Indeterminism

From Wikipedia, the free encyclopedia

Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or are not caused deterministically.

It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of libertarianism. In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic. Heisenberg's uncertainty principle and the "Born rule", proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay "Chance and Necessity". The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems.

Necessary but insufficient causation

Further information: Necessary and sufficient conditions

Indeterminists do not have to deny that causes exist. Instead, they can maintain that the only causes that exist are of a type that do not constrain the future to a single course; for instance, they can maintain that only necessary and not sufficient causes exist. The necessary/sufficient distinction works as follows:

If x is a necessary cause of y; then the presence of y implies that x definitely preceded it. The presence of x, however, does not imply that y will occur.

If x is a sufficient cause of y, then the presence of y implies that x may have preceded it. (However, another cause z may alternatively cause y. Thus the presence of y does not imply the presence of x, or z, or any other suspect.)

It is possible for everything to have a necessary cause, even while indeterminism holds and the future is open, because a necessary condition does not lead to a single inevitable effect. Indeterministic (or probabilistic) causation is a proposed possibility, such that "everything has a cause" is not a clear statement of indeterminism.

Probabilistic causation

Main article: Probabilistic causation

Interpreting causation as a deterministic relation means that if A causes B, then A must always be followed by B. In this sense, war does not cause deaths, nor does smoking cause cancer. As a result, many turn to a notion of probabilistic causation. Informally, A probabilistically causes B if A's occurrence increases the probability of B. This is sometimes interpreted to reflect the imperfect knowledge of a deterministic system but other times interpreted to mean that the causal system under study has an inherently indeterministic nature. (Propensity probability is an analogous idea, according to which probabilities have an objective existence and are not just limitations in a subject's knowledge).

It can be proved that realizations of any probability distribution other than the uniform one are mathematically equal to applying a (deterministic) function (namely, an inverse distribution function) on a random variable following the latter (i.e. an "absolutely random" one; the probabilities are contained in the deterministic element. A simple form of demonstrating it would be shooting randomly within a square and then (deterministically) interpreting a relatively large subsquare as the more probable outcome.

Intrinsic indeterminism versus unpredictability

A distinction is generally made between indeterminism and the mere inability to measure the variables (limits of precision). This is especially the case for physical indeterminism (as proposed by various interpretations of quantum mechanics). Yet some philosophers have argued that indeterminism and unpredictability are synonymous.

Philosophy

Ancient Greek philosophy

Leucippus

The oldest mention of the concept of chance is by the earliest philosopher of atomism, Leucippus, who said:

"The cosmos, then, became like a spherical form in this way: the atoms being submitted to a casual and unpredictable movement, quickly and incessantly".

Aristotle

Main article: Four causes

Aristotle described four possible causes (material, efficient, formal, and final). Aristotle's word for these causes was αἰτίαι (aitiai, as in aetiology), which translates as causes in the sense of the multiple factors responsible for an event. Aristotle did not subscribe to the simplistic "every event has a (single) cause" idea that was to come later.

In his Physics and Metaphysics, Aristotle said there were accidents (συμβεβηκός, sumbebekos) caused by nothing but chance (τύχη, tukhe). He noted that he and the early physicists found no place for chance among their causes.

We have seen how far Aristotle distances himself from any view which makes chance a crucial factor in the general explanation of things. And he does so on conceptual grounds: chance events are, he thinks, by definition unusual and lacking certain explanatory features: as such they form the complement class to those things which can be given full natural explanations.

— R.J. Hankinson, "Causes" in Blackwell Companion to Aristotle

Aristotle opposed his accidental chance to necessity:

Nor is there any definite cause for an accident, but only chance (τυχόν), namely an indefinite (ἀόριστον) cause.

It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will this be, or not? Yes, if this happens; otherwise not.

Pyrrhonism

The philosopher Sextus Empiricus described the Pyrrhonist position on causes as follows:

...we show the existence of causes are plausible, and if those, too, are plausible which prove that it is incorrect to assert the existence of a cause, and if there is no way to give preference to any of these over others – since we have no agreed-upon sign, criterion, or proof, as has been pointed out earlier – then, if we go by the statements of the Dogmatists, it is necessary to suspend judgment about the existence of causes, too, saying that they are no more existent than non-existent

Epicureanism

Epicurus argued that as atoms moved through the void, there were occasions when they would "swerve" (clinamen) from their otherwise determined paths, thus initiating new causal chains. Epicurus argued that these swerves would allow us to be more responsible for our actions, something impossible if every action was deterministically caused. For Epicureanism, the occasional interventions of arbitrary gods would be preferable to strict determinism.

Early modern philosophy

In 1729 theTestament of Jean Meslier states:

"The matter, by virtue of its own active force, moves and acts in blind manner".

Soon after Julien Offroy de la Mettrie in his L'Homme Machine. (1748, anon.) wrote:

"Perhaps, the cause of man's existence is just in existence itself? Perhaps he is by chance thrown in some point of this terrestrial surface without any how and why".

In his Anti-Sénèque [Traité de la vie heureuse, par Sénèque, avec un Discours du traducteur sur le même sujet, 1750] we read:

"Then, the chance has thrown us in life".

In the 19th century the French Philosopher Antoine-Augustin Cournot theorized chance in a new way, as series of not-linear causes. He wrote in Essai sur les fondements de nos connaissances (1851):

"It is not because of rarity that the chance is actual. On the contrary, it is because of chance they produce many possible others."

