Critique of Pure Reason

From Wikipedia, the free encyclopedia

Critique of Pure Reason

Title page of the 1781 edition
Author	Immanuel Kant
Original title	Critik a der reinen Vernunft
Translator	see below
Country	Germany
Language	German
Subject	Metaphysics
Published	1781
Pages	856 (first German edition)
a Kritik in modern German.

The Critique of Pure Reason (Kritik der reinen Vernunft) is a 1781 book by the German philosopher Immanuel Kant, in which the author seeks to determine the limits and scope of metaphysics. A heavily-revised second edition was published in 1787. Also referred to as Kant's "First Critique," it was followed by the Critique of Practical Reason (1788) and the Critique of Judgment (1790). In the preface to the first edition, Kant explains that by a "critique of pure reason" he means not "a critique of books and systems, but of the faculty of reason in general, in respect of all knowledge after which it may strive independently of all experience" and that he aims to reach a decision about "the possibility or impossibility of metaphysics". The First Critique is often viewed as culminating several centuries of early-modern philosophy, and inaugurating modern philosophy.

Kant builds on the work of empiricist philosophers such as John Locke and David Hume, as well as rationalists such as Gottfried Wilhelm Leibniz and Christian Wolff. He expounds new ideas on the nature of space and time, and tries to provide solutions to Hume's scepticism regarding human knowledge of the relation of cause and effect, and René Descartes' scepticism regarding knowledge of the external world. This is argued through the transcendental idealism of objects (as appearance) and their form of appearance. Kant regards the former "as mere representations and not as things in themselves", and the latter as "only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves". This grants the possibility of a priori knowledge, since objects as appearance "must conform to our cognition . . . which is to establish something about objects before they are given to us". Knowledge independent of experience Kant calls "a priori" knowledge, while knowledge obtained through experience is termed "a posteriori". According to Kant, a proposition is a priori if it is necessary and universal. A proposition is necessary if it could not possibly be false, and so cannot be denied without contradiction. A proposition is universal if it is true in all cases, and so does not admit of any exceptions. Knowledge gained a posteriori through the senses, Kant argues, never imparts absolute necessity and universality, because it is always possible that we might encounter an exception.

Kant claims to have discovered another attribute of propositions: the distinction between "analytic" and "synthetic" judgments. According to Kant, a proposition is analytic if the content of the predicate-concept of the proposition is already contained within the subject-concept of that proposition. For example, Kant considers the proposition "All bodies are extended" analytic, since the predicate-concept ('extended') is already contained within—or "thought in"—the subject-concept of the sentence ('body'). The distinctive character of analytic judgements was therefore that they can be known to be true simply by an analysis of the concepts contained in them; they are true by definition. In synthetic propositions, on the other hand, the predicate-concept is not already contained within the subject-concept. For example, Kant considers the proposition "All bodies are heavy" synthetic, since the concept 'body' does not already contain within it the concept 'weight'. Synthetic judgments therefore add something to a concept, whereas analytic judgments only explain what is already contained in the concept.

Prior to Kant, it was thought that all a priori knowledge must be analytic. Kant, however, argues that our knowledge of mathematics, of the first principles of natural science, and of metaphysics, is both a priori and synthetic. The peculiar nature of this knowledge, Kant argues, cries out for explanation. The central problem of the Critique is therefore to answer the question: "How are synthetic a priori judgements possible?" It is a "matter of life and death" to metaphysics and to human reason, Kant argues, that the grounds of this kind of knowledge be explained.

Though it received little attention when it was first published, the Critique later attracted attacks from both empiricist and rationalist critics, and became a source of controversy. It has exerted an enduring influence on Western philosophy, and helped to bring about the development of German idealism.

Background: early rationalism and Kant's rejection of Hume's empiricism

Before Kant, it was generally held that truths of reason must be analytic, meaning that what is stated in the predicate must already be present in the subject (for example, "An intelligent man is intelligent" or "An intelligent man is a man"). In either case, the judgment is analytic because it is ascertained by analyzing the subject. It was thought that all truths of reason, or necessary truths, are of this kind: that in all of them there is a predicate that is only part of the subject of which it is asserted. If this were so, attempting to deny anything that could be known a priori (for example, "An intelligent man is not intelligent" or "An intelligent man is not a man") would involve a contradiction. It was therefore thought that the law of contradiction is sufficient to establish all a priori knowledge.

David Hume (1711–1776) at first accepted the general view of rationalism about a priori knowledge. However, upon closer examination of the subject, Hume discovered that some judgments thought to be analytic, especially those related to cause and effect, were actually synthetic (i.e., no analysis of the subject will reveal the predicate). They thus depend exclusively upon experience and are therefore a posteriori.

Before Hume, rationalists had held that effect could be deduced from cause; Hume argued that it could not and from this inferred that nothing at all could be known a priori in relation to cause and effect. Kant (1724–1804), who was brought up under the auspices of rationalism, was deeply disturbed by Hume's skepticism. "Kant tells us that David Hume awakened him from his dogmatic slumbers."

Kant decided to find an answer and spent at least twelve years thinking about the subject. Although the Critique of Pure Reason was set down in written form in just four to five months, while Kant was also lecturing and teaching, the work is a summation of the development of Kant's philosophy throughout that twelve-year period.

Kant's work was stimulated by his decision to take seriously Hume's skeptical conclusions about such basic principles as cause and effect, which had implications for Kant's grounding in rationalism. In Kant's view, Hume's skepticism rested on the premise that all ideas are presentations of sensory experience. The problem that Hume identified was that basic principles such as causality cannot be derived from sense experience only: experience shows only that one event regularly succeeds another, not that it is caused by it.

In section VI ("The General Problem of Pure Reason") of the introduction to the Critique of Pure Reason, Kant explains that Hume stopped short of considering that a synthetic judgment could be made 'a priori'. Kant's goal was to find some way to derive cause and effect without relying on empirical knowledge. Kant rejects analytical methods for this, arguing that analytic reasoning cannot tell us anything that is not already self-evident, so his goal was to find a way to demonstrate how the synthetic a priori is possible.

To accomplish this goal, Kant argued that it would be necessary to use synthetic reasoning. However, this posed a new problem—how is it possible to have synthetic knowledge that is not based on empirical observation—that is, how are synthetic a priori truths possible? This question is exceedingly important, Kant maintains, because he contended that all important metaphysical knowledge is of synthetic a priori propositions. If it is impossible to determine which synthetic a priori propositions are true, he argues, then metaphysics as a discipline is impossible. The remainder of the Critique of Pure Reason is devoted to examining whether and how knowledge of synthetic a priori propositions is possible.

Synthetic a priori judgments

Immanuel Kant, lecturing to Russian officers—by I. Soyockina / V. Gracov, the Kant Museum, Kaliningrad

Kant argues that there are synthetic judgments such as the connection of cause and effect (e.g., "... Every effect has a cause.") where no analysis of the subject will produce the predicate. Kant reasons that statements such as those found in geometry and Newtonian physics are synthetic judgments. Kant uses the classical example of 7 + 5 = 12. No amount of analysis will find 12 in either 7 nor 5. Thus Kant arrives at the conclusion that all pure mathematics is synthetic though a priori; the number 7 is seven and the number 5 is five and the number 12 is twelve and the same principle applies to other numerals; in other words, they are universal and necessary. For Kant then, mathematics is synthetic judgment a priori. Conventional reasoning would have regarded such an equation to be analytic a priori by considering both 7 and 5 to be part of one subject being analyzed, however Kant looked upon 7 and 5 as two separate values, with the value of five being applied to that of 7 and synthetically arriving at the logical conclusion that they equal 12. This conclusion led Kant into a new problem as he wanted to establish how this could be possible: How is pure mathematics possible? This also led him to inquire whether it could be possible to ground synthetic a priori knowledge for a study of metaphysics, because most of the principles of metaphysics from Plato through to Kant's immediate predecessors made assertions about the world or about God or about the soul that were not self-evident but which could not be derived from empirical observation (B18-24). For Kant, all post-Cartesian metaphysics is mistaken from its very beginning: the empiricists are mistaken because they assert that it is not possible to go beyond experience and the dogmatists are mistaken because they assert that it is possible to go beyond experience through theoretical reason.

Therefore, Kant proposes a new basis for a science of metaphysics, posing the question: how is a science of metaphysics possible, if at all? According to Kant, only practical reason, the faculty of moral consciousness, the moral law of which everyone is immediately aware, makes it possible to know things as they are. This led to his most influential contribution to metaphysics: the abandonment of the quest to try to know the world as it is "in itself" independent of sense experience. He demonstrated this with a thought experiment, showing that it is not possible to meaningfully conceive of an object that exists outside of time and has no spatial components and is not structured in accordance with the categories of the understanding (Verstand), such as substance and causality. Although such an object cannot be conceived, Kant argues, there is no way of showing that such an object does not exist. Therefore, Kant says, the science of metaphysics must not attempt to reach beyond the limits of possible experience but must discuss only those limits, thus furthering the understanding of ourselves as thinking beings. The human mind is incapable of going beyond experience so as to obtain a knowledge of ultimate reality, because no direct advance can be made from pure ideas to objective existence.

Kant writes, "Since, then, the receptivity of the subject, its capacity to be affected by objects, must necessarily precede all intuitions of these objects, it can readily be understood how the form of all appearances can be given prior to all actual perceptions, and so exist in the mind a priori" (A26/B42). Appearance is then, via the faculty of transcendental imagination (Einbildungskraft), grounded systematically in accordance with the categories of the understanding. Kant's metaphysical system, which focuses on the operations of cognitive faculties (Erkenntnisvermögen), places substantial limits on knowledge not founded in the forms of sensibility (Sinnlichkeit). Thus it sees the error of metaphysical systems prior to the Critique as failing to first take into consideration the limitations of the human capacity for knowledge. According to Heidegger, transcendental imagination is what Kant also refers to as the unknown common root uniting sense and understanding, the two component parts of experience. Transcendental imagination is described in the first edition of the Critique of Pure Reason but Kant omits it from the second edition of 1787.

It is because he takes into account the role of people's cognitive faculties in structuring the known and knowable world that in the second preface to the Critique of Pure Reason Kant compares his critical philosophy to Copernicus' revolution in astronomy. Kant writes: "Hitherto it has been assumed that all our knowledge must conform to objects. But all attempts to extend our knowledge of objects by establishing something in regard to them a priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge" (Bxvi). Just as Copernicus revolutionized astronomy by taking the position of the observer into account, Kant's critical philosophy takes into account the position of the knower of the world in general and reveals its impact on the structure of the known world. Kant's view is that in explaining the movement of celestial bodies Copernicus rejected the idea that the movement is in the stars and accepted it as a part of the spectator. Knowledge does not depend so much on the object of knowledge as on the capacity of the knower.

Kant's transcendental idealism should be distinguished from idealistic systems such as that of George Berkeley. While Kant claimed that phenomena depend upon the conditions of sensibility, space and time, and on the synthesizing activity of the mind manifested in the rule-based structuring of perceptions into a world of objects, this thesis is not equivalent to mind-dependence in the sense of Berkeley's idealism. Kant defines transcendental idealism:

“	I understand by the transcendental idealism of all appearances the doctrine that they are all together to be regarded as mere representations and not things in themselves, and accordingly that time and space are only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves. To this idealism is opposed transcendental realism, which regards space and time as something given in themselves (independent of our sensibility).	”
— (CPR, A369)

Kant's approach

In Kant's view, a priori intuitions and concepts provide some a priori knowledge, which also provides the framework for a posteriori knowledge. Kant also believed that causality is a conceptual organizing principle imposed upon nature, albeit nature understood as the sum of appearances that can be synthesized according to a priori concepts.

In other words, space and time are a form of perceiving and causality is a form of knowing. Both space and time and conceptual principles and processes pre-structure experience.

Things as they are "in themselves"—the thing in itself or das Ding an sich—are unknowable. For something to become an object of knowledge, it must be experienced, and experience is structured by the mind—both space and time being the forms of intuition (Anschauung in German; for Kant, intuition is the process of sensing or the act of having a sensation) or perception, and the unifying, structuring activity of concepts. These aspects of mind turn things-in-themselves into the world of experience. There is never passive observation or knowledge.

According to Kant, the transcendental ego—the "Transcendental Unity of Apperception"—is similarly unknowable. Kant contrasts the transcendental ego to the empirical ego, the active individual self subject to immediate introspection. One is aware that there is an "I," a subject or self that accompanies one's experience and consciousness. Since one experiences it as it manifests itself in time, which Kant proposes is a subjective form of perception, one can know it only indirectly: as object, rather than subject. It is the empirical ego that distinguishes one person from another providing each with a definite character.

Contents

The Critique of Pure Reason is arranged around several basic distinctions. After the two Prefaces (the A edition Preface of 1781 and the B edition Preface of 1787) and the Introduction, the book is divided into the Doctrine of Elements and the Doctrine of Method:

The Doctrine of Elements sets out the a priori products of the mind, and the correct and incorrect use of these presentations. Kant further divides the Doctrine of Elements into the Transcendental Aesthetic and the Transcendental Logic, reflecting his basic distinction between sensibility and the understanding. In the Transcendental Aesthetic he argues that space and time are pure forms of intuition inherent in our faculty of sense. The Transcendental Logic is separated into the Transcendental Analytic and the Transcendental Dialectic:

• The Transcendental Analytic sets forth the appropriate uses of a priori concepts, called the categories, and other principles of the understanding, as conditions of the possibility of a science of metaphysics. The section titled the Metaphysical Deduction considers the origin of the categories. In the Transcendental Deduction, Kant then shows the application of the categories to experience. Next, the Analytic of Principles sets out arguments for the relation of the categories to metaphysical principles. This section begins with the Schematism, which describes how the imagination can apply pure concepts to the object given in sense perception. Next are arguments relating the a priori principles with the schematized categories.
• The Transcendental Dialectic describes the transcendental illusion behind the misuse of these principles in attempts to apply them to realms beyond sense experience. Kant’s most significant arguments are the Paralogisms of Pure Reason, the Antinomy of Pure Reason, and the Ideal of Pure Reason, aimed against, respectively, traditional theories of the soul, the universe as a whole, and the existence of God. In the Appendix to the Critique of Speculative Theology Kant describes the role of the transcendental ideas of reason.

The Doctrine of Method contains four sections. The first section, Discipline of Pure Reason, compares mathematical and logical methods of proof, and the second section, Canon of Pure Reason, distinguishes theoretical from practical reason.

