Cosmological argument

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In the philosophy of religion, a cosmological argument is an argument for the existence of God based upon observational and factual statements concerning the universe (or some general category of its natural contents) typically in the context of causation, change, contingency or finitude. In referring to reason and observation alone for its premises, and precluding revelation, this category of argument falls within the domain of natural theology. A cosmological argument can also sometimes be referred to as an argument from universal causation, an argument from first cause, the causal argument or the prime mover argument.

The concept of causation is a principal underpinning idea in all cosmological arguments, particularly in affirming the necessity for a First Cause. The latter is typically determined in philosophical analysis to be God, as identified within classical conceptions of theism.

The origins of the argument date back to at least Aristotle, developed subsequently within the scholarly traditions of Neoplatonism and early Christianity, and later under medieval Islamic scholasticism through the 9th to 12th centuries. It would eventually be re-introduced to Christian theology in the 13th century by Thomas Aquinas. In the 18th century, it would become associated with the principle of sufficient reason formulated by Gottfried Leibniz and Samuel Clarke, itself an exposition of the Parmenidean causal principle that "nothing comes from nothing".

Contemporary defenders of cosmological arguments include William Lane Craig, Robert Koons, John Lennox, Stephen Meyer, and Alexander Pruss.

History

Plato and Aristotle, depicted here in Raphael's The School of Athens, both developed first cause arguments.

Classical philosophy

Plato (c. 427–347 BC) and Aristotle (c. 384–322 BC) both posited first cause arguments, though each had certain notable caveats. In The Laws (Book X), Plato posited that all movement in the world and the Cosmos was "imparted motion". This required a "self-originated motion" to set it in motion and to maintain it. In Timaeus, Plato posited a "demiurge" of supreme wisdom and intelligence as the creator of the Cosmos.

Aristotle argued against the idea of a first cause, often confused with the idea of a "prime mover" or "unmoved mover" (πρῶτον κινοῦν ἀκίνητον or primus motor) in his Physics and Metaphysics. Aristotle argued in favor of the idea of several unmoved movers, one powering each celestial sphere, which he believed lived beyond the sphere of the fixed stars, and explained why motion in the universe (which he believed was eternal) had continued for an infinite period of time. Aristotle argued the atomist's assertion of a non-eternal universe would require a first uncaused cause – in his terminology, an efficient first cause – an idea he considered a nonsensical flaw in the reasoning of the atomists.

Like Plato, Aristotle believed in an eternal cosmos with no beginning and no end (which in turn follows Parmenides' famous statement that "nothing comes from nothing"). In what he called "first philosophy" or metaphysics, Aristotle did intend a theological correspondence between the prime mover and a deity; functionally, however, he provided an explanation for the apparent motion of the "fixed stars" (now understood as the daily rotation of the Earth). According to his theses, immaterial unmoved movers are eternal unchangeable beings that constantly think about thinking, but being immaterial, they are incapable of interacting with the cosmos and have no knowledge of what transpires therein. From an "aspiration or desire", the celestial spheres, imitate that purely intellectual activity as best they can, by uniform circular motion. The unmoved movers inspiring the planetary spheres are no different in kind from the prime mover, they merely suffer a dependency of relation to the prime mover. Correspondingly, the motions of the planets are subordinate to the motion inspired by the prime mover in the sphere of fixed stars. Aristotle's natural theology admitted no creation or capriciousness from the immortal pantheon, but maintained a defense against dangerous charges of impiety.

Plotinus, a third-century Platonist, taught that the One transcendent absolute caused the universe to exist simply as a consequence of its existence (creatio ex deo). His disciple Proclus stated "The One is God". Centuries later, the Islamic philosopher Avicenna (c. 980–1037) inquired into the question of being, in which he distinguished between essence (māhiyya) and existence (wuǧūd). He argued that the fact of existence could not be inferred from or accounted for by the essence of existing things, and that form and matter by themselves could not originate and interact with the movement of the Universe or the progressive actualization of existing things. Thus, he reasoned that existence must be due to an agent cause that necessitates, imparts, gives, or adds existence to an essence. To do so, the cause must coexist with its effect and be an existing thing.

Early Christian theology

Steven Duncan writes that the cosmological argument "was first formulated by a Greek-speaking Syriac Christian neo-Platonist, John Philoponus, who claims to find a contradiction between the Greek pagan insistence on the eternity of the world and the Aristotelian rejection of the existence of any actual infinite". Referring to the argument as the "'Kalam' cosmological argument", Duncan asserts that it "received its fullest articulation at the hands of [medieval] Muslim and Jewish exponents of Kalam ("the use of reason by believers to justify the basic metaphysical presuppositions of the faith").

Thomas Aquinas (c. 1225–1274) adapted and enhanced the argument he found in his reading of Aristotle, Avicenna (the Proof of the Truthful), and Maimonides to form one of the most influential versions of the cosmological argument. His conception of first cause was the idea that the Universe must be caused by something that is itself uncaused, which he claimed is that which we call God:

The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible. Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God.

Importantly, Aquinas' Five Ways, given the second question of his Summa Theologica, are not the entirety of Aquinas' demonstration that the Christian God exists. The Five Ways form only the beginning of Aquinas' Treatise on the Divine Nature.