Modern philosophy

Charles Peirce

Tychism (Greek: τύχη "chance") is a thesis proposed by the American philosopher Charles Sanders Peirce in the 1890s. It holds that absolute chance, also called spontaneity, is a real factor operative in the universe. It may be considered both the direct opposite of Albert Einstein's oft quoted dictum that: "God does not play dice with the universe" and an early philosophical anticipation of Werner Heisenberg's uncertainty principle.

Peirce does not, of course, assert that there is no law in the universe. On the contrary, he maintains that an absolutely chance world would be a contradiction and thus impossible. Complete lack of order is itself a sort of order. The position he advocates is rather that there are in the universe both regularities and irregularities.

Karl Popper comments that Peirce's theory received little contemporary attention, and that other philosophers did not adopt indeterminism until the rise of quantum mechanics.

Arthur Holly Compton

In 1931, Arthur Holly Compton championed the idea of human freedom based on quantum indeterminacy and invented the notion of amplification of microscopic quantum events to bring chance into the macroscopic world. In his somewhat bizarre mechanism, he imagined sticks of dynamite attached to his amplifier, anticipating the Schrödinger's cat paradox.

Reacting to criticisms that his ideas made chance the direct cause of our actions, Compton clarified the two-stage nature of his idea in an Atlantic Monthly article in 1955. First there is a range of random possible events, then one adds a determining factor in the act of choice.

A set of known physical conditions is not adequate to specify precisely what a forthcoming event will be. These conditions, insofar as they can be known, define instead a range of possible events from among which some particular event will occur. When one exercises freedom, by his act of choice he is himself adding a factor not supplied by the physical conditions and is thus himself determining what will occur. That he does so is known only to the person himself. From the outside one can see in his act only the working of physical law. It is the inner knowledge that he is in fact doing what he intends to do that tells the actor himself that he is free.

Compton welcomed the rise of indeterminism in 20th century science, writing:

In my own thinking on this vital subject I am in a much more satisfied state of mind than I could have been at any earlier stage of science. If the statements of the laws of physics were assumed correct, one would have had to suppose (as did most philosophers) that the feeling of freedom is illusory, or if [free] choice were considered effective, that the laws of physics ... [were] unreliable. The dilemma has been an uncomfortable one.

Together with Arthur Eddington in Britain, Compton was one of those rare distinguished physicists in the English speaking world of the late 1920s and throughout the 1930s arguing for the “liberation of free will” with the help of Heisenberg’s indeterminacy principle, but their efforts had been met not only with physical and philosophical criticism but most primarily with fierce political and ideological campaigns.

Karl Popper

In his essay Of Clouds and Clocks, included in his book Objective Knowledge, Popper contrasted "clouds", his metaphor for indeterministic systems, with "clocks", meaning deterministic ones. He sided with indeterminism, writing

I believe Peirce was right in holding that all clocks are clouds to some considerable degree — even the most precise of clocks. This, I think, is the most important inversion of the mistaken determinist view that all clouds are clocks

Popper was also a promoter of propensity probability.

Robert Kane

Kane is one of the leading contemporary philosophers on free will. Advocating what is termed within philosophical circles "libertarian freedom", Kane argues that "(1) the existence of alternative possibilities (or the agent's power to do otherwise) is a necessary condition for acting freely, and (2) determinism is not compatible with alternative possibilities (it precludes the power to do otherwise)". It is important to note that the crux of Kane's position is grounded not in a defense of alternative possibilities (AP) but in the notion of what Kane refers to as ultimate responsibility (UR). Thus, AP is a necessary but insufficient criterion for free will. It is necessary that there be (metaphysically) real alternatives for our actions, but that is not enough; our actions could be random without being in our control. The control is found in "ultimate responsibility".

What allows for ultimate responsibility of creation in Kane's picture are what he refers to as "self-forming actions" or SFAs — those moments of indecision during which people experience conflicting wills. These SFAs are the undetermined, regress-stopping voluntary actions or refrainings in the life histories of agents that are required for UR. UR does not require that every act done of our own free will be undetermined and thus that, for every act or choice, we could have done otherwise; it requires only that certain of our choices and actions be undetermined (and thus that we could have done otherwise), namely SFAs. These form our character or nature; they inform our future choices, reasons and motivations in action. If a person has had the opportunity to make a character-forming decision (SFA), he is responsible for the actions that are a result of his character.

Mark Balaguer

Mark Balaguer, in his book Free Will as an Open Scientific Problem argues similarly to Kane. He believes that, conceptually, free will requires indeterminism, and the question of whether the brain behaves indeterministically is open to further empirical research. He has also written on this matter "A Scientifically Reputable Version of Indeterministic Libertarian Free Will".

Science

See also: Philosophy of physics and indeterminism

Mathematics

In probability theory, a stochastic process, or sometimes random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible reality of how the process might evolve over time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.

Classical and relativistic physics

The idea that Newtonian physics proved causal determinism was highly influential in the early modern period. "Thus physical determinism [..] became the ruling faith among enlightened men; and everybody who did not embrace this new faith was held to be an obscurantist and a reactionary". However: "Newton himself may be counted among the few dissenters, for he regarded the solar system as imperfect, and consequently as likely to perish".

Classical chaos is not usually considered an example of indeterminism, as it can occur in deterministic systems such as the three-body problem.

John Earman has argued that most physical theories are indeterministic. For instance, Newtonian physics admits solutions where particles accelerate continuously, heading out towards infinity. By the time reversibility of the laws in question, particles could also head inwards, unprompted by any pre-existing state. He calls such hypothetical particles "space invaders".