The Divisions of Critique of Pure Reason
 
Dedication

1. First and second Prefaces

2. Introduction

3. Transcendental Doctrine of Elements

A. Transcendental Aesthetic

B. Transcendental Logic

(1) Transcendental Analytic

a. Analytic of Concepts

i. Metaphysical Deduction

ii. Transcendental Deduction

b. Analytic of Principles

i. Schematism (bridging chapter)

ii. System of Principles of Pure Understanding

a. Axioms of Intuition

b. Anticipations of Perception

c. Analogies of Experience

d. Postulates of Empirical Thought (Refutation of Idealism)

iii. Ground of Distinction of Objects into Phenomena and Noumena

iv. Appendix on the Amphiboly of the Concepts of Reflection

(2) Transcendental Dialectic: Transcendental Illusion

a. Paralogisms of Pure Reason

b. Antinomy of Pure Reason

c. Ideal of Pure Reason

d. Appendix to Critique of Speculative Theology

4. Transcendental Doctrine of Method

A. Discipline of Pure Reason

B. Canon of Pure Reason

C. Architectonic of Pure Reason

D. History of Pure Reason

Transcendental Doctrine of Elements

Transcendental Aesthetic

The Transcendental Aesthetic, as the Critique notes, deals with "all principles of a priori sensibility". As a further delimitation, it "constitutes the first part of the transcendental doctrine of elements, in contrast to that which contains the principles of pure thinking, and is named transcendental logic". In it, what is aimed at is "pure intuition and the mere form of appearances, which is the only thing that sensibility can make available a priori". It is thus an analytic of the a priori constitution of sensibility; through which "Objects are therefore given to us . . . , and it alone affords us intuitions". This in itself is an explication of the "pure form of sensible intuitions in general [that] is to be encountered in the mind a priori". Thus, pure form or intuition is the a priori "wherein all of the manifold of appearances is intuited in certain relations". from this, "a science of all principles of a priori sensibility [is called] the transcendental aesthetic". The above stems from the fact that "there are two stems of human cognition . . . namely sensibility and understanding". This division, as the critique notes, comes "closer to the language and the sense of the ancients, among whom the division of cognition into αισθητα και νοητα is very well known". An exposition on a priori intuitions is an analysis of the intentional constitution of sensibility. Since this lies a priori in the mind prior to actual object relation; "The transcendental doctrine of the senses will have to belong to the first part of the science of elements, since the conditions under which alone the objects of human cognition are given precede those under which those objects are thought".

Kant distinguishes between the matter and the form of appearances. The matter is "that in the appearance that corresponds to sensation" (A20/B34). The form is "that which so determines the manifold of appearance that it allows of being ordered in certain relations" (A20/B34). Kant's revolutionary claim is that the form of appearances—which he later identifies as space and time—is a contribution made by the faculty of sensation to cognition, rather than something that exists independently of the mind. This is the thrust of Kant's doctrine of the transcendental ideality of space and time.

Kant's arguments for this conclusion are widely debated among Kant scholars. Some see the argument as based on Kant's conclusions that our representation (Vorstellung) of space and time is an a priori intuition. From here Kant is thought to argue that our representation of space and time as a priori intuitions entails that space and time are transcendentally ideal. It is undeniable from Kant's point of view that in Transcendental Philosophy, the difference of things as they appear and things as they are is a major philosophical discovery. Others see the argument as based upon the question of whether synthetic a priori judgments are possible. Kant is taken to argue that the only way synthetic a priori judgments, such as those made in geometry, are possible is if space is transcendentally ideal.

In Section I (Of Space) of Transcendental Aesthetic in the Critique of Pure Reason Kant poses the following questions: What then are time and space? Are they real existences? Or, are they merely relations or determinations of things, such, however, as would equally belong to these things in themselves, though they should never become objects of intuition; or, are they such as belong only to the form of intuition, and consequently to the subjective constitution of the mind, without which these predicates of time and space could not be attached to any object? The answer that space and time are real existences belongs to Newton. The answer that space and time are relations or determinations of things even when they are not being sensed belongs to Leibniz. Both answers maintain that space and time exist independently of the subject's awareness. This is exactly what Kant denies in his answer that space and time belong to the subjective constitution of the mind.

Space and time

Kant gives two expositions of space and time: metaphysical and transcendental. The metaphysical expositions of space and time are concerned with clarifying how those intuitions are known independently of experience. The transcendental expositions attempt to show how the metaphysical conclusions might be applied to enrich our understanding.

In the transcendental exposition, Kant refers back to his metaphysical exposition in order to show that the sciences would be impossible if space and time were not kinds of pure a priori intuitions. He asks the reader to take the proposition, "two straight lines can neither contain any space nor, consequently, form a figure", and then to try to derive this proposition from the concepts of a straight line and the number two. He concludes that it is simply impossible (A47-48/B65). Thus, since this information cannot be obtained from analytic reasoning, it must be obtained through synthetic reasoning, i.e., a synthesis of concepts (in this case two and straightness) with the pure (a priori) intuition of space.

In this case, however, it was not experience that furnished the third term; otherwise, the necessary and universal character of geometry would be lost. Only space, which is a pure a priori form of intuition, can make this synthetic judgment, thus it must then be a priori. If geometry does not serve this pure a priori intuition, it is empirical, and would be an experimental science, but geometry does not proceed by measurements—it proceeds by demonstrations.

Kant rests his demonstration of the priority of space on the example of geometry. He reasons that therefore if something exists, it needs to be intelligible. If someone attacked this argument, he would doubt the universality of geometry (which Kant believes no honest person would do).

The other part of the Transcendental Aesthetic argues that time is a pure a priori intuition that renders mathematics possible. Time is not a concept, since otherwise it would merely conform to formal logical analysis (and therefore, to the principle of non-contradiction). However, time makes it possible to deviate from the principle of non-contradiction: indeed, it is possible to say that A and non-A are in the same spatial location if one considers them in different times, and a sufficient alteration between states were to occur (A32/B48). Time and space cannot thus be regarded as existing in themselves. They are a priori forms of sensible intuition.

The current interpretation of Kant states that the subject inherently possesses the underlying conditions to perceive spatial and temporal presentations. The Kantian thesis claims that in order for the subject to have any experience at all, then it must be bounded by these forms of presentations (Vorstellung). Some scholars have offered this position as an example of psychological nativism, as a rebuke to some aspects of classical empiricism.

Kant's thesis concerning the transcendental ideality of space and time limits appearances to the forms of sensibility—indeed, they form the limits within which these appearances can count as sensible; and it necessarily implies that the thing-in-itself is neither limited by them nor can it take the form of an appearance within us apart from the bounds of sensibility (A48-49/B66). Yet the thing-in-itself is held by Kant to be the cause of that which appears, and this is where an apparent paradox of Kantian critique resides: while we are prohibited from absolute knowledge of the thing-in-itself, we can impute to it a cause beyond ourselves as a source of representations within us. Kant's view of space and time rejects both the space and time of Aristotelian physics and the space and time of Newtonian physics.

Transcendental Logic

In the Transcendental Logic, there is a section (titled The Refutation of Idealism) that frees Kant's doctrine from any vestiges of subjective idealism, which would either doubt or deny the existence of external objects (B274-79). However, Senderowics warns that "... If the Refutation of Idealism indeed addresses a question left unanswered by the previous introductory pages of the Critique of Pure Reason, Kant's preceding comments contain a gap that needs to be bridged." Kant's distinction between the appearance and the thing-in-itself is not intended to imply that nothing knowable exists apart from consciousness, as with subjective idealism. Rather, it declares that knowledge is limited to phenomena as objects of a sensible intuition. In the Fourth Paralogism ("... A Paralogism is a logical fallacy"), Kant further certifies his philosophy as separate from that of subjective idealism by defining his position as a transcendental idealism in accord with empirical realism (A366–80), a form of direct realism. "The Paralogisms of Pure Reason" is the only chapter of the Dialectic that Kant rewrote for the second edition of the Critique of Pure Reason. In the first edition, the Fourth Paralogism offers a defence of transcendental idealism, which Kant reconsidered and relocated in the second edition.

Whereas the Transcendental Aesthetic was concerned with the role of the sensibility, the Transcendental Logic is concerned with the role of the understanding, which Kant defines as the faculty of the mind that deals with concepts. Knowledge, Kant argued, contains two components: intuitions, through which an object is given to us in sensibility, and concepts, through which an object is thought in understanding. In the Transcendental Aesthetic, he attempted to show that the a priori forms of intuition were space and time, and that these forms were the conditions of all possible intuition. It should therefore be expected that we should find similar a priori concepts in the understanding, and that these pure concepts should be the conditions of all possible thought. The Logic is divided into two parts: the Transcendental Analytic and the Transcendental Dialectic. The Analytic Kant calls a "logic of truth"; in it he aims to discover these pure concepts which are the conditions of all thought, and are thus what makes knowledge possible. The Transcendental Dialectic Kant calls a "logic of illusion"; in it he aims to expose the illusions that we create when we attempt to apply reason beyond the limits of experience.

The idea of a transcendental logic is that of a logic that gives an account of the origins of our knowledge as well as its relationship to objects. Kant contrasts this with the idea of a general logic, which abstracts from the conditions under which our knowledge is acquired, and from any relation that knowledge has to objects. According to Helge Svare "... It is important to keep in mind what Kant says here about logic in general, and transcendental logic in particular, being the product of abstraction, so that we are not misled when a few pages later he emphasizes the pure, non-empirical character of the transcendental concepts or the categories."

Kant's investigations in the Transcendental Logic lead him to conclude that the understanding and reason can only legitimately be applied to things as they appear phenomenally to us in experience. What things are in themselves as being noumenal, independent of our cognition, remains limited by what is known through phenomenal experience.

First Division: Transcendental Analytic

The Transcendental Analytic is divided into an Analytic of Concepts and an Analytic of Principles, as well as a third section concerned with the distinction between phenomena and noumena. In Chapter III (Of the ground of the division of all objects into phenomena and noumena) of the Transcendental Analytic, Kant generalizes the implications of the Analytic in regard to transcendent objects preparing the way for the explanation in the Transcendental Dialectic about thoughts of transcendent objects, Kant's detailed theory of the content (Inhalt) and origin of our thoughts about specific transcendent objects. The main sections of the Analytic of Concepts are The Metaphysical Deduction and The Transcendental Deduction of the Categories. The main sections of the Analytic of Principles are the Schematism, Axioms of Intuition, Anticipations of Perception, Analogies of Experience, Postulates and follow the same recurring tabular form:

	1. Quantity
2. Quality		3. Relation
	4. Modality

In the 2nd edition, these sections are followed by a section titled the Refutation of Idealism.

The Metaphysical Deduction

In the Metaphysical Deduction, Kant aims to derive twelve pure concepts of the understanding (which he calls "categories") from the logical forms of judgment. In the following section, he will go on to argue that these categories are conditions of all thought in general. Kant arranges the forms of judgment in a table of judgments, which he uses to guide the derivation of the table of categories.

The role of the understanding is to make judgments. In judgment, the understanding employs concepts which apply to the intuitions given to us in sensibility. Judgments can take different logical forms, with each form combining concepts in different ways. Kant claims that if we can identify all of the possible logical forms of judgment, this will serve as a "clue" to the discovery of the most basic and general concepts that are employed in making such judgments, and thus that are employed in all thought.

Logicians prior to Kant had concerned themselves to classify the various possible logical forms of judgment. Kant, with only minor modifications, accepts and adopts their work as correct and complete, and lays out all the logical forms of judgment in a table, reduced under four heads:

	1. Quantity of Judgements
2. Quality		3. Relation
	4. Modality

Under each head, there corresponds three logical forms of judgement:

	1. Quantity of Judgements Universal Particular Singular
2. Quality Affirmative Negative Infinite		3. Relation Categorical Hypothetical Disjunctive
	4. Modality Problematic Assertoric Apodeictic

This Aristotelian method for classifying judgments is the basis for his own twelve corresponding concepts of the understanding. In deriving these concepts, he reasons roughly as follows. If we are to possess pure concepts of the understanding, they must relate to the logical forms of judgement. However, if these pure concepts are to be applied to intuition, they must have content. But the logical forms of judgement are by themselves abstract and contentless. Therefore, to determine the pure concepts of the understanding we must identify concepts which both correspond to the logical forms of judgement, and are able to play a role in organising intuition. Kant therefore attempts to extract from each of the logical forms of judgement a concept which relates to intuition. For example, corresponding to the logical form of hypothetical judgement ('If p, then q'), there corresponds the category of causality ('If one event, then another'). Kant calls these pure concepts 'categories', echoing the Aristotelian notion of a category as a concept which is not derived from any more general concept. He follows a similar method for the other eleven categories, then represents them in the following table:

	1. Categories of Quantity Unity Plurality Totality
2. Categories of Quality Reality Negation Limitation		3. Categories of Relation Inherence and Subsistence (substance and accident) Causality and Dependence (cause and effect) Community (reciprocity between agent and patient)
	4. Categories of Modality Possibility—Impossibility Existence—Non-existence Necessity—Contingency

These categories, then, are the fundamental, primary, or native concepts of the understanding. These flow from, or constitute the mechanism of understanding and its nature, and are inseparable from its activity. Therefore, for human thought, they are universal and necessary, or a priori. As categories they are not contingent states or images of sensuous consciousness, and hence not to be thence derived. Similarly, they are not known to us independently of such consciousness or of sensible experience. On the one hand, they are exclusively involved in, and hence come to our knowledge exclusively through, the spontaneous activity of the understanding. This understanding is never active, however, until sensible data are furnished as material for it to act upon, and so it may truly be said that they become known to us "only on the occasion of sensible experience." For Kant, in opposition to Christian Wolff and Thomas Hobbes, the categories exist only in the mind.

These categories are "pure" conceptions of the understanding, in as much as they are independent of all that is contingent in sense. They are not derived from what is called the matter of sense, or from particular, variable sensations. However, they are not independent of the universal and necessary form of sense. Again, Kant, in the "Transcendental Logic," is professedly engaged with the search for an answer to the second main question of the Critique, How is pure physical science, or sensible knowledge, possible? Kant, now, has said, and, with reference to the kind of knowledge mentioned in the foregoing question, has said truly, that thoughts, without the content which perception supplies, are empty. This is not less true of pure thoughts, than of any others. The content which the pure conceptions, as categories of pure physical science or sensible knowledge, cannot derive from the matter of sense, they must and do derive from its pure form. And in this relation between the pure conceptions of the understanding and their pure content there is involved, as we shall see, the most intimate community of nature and origin between sense, on its formal side (space and time), and the understanding itself. For Kant, space and time are a priori intuitions. Out of a total of six arguments in favor of space as a priori intuition, Kant presents four of them in the Metaphysical Exposition of space: two argue for space a priori and two for space as intuition.