General principles

The infinite regress

A regress is a series of related elements, arranged in some type of sequence of succession, examined in backwards succession (regression) from a fixed point of reference. Depending on the type of regress, this retrograde examination may take the form of recursive analysis, in which the elements in a series are studied as products of prior, often simpler, elements. If there is no 'last member' in a regress (ie. no 'first member' in the series) it becomes an infinite regress, continuing in perpetuity. In the context of the cosmological argument the term 'regress' usually refers to causal regress, in which the series is a chain of cause and effect, with each element in the series arising from causal activity of the prior member. Some variants of the argument may also refer to temporal regress, wherein the elements are past events (discrete units of time) arranged in a temporal sequence.

An infinite regress argument attempts to establish the falsity of a proposition by showing that it entails an infinite regress that is vicious. The cosmological argument is a type of positive infinite regress argument given that it defends a proposition (in this case, the existence of a first cause) by arguing that its negation would lead to a vicious regress. An infinite regress may be vicious due to various reasons:

• Impossibility: Thought experiments such as Hilbert's Hotel are cited to demonstrate the metaphysical impossibilty of actual infinities existing in reality. By the same token, it may be argued that an infinite causal or temporal regress cannot occur in the real world.
• Implausibility: The regress contradicts empirical evidence (eg. for the finitude of the past) or basic principles such as Occam's razor.
• Explanatory failure: A failure of explanatory goals resulting in an infinite regress of explanations. This may arise in the case of logical fallacies such as begging the question or from an attempt to investigate causes concerning origins or fundamental principles.

Accidental and essential ordering of causes

Aquinas refers to the distinction found in Aristotle's Physics (8.5) that a series of causes may either be accidental or essential, though the designation of this terminology would follow later under John Duns Scotus at the turn of the 14th century.

In an accidentally ordered series of causes, earlier members need not continue exerting causal activity (having done so to progress the chain) for the series to continue. For example, in an ancestral lineage, the ancestors need no longer exist in order for their descendents to resume the bloodline. In an essential series, every prior member must maintain causal interrelationship in order for the series to continue: If a hand holds a stick that moves a rock along the ground, the rock would stop motion as soon as the hand or stick ceases to exist.

Based upon this distinction Frederick Copleston (1907-1994) characterises two types of causation: Causes in fieri, which cause an effect's becoming, or coming into existence, and causes in esse, which causally sustain an effect, in being, once it exists.

Two specific properties of an essentially ordered series have significance in the context of the cosmological argument:

• A first cause is essential: In the example illustrated above, the rock derives its causal power essentially from the stick, which derives its causal power essentially from the hand. Later members exercise no independent causal power in continuing the causal series.
• It requires that all causes in the series exist simultaneously in time, or timelessly.

Thomistic philosopher, R. P. Phillips comments on the characteristics of essential ordering:

"Each member of the series of causes possesses being solely by virtue of the actual present operation of a superior cause ... Life is dependent inter alia on a certain atmospheric pressure, this again on the continual operation of physical forces, whose being and operation depends on the position of the earth in the solar system, which itself must endure relatively unchanged, a state of being which can only be continuously produced by a definite—if unknown—constitution of the material universe. This constitution, however, cannot be its own cause ... We are thus irresistibly led to posit a first efficient cause which, while itself uncaused, shall impart causality to a whole series."

Versions of the argument

Aquinas's argument from contingency

In the scholastic era, Aquinas formulated the "argument from contingency", following Aristotle, in claiming that there must be something to explain the existence of the universe. Since the universe could, under different circumstances, conceivably not exist (ie. it is contingent) its existence must have a cause. This cause cannot be embodied in another contingent thing, but something that exists by necessity (ie. that must exist in order for anything else to exist). It is a form of argument from universal causation, therefore compatible with the conception of a universe that has no beginning in time. In other words, according to Aquinas, even if the universe has always existed, it still owes its continuing existence to an uncaused cause, he states: "... and this we understand to be God."

Aquinas's argument from contingency is formulated as the Third Way (Q2, A3) in the Summa Theologica. It may be expressed as follows:

1. There exist contingent things, for which non-existence is possible.
2. It is impossible for contingent things to always exist, so at some time they do not exist.
3. Therefore, if all things are contingent, then nothing would exist now.
4. There exists something rather than nothing.

He concludes thereupon that contingent beings are an insufficient explanation for the existence of other contingent beings. Furthermore, that there must exist a necessary being, whose non-existence is impossible, to explain the origination of all contingent beings.

5. Therefore, there exists a necessary being.
6. It is possible that a necessary being has a cause of its necessity in another necessary being.
7. The derivation of necessity between beings cannot regress to infinity (being an essentially ordered causal series).
8. Therefore, there exists a being that is necessary of itself, from which all necessity derives.
9. That being is whom everyone calls God.

Leibnizian cosmological argument

In 1714, German philosopher Gottfried Leibniz presented a variation of the cosmological argument based upon the principle of sufficient reason. He writes: "There can be found no fact that is true or existent, or any true proposition, without there being a sufficient reason for its being so and not otherwise, although we cannot know these reasons in most cases." Stating his argument succinctly:

"Why is there something rather than nothing? The sufficient reason ... is found in a substance which ... is a necessary being bearing the reason for its existence within itself."

Alexander Pruss formulates the argument as follows:

1. Every contingent fact has an explanation.
2. There is a contingent fact that includes all other contingent facts.
3. Therefore, there is an explanation of this fact.
4. This explanation must involve a necessary being.
5. This necessary being is God.