John D. Norton has suggested another indeterministic scenario, known as Norton's Dome, where a particle is initially situated on the exact apex of a dome.

Branching space-time is a theory uniting indeterminism and the special theory of relativity. The idea was originated by Nuel Belnap. The equations of general relativity admit of both indeterministic and deterministic solutions.

Boltzmann

Ludwig Boltzmann, was one of the founders of statistical mechanics and the modern atomic theory of matter. He is remembered for his discovery that the second law of thermodynamics is a statistical law stemming from disorder. He also speculated that the ordered universe we see is only a small bubble in much larger sea of chaos. The Boltzmann brain is a similar idea.

Evolution and biology

Darwinian evolution has an enhanced reliance on the chance element of random mutation compared to the earlier evolutionary theory of Herbert Spencer. However, the question of whether evolution requires genuine ontological indeterminism is open to debate.

In the essay Chance and Necessity (1970) Jacques Monod rejected the role of final causation in biology, instead arguing that a mixture of efficient causation and "pure chance" lead to teleonomy, or merely apparent purposefulness.

The Japanese theoretical population geneticist Motoo Kimura emphasises the role of indeterminism in evolution. According to neutral theory of molecular evolution: "at the molecular level most evolutionary change is caused by random drift of gene mutants that are equivalent in the face of selection.

Prigogine

In his 1997 book, The End of Certainty, Prigogine contends that determinism is no longer a viable scientific belief. "The more we know about our universe, the more difficult it becomes to believe in determinism." This is a major departure from the approach of Newton, Einstein and Schrödinger, all of whom expressed their theories in terms of deterministic equations. According to Prigogine, determinism loses its explanatory power in the face of irreversibility and instability.

Prigogine traces the dispute over determinism back to Darwin, whose attempt to explain individual variability according to evolving populations inspired Ludwig Boltzmann to explain the behavior of gases in terms of populations of particles rather than individual particles. This led to the field of statistical mechanics and the realization that gases undergo irreversible processes. In deterministic physics, all processes are time-reversible, meaning that they can proceed backward as well as forward through time. As Prigogine explains, determinism is fundamentally a denial of the arrow of time. With no arrow of time, there is no longer a privileged moment known as the "present," which follows a determined "past" and precedes an undetermined "future." All of time is simply given, with the future as determined or undetermined as the past. With irreversibility, the arrow of time is reintroduced to physics. Prigogine notes numerous examples of irreversibility, including diffusion, radioactive decay, solar radiation, weather and the emergence and evolution of life. Like weather systems, organisms are unstable systems existing far from thermodynamic equilibrium. Instability resists standard deterministic explanation. Instead, due to sensitivity to initial conditions, unstable systems can only be explained statistically, that is, in terms of probability.

Prigogine asserts that Newtonian physics has now been "extended" three times, first with the use of the wave function in quantum mechanics, then with the introduction of spacetime in general relativity and finally with the recognition of indeterminism in the study of unstable systems.

Quantum mechanics

Main article: Quantum indeterminacy

At one time, it was assumed in the physical sciences that if the behavior observed in a system cannot be predicted, the problem is due to lack of fine-grained information, so that a sufficiently detailed investigation would eventually result in a deterministic theory ("If you knew exactly all the forces acting on the dice, you would be able to predict which number comes up").

However, the advent of quantum mechanics removed the underpinning from that approach, with the claim that (at least according to the Copenhagen interpretation) the most basic constituents of matter at times behave indeterministically. This comes from the collapse of the wave function, in which the state of a system upon measurement cannot in general be predicted. Quantum mechanics only predicts the probabilities of possible outcomes, which are given by the Born rule. Non-deterministic behavior in wave function collapse is not only a feature of the Copenhagen interpretation, with its observer-dependence, but also of objective collapse and other theories.

Opponents of quantum indeterminism suggested that determinism could be restored by formulating a new theory in which additional information, so-called hidden variables, would allow definite outcomes to be determined. For instance, in 1935, Einstein, Podolsky and Rosen wrote a paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" arguing that such a theory was in fact necessary to preserve the principle of locality. In 1964, John S. Bell was able to define a theoretical test for these local hidden variable theories, which was reformulated as a workable experimental test through the work of Clauser, Horne, Shimony and Holt. The negative result of the 1980s tests by Alain Aspect ruled such theories out, provided certain assumptions about the experiment hold. Thus any interpretation of quantum mechanics, including deterministic reformulations, must either reject locality or reject counterfactual definiteness altogether. David Bohm's theory is the main example of a non-local deterministic quantum theory.

The many-worlds interpretation is said to be deterministic, but experimental results still cannot be predicted: experimenters do not know which 'world' they will end up in. Technically, counterfactual definiteness is lacking.

A notable consequence of quantum indeterminism is the Heisenberg uncertainty principle, which prevents the simultaneous accurate measurement of all a particle's properties.

Cosmology

Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. Currently, the most widely accepted explanation for their origin is in the context of cosmic inflation. According to the inflationary paradigm, the exponential growth of the scale factor during inflation caused quantum fluctuations of the inflaton field to be stretched to macroscopic scales, and, upon leaving the horizon, to "freeze in". At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the initial conditions for structure formation.

Neuroscience

Neuroscientists such as Björn Brembs and Christof Koch believe thermodynamically stochastic processes in the brain are the basis of free will, and that even very simple organisms such as flies have a form of free will. Similar ideas are put forward by some philosophers such as Robert Kane.