The Transcendental Deduction

In the Transcendental Deduction, Kant aims to show that the categories derived in the Metaphysical Deduction are conditions of all possible experience. He achieves this proof roughly by the following line of thought: all representations must have some common ground if they are to be the source of possible knowledge (because extracting knowledge from experience requires the ability to compare and contrast representations that may occur at different times or in different places). This ground of all experience is the self-consciousness of the experiencing subject, and the constitution of the subject is such that all thought is rule-governed in accordance with the categories. It follows that the categories feature as necessary components in any possible experience.

	1.Axioms of intuition
2.Anticipations of perception		3.Analogies of experience
	4.Postulates of empirical thought in general

The Schematism

In order for any concept to have meaning, it must be related to sense perception. The 12 categories, or a priori concepts, are related to phenomenal appearances through schemata. Each category has a schema. It is a connection through time between the category, which is an a priori concept of the understanding, and a phenomenal a posteriori appearance. These schemata are needed to link the pure category to sensed phenomenal appearances because the categories are, as Kant says, heterogeneous with sense intuition. Categories and sensed phenomena, however, do share one characteristic: time. Succession is the form of sense impressions and also of the Category of causality. Therefore, time can be said to be the schema of Categories or pure concepts of the understanding. According to Heidegger, for Kant "... The schemata of pure concepts of understanding, the categories, are a priori time-determinations and as such they are a transcendental product of the pure power of imagination."

The Refutation of Idealism

In order to answer criticisms of the Critique of Pure Reason that Transcendental Idealism denied the reality of external objects, Kant added a section to the second edition (1787) titled "The Refutation of Idealism" that turns the "game" of idealism against itself by arguing that self-consciousness presupposes external objects in space. Defining self-consciousness as a determination of the self in time, Kant argues that all determinations of time presuppose something permanent in perception and that this permanence cannot be in the self, since it is only through the permanence that one's existence in time can itself be determined. This argument inverted the supposed priority of inner over outer experience that had dominated philosophies of mind and knowledge since René Descartes. In Book II, chapter II, section III of the Transcendental Analytic, right under "The Postulates of Empirical Thought", Kant adds his well-known "Widerlegung des Idealismus" (Refutation of Idealism) where he refutes both Descartes' problematic idealism and Berkeley's dogmatic idealism. According to Kant, in problematic idealism the existence of objects is doubtful or impossible to prove while in dogmatic idealism, the existence of space and therefore of spatial objects is impossible. In contradistinction, Kant holds that external objects may be directly perceived and that such experience is a necessary presupposition of self-consciousness.

Appendix: Amphiboly of Concepts of Reflection

As an Appendix to the First Division of Transcendental Logic, Kant intends the "Amphiboly of the Conceptions of Reflection" to be a critique of Leibniz's metaphysics and a prelude to Transcendental Dialectic, the Second Division of Transcendental Logic. Kant introduces a whole set of new ideas called "concepts of reflection": identity/difference, agreement/opposition, inner/outer and matter/form. According to Kant, the categories do have but these concepts have no synthetic function in experience. These special concepts just help to make comparisons between concepts judging them either different or the same, compatible or incompatible. It is this particular action of making a judgement that Kant calls "logical reflection." As Kant states: "Through observation and analysis of appearances we penetrate to nature's inner recesses, and no one can say how far this knowledge may in time extend. But with all this knowledge, and even if the whole of nature were revealed to us, we should still never be able to answer those transcendental questions which go beyond nature. The reason of this is that it is not given to us to observe our own mind with any other intuition than that of inner sense; and that it is yet precisely in the mind that the secret of the source of our sensibility is located. The relation of sensibility to an object and what the transcendental ground of this [objective] unity may be, are matters undoubtedly so deeply concealed that we, who after all know even ourselves only through inner sense and therefore as appearance, can never be justified in treating sensibility as being a suitable instrument of investigation for discovering anything save always still other appearances – eager as we yet are to explore their non-sensible cause."

Second Division: Transcendental Dialectic

Following the systematic treatment of a priori knowledge given in the transcendental analytic, the transcendental dialectic seeks to dissect dialectical illusions. Its task is effectively to expose the fraudulence of the non-empirical employment of the understanding. The Transcendental Dialectic shows how pure reason should not be used. According to Kant, the rational faculty is plagued with dialectic illusions as man attempts to know what can never be known.

This longer but less dense section of the Critique is composed of five essential elements, including an Appendix, as follows: (a) Introduction (to Reason and the Transcendental Ideas), (b) Rational Psychology (the nature of the soul), (c) Rational Cosmology (the nature of the world), (d) Rational Theology (God), and (e) Appendix (on the constitutive and regulative uses of reason).

In the introduction, Kant introduces a new faculty, human reason, positing that it is a unifying faculty that unifies the manifold of knowledge gained by the understanding. Another way of thinking of reason is to say that it searches for the 'unconditioned'; Kant had shown in the Second Analogy that every empirical event has a cause, and thus each event is conditioned by something antecedent to it, which itself has its own condition, and so forth. Reason seeks to find an intellectual resting place that may bring the series of empirical conditions to a close, to obtain knowledge of an 'absolute totality' of conditions, thus becoming unconditioned. All in all, Kant ascribes to reason the faculty to understand and at the same time criticize the illusions it is subject to.

The paralogisms of pure reason

One of the ways that pure reason erroneously tries to operate beyond the limits of possible experience is when it thinks that there is an immortal Soul in every person. Its proofs, however, are paralogisms, or the results of false reasoning.

The soul is substance

Every one of my thoughts and judgments is based on the presupposition "I think." "I" is the subject and the thoughts are the predicates. Yet I should not confuse the ever-present logical subject of my every thought with a permanent, immortal, real substance (soul). The logical subject is a mere idea, not a real substance. Unlike Descartes who believes that the soul may be known directly through reason, Kant asserts that no such thing is possible. Descartes declares cogito ergo sum but Kant denies that any knowledge of "I" may be possible. "I" is only the background of the field of apperception and as such lacks the experience of direct intuition that would make self-knowledge possible. This implies that the self in itself could never be known. Like Hume, Kant rejects knowledge of the "I" as substance. For Kant, the "I" that is taken to be the soul is purely logical and involves no intuitions. The "I" is the result of the a priori consciousness continuum not of direct intuition a posteriori. It is apperception as the principle of unity in the consciousness continuum that dictates the presence of "I" as a singular logical subject of all the representations of a single consciousness. Although "I" seems to refer to the same "I" all the time, it is not really a permanent feature but only the logical characteristic of a unified consciousness.

The soul is simple

The only use or advantage of asserting that the soul is simple is to differentiate it from matter and therefore prove that it is immortal, but the substratum of matter may also be simple. Since we know nothing of this substratum, both matter and soul may be fundamentally simple and therefore not different from each other. Then the soul may decay, as does matter. It makes no difference to say that the soul is simple and therefore immortal. Such a simple nature can never be known through experience. It has no objective validity. According to Descartes, the soul is indivisible. This paralogism mistakes the unity of apperception for the unity of an indivisible substance called the soul. It is a mistake that is the result of the first paralogism. It is impossible that thinking (Denken) could be composite for if the thought by a single consciousness were to be distributed piecemeal among different consciousnesses, the thought would be lost. According to Kant, the most important part of this proposition is that a multi-faceted presentation requires a single subject. This paralogism misinterprets the metaphysical oneness of the subject by interpreting the unity of apperception as being indivisible and the soul simple as a result. According to Kant, the simplicity of the soul as Descartes believed cannot be inferred from the "I think" as it is assumed to be there in the first place. Therefore, it is a tautology.

The soul is a person

In order to have coherent thoughts, I must have an "I" that is not changing and that thinks the changing thoughts. Yet we cannot prove that there is a permanent soul or an undying "I" that constitutes my person. I only know that I am one person during the time that I am conscious. As a subject who observes my own experiences, I attribute a certain identity to myself, but, to another observing subject, I am an object of his experience. He may attribute a different persisting identity to me. In the third paralogism, the "I" is a self-conscious person in a time continuum, which is the same as saying that personal identity is the result of an immaterial soul. The third paralogism mistakes the "I", as unit of apperception being the same all the time, with the everlasting soul. According to Kant, the thought of "I" accompanies every personal thought and it is this that gives the illusion of a permanent I. However, the permanence of "I" in the unity of apperception is not the permanence of substance. For Kant, permanence is a schema, the conceptual means of bringing intuitions under a category. The paralogism confuses the permanence of an object seen from without with the permanence of the "I" in a unity of apperception seen from within. From the oneness of the apperceptive "I" nothing may be deduced. The "I" itself shall always remain unknown. The only ground for knowledge is the intuition, the basis of sense experience.

The soul is separated from the experienced world

The soul is not separate from the world. They exist for us only in relation to each other. Whatever we know about the external world is only a direct, immediate, internal experience. The world appears, in the way that it appears, as a mental phenomenon. We cannot know the world as a thing-in-itself, that is, other than as an appearance within us. To think about the world as being totally separate from the soul is to think that a mere phenomenal appearance has independent existence outside of us. If we try to know an object as being other than an appearance, it can only be known as a phenomenal appearance, never otherwise. We cannot know a separate, thinking, non-material soul or a separate, non-thinking, material world because we cannot know things, as to what they may be by themselves, beyond being objects of our senses. The fourth paralogism is passed over lightly or not treated at all by commentators. In the first edition of the Critique of Pure Reason, the fourth paralogism is addressed to refuting the thesis that there is no certainty of the existence of the external world. In the second edition of the Critique of Pure Reason, the task at hand becomes the Refutation of Idealism. Sometimes, the fourth paralogism is taken as one of the most awkward of Kant's invented tetrads. Nevertheless, in the fourth paralogism, there is a great deal of philosophizing about the self that goes beyond the mere refutation of idealism. In both editions, Kant is trying to refute the same argument for the non-identity of mind and body. In the first edition, Kant refutes the Cartesian doctrine that there is direct knowledge of inner states only and that knowledge of the external world is exclusively by inference. Kant claims mysticism is one of the characteristics of Platonism, the main source of dogmatic idealism. Kant explains skeptical idealism by developing a syllogism called "The Fourth Paralogism of the Ideality of Outer Relation:"

• If that whose existence can be inferred only as a cause of given perceptions has only a doubtful existence.
• And the existence of outer appearances cannot be immediately perceived but can be inferred only as the cause of given perceptions.
• Then, the existence of all objects of outer sense is doubtful.

Kant may have had in mind an argument by Descartes:

• My own existence is not doubtful
• But the existence of physical things is doubtful
• Therefore, I am not a physical thing.

It is questionable that the fourth paralogism should appear in a chapter on the soul. What Kant implies about Descartes' argument in favor of the immaterial soul is that the argument rests upon a mistake on the nature of objective judgement not on any misconceptions about the soul. The attack is mislocated.

These Paralogisms cannot be proven for speculative reason and therefore can give no certain knowledge about the Soul. However, they can be retained as a guide to human behavior. In this way, they are necessary and sufficient for practical purposes. In order for humans to behave properly, they can suppose that the soul is an imperishable substance, it is indestructibly simple, it stays the same forever, and it is separate from the decaying material world. On the other hand, anti-rationalist critics of Kant's ethics consider it too abstract, alienating, altruistic or detached from human concern to actually be able to guide human behavior. It is then that the Critique of Pure Reason offers the best defense, demonstrating that in human concern and behavior, the influence of rationality is preponderant.

The antinomy of pure reason

Kant presents the four antinomies of reason in the Critique of Pure Reason as going beyond the rational intention of reaching a conclusion. For Kant, an antinomy is a pair of faultless arguments in favor of opposite conclusions. Historically, Gottfried Leibniz and Samuel Clarke (Newton's spokesman) had just recently engaged in a titanic debate of unprecedented repercussions. Kant's formulation of the arguments was affected accordingly.

The Ideas of Rational Cosmology are dialectical. They result in four kinds of opposing assertions, each of which is logically valid. The antinomy, with its resolution, is as follows:

• Thesis: The world has, as to time and space, a beginning (limit).
• Antithesis: The world is, as to time and space, infinite.

Both are false. The world is an object of experience. Neither statement is based on experience.

• Thesis: Everything in the world consists of elements that are simple.
• Antithesis: There is no simple thing, but everything is composite.

Both are false. Things are objects of experience. Neither statement is based on experience.

• Thesis: There are in the world causes through freedom.
• Antithesis: There is no freedom, but all is nature.

Both may be true. The thesis may be true of things-in-themselves (other than as they appear). The antithesis may be true of things as they appear.

• Thesis: In the series of the world-causes there is some necessary being.
• Antithesis: There is nothing necessary in the world, but in this series all is contingent.

Both may be true. The thesis may be true of things-in-themselves (other than as they appear). The antithesis may be true of things as they appear.

According to Kant, rationalism came to fruition by defending the thesis of each antinomy while empiricism evolved into new developments by working to better the arguments in favor of each antithesis.

Pure reason

Pure reason mistakenly goes beyond its relation to possible experience when it concludes that there is a Being who is the most real thing (ens realissimum) conceivable. This ens realissimum is the philosophical origin of the idea of God. This personified object is postulated by Reason as the subject of all predicates, the sum total of all reality. Kant called this Supreme Being, or God, the Ideal of Pure Reason because it exists as the highest and most complete condition of the possibility of all objects, their original cause and their continual support. However, Kant's explication of the theological idea is notoriously unfathomable.

Refutation of the ontological proof of God's existence of Anselm of Canterbury

The ontological proof can be traced back to Anselm of Canterbury (1033–1109). Anselm presented the proof in chapter II of a short treatise titled "Discourse on the existence of God." It was not Kant but the monk Gaunilo and later the Scholastic Thomas Aquinas who first challenged the logical consistency of the proof. Aquinas went on to provide his own proofs for the existence of God in what are known as the Five Ways.

The ontological proof considers the concept of the most real Being (ens realissimum) and concludes that it is necessary. The ontological argument states that God exists because he is perfect. If he didn't exist, he would be less than perfect. Existence is assumed to be a predicate or attribute of the subject, God, but Kant asserted that existence is not a predicate. Existence or Being is merely the infinitive of the copula or linking, connecting verb "is" in a declarative sentence. It connects the subject to a predicate. "Existence is evidently not a real predicate ... The small word is, is not an additional predicate, but only serves to put the predicate in relation to the subject." (A599) Also, we cannot accept a mere concept or mental idea as being a real, external thing or object. The Ontological Argument starts with a mere mental concept of a perfect God and tries to end with a real, existing God.