Premise 1 expresses the principle of sufficient reason (PSR). In premise 2, Leibniz proposes the existence of a logical conjunction of all contingent facts. This may be regarded as the sum total of all contingent reality, referred to in later literature as the Big Conjunctive Contingent Fact (BCCF). Premise 3 applies the PSR to the BCCF, given that it too, as a contingency, has a sufficient explanation. It follows, in statement 4, that the explanation of the BCCF must be necessary, not contingent, given that the BCCF incorporates all contingent facts.

Statement 5 proposes that the necessary being explaining the totality of contingent facts is God. Philosophers of religion, such as Joshua Rasmussen and T. Ryan Byerly, have argued in defence of the inference from 4 to 5.

Duns Scotus's argument

Inspired by Aquinas's argument of the unmoved mover, this metaphysical argument for the existence of God was formulated by influential Medieval Christian theologian Duns Scotus (1265/66–1308). Like other philosophers and theologians, Scotus believed that his statement for God's existence could be considered separate to that of Aquinas. The form of the argument can be summarised as follows:

1. An effect cannot be produced by itself.
2. An effect cannot be produced by nothing.
3. A circle of causes is impossible.
4. Therefore, an effect must be produced by something else.
5. An accidentally ordered causal series cannot exist without an essentially ordered series.

1. Each member in an accidentally ordered series (except a possible first) exists via causal activity of a prior member.
2. That causal activity is exercised by virtue of a certain form.
3. Therefore, that form is required by each member to effect causation.
4. The form itself is not a member of the series.
5. Therefore [c,d], accidentally ordered causes cannot exist without higher-order (essentially ordered) causes.

6. An essentially ordered causal series cannot regress to infinity.
7. Therefore [4,5,6], there exists a first agent.

Scotus affirms, in premise 5, that an accidentally ordered series of causes is impossible without higher-order laws and processes that govern the basic nature of all causal activity, which he characterises as essentially ordered causes. Premise 6 continues, in accordance with Aquinas's discourses on the Second Way and Third Way, that an essentially ordered series of causes cannot be an infinite regress.

On this he posits that, if it is merely possible that a first agent exists, then it is necessarily true that a first agent exists, given that the non-existence of a first agent entails the impossibility of its own existence (by virtue of being a first cause in the chain). Establishing this as basis, he argues that it is not impossible for a being to exist that is causeless by virtue of ontological perfection.

With the formulation of this argument, Scotus establishes the first component of his 'triple primacy': The characterisation of a being that is first in efficient causality, final causality and pre-eminence, or maximal excellence, which he ascribes to God.

Kalam cosmological argument

Main article: Kalam cosmological argument

A modern formulation of the cosmological argument that proposes, as its central thesis, the impossibility of an infinite temporal regress of events (or a past-eternal universe). Its premises defend the finitude of the past through both philosophical and scientific arguments. Many of these ideas originate in the writings of early Christian theologian John Philoponus (490–570 AD), developed within the proceedings of medieval Islamic scholasticism through the 9th to 12th centuries, eventually returning to Christian theological scholarship in the 13th century.

They were revitalised for modern academic discourse by philosopher and theologian William Lane Craig through publications such as The Kalām Cosmological Argument (1979) and the Blackwell Companion to Natural Theology (2009). The form of the argument popularised by Craig is expressed in two parts, as an initial deductive syllogism followed by philosophical analysis of its conclusion.

Initial syllogism

1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

Philosophical analysis of the conclusion

Craig argues that the cause of the universe necessarily embodies specific properties in creating the universe ex nihilo and in effecting creation from a timeless state (implying free agency). Based upon this analysis, he appends a further premise and conclusion:

4. If the universe has a cause, then an uncaused, personal Creator of the universe exists who sans (without) the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
5. Therefore, an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.

For scientific evidence of the finitude of the past, Craig appeals to the Borde-Guth-Vilenkin theorem, which posits a past boundary to cosmic inflation, and the general consensus on the standard model of cosmology, referring to the origin of the universe in the Big Bang.

For philosophical evidence, he cites the Hilbert's Hotel thought experiment and the tale of Tristram Shandy as proofs (respectively) of the impossibility of actual infinities existing in reality and of forming an actual infinite by successive addition. He concludes that past events, comprising a series of events that are, (a) instantiated in reality, (b) formed by successive addition, cannot be actually infinite.

He remarks upon the theological implications that follow from the final conclusion of this argument:

"... our whole universe was caused to exist by something beyond it and greater than it. For it is no secret that one of the most important conceptions of what theists mean by 'God' is Creator of heaven and earth."

Criticism and discourse

"What caused the first cause?"

One objection to the argument asks why a first cause is unique in that it does not require any causes. Proponents argue that the first cause is exempt from having a cause, as this is part of what it is to be the first cause, while opponents argue that this is special pleading or otherwise untrue. Critics often press that arguing for the first cause's exemption raises the question of why the first cause is indeed exempt, whereas defenders maintain that this question has been answered by the various arguments, emphasizing that none of the major cosmological arguments rests on the premise that everything has a cause, and so the question does not address the actual premises of an argument and rests on a misunderstanding of them.

Andrew Loke states that, according to the Kalam cosmological argument, only things which begin to exist require a cause. On the other hand, something that is without beginning has always existed and therefore does not require a cause. Loke and William Lane Craig argue that an infinite regress of causes is impossible, therefore, that there must be a first uncaused cause, even if one posits a plurality of causes of the universe. Craig argues further that Occam's razor may be employed to remove unneeded further causes of the universe to leave a single uncaused cause.