Despite recognizing indeterminism to be a very low-level, necessary prerequisite, Björn Brembs says that it's not even close to being sufficient for addressing things like morality and responsibility.

Other views

Against Einstein and others who advocated determinism, indeterminism—as championed by the English astronomer Sir Arthur Eddington—says that a physical object has an ontologically undetermined component that is not due to the epistemological limitations of physicists' understanding. The uncertainty principle, then, would not necessarily be due to hidden variables but to an indeterminism in nature itself.

Determinism and indeterminism are examined in Causality and Chance in Modern Physics by David Bohm. He speculates that, since determinism can emerge from underlying indeterminism (via the law of large numbers), and that indeterminism can emerge from determinism (for instance, from classical chaos), the universe could be conceived of as having alternating layers of causality and chaos.

Ancient Greek philosophy

From Wikipedia, the free encyclopedia

 

Ancient Greek philosophy arose in the 6th century BC. Philosophy was used to make sense of the world using reason. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics. Greek philosophy continued throughout the Hellenistic period and later evolved into Roman philosophy.Greek philosophy has influenced much of Western culture since its inception, and can be found in many aspects of public education. Alfred North Whitehead once noted: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato". Clear, unbroken lines of influence lead from ancient Greek and Hellenistic philosophers to Roman philosophy, Early Islamic philosophy, Medieval Scholasticism, the European Renaissance and the Age of Enlightenment.

Greek philosophy was influenced to some extent by the older wisdom literature and mythological cosmogonies of the ancient Near East, though the extent of this influence is widely debated. The classicist Martin Litchfield West states, "contact with oriental cosmology and theology helped to liberate the early Greek philosophers' imagination; it certainly gave them many suggestive ideas. But they taught themselves to reason. Philosophy as we understand it is a Greek creation".

Subsequent philosophic tradition was so influenced by Socrates as presented by Plato that it is conventional to refer to philosophy developed prior to Socrates as pre-Socratic philosophy. The periods following this, up to and after the wars of Alexander the Great, are those of "Classical Greek" and "Hellenistic philosophy", respectively.

Early Greek Philosophy (or pre-Socratic philosophy)

Main article: Pre-Socratic philosophy

The convention of terming those philosophers who were active prior to the death of Socrates as the pre-Socratics gained currency with the 1903 publication of Hermann Diels' Fragmente der Vorsokratiker, although the term did not originate with him. The term is considered useful because what came to be known as the "Athenian school" (composed of Socrates, Plato, and Aristotle) signaled the rise of a new approach to philosophy; Friedrich Nietzsche's thesis that this shift began with Plato rather than with Socrates (hence his nomenclature of "pre-Platonic philosophy") has not prevented the predominance of the "pre-Socratic" distinction.

Since 2016, however, current scholarship has transitioned from calling philosophy before the Athenian school "pre-Socratic" to simply "Early Greek Philosophy". André Laks and Glenn W. Most have been partly responsible for popularizing this shift in describing the era preceding the Athenian School through their comprehensive, nine volume Loeb editions of Early Greek Philosophy. In their first volume, they distinguish their systematic approach from that of Hermann Diels, beginning with the choice of "Early Greek Philosophy" over "pre-Socratic philosophy" most notably because Socrates is contemporary and sometimes even prior to philosophers traditionally considered "pre-Socratic" (e.g., the Atomists).

The early Greek philosophers (or "pre-Socratics") were primarily concerned with cosmology, ontology, and mathematics. They were distinguished from "non-philosophers" insofar as they rejected mythological explanations in favor of reasoned discourse.

Milesian school

Main article: Milesian school

Thales of Miletus, regarded by Aristotle as the first philosopher, held that all things arise from a single material substance, water. It is not because he gave a cosmogony that John Burnet calls him the "first man of science", but because he gave a naturalistic explanation of the cosmos and supported it with reasons. According to tradition, Thales was able to predict an eclipse and taught the Egyptians how to measure the height of the pyramids.

Thales inspired the Milesian school of philosophy and was followed by Anaximander, who argued that the substratum or arche could not be water or any of the classical elements but was instead something "unlimited" or "indefinite" (in Greek, the apeiron). He began from the observation that the world seems to consist of opposites (e.g., hot and cold), yet a thing can become its opposite (e.g., a hot thing cold). Therefore, they cannot truly be opposites but rather must both be manifestations of some underlying unity that is neither. This underlying unity (substratum, arche) could not be any of the classical elements, since they were one extreme or another. For example, water is wet, the opposite of dry, while fire is dry, the opposite of wet. This initial state is ageless and imperishable, and everything returns to it according to necessity. Anaximenes in turn held that the arche was air, although John Burnet argues that by this, he meant that it was a transparent mist, the aether. Despite their varied answers, the Milesian school was searching for a natural substance that would remain unchanged despite appearing in different forms, and thus represents one of the first scientific attempts to answer the question that would lead to the development of modern atomic theory; "the Milesians," says Burnet, "asked for the φύσις of all things."

Xenophanes

Main article: Xenophanes

Xenophanes was born in Ionia, where the Milesian school was at its most powerful and may have picked up some of the Milesians' cosmological theories as a result. What is known is that he argued that each of the phenomena had a natural rather than divine explanation in a manner reminiscent of Anaximander's theories and that there was only one god, the world as a whole, and that he ridiculed the anthropomorphism of the Greek religion by claiming that cattle would claim that the gods looked like cattle, horses like horses, and lions like lions, just as the Ethiopians claimed that the gods were snub-nosed and black and the Thracians claimed they were pale and red-haired.