The argument is essentially deductive in nature. Given a certain fact, it proceeds to infer another from it. The method pursued, then, is that of deducing the fact of God's being from the a priori idea of him. If man finds that the idea of God is necessarily involved in his self-consciousness, it is legitimate for him to proceed from this notion to the actual existence of the divine being. In other words, the idea of God necessarily includes existence. It may include it in several ways. One may argue, for instance, according to the method of Descartes, and say that the conception of God could have originated only with the divine being himself, therefore the idea possessed by us is based on the prior existence of God himself. Or we may allege that we have the idea that God is the most necessary of all beings—that is to say, he belongs to the class of realities; consequently it cannot but be a fact that he exists. This is held to be proof per saltum. A leap takes place from the premise to the conclusion, and all intermediate steps are omitted. The implication is that premise and conclusion stand over against one another without any obvious, much less necessary, connection. A jump is made from thought to reality. Kant here objects that being or existence is not a mere attribute that may be added onto a subject, thereby increasing its qualitative content. The predicate, being, adds something to the subject that no mere quality can give. It informs us that the idea is not a mere conception, but is also an actually existing reality. Being, as Kant thinks, actually increases the concept itself in such a way as to transform it. You may attach as many attributes as you please to a concept; you do not thereby lift it out of the subjective sphere and render it actual. So you may pile attribute upon attribute on the conception of God, but at the end of the day you are not necessarily one step nearer his actual existence. So that when we say God exists, we do not simply attach a new attribute to our conception; we do far more than this implies. We pass our bare concept from the sphere of inner subjectivity to that of actuality. This is the great vice of the Ontological argument. The idea of ten dollars is different from the fact only in reality. In the same way the conception of God is different from the fact of his existence only in reality. When, accordingly, the Ontological proof declares that the latter is involved in the former, it puts forward nothing more than a mere statement. No proof is forthcoming precisely where proof is most required. We are not in a position to say that the idea of God includes existence, because it is of the very nature of ideas not to include existence.

Kant explains that being not being a predicate could not characterize a thing. Logically, it is the copula of a judgment. In the proposition, "God is almighty", the copula "is" does not add a new predicate; it only unites a predicate to a subject. To take God with all its predicates and say that "God is" is equivalent to "God exists" or that "There is a God" is to jump to a conclusion as no new predicate is being attached to God. The content of both subject and predicate is one and the same. According to Kant then, existence is not really a predicate. Therefore, there is really no connection between the idea of God and God's appearance or disappearance. No statement about God whatsoever may establish God's existence. Kant makes a distinction between "in intellectus" (in mind) and "in re" (in reality or in fact) so that questions of being are a priori and questions of existence are resolved a posteriori.

Refutation of the cosmological ("prime mover") proof of God's existence

The cosmological proof considers the concept of an absolutely necessary Being and concludes that it has the most reality. In this way, the cosmological proof is merely the converse of the ontological proof. Yet the cosmological proof purports to start from sense experience. It says, "If anything exists in the cosmos, then there must be an absolutely necessary Being. " It then claims that there is only one concept of an absolutely necessary object. That is the concept of a Supreme Being who has maximum reality. Only such a supremely real being would be necessary and independently sufficient without compare, but this is the Ontological Proof again, which was asserted a priori without sense experience.

Summarizing the cosmological argument further, it may be stated as follows: "Contingent things exist—at least I exist; and as they are not self-caused, nor capable of explanation as an infinite series, it is requisite to infer that a necessary being, on whom they depend, exists." Seeing that this being exists, he belongs to the realm of reality. Seeing that all things issue from him, he is the most necessary of beings, for only a being who is self-dependent, who possesses all the conditions of reality within himself, could be the origin of contingent things. And such a being is God. This proof is invalid for three chief reasons. First, it makes use of a category, namely, Cause. And, as has been already pointed out, it is not possible to apply this, or any other, category except to the matter given by sense under the general conditions of space and time. If, then, we employ it in relation to Deity, we try to force its application in a sphere where it is useless, and incapable of affording any information. Once more, we are in the now familiar difficulty of the paralogism of Rational Psychology or of the Antinomies. The category has meaning only when applied to phenomena. Yet God is a noumenon. Second, it mistakes an idea of absolute necessity—an idea that is nothing more than an ideal—for a synthesis of elements in the phenomenal world or world of experience. This necessity is not an object of knowledge, derived from sensation and set in shape by the operation of categories. It cannot be regarded as more than an inference. Yet the cosmological argument treats it as if it were an object of knowledge exactly on the same level as perception of any thing or object in the course of experience. Thirdly, it presupposes the Ontological argument, already proved false. It does this, because it proceeds from the conception of the necessity of a certain being to the fact of his existence. Yet it is possible to take this course only if idea and fact are convertible with one another, and it has just been proved that they are not so convertible.

Physico-theological ("watch maker") proof of God's existence

The physico-theological proof of God's existence is supposed to be based on a posteriori sensed experience of nature and not on mere a priori abstract concepts. It observes that the objects in the world have been intentionally arranged with great wisdom. The fitness of this arrangement could never have occurred randomly, without purpose. The world must have been caused by an intelligent power. The unity of the relation between all of the parts of the world leads us to infer that there is only one cause of everything. That one cause is a perfect, mighty, wise, and self-sufficient Being. This physico-theology does not, however, prove with certainty the existence of God. For this, we need something absolutely necessary that consequently has all-embracing reality, but this is the Cosmological Proof, which concludes that an all-encompassing real Being has absolutely necessary existence. All three proofs can be reduced to the Ontological Proof, which tried to make an objective reality out of a subjective concept.

In the Critique of Pure Reason, Kant abandons the attempt to prove the existence of God although Kant's real intention is to attempt to disprove the non-existence of God. Rather than proving the existence of God, Kant is really trying to disprove the non-existence of God since no one can prove the non-existence of God. In abandoning any attempt to prove the existence of God, Kant declares the three proofs of rational theology known as the ontological, the cosmological and the physico-theological as quite untenable.

II. Transcendental Doctrine of Method

The second book in the Critique, and by far the shorter of the two, attempts to lay out the formal conditions of the complete system of pure reason.

In the Transcendental Dialectic, Kant showed how pure reason is improperly used when it is not related to experience. In the Method of Transcendentalism, he explained the proper use of pure reason.

The discipline of pure reason

In section I, the discipline of pure reason in the sphere of dogmatism, of chapter I, the discipline of pure reason, of Part II, transcendental discipline of method, of the Critique of Pure Reason, Kant enters into the most extensive discussion of the relationship between mathematical theory and philosophy.

Discipline is the restraint, through caution and self-examination, that prevents philosophical pure reason from applying itself beyond the limits of possible sensual experience. Philosophy cannot possess dogmatic certainty. Philosophy, unlike mathematics, cannot have definitions, axioms or demonstrations. All philosophical concepts must be ultimately based on a posteriori, experienced intuition. This is different from algebra and geometry, which use concepts that are derived from a priori intuitions, such as symbolic equations and spatial figures. Kant's basic intention in this section of the text is to describe why reason should not go beyond its already well-established limits. In section I, the discipline of pure reason in the sphere of dogmatism, Kant clearly explains why philosophy cannot do what mathematics can do in spite of their similarities. Kant also explains that when reason goes beyond its own limits, it becomes dogmatic. For Kant, the limits of reason lie in the field of experience as, after all, all knowledge depends on experience. According to Kant, a dogmatic statement would be a statement that reason accepts as true even though it goes beyond the bounds of experience.

Restraint should be exercised in the polemical use of pure reason. Kant defined this polemical use as the defense against dogmatic negations. For example, if it is dogmatically affirmed that God exists or that the soul is immortal, a dogmatic negation could be made that God doesn't exist or that the soul is not immortal. Such dogmatic assertions can't be proved. The statements are not based on possible experience. In section II, the discipline of pure reason in polemics, Kant argues strongly against the polemical use of pure reason. The dogmatic use of reason would be the acceptance as true of a statement that goes beyond the bounds of reason while the polemic use of reason would be the defense of such statement against any attack that could be raised against it. For Kant, then, there cannot possibly be any polemic use of pure reason. Kant argues against the polemic use of pure reason and considers it improper on the grounds that opponents cannot engage in a rational dispute based on a question that goes beyond the bounds of experience.

Kant claimed that adversaries should be freely allowed to speak reason. In return, they should be opposed through reason. Dialectical strife leads to an increase of reason's knowledge. Yet there should be no dogmatic polemical use of reason. The critique of pure reason is the tribunal for all of reason's disputes. It determines the rights of reason in general. We should be able to openly express our thoughts and doubts. This leads to improved insight. We should eliminate polemic in the form of opposed dogmatic assertions that cannot be related to possible experience.

According to Kant, the censorship of reason is the examination and possible rebuke of reason. Such censorship leads to doubt and skepticism. After dogmatism produces opposing assertions, skepticism usually occurs. The doubts of skepticism awaken reason from its dogmatism and bring about an examination of reason's rights and limits. It is necessary to take the next step after dogmatism and skepticism. This is the step to criticism. By criticism, the limits of our knowledge are proved from principles, not from mere personal experience.

If criticism of reason teaches us that we can't know anything unrelated to experience, can we have hypotheses, guesses, or opinions about such matters? We can only imagine a thing that would be a possible object of experience. The hypotheses of God or a soul cannot be dogmatically affirmed or denied, but we have a practical interest in their existence. It is therefore up to an opponent to prove that they don't exist. Such hypotheses can be used to expose the pretensions of dogmatism. Kant explicitly praises Hume on his critique of religion for being beyond the field of natural science. However, Kant goes so far and not further in praising Hume basically because of Hume's skepticism. If only Hume would be critical rather than skeptical, Kant would be all-praises. In concluding that there is no polemical use of pure reason, Kant also concludes there is no skeptical use of pure reason. In section II, the discipline of pure reason in polemics, in a special section, scepticism not a permanent state for human reason, Kant mentions Hume but denies the possibility that skepticism could possibly be the final end of reason or could possibly serve its best interests.

Proofs of transcendental propositions about pure reason (God, soul, free will, causality, simplicity) must first prove whether the concept is valid. Reason should be moderated and not asked to perform beyond its power. The three rules of the proofs of pure reason are: (1) consider the legitimacy of your principles, (2) each proposition can have only one proof because it is based on one concept and its general object, and (3) only direct proofs can be used, never indirect proofs (e.g., a proposition is true because its opposite is false). By attempting to directly prove transcendental assertions, it will become clear that pure reason can gain no speculative knowledge and must restrict itself to practical, moral principles. The dogmatic use of reason is called into question by the skeptical use of reason but skepticism does not present a permanent state for human reason. Kant proposes instead a critique of pure reason by means of which the limitations of reason are clearly established and the field of knowledge is circumscribed by experience. According to the rationalists and skeptics, there are analytic judgments a priori and synthetic judgments a posteriori. Analytic judgments a posteriori do not really exist. Added to all these rational judgments is Kant's great discovery of the synthetic judgment a priori.

The canon of pure reason

The canon of pure reason is a discipline for the limitation of pure reason. The analytic part of logic in general is a canon for the understanding and reason in general. However, the Transcendental Analytic is a canon of the pure understanding for only the pure understanding is able to judge synthetically a priori.

The speculative propositions of God, immortal soul, and free will have no cognitive use but are valuable to our moral interest. In pure philosophy, reason is morally (practically) concerned with what ought to be done if the will is free, if there is a God, and if there is a future world. Yet, in its actual practical employment and use, reason is only concerned with the existence of God and a future life. Basically, the canon of pure reason deals with two questions: Is there a God? Is there a future life? These questions are translated by the canon of pure reason into two criteria: What ought I to do? and What may I hope for? yielding the postulates of God's own existence and a future life, or life in the future.

The greatest advantage of the philosophy of pure reason is negative, the prevention of error. Yet moral reason can provide positive knowledge. There can't be a canon, or system of a priori principles, for the correct use of speculative reason. However, there can be a canon for the practical (moral) use of reason.

Reason has three main questions and answers:

1. What can I know? We cannot know, through reason, anything that can't be a possible sense experience; ("that all our knowledge begins with experience there can be no doubt")
2. What should I do? Do that which will make you deserve happiness;
3. What may I hope? We can hope to be happy as far as we have made ourselves deserving of it through our conduct.

Reason tells us that there is a God, the supreme good, who arranges a future life in a moral world. If not, moral laws would be idle fantasies. Our happiness in that intelligible world will exactly depend on how we have made ourselves worthy of being happy. The union of speculative and practical reason occurs when we see God's reason and purpose in nature's unity of design or general system of ends. The speculative extension of reason is severely limited in the transcendental dialectics of the Critique of Pure Reason, which Kant would later fully explore in the Critique of Practical Reason.

In the transcendental use of reason, there can be neither opinion nor knowledge. Reason results in a strong belief in the unity of design and purpose in nature. This unity requires a wise God who provides a future life for the human soul. Such a strong belief rests on moral certainty, not logical certainty. Even if a person has no moral beliefs, the fear of God and a future life acts as a deterrent to evil acts, because no one can prove the non-existence of God and an afterlife. Does all of this philosophy merely lead to two articles of faith, namely, God and the immortal soul? With regard to these essential interests of human nature, the highest philosophy can achieve no more than the guidance, which belongs to the pure understanding. Some would even go so far as to interpret the Transcendental Analytic of the Critique of Pure Reason as a return to the Cartesian epistemological tradition and a search for truth through certainty.

The Architectonic of Pure Reason

All knowledge from pure reason is architectonic in that it is a systematic unity. The entire system of metaphysics consists of: (1.) Ontology—objects in general; (2.) Rational Physiology—given objects; (3.) Rational cosmology—the whole world; (4.) Rational Theology—God. Metaphysics supports religion and curbs the extravagant use of reason beyond possible experience. The components of metaphysics are criticism, metaphysics of nature, and metaphysics of morals. These constitute philosophy in the genuine sense of the word. It uses science to gain wisdom. Metaphysics investigates reason, which is the foundation of science. Its censorship of reason promotes order and harmony in science and maintains metaphysics' main purpose, which is general happiness. In chapter III, the architectonic of pure reason, Kant defines metaphysics as the critique of pure reason in relation to pure a priori knowledge. Morals, analytics and dialectics for Kant constitute metaphysics, which is philosophy and the highest achievement of human reason.