"Why can't the universe be causeless?"

It is argued that the premise of causality has been arrived at via a posteriori (inductive) reasoning, which is dependent on experience. David Hume highlighted this problem of induction and argued that causal relations are not true a priori. However, as to whether inductive or deductive reasoning is more valuable remains a matter of debate, with the general conclusion being that neither is prominent. Opponents of the cosmological argument argue that it is unwise to draw conclusions from an extrapolation of causality beyond experience, therefore, that the causal principle does not apply to the origin of the universe.

Philosopher Robert Koons argues that to deny causation is to deny all empirical ideas – for example, if we know our own hand, we know it because of the chain of causes including light being reflected upon one's eyes, stimulating the retina and sending a message through the optic nerve into your brain. He summarised the purpose of the argument as "that if you don't buy into theistic metaphysics, you're undermining empirical science. The two grew up together historically and are culturally and philosophically inter-dependent ... If you say I just don't buy this causality principle – that's going to be a big big problem for empirical science."

"Why should the cause be God?"

According to this objection, the basic cosmological argument merely establishes that a first cause exists, not that it has the attributes of a theistic god, such as omniscience, omnipotence, and omnibenevolence. This is why the argument is often expanded to assert that at least some of these attributes are necessarily true, for instance in the modern Kalam argument given above.

Defenders of the cosmological arguments also reply that theologians of note are aware of the need to additionally prove other attributes of the first cause beyond that one exists. One notable example of this is found in Aquinas' Summa Theologiae in which much of the first part (Prima Pars) is devoted to establishing the attributes of this first cause, such as its uniqueness, perfection, and intelligence. Thus defenders of cosmological arguments would reply that while it is true that the cosmological argument only establishes a first cause, this is merely the first step which then allows for the demonstration of the other theistic attributes.

Timeless origin of the universe

Some cosmologists and physicists, such as Carlo Rovelli, argue that a challenge to the cosmological argument is the nature of time: "One finds that time just disappears from the Wheeler–DeWitt equation." The Big Bang theory states that it is the point in which all dimensions came into existence, the start of both space and time. Then, the question "What was there before the Universe?" makes no sense; the concept of "before" becomes meaningless when considering a situation without time.^[61] This has been put forward by J. Richard Gott III, James E. Gunn, David N. Schramm, and Beatrice Tinsley, who said that asking what occurred before the Big Bang is like asking what is north of the North Pole. However, some cosmologists and physicists attempt to investigate causes for the Big Bang, using such scenarios as the collision of membranes. Philosopher Edward Feser argues that most of the classical philosophers' cosmological arguments for the existence of God do not depend on the Big Bang or whether the universe had a beginning. The question is not about what got things started, or how long they have been going, but rather what keeps them going.

Avoiding an infinite regress

David Hume and later Paul Edwards have invoked a similar principle in their criticisms of the cosmological argument. William L. Rowe has called this the Hume-Edwards principle:

If the existence of every member of a set is explained, the existence of that set is thereby explained.

Nevertheless, David White argues that the notion of an infinite causal regress providing a proper explanation is fallacious. Furthermore, in Hume's Dialogues Concerning Natural Religion, the character Demea states that even if the succession of causes is infinite, the whole chain still requires a cause. To explain this, suppose there exists a causal chain of infinite contingent beings. If one asks the question, "Why are there any contingent beings at all?", it does not help to be told that "There are contingent beings because other contingent beings caused them." That answer would just presuppose additional contingent beings. An adequate explanation of why some contingent beings exist would invoke a different sort of being, a necessary being that is not contingent. A response might suppose each individual is contingent but the infinite chain as a whole is not, or the whole infinite causal chain is its own cause.

Edward Feser argues that an essentially ordered series of causes cannot regress to infinity, even if it may be theoretically possible for accidentally ordered causes to do so. Severinsen argues that there is an "infinite" and complex causal structure. White tried to introduce an argument "without appeal to the principle of sufficient reason and without denying the possibility of an infinite causal regress". A number of other arguments have been offered to demonstrate that an actual infinite regress cannot exist, viz. the argument for the impossibility of concrete actual infinities, the argument for the impossibility of traversing an actual infinite, the argument from the lack of capacity to begin to exist, and various arguments from paradoxes.

Causal loop arguments

Some objections to the cosmological argument refer to the possibility of loops in the structure of cause and effect that would avoid the need for a First Cause. Gott and Li refer to the curvature of spacetime and closed timelike curves as possible mechanisms by which the universe may bring about its own existence. Richard Hanley contends that causal loops are neither logically nor physically impossible, remarking: "[In timed systems] the only possibly objectionable feature that all causal loops share is that coincidence is required to explain them." However, Andrew Loke argues that there is insufficient evidence to postulate a causal loop of the type that would avoid a First Cause. He asserts that such a mechanism would suffer from the problem of vicious circularity, rendering it metaphysically impossible.

Infinite regress

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An illustration of infinite regress

An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor.

In the epistemic regress, for example, a belief is justified because it is based on another belief that is justified. But this other belief is itself in need of one more justified belief for itself to be justified and so on. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress.

For such an argument to be successful, it must demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. There are different ways in which a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of metaphysical impossibility. Other forms occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve.

Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy. While some philosophers have explicitly defended theories with infinite regresses, the more common strategy has been to reformulate the theory in question in a way that avoids the regress. One such strategy is foundationalism, which posits that there is a first element in the series from which all the other elements arise but which is not itself explained this way. Another way is coherentism, which is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network.

Infinite regress arguments have been made in various areas of philosophy. Famous examples include the cosmological argument and Bradley's regress.

Definition

An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. This principle can often be expressed in the following form: X is F because X stands in R to Y and Y is F. X and Y stand for objects, R stands for a relation and F stands for a property in the widest sense. In the epistemic regress, for example, a belief is justified because it is based on another belief that is justified. But this other belief is itself in need of one more justified belief for itself to be justified and so on. Or in the cosmological argument, an event occurred because it was caused by another event that occurred before it, which was itself caused by a previous event, and so on. This principle by itself is not sufficient: it does not lead to a regress if there is no X that is F. This is why an additional triggering condition has to be fulfilled: there has to be an X that is F for the regress to get started. So the regress starts with the fact that X is F. According to the recursive principle, this is only possible if there is a distinct Y that is also F. But in order to account for the fact that Y is F, we need to posit a Z that is F and so on. Once the regress has started, there is no way of stopping it since a new entity has to be introduced at each step in order to make the previous step possible.

An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. The mere existence of an infinite regress by itself is not a proof for anything. So in addition to connecting the theory to a recursive principle paired with a triggering condition, the argument has to show in which way the resulting regress is vicious. For example, one form of evidentialism in epistemology holds that a belief is only justified if it is based on another belief that is justified. An opponent of this theory could use an infinite regress argument by demonstrating (1) that this theory leads to an infinite regress (e.g. by pointing out the recursive principle and the triggering condition) and (2) that this infinite regress is vicious (e.g. by showing that it is implausible given the limitations of the human mind). In this example, the argument has a negative form since it only denies that another theory is true. But it can also be used in a positive form to support a theory by showing that its alternative involves a vicious regress. This is how the cosmological argument for the existence of God works: it claims that positing God's existence is necessary in order to avoid an infinite regress of causes.

Viciousness

For an infinite regress argument to be successful, it has to show that the involved regress is vicious. A non-vicious regress is called virtuous or benign. Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy. In most cases, it is not self-evident whether an infinite regress is vicious or not. The truth regress constitutes an example of an infinite regress that is not vicious: if the proposition "P" is true, then the proposition that "It is true that P" is also true and so on. Infinite regresses pose a problem mostly if the regress concerns concrete objects. Abstract objects, on the other hand, are often considered to be unproblematic in this respect. For example, the truth-regress leads to an infinite number of true propositions or the Peano axioms entail the existence of infinitely many natural numbers. But these regresses are usually not held against the theories that entail them.

There are different ways how a regress can be vicious. The most serious type of viciousness involves a contradiction in the form of metaphysical impossibility. Other types occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. The vice of an infinite regress can be local if it causes problems only for certain theories when combined with other assumptions, or global otherwise. For example, an otherwise virtuous regress is locally vicious for a theory that posits a finite domain. In some cases, an infinite regress is not itself the source of the problem but merely indicates a different underlying problem.

Impossibility

Infinite regresses that involve metaphysical impossibility are the most serious cases of viciousness. The easiest way to arrive at this result is by accepting the assumption that actual infinities are impossible, thereby directly leading to a contradiction. This anti-infinitists position is opposed to infinity in general, not just specifically to infinite regresses. But it is open to defenders of the theory in question to deny this outright prohibition on actual infinities. For example, it has been argued that only certain types of infinities are problematic in this way, like infinite intensive magnitudes (e.g. infinite energy densities). But other types of infinities, like infinite cardinality (e.g. infinitely many causes) or infinite extensive magnitude (e.g. the duration of the universe's history) are unproblematic from the point of view of metaphysical impossibility. While there may be some instances of viciousness due to metaphysical impossibility, most vicious regresses are problematic because of other reasons.

Implausibility

A more common form of viciousness arises from the implausibility of the infinite regress in question. This category often applies to theories about human actions, states or capacities. This argument is weaker than the argument from impossibility since it allows that the regress in question is possible. It only denies that it is actual. For example, it seems implausible due to the limitations of the human mind that there are justified beliefs if this entails that the agent needs to have an infinite amount of them. But this is not metaphysically impossible, e.g. if it is assumed that the infinite number of beliefs are only non-occurrent or dispositional while the limitation only applies to the number of beliefs one is actually thinking about at one moment. Another reason for the implausibility of theories involving an infinite regress is due to the principle known as Ockham's razor, which posits that we should avoid ontological extravagance by not multiplying entities without necessity. Considerations of parsimony are complicated by the distinction between quantitative and qualitative parsimony: concerning how many entities are posited in contrast to how many kinds of entities are posited. For example, the cosmological argument for the existence of God promises to increase quantitative parsimony by positing that there is one first cause instead of allowing an infinite chain of events. But it does so by decreasing qualitative parsimony: it posits God as a new type of entity.