Xenophanes was highly influential to subsequent schools of philosophy. He was seen as the founder of a line of philosophy that culminated in Pyrrhonism, possibly an influence on Eleatic philosophy, and a precursor to Epicurus' total break between science and religion.

Pythagoreanism

Main article: Pythagoreanism

Pythagoras lived at approximately the same time that Xenophanes did and, in contrast to the latter, the school that he founded sought to reconcile religious belief and reason. Little is known about his life with any reliability, however, and no writings of his survive, so it is possible that he was simply a mystic whose successors introduced rationalism into Pythagoreanism, that he was simply a rationalist whose successors are responsible for the mysticism in Pythagoreanism, or that he was actually the author of the doctrine; there is no way to know for certain.

Pythagoras is said to have been a disciple of Anaximander and to have imbibed the cosmological concerns of the Ionians, including the idea that the cosmos is constructed of spheres, the importance of the infinite, and that air or aether is the arche of everything. Pythagoreanism also incorporated ascetic ideals, emphasizing purgation, metempsychosis, and consequently a respect for all animal life; much was made of the correspondence between mathematics and the cosmos in a musical harmony. Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.

Heraclitus

Main article: Heraclitus

Heraclitus must have lived after Xenophanes and Pythagoras, as he condemns them along with Homer as proving that much learning cannot teach a man to think; since Parmenides refers to him in the past tense, this would place him in the 5th century BC. Contrary to the Milesian school, which posits one stable element as the arche, Heraclitus taught that panta rhei ("everything flows"), the closest element to this eternal flux being fire. All things come to pass in accordance with Logos, which must be considered as "plan" or "formula", and "the Logos is common". He also posited a unity of opposites, expressed through dialectic, which structured this flux, such as that seeming opposites in fact are manifestations of a common substrate to good and evil itself.

Heraclitus called the oppositional processes ἔρις (eris), "strife", and hypothesized that the apparently stable state of δίκη (dikê), or "justice", is the harmonic unity of these opposites.

Eleatic philosophy

Main article: Eleatics

Parmenides of Elea cast his philosophy against those who held "it is and is not the same, and all things travel in opposite directions,"—presumably referring to Heraclitus and those who followed him. Whereas the doctrines of the Milesian school, in suggesting that the substratum could appear in a variety of different guises, implied that everything that exists is corpuscular, Parmenides argued that the first principle of being was One, indivisible, and unchanging. Being, he argued, by definition implies eternality, while only that which is can be thought; a thing which is, moreover, cannot be more or less, and so the rarefaction and condensation of the Milesians is impossible regarding Being; lastly, as movement requires that something exist apart from the thing moving (viz. the space into which it moves), the One or Being cannot move, since this would require that "space" both exist and not exist. While this doctrine is at odds with ordinary sensory experience, where things do indeed change and move, the Eleatic school followed Parmenides in denying that sense phenomena revealed the world as it actually was; instead, the only thing with Being was thought, or the question of whether something exists or not is one of whether it can be thought.

In support of this, Parmenides' pupil Zeno of Elea attempted to prove that the concept of motion was absurd and as such motion did not exist. He also attacked the subsequent development of pluralism, arguing that it was incompatible with Being. His arguments are known as Zeno's paradoxes.

Pluralism and atomism

The power of Parmenides' logic was such that some subsequent philosophers abandoned the monism of the Milesians, Xenophanes, Heraclitus, and Parmenides, where one thing was the arche. In place of this, they adopted pluralism, such as Empedocles and Anaxagoras. There were, they said, multiple elements which were not reducible to one another and these were set in motion by love and strife (as in Empedocles) or by Mind (as in Anaxagoras). Agreeing with Parmenides that there is no coming into being or passing away, genesis or decay, they said that things appear to come into being and pass away because the elements out of which they are composed assemble or disassemble while themselves being unchanging.

Leucippus also proposed an ontological pluralism with a cosmogony based on two main elements: the vacuum and atoms. These, by means of their inherent movement, are crossing the void and creating the real material bodies. His theories were not well known by the time of Plato, however, and they were ultimately incorporated into the work of his student, Democritus.

Sophism

Main article: Sophists

Sophism arose from the juxtaposition of physis (nature) and nomos (law). John Burnet posits its origin in the scientific progress of the previous centuries which suggested that Being was radically different from what was experienced by the senses and, if comprehensible at all, was not comprehensible in terms of order; the world in which people lived, on the other hand, was one of law and order, albeit of humankind's own making. At the same time, nature was constant, while what was by law differed from one place to another and could be changed.

The first person to call themselves a sophist, according to Plato, was Protagoras, whom he presents as teaching that all virtue is conventional. It was Protagoras who claimed that "man is the measure of all things, of the things that are, that they are, and of the things that are not, that they are not," which Plato interprets as a radical perspectivism, where some things seem to be one way for one person (and so actually are that way) and another way for another person (and so actually are that way as well); the conclusion being that one cannot look to nature for guidance regarding how to live one's life.

Protagoras and subsequent sophists tended to teach rhetoric as their primary vocation. Prodicus, Gorgias, Hippias, and Thrasymachus appear in various dialogues, sometimes explicitly teaching that while nature provides no ethical guidance, the guidance that the laws provide is worthless, or that nature favors those who act against the laws.