The history of pure reason

Kant writes that metaphysics began with the study of the knowledge of God and the nature of a future world. It was concluded early that good conduct would result in happiness in another world as arranged by God. The object of rational knowledge was investigated by sensualists (Epicurus), and intellectualists (Plato). Sensualists claimed that only the objects of the senses are real. Intellectualists asserted that true objects are known only by the understanding mind. Aristotle and Locke thought that the pure concepts of reason are derived only from experience. Plato and Leibniz contended that they come from reason, not sense experience, which is illusory. Epicurus never speculated beyond the limits of experience. Locke, however, said that the existence of God and the immortality of the soul could be proven. Those who follow the naturalistic method of studying the problems of pure reason use their common, sound, or healthy reason, not scientific speculation. Others, who use the scientific method, are either dogmatists (Wolff) or skeptics (Hume). In Kant's view, all of the above methods are faulty. The method of criticism remains as the path toward the completely satisfying answers to the metaphysical questions about God and the future life in another world.

Terms and phrases

• a priori versus a posteriori
• Analytic versus synthetic
• Appearance
• Category
• concept versus object of sense perception
• Empirical versus pure
• intuition
• Manifold of the appearances
• Object
• Phenomena versus noumena
• Schema
• Transcendental idealism
• variant translations of Vorstellung: presentation or representation

Intuition and concept

Kant distinguishes between two different fundamental types of representation: intuitions and concepts:

1. Concepts are "mediate representations" (see A68/B93). Mediate representations represent things by representing general characteristics of things. For example, consider a particular chair. The concepts "brown," "wooden," "chair," and so forth are, according to Kant, mediate representations of the chair. They can represent the chair by representing general characteristics of the chair: being brown, being wooden, being a chair, and so forth.
2. Intuitions are "immediate representations" (see B41), that is, representations that represent things directly. One's perception of the chair is, according to Kant, an immediate representation. The perception represents the chair directly, and not by means of any general characteristics.

A diagram of Immanuel Kant's system of thought

Kant divides intuitions in the following ways:

• Kant distinguishes intuitions into pure intuitions and empirical intuitions. Empirical intuitions are intuitions that contain sensation. Pure intuitions are intuitions that do not contain any sensation (A50/B74). An example of an empirical intuition would be one's perception of a chair or another physical object. All such intuitions are immediate representations that have sensation as part of the content of the representation. The pure intuitions are, according to Kant, those of space and time, which are our mind's subjective condition of coordinating sensibilia. Our representations of space and time are not objective and real, but immediate representations that do not include sensation within those representations. Thus both are pure intuitions.
• Kant also divides intuitions into two groups in another way. Some intuitions require the presence of their object, i.e. of the thing represented by the intuition. Other intuitions do not. (The best source for these distinctions is Kant's Lectures on Metaphysics.) We might think of these in non-Kantian terms as first, perceptions, and second, imaginations (see B151). An example of the former: one's perception of a chair. An example of the latter: one's memory (Gedachtnis/Erinnerung) of a chair that has subsequently been destroyed. Throughout the Transcendental Aesthetic, Kant seems to restrict his discussion to intuitions of the former type: intuitions that require the presence of their object.

Kant also distinguished between a priori (pure) and a posteriori (empirical) concepts.

Tables of principles and categories of understanding in the critique

Kant borrowed the term "categories" from Aristotle, but with the concession that Aristotle's own categorizations were faulty. Aristotle's imperfection is apparent from his inclusion of "some modes of pure sensibility (quando, ubi, situs, also prius, simul), also an empirical concept (motus), none of which can belong to this genealogical register of the understanding."

Kant's divisions, however, are guided by his search in the mind for what makes synthetic a priori judgments possible.

FUNCTION OF THOUGHT IN JUDGMENT	CATEGORIES OF UNDERSTANDING	PRINCIPLES OF PURE UNDERSTANDING
Quantity	Quantity
Universal Particular Singular	Unity Plurality Totality	Axioms of Intuition
Quality	Quality
Affirmative Negative Infinite	Reality Negation Limitation	Anticipations of Perception
Relation	Relation
Categorical Hypothetical Disjunctive	Of Inherence and Subsistence (substantia et accidens) Of Causality and Dependence (cause and effect) Of Community (reciprocity between the agent and patient)	Analogies of Experience
Modality	Modality
Problematical Assertorical Apodeictical	Possibility-Impossibility Existence-Non-existence Necessity-Contingence	Postulates of Empirical Thought in General

Reception

Early responses: 1781–1793

The Critique of Pure Reason was the first of Kant's works to become famous. According to Frederick C. Beiser, the work helped to discredit rationalist metaphysics of the kind associated with Leibniz and Wolff which had appeared to provide a priori knowledge of the existence of God, although Beiser notes that this school of thought was already in decline by the time the Critique of Pure Reason was published. In his view, Kant's philosophy became successful in the early 1790s partly because Kant's doctrine of "practical faith" seemed to provide a justification for moral, religious, and political beliefs without an a priori knowledge of God. However, the Critique of Pure Reason received little attention when it was first published. Kant did not expect reviews from anyone qualified to appraise the work, and initially heard only complaints about its obscurity. The theologian and philosopher Johann Friedrich Schultz wrote that the public saw the work as "a sealed book" consisting in nothing but "hieroglyphics". The first review appeared in the Zugaben zu den Göttinger gelehrte Anzeigen in 1782. The review, which denied that there is any distinction between Kant's idealism and that of Berkeley, was anonymous and became notorious. Kant reformulated his views because of it, redefining his transcendental idealism in the Prolegomena to Any Future Metaphysics (1783) and the second edition of the Critique of Pure Reason. The review was denounced by Kant, but defended by Kant's empiricist critics, and the resulting controversy drew attention to the Critique of Pure Reason.

Kant believed that the anonymous review was biased and deliberately misunderstood his views. He discussed it in an appendix of the Prolegomena, accusing its author of failing to understand or even address the main issue addressed in the Critique of Pure Reason, the possibility of synthetic a priori judgments, and insisting on the distinction between transcendental idealism and the idealism of Berkeley. In a letter to Kant, the philosopher Christian Garve admitted to having written the review, which he disowned due to editorial changes outside his control. Though Garve did not inform Kant of this, the changes were made by J. G. Feder. Following the controversy over Garve's review, there were no more reviews of the Critique of Pure Reason in 1782 except for a brief notice. The work received greater attention only in 1784, when Shultz's commentary was published and a review by the philosopher and historian of philosophy Dietrich Tiedemann was published in the Hessische Beyträge zur Gelehrsamkeit und Kunst. Tiedemann attacked the possibility of the synthetic a priori and defended the possibility of metaphysics. He denied the synthetic status of mathematical judgments, maintaining that they can be shown to be analytic if the subject term is analyzed in full detail, and criticized Kant's theory of the a priori nature of space, asking how it was possible to distinguish one place from another when the parts of absolute space are identical in themselves. Kant's issued a hostile reaction. Kant maintained that Tiedemann did not understand the problems facing the critical philosophy.

Christian Gottlieb Selle, an empiricist critic of Kant influenced by Locke to whom Kant had sent one of the complimentary copies of the Critique of Pure Reason, was disappointed by the work, considering it a reversion to rationalism and scholasticism, and began a polemical campaign against Kant, arguing against the possibility of all a priori knowledge. His writings received widespread attention and created controversy. Though Kant was unable to write a reply to Selle, he did engage in a public dispute with Feder, after learning of Feder's role in the review published in Zugaben zu den Göttinger gelehrte Anzeigen. In 1788, Feder published Ueber Raum und Causalität: Zur Prüfung der kantischen Philosophie, a polemic against the Critique of Pure Reason in which he argued that Kant employed a "dogmatic method" and was still employing the methodology of rationalist metaphysics, and that Kant's transcendental philosophy transcends the limits of possible experience. Feder believed that Kant's fundamental error was his contempt for "empirical philosophy", which explains the faculty of knowledge according to the laws of nature. With Christian Meiners, he edited a journal, the Philosophische Bibliothek, opposed to Kantianism.

Feder's campaign against Kant was unsuccessful and the Philosophische Bibliothek ceased publication after only a few issues. Other critics of Kant continued to argue against the Critique of Pure Reason, with Gottlob August Tittel, who was influenced by Locke, publishing several polemics against Kant, who, although worried by some of Tittel's criticisms, addressed him only in a footnote in the preface to the Critique of Practical Reason. Tittel was one of the first to make criticisms of Kant, such as those concerning Kant's table of categories, the categorical imperative, and the problem of applying the categories to experience, that have continued to be influential. The philosopher Adam Weishaupt, founder and leader of the secret society the Illuminati, and an ally of Feder, also published several polemics against Kant, which attracted controversy and generated excitement. Weishaupt charged that Kant's philosophy leads to complete subjectivism and the denial of all reality independent of passing states of consciousness, a view he considered self-refuting. Herman Andreas Pistorius was another empiricist critic of Kant. Kant took Pistorius more seriously than his other critics and believed that he had made some of the most important objections to the Critique of Pure Reason. Beiser writes that many sections of the Critique of Practical Reason are "disguised polemics against Pistorius". Pistorius argued that, if Kant were consistent, his form of idealism would not be an improvement over that of Berkeley, and that Kant's philosophy contains internal contradictions.

Though the followers of Wolff, such as J. G. E. Maass, J. F. Flatt, and J. A. Ulrich, initially ignored the Critique of Pure Reason, they began to publish polemics against Kant in 1788. The theologian Johann Augustus Eberhard began to publish the Philosophisches Magazin, which was dedicated to defending Wolff's philosophy. The Wolffian critics argued that Kant's philosophy inevitably ends in skepticism and the impossibility of knowledge, defended the possibility of rational knowledge of the supersensible world as the only way of avoiding solipsism. They maintained that the criterion Kant proposed to distinguish between analytic and synthetic judgments had been known to Leibniz and was useless, since it was too vague to determine which judgments are analytic or synthetic in specific cases. These arguments led to a controversy between the Wolffians and Kant's followers over the originality and adequacy of Kant's criterion. The Wolffian campaign against Kant was ultimately unsuccessful. Beiser argues that the decisive reason for Kant's victory over the Wolffians was the French Revolution, writing that, "The political revolution in France seemed to find its abstract formulation with the philosophical revolution in Germany." Specifically, he concludes that the principle of autonomy, which has an important role in Kant's ethics, appeared to express and justify the egalitarian demands behind the French Revolution.

Later responses

The Critique of Pure Reason has exerted an enduring influence on Western philosophy. The constructive aspect of the work, Kant's attempt to ground the conditions for the possibility of objects in the conditions of experience, helped bring about the development of German idealism. However, the work's destructive potential influenced Young Hegelians such as Bruno Bauer, Ludwig Feuerbach, and Karl Marx, and also Friedrich Nietzsche, whose philosophy has been seen as a form of "radical Kantianism" by Howard Caygill. Other interpretations of the Critique by philosophers and historians of philosophy have stressed different aspects of the work. The late 19th-century neo-Kantians Hermann Cohen and Heinrich Rickert focused on its philosophical justification of science, Martin Heidegger and Heinz Heimsoeth on aspects of ontology, and Peter Strawson on the limits of reason within the boundaries of sensory experience. Hannah Arendt and Jean-François Lyotard dealt with its work of orientation of a limited understanding in the field of world history.

Referencing

The A and B numbers used as standard references refer to the page numbers of the first (1781) and second (1787) German editions respectively. Sometimes NKS numbers are used to refer to pages of the Norman Kemp Smith English translation (St. Martin's Press, Macmillan, 1929).

English translations

Critique of Pure Reason. Translated by Francis Haywood. William Pickering. 1838. (first English translation)

Critique of Pure Reason. Translated by J. M. D. Meiklejohn. 1855 – via Project Gutenberg.

Critique of Pure Reason. Translated by Thomas Kingsmill Abbott. 1873.

Critique of Pure Reason. Translated by Friedrich Max Müller. The Macmillian Company. 1881. (Introduction by Ludwig Noiré)

Critique of Pure Reason. Translated by Norman Kemp Smith. Palgrave Macmillan. 1929. ISBN 1-4039-1194-0. Archived from the original on 2009-04-27.

Critique of Pure Reason. Translated by Wolfgang Schwartz. Scientia Verlag und Antiquariat. 1982. ISBN 978-3-5110-9260-3.

Critique of Pure Reason, Abridged. Translated by Werner S. Pluhar. Hackett Publishing. 1999. ISBN 978-1-6246-6605-6.

Critique of Pure Reason. Translated and edited by Paul Guyer and Allen W. Wood. Cambridge University Press. 1999. ISBN 978-0-5216-5729-7.

Critique of Pure Reason. Translated by Marcus Weigelt. Penguin Books. 2007. ISBN 978-0-1404-4747-7.

Gifted education

From Wikipedia, the free encyclopedia

Gifted education (also known as Gifted and Talented Education (GATE), Talented and Gifted (TAG), or G/T) is a broad term for special practices, procedures, and theories used in the education of children who have been identified as gifted or talented.

The main approaches to gifted education are enrichment and acceleration. An enrichment program teaches additional, related material, but keeps the student progressing through the curriculum at the same rate. For example, after the gifted students have completed the normal work in the curriculum, an enrichment program might provide them with additional details about a subject in the curriculum. An acceleration program advances the student through the standard curriculum faster than normal. When gifted students have completed the normal work, they move on to the next subject in the curriculum, even though the rest of the class is still working on the first subject.

There is no standard global definition of what a gifted student is. Multiple definitions of giftedness are used by different groups. Most of these definitions select the students who are the most skilled or talented in a given area, e.g., the students with the most skill or talent in music, language, logical reasoning, or mathematics. The percentage of students selected varies, generally with 10% or fewer being selected for gifted education programs. However, since students vary in their aptitudes and achievements, a student who is not gifted in one area, such as music, may be considered gifted in another, such as language. Consequently, even if all programs agreed to include only the top 5% of students in their area, more than just 5% of students would be identified as gifted.

History

Classical era to Renaissance

Gifted and talented education dates back thousands of years. Plato (c. 427–c. 347 BCE) advocated providing specialized education for intellectually gifted young men and women. In China's Tang Dynasty (580-618 CE), child prodigies were summoned to the imperial court for specialized education. Throughout the Renaissance, those who exhibited creative talent in art, architecture, and literature were supported by both the government and private patronage.