Failure to explain

Another form of viciousness applies not to the infinite regress by itself but to it in relation to the explanatory goals of a theory. Theories are often formulated with the goal of solving a specific problem, e.g. of answering the question why a certain type of entity exists. One way how such an attempt can fail is if the answer to the question already assumes in disguised form what it was supposed to explain. This is akin to the informal fallacy of begging the question. From the perspective of a mythological world view, for example, one way to explain why the earth seems to be at rest instead of falling down is to hold that it rests on the back of a giant turtle. In order to explain why the turtle itself is not in free fall, another even bigger turtle is posited and so on, resulting in a world that is turtles all the way down. Despite its shortcomings in clashing with modern physics and due to its ontological extravagance, this theory seems to be metaphysically possible assuming that space is infinite. One way to assess the viciousness of this regress is to distinguish between local and global explanations. A local explanation is only interested in explaining why one thing has a certain property through reference to another thing without trying to explain this other thing as well. A global explanation, on the other hand, tries to explain why there are any things with this property at all. So as a local explanation, the regress in the turtle theory is benign: it succeeds in explaining why the earth is not falling. But as a global explanation, it fails because it has to assume rather than explain at each step that there is another thing that is not falling. It does not explain why nothing at all is falling.

It has been argued that infinite regresses can be benign under certain circumstances despite aiming at global explanation. This line of thought rests on the idea of the transmission involved in the vicious cases: it is explained that X is F because Y is F where this F was somehow transmitted from Y to X. The problem is that to transfer something, it first must be possessed, so the possession is presumed rather than explained. For example, in trying to explain why one's neighbor has the property of being the owner of a bag of sugar, it is revealed that this bag was first in someone else's possession before it was transferred to the neighbor and that the same is true for this and every other previous owner. This explanation is unsatisfying since ownership is presupposed at every step. In non-transmissive explanations, however, Y is still the reason for X being F and Y is also F but this is just seen as a contingent fact. This line of thought has been used to argue that the epistemic regress is not vicious. From a Bayesian point of view, for example, justification or evidence can be defined in terms of one belief raising the probability that another belief is true. The former belief may also be justified but this is not relevant for explaining why the latter belief is justified.

Responses to infinite regress arguments

Philosophers have responded to infinite regress arguments in various ways. The criticized theory can be defended, for example, by denying that an infinite regress is involved. Infinitists, on the other hand, embrace the regress but deny that it is vicious. Another response is to modify the theory in order to avoid the regress. This can be achieved in the form of foundationalism or of coherentism.

Foundationalism

Traditionally, the most common response is foundationalism. It posits that there is a first element in the series from which all the other elements arise but which is not itself explained this way. So from any given position, the series can be traced back to elements on the most fundamental level, which the recursive principle fails to explain. This way an infinite regress is avoided. This position is well-known from its applications in the field of epistemology. Foundationalist theories of epistemic justification state that besides inferentially justified beliefs, which depend for their justification on other beliefs, there are also non-inferentially justified beliefs. The non-inferentially justified beliefs constitute the foundation on which the superstructure consisting of all the inferentially justified beliefs rests. Acquaintance theories, for example, explain the justification of non-inferential beliefs through acquaintance with the objects of the belief. On such a view, an agent is inferentially justified to believe that it will rain tomorrow based on the belief that the weather forecast told so. They are non-inferentially justified in believing that they are in pain because they are directly acquainted with the pain. So a different type of explanation (acquaintance) is used for the foundational elements.

Another example comes from the field of metaphysics concerning the problem of ontological hierarchy. One position in this debate claims that some entities exist on a more fundamental level than other entities and that the latter entities depend on or are grounded in the former entities. Metaphysical foundationalism is the thesis that these dependence relations do not form an infinite regress: that there is a most fundamental level that grounds the existence of the entities from all other levels. This is sometimes expressed by stating that the grounding-relation responsible for this hierarchy is well-founded.

Coherentism

Coherentism, mostly found in the field of epistemology, is another way to avoid infinite regresses. It is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network. For example, coherentist theories of epistemic justification hold that beliefs are justified because of the way they hang together: they cohere well with each other. This view can be expressed by stating that justification is primarily a property of the system of beliefs as a whole. The justification of a single belief is derivative in the sense that it depends on the fact that this belief belongs to a coherent whole. Laurence BonJour is a well-known contemporary defender of this position.

Examples

Aristotle

Aristotle argued that knowing does not necessitate an infinite regress because some knowledge does not depend on demonstration:

Some hold that owing to the necessity of knowing the primary premises, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premises. The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand – they say – the series terminates and there are primary premises, yet these are unknowable because incapable of demonstration, which according to them is the only form of knowledge. And since thus one cannot know the primary premises, knowledge of the conclusions which follow from them is not pure scientific knowledge nor properly knowing at all, but rests on the mere supposition that the premises are true. The other party agrees with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal. Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premises from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) Such, then, is our doctrine, and in addition, we maintain that besides scientific knowledge there is its original source which enables us to recognize the definitions.

— Aristotle, Posterior Analytics I.3 72b1–15

Philosophy of mind

Gilbert Ryle argues in the philosophy of mind that mind-body dualism is implausible because it produces an infinite regress of "inner observers" when trying to explain how mental states are able to influence physical states.