Classical Greek philosophy

Socrates

Main article: Socrates

Four Greek philosophers: Socrates, Antisthenes, Chrysippos, Epicurus; British Museum

Socrates, believed to have been born in Athens in the 5th century BC, marks a watershed in ancient Greek philosophy. Athens was a center of learning, with sophists and philosophers traveling from across Greece to teach rhetoric, astronomy, cosmology, and geometry.

While philosophy was an established pursuit prior to Socrates, Cicero credits him as "the first who brought philosophy down from the heavens, placed it in cities, introduced it into families, and obliged it to examine into life and morals, and good and evil." By this account he would be considered the founder of political philosophy. The reasons for this turn toward political and ethical subjects remain the object of much study.

The fact that many conversations involving Socrates (as recounted by Plato and Xenophon) end without having reached a firm conclusion, or aporetically, has stimulated debate over the meaning of the Socratic method. Socrates is said to have pursued this probing question-and-answer style of examination on a number of topics, usually attempting to arrive at a defensible and attractive definition of a virtue.

While Socrates' recorded conversations rarely provide a definite answer to the question under examination, several maxims or paradoxes for which he has become known recur. Socrates taught that no one desires what is bad, and so if anyone does something that truly is bad, it must be unwillingly or out of ignorance; consequently, all virtue is knowledge. He frequently remarks on his own ignorance (claiming that he does not know what courage is, for example). Plato presents him as distinguishing himself from the common run of mankind by the fact that, while they know nothing noble and good, they do not know that they do not know, whereas Socrates knows and acknowledges that he knows nothing noble and good.

The great statesman Pericles was closely associated with this new learning and a friend of Anaxagoras, however, and his political opponents struck at him by taking advantage of a conservative reaction against the philosophers; it became a crime to investigate the things above the heavens or below the earth, subjects considered impious. Anaxagoras is said to have been charged and to have fled into exile when Socrates was about twenty years of age. There is a story that Protagoras, too, was forced to flee and that the Athenians burned his books. Socrates, however, is the only subject recorded as charged under this law, convicted, and sentenced to death in 399 BC (see Trial of Socrates). In the version of his defense speech presented by Plato, he claims that it is the envy he arouses on account of his being a philosopher that will convict him.

Numerous subsequent philosophical movements were inspired by Socrates or his younger associates. Plato casts Socrates as the main interlocutor in his dialogues, deriving from them the basis of Platonism (and by extension, Neoplatonism). Plato's student Aristotle in turn criticized and built upon the doctrines he ascribed to Socrates and Plato, forming the foundation of Aristotelianism. Antisthenes founded the school that would come to be known as Cynicism and accused Plato of distorting Socrates' teachings. Zeno of Citium in turn adapted the ethics of Cynicism to articulate Stoicism. Epicurus studied with Platonic and Pyrrhonist teachers before renouncing all previous philosophers (including Democritus, on whose atomism the Epicurean philosophy relies). The philosophic movements that were to dominate the intellectual life of the Roman Empire were thus born in this febrile period following Socrates' activity, and either directly or indirectly influenced by him. They were also absorbed by the expanding Muslim world in the 7th through 10th centuries AD, from which they returned to the West as foundations of Medieval philosophy and the Renaissance, as discussed below.

Plato

Main article: Plato

Plato was an Athenian of the generation after Socrates. Ancient tradition ascribes thirty-six dialogues and thirteen letters to him, although of these only twenty-four of the dialogues are now universally recognized as authentic; most modern scholars believe that at least twenty-eight dialogues and two of the letters were in fact written by Plato, although all of the thirty-six dialogues have some defenders. A further nine dialogues are ascribed to Plato but were considered spurious even in antiquity.

Plato's dialogues feature Socrates, although not always as the leader of the conversation. (One dialogue, the Laws, instead contains an "Athenian Stranger".) Along with Xenophon, Plato is the primary source of information about Socrates' life and beliefs and it is not always easy to distinguish between the two. While the Socrates presented in the dialogues is often taken to be Plato's mouthpiece, Socrates' reputation for irony, his caginess regarding his own opinions in the dialogues, and his occasional absence from or minor role in the conversation serve to conceal Plato's doctrines. Much of what is said about his doctrines is derived from what Aristotle reports about them.

The political doctrine ascribed to Plato is derived from the Republic, the Laws, and the Statesman. The first of these contains the suggestion that there will not be justice in cities unless they are ruled by philosopher kings; those responsible for enforcing the laws are compelled to hold their women, children, and property in common; and the individual is taught to pursue the common good through noble lies; the Republic says that such a city is likely impossible, however, generally assuming that philosophers would refuse to rule and the people would refuse to compel them to do so.

Whereas the Republic is premised on a distinction between the sort of knowledge possessed by the philosopher and that possessed by the king or political man, Socrates explores only the character of the philosopher; in the Statesman, on the other hand, a participant referred to as the Eleatic Stranger discusses the sort of knowledge possessed by the political man, while Socrates listens quietly. Although rule by a wise man would be preferable to rule by law, the wise cannot help but be judged by the unwise, and so in practice, rule by law is deemed necessary.

Both the Republic and the Statesman reveal the limitations of politics, raising the question of what political order would be best given those constraints; that question is addressed in the Laws, a dialogue that does not take place in Athens and from which Socrates is absent. The character of the society described there is eminently conservative, a corrected or liberalized timocracy on the Spartan or Cretan model or that of pre-democratic Athens.

Plato's dialogues also have metaphysical themes, the most famous of which is his theory of forms. It holds that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through our physical senses, possess the highest and most fundamental kind of reality. He argued extensively in the Phaedo, Phaedrus, and Republic for the immortality of the soul, and he believed specifically in reincarnation.