Sir Francis Galton

One of the earliest Western studies of human abilities was conducted by Sir Francis Galton, who between 1888 and 1894 developed and compiled measurements of over 7,500 individuals to gauge their natural intellectual abilities. In his studies he determined that if a parent deviates from the norm, so will the child, but to a lesser extent, one of the earliest observed examples of regression toward the mean. Galton believed that individuals could be improved through interventions in heredity, a movement he named eugenics. He categorized people into gifted, capable, average, or degenerate, and recommended breeding between the first two categories, and forced abstinence for the latter two. His term for the most intelligent and talented people was "eminent," and after studying England's most prominent families, concluded that one's eminence was directly related to his direct hereditary line.

Lewis Terman

At Stanford University in 1918, Lewis Terman adapted Alfred Binet's Binet-Simon intelligence test into the Stanford-Binet test, and introduced intelligence quotient (IQ) scoring for the test. According to Terman, the IQ was one's mental age compared to one's chronological age, based on the mental age norms he compiled after studying a sample of children.^[4] He defined intelligence as "the ability to carry on abstract thinking". During World War I Terman was a commissioned officer of the United States Army, and collaborated with other psychologists in developing intelligence tests for new recruits to the armed forces. For the first time, intelligence testing was given to a wide population of drafted soldiers.

After the war, Terman undertook an extensive longitudinal study of 643 children in California who scored at IQ 140 or above, the Genetic Studies of Genius, continuing to evaluate them throughout their lives. Subjects of these case studies were called "Termites" and the studies contacted the children in 1921, and again in 1930, 1947, and 1959 after his death. Terman's studies have to date been the most extensive on high-functioning children, and are still quoted in psychological literature today. Terman claimed to have disproven common misconceptions, such as that highly intelligent children were prone to ill physical and mental health, that their intelligence burned out early in their lives, or that they either achieved greatly or underachieved.

Leta Hollingworth

A professional colleague of Terman's, Leta Hollingworth was the first in the United States to study how best to serve students who showed evidence of high performance on tests. Although recognizing Terman's and Galton's beliefs that heredity played a vital role in intelligence, Hollingworth gave similar credit to home environment and school structure. Hollingworth worked to dispel the pervasive belief that "bright children take care of themselves" and emphasized the importance of early identification, daily contact, and grouping gifted children with others with similar abilities. Hollingworth performed an 18-year-long study of 50 children in New York City who scored 155 or above on the Stanford-Binet, and studied smaller groups of children who scored above a 180. She also ran a school in New York City for bright students that employed a curriculum of student-led exploration, as opposed to a teacher providing students with a more advanced curriculum they would encounter later in life.

The Cold War

One unforeseen result of the launch of Sputnik by the Soviet Union was the immediate emphasis on education for bright students in the United States, and this settled the question whether the federal government should get involved in public education at all. The National Defense Education Act (NDEA) was passed by Congress in 1958 with $1 billion US to bolster science, math, and technology in public education. Educators immediately pushed to identify gifted students and serve them in schools. Students chosen for gifted services were given intelligence tests with a strict cutoff, usually at 130, which meant that students who scored below the 130 were not identified.

Marland Report

The impact of the NDEA was evident in schools for years after, but a study on how effective education was meeting the needs of gifted students was initiated by the United States Department of Education in 1969. The Marland Report, completed in 1972, for the first time presented a general definition of giftedness, and urged districts to adopt it. The report also allowed students to show high functioning on talents and skills not measurable by an intelligence test. The Marland Report defined gifted as "Children capable of high performance include those with demonstrated achievement and/or potential ability in any of the following areas, singly or in combination:

• General intellectual ability,
• Specific academic aptitude,
• Creative or productive thinking,
• Leadership ability,
• Visual and performing arts, or
• Psychomotor ability."

The report's definition continues to be the basis of the definition of giftedness in most districts and states.

A Nation at Risk

In 1983, the result of an 18-month-long study of secondary students was published as A Nation at Risk, and claimed that students in the United States were no longer receiving superior education, and in fact, could not compete with students from other developed countries in many academic exercises. One of the recommendations the book made was to increase services to gifted education programs, citing curriculum enrichment or acceleration specifically. The US federal government was also urged to create standards for the identification and servicing of gifted students.

Jacob Javits Gifted and Talented Students Education Act

The Jacob Javits Gifted and Talented Students Education Act was passed in 1988 as part of the Elementary and Secondary Education Act (ESEA). Instead of funding district-level gifted education programs, the Javits Act instead has three primary components: the research of effective methods of testing, identification, and programming, which is performed at the National Research Center on the Gifted and Talented; the awarding of grants to colleges, states, and districts that focus on underrepresented populations of gifted students; and grants awarded to state and districts for program implementation.

Annual funding for grants must be passed by US Congress, and totaled $9.6 million US in 2007, but the money isn't promised. While he was President, George W. Bush eliminated the money every year of his term, but members of Congress overrode the president to make sure the grant money was distributed.

No Child Left Behind

The most recent US federal education initiative was signed into law in 2002. The goal of No Child Left Behind (NCLB) is to bring proficiency of all students to grade level, but critics note it does not address the needs of gifted students who perform above grade level. The act imposes punishments on schools, administrators, and teachers when students do not achieve to the plan's designs, but does not address any achievement standards for high functioning students, forcing schools and teachers to spend their time with low achieving students. An article in The Washington Post declared, "The unmistakable message to teachers -- and to students -- is that it makes no difference whether a child barely meets the proficiency standard or far exceeds it." Gifted services have been recently eroding as a result of the new legislation, according to a 2006 article in The New York Times.

A Nation Deceived

In 2004, the John Templeton Foundation sponsored a report titled A Nation Deceived: How Schools Hold Back America's Brightest Students, highlighting the disparity between the research on acceleration (which generally supports it, both from an academic and a psychological point of view), and the educational practices in the US that are often contrary to the conclusions of that research. The Institute for Research and Policy on Acceleration (IRPA) was established in 2006 at The Connie Belin & Jacqueline N. Blank International Center for Gifted Education and Talent Development at the University of Iowa College of Education through the support of the John Templeton Foundation following the publication of this report.

Studies of giftedness

The development of early intelligence tests by Alfred Binet led to the Stanford-Binet IQ test developed by Lewis Terman. Terman began long-term studies of gifted children with a view to checking if the popular view "early ripe, early rot" was true. The Terman Genetic Studies of Genius longitudinal study has been described by successor researchers who conducted the study after Terman's death and also by an independent researcher who had full access to the study files.

Modern studies by James and Kulik conclude that gifted students benefit least from working in a mixed-level class, and benefit most from learning with other similarly advanced students in accelerated or enriched classes.

Definition of giftedness

Educational authorities differ on the definition of giftedness: even when using the same IQ test to define giftedness, they may disagree on what gifted means - one may take up the top 2 percent of the population, another might take up the top 5 percent of a population, which may be within a state, district, or school. Within a single school district, there can be substantial differences in the distribution of measured IQ. (The IQ for the top percentile at a high-performing school may be quite different from that at a lower performing school.)

Dr Peter Marshall

Dr Peter Marshall obtained his doctorate in 1995, for research carried out in this field in the years from 1986. At the time, he was the first Research Director of The Mensa Foundation for Gifted Children. His work challenged the difficult childhood hypothesis, concluding that gifted children, by and large, do not have any more difficult childhoods than mainstream children and, in fact, that where they do, their giftedness probably helps them cope better than mainstream children. His thesis is published under the title Growing up Gifted – Triangulations with the Gulbenkian Project and provided the material for his subsequent book Educating a Gifted Child.

He has acted as consultant to schools and local education authorities such as Cumbria County Council and Blackburn, Hyndburn and Ribble Valley Health Authority and Thorncliffe Grammar in Barrow in Furness and he has been chosen to give the Mensa Lecture on the Subject at Trinity College Cambridge in August 2018.

In his book, Educating a Gifted Child, he analyses a large range of causes of underachievement, explains the social attitudes to giftedness, lists the range of non-intellective aspects of giftedness, and explores the concepts of intelligence and IQ tests.

Dr Marshall is the President of The International Association for High Ability (IAFHA), which aims to help gifted individuals from all backgrounds to fulfil their potential for the benefit of themselves, their society and the human race in general.

In Identifying Gifted Children: A Practical Guide, Susan K. Johnsen (2004) explains that gifted children all exhibit the potential for high performance in the areas included in the United States federal definition of gifted and talented students:

The term 'gifted and talented' when used in respect to students, children, or youth means [those who show] evidence of high performance capability in areas such as intellectual, creative, artistic, or leadership capacity, or in specific academic fields, and who require services or activities not ordinarily provided by the school in order to fully develop such capabilities.

— P.L. 103–382, Title XIV, p. 388

The National Association for Gifted Children in the United States defines giftedness as:

Gifted individuals are those who demonstrate outstanding levels of aptitude (defined as an exceptional ability to reason and learn) or competence (documented performance or achievement in top 10% or rarer) in one or more domains. Domains include any structured area of activity with its own symbol system (e.g., mathematics, music, language) and/or set of sensorimotor skills (e.g., painting, dance, sports).
The development of ability or talent is a lifelong process. It can be evident in young children as exceptional performance on tests and/or other measures of ability or as a rapid rate of learning, compared to other students of the same age, or in actual achievement in a domain. As individuals mature through childhood to adolescence, however, achievement and high levels of motivation in the domain become the primary characteristics of their giftedness. Various factors can either enhance or inhibit the development and expression of abilities.

This definition has been adopted in part or completely by the majority of the states in the United States. Most have some definition similar to that used in the State of Texas, whose definition states:

"[The phrase] 'gifted and talented student' means a child or youth who performs at or shows the potential for performing at a remarkably high level of accomplishment when compared to others of the same age, experience, or environment, and who:

• exhibits high performance capability in an intellectual, creative, or artistic area;
• possesses an unusual capacity for leadership; or
• excels in a specific academic field."
  — 74th legislature of the State of Texas, Chapter 29, Subchapter D, Section 29.121

The major characteristics of these definitions are (a) the diversity of areas in which performance may be exhibited (e.g., intellectual, creative, artistic, leadership, academic), (b) the comparison with other groups (e.g., those in general education classrooms or of the same age, experience, or environment), and (c) the use of terms that imply a need for development of the gift (e.g., capability and potential).

Reliance on IQ

In her book, Identifying Gifted Children: A Practical Guide, Susan K. Johnsen (2004) writes that schools should use a variety of measures of students' capability and potential when identifying gifted children. These measures may include portfolios of student work, classroom observations, achievement measures, and intelligence scores. Most educational professionals accept that no single measure can be used in isolation to accurately identify every gifted child.

Even if the notion of IQ is generally useful for identifying academically talented students who would benefit from further services, the question of the cutoff point for giftedness is still important. As noted above, different authorities often define giftedness differently.

Global implementation

Australia

Public gifted education in Australia varies significantly from state to state. New South Wales has 95 primary schools with opportunity classes catering to students in year 5 and 6. New South Wales also has 17 fully selective secondary schools and 25 partially selective secondary schools. Western Australia has selective programs in 17 high schools, including Perth Modern School, a fully selective school. Queensland has 3 Queensland Academies catering to students in years 10,11 and 12. South Australia has programs in 3 public high schools catering to students in years 8,9 and 10, including Glenunga International High School. The Victorian Government commissioned a parliamentary inquiry into the education of gifted and talented children in 2012. One recommendation from the inquiry was for the Victorian Government to list the schools with programs, but the government has not implemented this recommendation. Some private schools have developed programs for gifted children.

State/Territory	Public Primary Schools with Programs	Partially Selective Public High Schools	Fully Selective Public High Schools
New South Wales	95	25	17
Western Australia	0	16	1
Queensland	0	0	3
South Australia	0	3	0
Victoria	?	?	6
Tasmania	0	0	0
Australian Capital Territory	0	0	0
Northern Territory	0	0	0

Canada

Queen Elizabeth High School in Calgary offers the GATE Program to both Division 3 and 4 (in total, Grades 7-12)

The Calgary Board of Education (CBE), in Calgary, Alberta, has various elementary, middle and high schools offering the GATE Program, standing for Gifted and Talented Education, for Grades 4-12, or Divisions 2-4. The program for students, who, through an IQ test, ranked in the Very Superior Range; falling into Gifted or Genius. For each of the three divisions, there are 2 schools offering GATE, one for the North Side of the city (CBE Areas I, II and III) and one for the South Side (CBE Areas IV and V). For Division 2, or Grades 4-6, it is available at Hillhurst Elementary School for the North and Nellie McClung Elementary School for the South. For Division 3, or Grades 7-9, it is available at Queen Elizabeth High School for the North and John Ware Junior High School for the South. For Division 3, or Grades 10-12, Queen Elizabeth High School, which is a joint Junior High-Senior High offers it for the North and Henry Wise Wood Senior High School offers it for the south. GATE classes go more in depth and learns some curriculum for the following grade level, with tougher assignments and a faster learning pace. They benefit from being around students like them. These students attend the school alongside regular students and those in other programs (e.g. IB, AP.) In the 2014-15 school year, students from Grades 4-7 in the south will be attending Louis Riel Junior High School, already home to a science program, and students in the regular program there will be moved to Nellie McClung and John Ware. Students at John Ware will be phased out: eighth grade GATE will end in June 2015, and ninth grade GATE will end in 2016, while GATE will be expanding to Grade 9 at Louis Riel by September 2016. Prior to John Ware, the GATE program was housed at Elboya. A large number of teachers from Nellie McClung and John Ware will be moving to the new location, which was picked to deal with student population issues and to concentrate resources.

Notable alumni of the CBE GATE Program include the 36th mayor of Calgary, Naheed Nenshi, from Queen Elizabeth High School.

Naheed Nenshi, a mayor of Calgary and an alumnus of the CBE GATE Program.

Vancouver Board of Education's gifted program is called Multi-Age Cluster Class or MACC.[1] This is a full-time program for highly gifted elementary students from grades 4 to 7. Through project-based learning, students are challenged to use higher order thinking skills. Another focus of the program is autonomous learning; students are encouraged to self-monitor, self-reflect and seek out enrichment opportunities. Entrance to the program is initiated through referral followed by a review by a screening committee. IQ tests are used but not exclusively. Students are also assessed by performance, cognitive ability tests, and motivation. There are 4 MACC's in Vancouver: grade 4/5 and grade 6/7 at Sir William Osler Elementary, grade 5/6/7 at Tecumseh Elementary, and a French Immersion grade 5/6/7 at Kerrisdale Elementary.

At a lower scale, the Peel District School Board operates its Regional Enhanced Program at The Woodlands School, Lorne Park Secondary School, Glenforest Secondary School, Heart Lake Secondary School and Humberview Secondary School to provide students an opportunity to develop and explore skills in a particular area of interest. Students identified as gifted (which the PDSB classifies as "enhanced") may choose to attend the nearest of these high schools instead of their assigned home high school. In the Regional Enhanced Program, enhanced students take core courses (primarily, but not limited to English, mathematics, and the sciences) in an environment surrounded by fellow enhanced peers. The classes often contain modified assignments that encourage students to be creative.