Knotted polymers

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Knotted_polymers

Single Chain Cyclized/Knotted Polymers are a new class of polymer architecture with a general structure consisting of multiple intramolecular cyclization units within a single polymer chain. Such a structure was synthesized via the controlled polymerization of multivinyl monomers, which was first reported in Dr. Wenxin Wang's research lab. These multiple intramolecular cyclized/knotted units mimic the characteristics of complex knots found in proteins and DNA which provide some elasticity to these structures. Of note, 85% of elasticity in natural rubber is due to knot-like structures within its molecular chain.
An intramolecular cyclization reaction is where the growing polymer chain reacts with a vinyl functional group on its own chain, rather than with another growing chain in the reaction system. In this way the growing polymer chain covalently links to itself in a fashion similar to that of a knot in a piece of string. As such, single chain cyclized/knotted polymers consist of many of these links (intramolecularly cyclized), as opposed to other polymer architectures including branched and crosslinked polymers that are formed by two or more polymer chains in combination.

Figure 1. Single chain cyclized/knotted polymer, analogous to a Celtic knot.

Linear polymers can also fold into knotted topologies via non-covalent linkages. Knots and slipknots have been identified in naturally evolved polymers such as proteins as well. Circuit topology and knot theory formalise and classify such molecular conformations.

Synthesis

Deactivation enhanced ATRP

A simple modification to atom transfer radical polymerization (ATRP) was introduced in 2007 to kinetically control the polymerization by increasing the ratio of inactive copper(II) catalyst to active copper(I) catalyst. The modification to this strategy is termed deactivation enhanced ATRP, whereby different ratios of copper(II)/copper(I) are added. Alternatively a copper(II) catalyst may be used in the presence of small amounts of a reducing agent such as ascorbic acid to produce low percentages of copper(I) in situ and to control the ratio of copper (II)/copper (I). Deactivation enhanced ATRP features the decrease of the instantaneous kinetic chain length ν as defined by:${\displaystyle \nu =\frac{R_{\text{p}}}{R_{\text{deac}}}=\frac{k_{\text{p}}[\text{M}][\text{P}]}{k_{\text{deac}}[{\text{Cu}}^{\text{II}}][\text{P}]}=\frac{k_{\text{p}}[\text{M}]}{k_{\text{deac}}[{\text{Cu}}^{\text{II}}]}}$,
meaning an average number of monomer units are added to a propagating chain end during each activation/deactivation cycle, The resulting chain growth rate is slowed down to allow sufficient control over the reaction thus greatly increasing the percentage of multi-vinyl monomers in the reaction system (even up to 100 percent (homopolymerization)).

Polymerization process

Typically, single chain cyclized/knotted polymers are synthesized by deactivation enhanced ATRP of multivinyl monomers via kinetically controlled strategy. There are several main reactions during this polymerization process: initiation, activation, deactivation, chain propagation, intramolecular cyclization and intermolecular crosslinking. The polymerization process is explained in Figure 2.

Figure 2. Single chain cyclized/knotted polymers synthesis approach.

In a similar way to normal ATRP, the polymerization is started by initiation to produce a free radical, followed by chain propagation and reversible activation/deactivation equilibrium. Unlike the polymerization of single vinyl monomers, for the polymerization of multivinyl monomers, the chain propagation occurs between the active centres and one of the vinyl groups from the free monomers. Therefore, multiple unreacted pendent vinyl groups are introduced into the linear primary polymer chains, resulting in a high local/spatial vinyl concentration. As the chain grows, the propagating centre reacts with their own pendent vinyl groups to form intramolecular cyclized rings (i.e. intramolecular cyclization). The unique alternating chain propagation/intramolecular cyclization process eventually leads to the single chain cyclized/knotted polymer architecture.

Intramolecular cyclization or intermolecular crosslinking

It is worthy to note that due to the multiple reactive sites of the multivinyl monomers, plenty of unreacted pendent vinyl groups are introduced to linear primary polymer chains. These pendent vinyl groups have the potential to react with propagating active centres either from their own polymer chain or others. Therefore, both of the intramolecular cyclization and intermolecular crosslinking might occur in this process.

Using the deactivation enhanced strategy, a relatively small instantaneous kinetic chain length limits the number of vinyl groups that can be added to a propagating chain end during each activation/deactivation cycles and thus keeps the polymer chains growing in a limited space. In this way, unlike what happens in free radical polymerization (FRP), the formation of huge polymer chains and large-scale combinations at early reaction stages is avoided. Therefore, a small instantaneous kinetic chain length is the prerequisite for further manipulation of intramolecular cyclization or intermolecular crosslinking. Based on the small instantaneous kinetic chain length, regulation of different chain dimensions and concentrations would lead to distinct reaction types. A low ratio of initiator to monomer would result in the formation of longer chains but of a lower chain concentration, This scenario would no doubt increases the chances of intramolecular cyclization due to the high local/spatial vinyl concentration within the growth boundary. Although the opportunity for intermolecular reactions can increase as the polymer chains grow, the likelihood of this occurring at the early stage of reactions is minimal due to the low chain concentration, which is why single chain cyclized/knotted polymers can form. However, in contrast, a high initiator concentration not only diminishes the chain dimension during the linear-growth phase thus suppressing the intramolecular cyclization, but it also increases the chain concentration within the system so that pendent vinyl groups in one chain are more likely to fall into the growth boundary of another chain. Once the monomers are converted to short chains, the intermolecular combination increases and allows the formation of hyperbranched structures with a high density of branching and vinyl functional groups.

Note

• The monomer concentration is important for the synthesis of single chain cyclized/knotted polymers, but the kinetic chain length is the key determining factor for synthesis.