Plato often uses long-form analogies (usually allegories) to explain his ideas; the most famous is perhaps the Allegory of the Cave. It likens most humans to people tied up in a cave, who look only at shadows on the walls and have no other conception of reality. If they turned around, they would see what is casting the shadows (and thereby gain a further dimension to their reality). If some left the cave, they would see the outside world illuminated by the sun (representing the ultimate form of goodness and truth). If these travelers then re-entered the cave, the people inside (who are still only familiar with the shadows) would not be equipped to believe reports of this 'outside world'. This story explains the theory of forms with their different levels of reality, and advances the view that philosopher-kings are wisest while most humans are ignorant. One student of Plato, Aristotle, who would become another of the most influential philosophers of all time, stressed the implication that understanding relies upon first-hand observation.

Aristotle

Main article: Aristotle

See also: Aristotelianism

Aristotle moved to Athens from his native Stageira in 367 BC and began to study philosophy (perhaps even rhetoric, under Isocrates), eventually enrolling at Plato's Academy. He left Athens approximately twenty years later to study botany and zoology, became a tutor of Alexander the Great, and ultimately returned to Athens a decade later to establish his own school: the Lyceum. At least twenty-nine of his treatises have survived, known as the corpus Aristotelicum, and address a variety of subjects including logic, physics, optics, metaphysics, ethics, rhetoric, politics, poetry, botany, and zoology.

Aristotle is often portrayed as disagreeing with his teacher Plato (e.g., in Raphael's School of Athens). He criticizes the regimes described in Plato's Republic and Laws, and refers to the theory of forms as "empty words and poetic metaphors". He is generally presented as giving greater weight to empirical observation and practical concerns.

Aristotle's fame was not great during the Hellenistic period, when Stoic logic was in vogue, but later peripatetic commentators popularized his work, which eventually contributed heavily to Islamic, Jewish, and medieval Christian philosophy. His influence was such that Avicenna referred to him simply as "the Master"; Maimonides, Alfarabi, Averroes, and Aquinas as "the Philosopher".

Aristotle opposed the utopian style of theorizing, deciding to rely on the understood and observed behaviors of people in reality to formulate his theories. Stemming from an underlying moral assumption that life is valuable, the philosopher makes a point that scarce resources ought to be responsibly allocated to reduce poverty and death. This 'fear of goods' led Aristotle to exclusively support 'natural' trades in which personal satiation was kept at natural limit of consumption. 'Unnatural' trade, as opposed to the intended limit, was classified as the acquisition of wealth to attain more wealth instead of to purchase more goods. Cutting more along the grain of reality, Aristotle did not only set his mind on how to give people direction to make the right choices but wanted each person equipped with the tools to perform this moral duty. In his own words, "Property should be in a certain sense common, but, as a general rule, private; for, when everyone has a distinct interest, men will not complain of one another, and they will make more progress because everyone will be attending to his own business... And further, there is the greatest pleasure in doing a kindness or service to friends or guests or companions, which can only be rendered when a man has private property. These advantages are lost by excessive unification of the state."

Cynicism

Main article: Cynicism (philosophy)

Cynicism was founded by Antisthenes, who was a disciple of Socrates, as well as Diogenes, his contemporary. Their aim was to live according to nature and against convention. Antisthenes was inspired by the ascetism of Socrates, and accused Plato of pride and conceit. Diogenes, his follower, took the ideas to their limit, living in extreme poverty and engaging in anti-social behaviour. Crates of Thebes was, in turn, inspired by Diogenes to give away his fortune and live on the streets of Athens.

Cyrenaicism

Main article: Cyrenaics

The Cyrenaics were founded by Aristippus of Cyrene, who was a pupil of Socrates. The Cyrenaics were hedonists and held that pleasure was the supreme good in life, especially physical pleasure, which they thought more intense and more desirable than mental pleasures. Pleasure is the only good in life and pain is the only evil. Socrates had held that virtue was the only human good, but he had also accepted a limited role for its utilitarian side, allowing pleasure to be a secondary goal of moral action. Aristippus and his followers seized upon this, and made pleasure the sole final goal of life, denying that virtue had any intrinsic value.

Megarians

Main article: Megarian school

The Megarian school flourished in the 4th century BC. It was founded by Euclides of Megara, one of the pupils of Socrates. Its ethical teachings were derived from Socrates, recognizing a single good, which was apparently combined with the Eleatic doctrine of Unity. Their work on modal logic, logical conditionals, and propositional logic played an important role in the development of logic in antiquity, and were influences on the subsequent creation of Stoicism and Pyrrhonism.

Hellenistic philosophy

Main article: Hellenistic philosophy

See also: Ancient Roman philosophy

The philosopher Pyrrho of Elis, in an anecdote taken from Sextus Empiricus' Outlines of Pyrrhonism

 

(upper) PIRRHO • HELIENSIS •
PLISTARCHI • FILIVS
translation (from Latin): Pyrrho • Greek • Son of Plistarchus

(middle) OPORTERE • SAPIENTEM
HANC ILLIVS IMITARI
SECVRITATEM translation (from Latin): It is right wisdom then that all imitate this security (Pyrrho pointing at a peaceful pig munching his food)

(lower) Whoever wants to apply the real wisdom, shall not mind trepidation and misery

During the Hellenistic and Roman periods, many different schools of thought developed in the Hellenistic world and then the Greco-Roman world. There were Greeks, Romans, Egyptians, Syrians and Arabs who contributed to the development of Hellenistic philosophy. Elements of Persian philosophy and Indian philosophy also had an influence. The spread of Christianity throughout the Roman world, followed by the spread of Islam, ushered in the end of Hellenistic philosophy and the beginnings of Medieval philosophy, which was dominated by the three Abrahamic traditions: Jewish philosophy, Christian philosophy, and early Islamic philosophy.