Ecuador

In Ecuador, Centro Ecuatoriano para el Desarrollo del Alto Potencial started in 2018 as the first all around gifted children educational program in the country. The center offers evaluations, extracurricular activities and one to one psychological tutoring that helps with the academic and social skills of gifted children. The center's mission is to develop and deliver high quality academic and psychosocial programs for the integral development of gifted and talented children in Ecuador.

Hong Kong

Definition of Giftedness in Hong Kong

The Education Commission Report No.4  issued in 1990 recommended a policy on gifted education for schools in Hong Kong and suggested that a broad definition of giftedness using multiple criteria should be adopted.

Gifted children generally have exceptional achievement or potential in one or more of the following domains:

• a high level of measured intelligence;
• specific academic aptitude in a subject area;
• creative thinking;
• superior talent in visual and performing arts;
• natural leadership of peers; and
• psychomotor ability - outstanding performance or ingenuity in athletics, mechanical skills or other areas requiring gross or fine motor coordination.

The multi-dimensional aspect of intelligence has been promoted by Professor Howard Gardner from the Harvard Graduate School of Education in his Theory of Multiple Intelligences. In his introduction to the tenth anniversary edition of his classic work Frames of Mind. The theory of multiple intelligences, he says:

In the heyday of the psychometric and behaviorist eras, it was generally believed that intelligence was a single entity that was inherited; and that human beings - initially a blank slate - could be trained to learn anything, provided that it was presented in an appropriate way. Nowadays an increasing number of researchers believe precisely the opposite; that there exists a multitude of intelligences, quite independent of each other; that each intelligence has its own strengths and constraints; that the mind is far from unencumbered at birth; and that it is unexpectedly difficult to teach things that go against early 'naive' theories of that challenge the natural lines of force within an intelligence and its matching domains. (Gardner 1993: xxiii)

Howard Gardner initially formulated a list of seven intelligences, but later added an eighth, that are intrinsic to the human mind: linguistic, logical/mathematical, visual/spatial, musical, bodily kinesthetic, intrapersonal, interpersonal, and naturalist intelligences. It has become widely accepted at both local and international scales to adopt a broad definition of giftedness using multiple criteria to formulate gifted education policy.

The Mission and Principles of Gifted Education Policy in Hong Kong

The mission of gifted education is to systematically and strategically explore and develop the potential of gifted students. Gifted learners are to be provided with opportunities to receive education at appropriate levels in a flexible teaching and learning environment. The guiding principles for gifted education in Hong Kong are:

• Nurturing multiple intelligences as a requirement of basic education for all students and an essential part of the mission for all schools
• The needs of gifted children are best met within their own schools though it is recognized that opportunities to learn with similarly gifted students are important. Schools have an obligation to provide stimulating and challenging learning opportunities for their students
• The identification of gifted students should recognize the breadth of multiple intelligences
• Schools should ensure that the social and emotional, as well as the intellectual, needs of gifted children are recognized and met.

India

In India, Jnana Prabodhini Prashala started in 1968, is probably the first school for gifted education. The motto is motivating intelligence for social change. The school, located in central Pune, admits 80 students each year, after thorough testing, which includes two written papers and an interview. The psychology department of Jnana Prabodhini has worked on J. P. Guilford's model of Intelligence.

Iran

National Organization for Development of Exceptional Talents (NODET, also known as SAMPAD, Persian: سمپاد, which stands for سازمان ملی پرورش استعدادهای درخشان in Persian) are national Middle and High Schools in Iran developed specifically for the development of exceptionally talented students in Iran. NODET was first established in 1976 and re-established in 1987.

Admission to NODET schools is selective and based on a comprehensive nationwide entrance examination procedure.

Every year thousands of students apply to enter the schools, from which less than 5% are chosen for the 99 middle schools and 98 high-schools within the country. All applicants must have a minimum GPA of 19 (out of 20) for attending the entrance exam. In 2006, 87,081 boys and 83,596 girls from 56 cities applied, and finally 6,888 students were accepted for the 2007 middle schools. The admission process is much more selective in big cities like Tehran, Isfahan, Mashhad and Karaj in which less than 150 students are accepted after two exams and interviews, out of over 50,000 applicants.

Top schools of NODET (and also Iran's top) are Allameh Helli High School and Shahid Madani High School (in Tabriz), Farzanegan High School located in Tehran, Shahid Ejei High School located in Isfahan, Shahid Hashemi Nejad High School located in Mashhad and Shahid Soltani School located in Karaj. Courses taught in NODET schools are college-level in fields such as Biology, Chemistry, Mathematics, Physics and English Language. The best teachers of the ministry of education are chosen mainly by the school's principal and faculty to teach at NODET schools. Schools mainly have only two majors (normal schools have three majors), math-physics and experimental sciences (like math-physics but having biology as the main course). Even though social sciences are taught, there is much less emphasis on these subjects due to the lack of interest in both students and the organization.

Norway

Norway has no centre for gifted or talented children or youth. However, there is the privately run Barratt Due Institute of Music who offers musical kindergarten, evening school and college for highly talented young musicians. There is also the public secondary school for talents in ballet at Ruseløkka school in Oslo, who admits the 15 top dancers. On athletics, Privately run Norwegian Elite Sports Gymnasium (NTG) offers secondary school for talents in five locations in Norway. This account might not be complete.

Republic of Korea

Following the Gifted Education Promotion Law (영재교육진흥법) in the year 2000, the Ministry of Education, Science, and Technology (MEST) founded the National Research Center for Gifted and Talented Education (NRCGTE) in 2002 to ensure effective implementation of gifted education research, development, and policy. The center is managed by the Korean Educational Development Institute (KEDI). Presently twenty-five universities conduct gifted and talented education research in some form; for example, Seoul National University is conducting Science-gifted Education Center, and KAIST is conducting Global Institute For Talented Education (GIFTED), the Korean Society for the Gifted and Talented (한국영재교육학회) and the Korean Society for the Gifted (사단법인 한국영재학회).

Education for the scientifically gifted in Korea can be traced back to the 1983 government founding of Gyeonggi Science High School.^[39] Following three later additions (Korea Science Academy of KAIST; Seoul Science High School and Daegu Science High School), approximately 1,500, or 1 in 1,300 (0.08 percent) of high school students are currently enrolled among its four gifted academies. By 2008, about 50,000, or 1 in 140 (0.7 percent) of elementary and middle school students participated in education for the gifted. In 2005, a program was undertaken to identify and educate gifted children of socioeconomically underprivileged people. Since then, more than 1,800 students have enrolled in the program.

Gradually the focus has expanded over time to cover informatics, arts, physical education, creative writing, humanities, and social sciences, leading to the 2008 creation of the government funded Korean National Institute for the Gifted Arts. To pluralize the need for trained professional educators, teachers undergo basic training (60 hours), advanced training (120 hours), and overseas training (60 hours) to acquire skills necessary to teach gifted youth.

Singapore

In Singapore, the Gifted Education Programme (GEP) was introduced in 1984 and is offered in the upper primary years (Primary 4-6, ages 10–12). Pupils undergo rigorous testing in Primary 3 (age 9) for admission into the GEP for Primary 4 to 6. About 1% of the year's cohort are admitted into the programme. The GEP is offered at selected schools, meaning that these pupils attend school alongside their peers in the mainstream curriculum but attend separate classes for certain subjects. As of the 2016 academic year, there are 9 primary schools which offer the GEP.

Slovakia

The School for Gifted Children in Bratislava was established in 1998. It offers education known as APROGEN - Alternative Program for Gifted Education.

United Kingdom

In England, schools are expected to identify 5-10% of students who are gifted and/or talented in relation to the rest of the cohort in that school—an approach that is pragmatic (concerned with ensuring schools put in place some provision for their most able learners) rather than principled (in terms of how to best understand giftedness). The term gifted applies to traditional academic subjects, and talented is used in relation to high levels of attainment in the creative arts and sports. The National Academy for Gifted and Talented Youth ran from 2002 to 2007 at the University of Warwick. Warwick University decided not to reapply for the contract to run NAGTY in 2007, instead introducing its own programme, the International Gateway for Gifted Youth in 2008. In January 2010, the government announced that NAGTY was to be scrapped the following month.

United States

In the United States, each state department of education determines if the needs of gifted students will be addressed as a mandatory function of public education. If so, the state determines the definition of which students will be identified and receive services, but may or may not determine how they shall receive services. If a state does not consider gifted education mandatory, individual districts may, thus the definition of what gifted is varies from state or district.

In contrast with special education, gifted education is not regulated on a federal level, although recommendations by the US Department of Education are offered. As such, funding for services is not consistent from state to state, and although students may be identified, the extent to which they receive services can vary widely depending upon a state or district's budget.

Gifted education programs are also offered at various private schools. For example, The Mirman School caters to children with an IQ of 138 and above.

Commonly used terms

Differentiation

Modification of a gifted student’s curriculum to accommodate their specific needs. This may include changing the content or ability level of the material.

Affective curriculum

A curriculum that is designed to teach gifted students about emotions, self-esteem, and social skills. This can be valuable for all students, especially those who have been grouped with much older students, or who have been rejected by their same-age, but academically typical, peers.

Heterogeneous grouping

A strategy that groups students of varied ability, preparedness, or accomplishment in a single classroom environment. Usually this terminology is applied to groupings of students in a particular grade, especially in elementary school. For example, students in fifth grade would be heterogeneously grouped in math if they were randomly assigned to classes instead of being grouped by demonstrated subject mastery. Heterogeneous grouping is sometimes claimed to provide a more effective instructional environment for less prepared students.

Homogeneous grouping

A strategy that groups students by specific ability, preparedness, or interest within a subject area. Usually this terminology is applied to groupings of students in a particular grade, especially in elementary school. For example, students in fifth grade would be homogeneously grouped in math if they were assigned to classes based on demonstrated subject mastery rather than being randomly assigned. Homogeneous grouping can provide more effective instruction for the most prepared students.

Individualized Education Program (IEP)

A written document that addresses a student's specific individual needs. It may specify accommodations, materials, or classroom instruction. IEPs are often created for students with disabilities, who are required by law to have an IEP when appropriate. Most states are not required to have IEPs for students who are only identified as gifted. Some students may be intellectually gifted in addition to having learning and/or attentional disabilities, and may have an IEP that includes, for instance, enrichment activities as a means of alleviating boredom or frustration, or as a reward for on-task behavior. In order to warrant such an IEP, a student needs to be diagnosed with a separate emotional or learning disability that is not simply the result of being unchallenged in a typical classroom. These are also known as Individual Program Plans, or IPPs.

Forms

Attempts to provide gifted education can be classified in several ways. Most gifted students benefit from a combination of approaches at different times.

Hobby

Activities such as reading, creative writing, sport, computer games, chess, music, dance, foreign languages, and art give an extra intellectual challenge outside of school hours. For some GATE students, (if they are a top level) the district might send a letter containing a suggestion of skipping a grade.

Enrichment

On the primary school level, students spend all class time with their peers, but receive extra material to challenge them. Enrichment may be as simple as a modified assignment provided by the regular classroom teacher, or it might include formal programs such as Odyssey of the Mind, Destination Imagination or academic competitions such as Brain Bowl, Future Problem Solving, Science Olympiad, National History Day, science fairs, or spelling bees. Programmes of enrichment activities may also be organised outside the school day (e.g. the ASCEND project in secondary science education ). This work is done in addition to, and not instead of, any regular school work assigned. Critics of this approach argue that it requires gifted students to do more work instead of the same amount at an advanced level. On the secondary school level sometimes an option is to take more courses like English, Spanish, Latin, Philosophy, Science, etc., or to engage in extra curricular activities. Some perceive there to be a necessary choice between enrichment and acceleration, as if the two were mutually exclusive alternatives. However, other researchers see the two as complements to each other.

Compacting

The regular school material is compacted by pretesting the student to establish which skills and content have already been mastered. Pretests can be presented on a daily basis (pupils doing the most difficult items on a worksheet first and skipping the rest if they are performed correctly), or before a week or longer unit of instructional time. When a student demonstrates an appropriate level of proficiency, further repetitive practice can be safely skipped, thus reducing boredom and freeing up time for the student to work on more challenging material.

Self-pacing

Self-pacing methods, such as the Montessori Method, use flexible grouping practices to allow children to advance at their own pace. Self-pacing can be beneficial for all children and is not targeted specifically at those identified as gifted or talented, but it can allow children to learn at a highly accelerated rate. Directed Studies are usually based on self-pacing.

Acceleration

Pupils are advanced to a higher-level class covering material more suited to their abilities and preparedness. This may take the form of skipping grades or completing normal curriculum in a shorter-than-normal period of time ("telescoping"). Subject acceleration (also called partial acceleration) is a flexible approach which can advance a student in one field, such as mathematics or language, without changing other studies, such as history or science. This type of acceleration is usually based upon achievement testing, rather than IQ.

Some colleges offer early entrance programs that give gifted younger students the opportunity to attend college early. In the U.S., many community colleges allow advanced students to enroll with the consent of school officials and the pupils' parents.

Acceleration presents gifted children academic material from established curricula that is commensurate with their ability and preparedness, and for this reason is a low-cost option from the perspective of the school. This may result in a small number of children taking classes targeted at older children. However, for the majority of gifted students, acceleration is beneficial both academically and socially. "Radical acceleration (acceleration by two or more years) is effective academically and socially for highly gifted students." Some advocates have argued that the disadvantages of being retained in a standard mixed-ability classroom are substantially worse than any shortcomings of acceleration. For example, psychologist Miraca Gross reports: "the majority of these children [retained in a typical classroom] are socially rejected [by their peers with typical academic talents], isolated, and deeply unhappy. Children of  180+ who are retained in the regular classroom are even more seriously at risk and experience severe emotional distress." These accelerated children should be placed together in one class if possible. Research suggests that acceleration might have an impact long after students graduate from high school. For example, one study shows that high-IQ individuals who experienced full-grade acceleration earned higher incomes as adults.