Pyrrhonism

Main article: Pyrrhonism

Pyrrho of Elis, a Democritean philosopher, traveled to India with Alexander the Great's army where Pyrrho was influenced by Buddhist teachings, most particularly the three marks of existence. After returning to Greece, Pyrrho started a new school of philosophy, Pyrrhonism, which taught that it is one's opinions about non-evident matters (i.e., dogma) that prevent one from attaining eudaimonia. Pyrrhonism places the attainment of ataraxia (a state of equanimity) as the way to achieve eudaimonia. To bring the mind to ataraxia Pyrrhonism uses epoché (suspension of judgment) regarding all non-evident propositions. Pyrrhonists dispute that the dogmatists – which includes all of Pyrrhonism's rival philosophies – have found truth regarding non-evident matters. For any non-evident matter, a Pyrrhonist makes arguments for and against such that the matter cannot be concluded, thus suspending belief and thereby inducing ataraxia.

Epicureanism

Main article: Epicureanism

Epicurus studied in Athens with Nausiphanes, who was a follower of Democritus and a student of Pyrrho of Elis. He accepted Democritus' theory of atomism, with improvements made in response to criticisms by Aristotle and others. His ethics were based on "the pursuit of pleasure and the avoidance of pain". This was, however, not simple hedonism, as he noted that "We do not mean the pleasures of the prodigal or of sensuality . . . we mean the absence of pain in the body and trouble in the mind".

Stoicism

Main article: Stoicism

The founder of Stoicism, Zeno of Citium, was taught by Crates of Thebes, and he took up the Cynic ideals of continence and self-mastery, but applied the concept of apatheia (indifference) to personal circumstances rather than social norms, and switched shameless flouting of the latter for a resolute fulfillment of social duties. Logic and physics were also part of early Stoicism, further developed by Zeno's successors Cleanthes and Chrysippus. Their metaphysics was based in materialism, which was structured by logos, reason (but also called God or fate). Their logical contributions still feature in contemporary propositional calculus. Their ethics was based on pursuing happiness, which they believed was a product of 'living in accordance with nature'. This meant accepting those things which one could not change. One could therefore choose whether to be happy or not by adjusting one's attitude towards their circumstances, as the freedom from fears and desires was happiness itself.

Platonism

Main article: Platonism

Academic skepticism

Main article: Academic skepticism

Around 266 BC, Arcesilaus became head of the Platonic Academy, and adopted skepticism as a central tenet of Platonism, making Platonism nearly the same as Pyrrhonism. After Arcesilaus, Academic skepticism diverged from Pyrrhonism. This skeptical period of ancient Platonism, from Arcesilaus to Philo of Larissa, became known as the New Academy, although some ancient authors added further subdivisions, such as a Middle Academy. The Academic skeptics did not doubt the existence of truth; they just doubted that humans had the capacities for obtaining it. They based this position on Plato's Phaedo, sections 64–67, in which Socrates discusses how knowledge is not accessible to mortals. While the objective of the Pyrrhonists was the attainment of ataraxia, after Arcesilaus the Academic skeptics did not hold up ataraxia as the central objective. The Academic skeptics focused on criticizing the dogmas of other schools of philosophy, in particular of the dogmatism of the Stoics. They acknowledged some vestiges of a moral law within, at best but a plausible guide, the possession of which, however, formed the real distinction between the sage and the fool. Slight as the difference may appear between the positions of the Academic skeptics and the Pyrrhonists, a comparison of their lives leads to the conclusion that a practical philosophical moderation was the characteristic of the Academic skeptics whereas the objectives of the Pyrrhonists were more psychological.

Middle Platonism

Main article: Middle Platonism

Following the end of the skeptical period of the Academy with Antiochus of Ascalon, Platonic thought entered the period of Middle Platonism, which absorbed ideas from the Peripatetic and Stoic schools. More extreme syncretism was done by Numenius of Apamea, who combined it with Neopythagoreanism.

Neoplatonism

Main article: Neoplatonism

Also affected by the neopythagoreans, the neoplatonists, first of them Plotinus, argued that mind exists before matter, and that the universe has a singular cause which must therefore be a single mind. As such, neoplatonism became essentially a religion, and had great impact on Gnosticism and Christian theology.

Transmission of Greek philosophy in the medieval period

Main article: Arab transmission of the Classics to the West

See also: Early Islamic philosophy and Latin translations of the 12th century

During the Middle Ages, Greek ideas were largely forgotten in Western Europe due to the decline in literacy during the Migration Period. In the Byzantine Empire, however, Greek ideas were preserved and studied. Islamic philosophers such as Al-Kindi (Alkindus), Al-Farabi (Alpharabius), Ibn Sina (Avicenna) and Ibn Rushd (Averroes) also reinterpreted these works after the caliphs authorized the gathering of Greek manuscripts and hired translators to increase their prestige. During the High Middle Ages Greek philosophy re-entered the West through both translations from Arabic to Latin and original Greek manuscripts from the Byzantine Empire. The re-introduction of these philosophies, accompanied by the new Arabic commentaries, had a great influence on Medieval philosophers such as Thomas Aquinas.