Colloquium

Like acceleration, colloquium provides advanced material for high school students. In colloquium, students take Advanced Placement courses. However, colloquium is different from AP classes because students are usually given more projects than students in AP classes. Students in colloquium also generally study topics more in depth and sometimes in a different way than students enrolled in AP classes do. Colloquium is a form that takes place in a traditional public school. In colloquium, subjects are grouped together. Subjects are taught at different times of the day; however, usually what is being taught in one subject will connect with another subject. For example, if the students are learning about colonial America in History, then they might also be analyzing text from The Scarlet Letter in English. Some schools may only have colloquium in certain subjects. In schools where colloquium is only offered in English and History, colloquium students usually take Advanced Placement courses in math and science and vice versa.

Pull-Out

Gifted students are pulled out of a heterogeneous classroom to spend a portion of their time in a gifted class. These programs vary widely, from carefully designed half-day academic programs to a single hour each week of educational challenges. Generally, these programs are ineffective at promoting academic advancement unless the material covered contains extensions and enrichment to the core curriculum. The majority of pull-out programs include an assortment of critical thinking drills, creative exercises, and subjects typically not introduced in standard curricula. Much of the material introduced in Gifted pull-out programs deals with the study of Logic, and its application to fields ranging from Philosophy to Mathematics. Students are encouraged to apply these empirical reasoning skills to every aspect of their education both in and outside of class. In some elementary classes such as math, students divide classes based on level: highest (gifted), median and lowest.

Cluster Grouping

Cluster grouping is the gathering of four to six gifted and talented and/or high achieving students in a single classroom for the entire school day. Cluster teachers are specially trained in differentiating for gifted learners. Clusters are typically used in upper elementary grades. Within a cluster group, instruction may include enrichment and extensions, higher-order thinking skills, pretesting and differentiation, compacting, an accelerated pace, and more complexity in content.

Summer Enrichment Programs (United States)

These offer a variety of courses that mainly take place in the summer. Summer schools are popular in the United States. Entrance fees are required for such programs, and programs typically focus on one subject, or class, for the duration of the camp.

Several examples of this type of program are:

• University of Iowa College of Education's Belin-Blank Honors Center
• Wesleyan Summer Gifted Program at West Virginia Wesleyan College
• The College of William and Mary, Precollegiate Programs, Williamsburg, VA
• Montclair State University, Academcially Gifted and Talented program, Montclair, NJ
• GERI: Gifted Education Resource Institute, Purdue University
• The Johns Hopkins University
• C-MITES
• Center for Talented Youth
• CTYI
• Center for Talent Development
• Plymouth Antiquarian Society
• Summer Enrichment Workshop - University of Alabama-Tuscaloosa
• Western Kentucky University Center for Gifted Studies

There are also several websites that list summer enrichment programs:

• Purdue University GERI Youth Programs
• Summer Institute for the Gifted
• National Association for Gifted Children
• National Society for the Gifted and Talented

Within the United States, in addition to programs designed by the state, some counties also choose to form their own Talented and Gifted Programs. Sometimes this means that an individual county will form its own TAG program; sometimes several counties will come together if not enough gifted students are present in a single county. Generally, a TAG program focuses on a specific age group, particularly the local TAG programs. This could mean elementary age, high school age, or by years such as ages 9 through 14.

These classes are generally organized so that students have the opportunity to choose several courses they wish to participate in. Courses offered often vary between subjects, but are not typically strictly academically related to that subject. For example, a TAG course that could be offered in history could be the students learning about a certain event and then acting it out in a performance to be presented to parents on the last night of the program. These courses are designed to challenge the students to think in new ways and not merely to be lectured as they are in school.

Full-time separate classes or schools

Some gifted students are educated in either a separate class or a separate school. These classes and schools are sometimes called "congregated gifted programs" or "dedicated gifted programs."
Some independent schools have a primary mission to serve the needs of the academically gifted. Such schools are relatively scarce and often difficult for families to locate. Some of these schools can be located on the Wikipedia article entitled: "List of gifted and talented programmes". Another resource for locating gifted schools in the United States can be found on the National Association for Gifted Children's "Resource Directory" accessible through their home page. Such schools often need to work to guard their mission from occasional charges of elitism, support the professional growth and training of their staff, write curriculum units that are specifically designed to meet the social, emotional, and academic talents of their students, and educate their parent population at all ages.

Some gifted and talented classes offer self-directed or individualized studies, where the students lead a class themselves and decide on their own task, tests, and all other assignments. These separate classes or schools tend to be more expensive than regular classes, due to smaller class sizes and lower student-to-teacher rations. Not-for-profit (non-profit) schools often can offer lower costs than for-profit schools. Either way, they are in high demand and parents have to pay part of the costs.

Homeschooling in the US

An umbrella term encompassing myriad educational options for gifted children: part-time schooling; school at home; classes, groups, mentors and tutors; and unschooling. In many US states, the population of gifted students who are being homeschooled is rising quite rapidly, as school districts responding to budgetary issues and standards-based policies are cutting what limited gifted education programs remain extant, and families seek educational opportunities that are tailored to each child's unique needs.

Identifying gifted children

The term "Gifted Assessment" is typically applied to a process of using norm-referenced psychometric tests administered by a qualified psychologist or psychometrist with the goal of identifying children whose intellectual functioning is significantly advanced as compared to the appropriate reference group (i.e., individuals of their age, gender, and country). The cut-off score for differentiating this group is usually determined by district school boards and can differ slightly from area to area, however, the majority defines this group as students scoring in the top 2 percentiles on one of the accepted tests of intellectual (cognitive) functioning or IQ. Some school boards also require a child to demonstrate advanced academic standing on individualized achievement tests and/ or through their classroom performance. Identifying gifted children is often difficult but is very important because typical school teachers are not qualified to educate a gifted student. This can lead to a situation where a gifted child is bored, underachieves and misbehaves in class.

Individual IQ testing is usually the optimal method to identify giftedness among children. However it does not distinguish well among those found to be gifted. Therefore, examiners prefer using a variety of tests to first identify giftedness and then further differentiate. This is often done by using individual IQ tests and then group or individual achievement tests. There is no standard consensus on which tests to use, as each test is better suited for a certain role.

The two most popular tests for identifying giftedness in the school-age population are the WISC IV and the SB5. The WIAT III is considered the most popular academic achievement test to determine a child's aggregate learned knowledge.

Although a newer WISC version, the WISC V, was developed in late 2014, the WISC IV is still the most commonplace test. It has been translated into several languages including Spanish, Portuguese, Norwegian, Swedish, French, German, Dutch, Japanese, Chinese, Korean, and Italian. The WISC-IV assesses a child's cognitive abilities, with respect to age group. Coupled with results from other tests, the WISC accurately depicts a child's developmental and psychological needs for the future.

The SB5 is an intelligence test that determines cognitive abilities and can be administered to persons in virtually any age group. It assesses a series of intelligence indicators including fluid reasoning, general knowledge, quantitative reasoning, spatial processing, and working memory. The SB5 makes use of both verbal and nonverbal testing.

The WIAT-III cannot assess all components of learned knowledge, but does give an understanding of a child's ability to acquire skills and knowledge through formal education. This test measures aspects of the learning process that take place in a traditional school setting in reading, writing, math, and oral language. Although the WIAT-III tests a wide range of material, it is designed primarily to assess children's learning before adolescence.

Versions of these tests exist for each age group. However it is recommended to begin assessment as early as possible, with approximately eight years of age being the optimal time to test. Testing allows identification of specific needs of students and help to plan an education early.

Out-of-group achievement testing (such as taking the SAT or ACT early) can also help to identify these students early on (see SMPY) and is implemented by various talent search programs in use by education programs. Out-of-group testing can also help to differentiate children who have scored in the highest percentiles in a single IQ test.

Testing alone cannot accurately identify every gifted child. Teacher and parent nominations are essential additions to the objective information provided by grades and scores. Parents are encouraged to keep portfolios of their children's work, and documentation of their early signs of gifted behavior.

Controversies

Controversies concerning gifted education are varied and often highly politicized. They are as basic as agreeing upon the appropriateness of the term 'gifted' or the definition of 'giftedness'. For example, does 'giftedness' refer to performance or potential (such as inherent intelligence)? Many students do not exhibit both at the same time.

Measures of general intelligence also remain controversial. Early IQ tests were notorious for producing higher IQ scores for privileged races and classes and lower scores for disadvantaged subgroups. Although IQ tests have changed substantially over the past half century, and many objections to the early tests have been addressed by 'culture neutral' tests (such as the Raven test), IQ testing remains controversial. Regardless of the tests used to identify children for gifted programs, many school districts in the United States still have disproportionately more White and Asian American students enrolled in their gifted programs, while Hispanic and African American students are usually underrepresented. However, research shows that this may be not be a fault of tests, but rather a result of the achievement gap in the United States.

Some schools and districts only accept IQ tests as evidence of giftedness. This brings scrutiny to the fact that many affluent families can afford to consult with an educational psychologist to test their children, whereas families with a limited income cannot afford the test and must depend on district resources.

Gender

Another area of controversy has been the marginalization of gifted females with studies attributing it to self-efficacy, acculturation and biological differences in aptitude between boys and girls for advanced maths.

Class and ethnicity

Gifted programs are often seen as being elitist in places where the majority of students receiving gifted services are from a privileged background. Identifying and serving gifted children from poverty presents unique challenges, ranging from emotional issues arising from a family's economic insecurity, to gaps in pre-school cognitive development due to the family's lack of education and time.

In New York City experience has shown that basing admission to gifted and talented programs on tests of any sort can result in selection of substantially more middle-class and white or Asian students and development of more programs in schools that such students attend.

Appropriateness of forms of gifted education

This is the most hotly debated aspect of gifted education. Some people believe that gifted education resources lack availability and flexibility. They feel that in the alternative methods of gifted education, the gifted students "miss out" on having a "normal" childhood, at least insofar as "normal childhood" is defined as attending school in a mixed-ability classroom. Others believe that gifted education allows gifted students to interact with peers that are on their level, be adequately challenged, and leaves them better equipped to take on the challenges of life.

Another facet of this controversy is the effectiveness of the programs dependent upon resources that are pushed more toward students who are struggling. Gifted Education is not mandated in many states, making it elective for districts to earmark money for. Many lower-achieving districts and schools must make crisis decisions on programs that are not high priorities. As a result, gifted students at these schools are not served, or not served effectively.

Emotional aspects

While giftedness is seen as an academic advantage, psychologically it can pose other challenges for the gifted individual. A person who is intellectually advanced may or may not be advanced in other areas. Each individual student needs to be evaluated for physical, social, and emotional skills without the traditional prejudices which prescribe either "compensatory" weaknesses or "matching" advancement in these areas.

It is a common misconception that gifted students are universally gifted in all areas of academics, and these misconceptions can have a variety of negative emotional effects on a gifted child. Unrealistically high expectations of academic success are often placed on gifted students by both parents and teachers. This pressure can cause gifted students to experience high levels of anxiety, to become perfectionists, and to develop a fear of failure. Gifted students come to define themselves and their identity through their giftedness, which can be problematic as their entire self-concept can be shaken when they do not live up to the unrealistically high expectations of others.

A person with significant academic talents often finds it difficult to fit in with schoolmates. These pressures often wane during adulthood, but they can leave a significant negative impact on emotional development.

Social pressures can cause children to "play down" their intelligence in an effort to blend in with other students. "Playing down" is a strategy often used by students with clinical depression and is seen somewhat more frequently in socially acute adolescents. This behavior is usually discouraged by educators when they recognize it. Unfortunately, the very educators who want these children to challenge themselves and to embrace their gifts and talents are often the same people who are forced to discourage them in a mixed-ability classroom, through mechanisms like refusing to call on the talented student in class so that typical students have an opportunity to participate.

Students who are young, enthusiastic or aggressive are more likely to attract attention and to disrupt the class by working ahead, giving the correct answers all the time, asking for new assignments, or finding creative ways to entertain themselves while the rest of the class finishes an assignment. This behavior can be mistaken for ADHD.

Many parents of gifted find that it is the social-emotional aspect of their children's lives that needs support. Schools and Talent Development programs often focus on academic enrichment rather than providing time for gifted kids to have the social interaction with true peers that is required for healthy development. National organizations such as Supporting Emotional Needs of the Gifted SENG as well as local organizations, have emerged in an effort to meet these needs.

It can also happen that some unidentified gifted students will get bored in regular class, daydream and lose track of where the class is in a lecture, and the teacher becomes convinced that the student is slow and struggling with the material.

Finally, G&T students are statistically somewhat more likely to be diagnosed with a mental disorder such as bipolar disorder and to become addicted to drugs or alcohol. G&T students also have a higher chance of co-occurring learning disability. Gifted students with learning disability are often called twice exceptional. These students can require special attention in school.

Test preparation

In the United States, particularly in New York City where qualifying children as young as 4 are enrolled in enriched kindergarten classes offered by the public schools, a test preparation industry has grown up which closely monitors the nature of tests given to prospective students of gifted and talented programs. This can result in admission of significant numbers of students into programs who lack superior natural intellectual talent and exclusion of naturally talented students who did not participate in test preparation or lacked the resources to do so.

It is virtually impossible to train a child for a WISC test or other gifted test. Some websites are known for publishing test questions and answers, although using these is considered illegal since it is highly confidential information. It would also be disastrous if a non-gifted student was placed in a gifted program. Reviewing actual test questions can confuse children and stifles their natural thinking process, however reviewing similar style questions is a possibility.

Private gifted assessment is usually expensive and educators recommend that parents take advantage of online screening tests to give a preliminary indication of potential giftedness. Another way to screen for giftedness before requesting a psychological assessment is to do a curriculum-based assessment. Curriculum-based assessment is a form of achievement testing that focuses specifically on what the child has been exposed to in their academic career. It can be done through school or a private educational center. Although this can determine if a child's performance in school potentially signifies giftedness, there are complications. For example, if a child changes school districts or country of residence, the different terminology of curriculum could hold that child back. Secondly, discrepancies between school districts, along with public and private education, create a very wide range of potential knowledge bases.

Justification

Researchers and practitioners in gifted education contend that, if education were to follow the medical maxim of "first, do no harm," then no further justification would be required for providing resources for gifted education as they believe gifted children to be at-risk. The notion that gifted children are "at-risk" was publicly declared in the Marland Report in 1972:

Gifted and Talented children are, in fact, deprived and can suffer psychological damage and permanent impairment of their abilities to function well which is equal to or greater than the similar deprivation suffered by any other population with special needs served by the Office of Education.
(pp. xi-xii)

Three decades later, a similar statement was made by researchers in the field:

National efforts to increase the availability of a variety of appropriate instructional and out-of-school provisions must be a high priority since research indicates that many of the emotional or social difficulties gifted students experience disappear when their educational climates are adapted to their level and pace of learning." [emphasis added]