Applications

Single chain cyclized polymers consist of multiple cyclized rings which afford them some unique properties, including high density, low intrinsic viscosity, low translational friction coefficients, high glass transition temperatures, and excellent elasticity of the formed network. In particular, an abundance of internal space makes the single chain cyclized polymers ideal candidates as efficient cargo-carriers.

Gene delivery

It is well established that the macromolecular structure of nonviral gene delivery vectors alters their transfection efficacy and cytotoxicity. The cyclized structure has been proven to reduce cytotoxicity and increase circulation time for drug and gene delivery applications. The unique structure of cyclizing chains provides the single chain cyclized polymers a different method of interaction between the polymer and plasmid DNA, and results in a general trend of higher transfection capabilities than branched polymers. Moreover, due to the nature of the single chain structure, this cyclized polymer can “untie” to a linear chain under reducing conditions. Transfection profiles on astrocytes comparing 25 kDa-PEI, SuperFect® and Lipofectamine®2000 and cyclized polymer showed greater efficiency and cell viability whilst maintaining neural cell viability above 80% four days post transfections.

Magi

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Magi

Zoroastrian priests (Magi) carrying barsoms. Statuettes from the Oxus Treasure of the Achaemenid Empire, 4th century BC

Magi (PLUR), or magus (SING), is the term for priests in Zoroastrianism and earlier Iranian religions. The earliest known use of the word magi is in the trilingual inscription written by Darius the Great, known as the Behistun Inscription. Old Persian texts, predating the Hellenistic period, refer to a magus as a Zurvanic, and presumably Zoroastrian, priest.

Pervasive throughout the Eastern Mediterranean and Western Asia until late antiquity and beyond, mágos (μάγος) was influenced by (and eventually displaced) Greek goēs (γόης), the older word for a practitioner of magic, with a meaning expanded to include astronomy, astrology, alchemy, and other forms of esoteric knowledge. This association was in turn the product of the Hellenistic fascination for Pseudo-Zoroaster, who was perceived by the Greeks to be the Chaldean founder of the Magi and inventor of both astrology and magic, a meaning that still survives in the modern-day words "magic" and "magician".

In the Gospel of Matthew, "μάγοι" (magoi) from the east do homage to the Christ Child, and the transliterated plural "magi" entered English from Latin in this context around 1200 CE (this particular use is also commonly rendered in English as "kings" and more often in recent times as "wise men"). The singular "magus" appears considerably later, when it was borrowed from Old French in the late 14th century with the meaning magician.

Hereditary Zoroastrian priesthood has survived in India and Iran. They are termed Herbad, Mobad (Magupat, i.e. chief of the Maga), and Dastur depending on the rank.

Iranian sources

Zoroastrian Magus carrying barsom from the Oxus Treasure of the Achaemenid Empire, 4th century BC

The term only appears twice in Iranian texts from before the 5th century BC, and only one of these can be dated with precision. This one instance occurs in the trilingual Behistun inscription of Darius the Great, and which can be dated to about 520 BC. In this trilingual text, certain rebels have magian as an attribute; in the Old Persian portion as maγu- (generally assumed to be a loan word from Median). The meaning of the term in this context is uncertain.

The other instance appears in the texts of the Avesta, the sacred literature of Zoroastrianism. In this instance, which is in the Younger Avestan portion, the term appears in the hapax moghu.tbiš, meaning "hostile to the moghu", where moghu does not (as was previously thought) mean "magus", but rather "a member of the tribe" or referred to a particular social class in the proto-Iranian language and then continued to do so in Avestan.

An unrelated term, but previously assumed to be related, appears in the older Gathic Avestan language texts. This word, adjectival magavan meaning "possessing maga-", was once the premise that Avestan maga- and Median (i.e. Old Persian) magu- were coeval (and also that both these were cognates of Vedic Sanskrit magha-). While "in the Gathas the word seems to mean both the teaching of Zoroaster and the community that accepted that teaching", and it seems that Avestan maga- is related to Sanskrit magha-, "there is no reason to suppose that the western Iranian form magu (Magus) has exactly the same meaning" as well. But it "may be, however", that Avestan moghu (which is not the same as Avestan maga-) "and Medean magu were the same word in origin, a common Iranian term for 'member of the tribe' having developed among the Medes the special sense of 'member of the (priestly) tribe', hence a priest."

Some examples of the use of magi in Persian poetry, are present in the poems of Hafez. There are two frequent terms used by him, first one is Peer-e Moghan (literally "the old man of the magi") and second one is Deyr-e Moghan (literally "the monastery of the magi").

Greco-Roman sources

Classical Greek

The oldest surviving Greek reference to the magi – from Greek μάγος (mágos, plural: magoi) – might be from 6th century BC Heraclitus (apud Clemens Protrepticus 2.22.2), who curses the magi for their "impious" rites and rituals. A description of the rituals that Heraclitus refers to has not survived, and there is nothing to suggest that Heraclitus was referring to foreigners.

Better preserved are the descriptions of the mid-5th century BC Herodotus, who in his portrayal of the Iranian expatriates living in Asia Minor uses the term "magi" in two different senses. In the first sense (Histories 1.101), Herodotus speaks of the magi as one of the tribes/peoples (ethnous) of the Medes. In another sense (1.132), Herodotus uses the term "magi" to generically refer to a "sacerdotal caste", but "whose ethnic origin is never again so much as mentioned." According to Robert Charles Zaehner, in other accounts, "we hear of Magi not only in Persia, Parthia, Bactria, Chorasmia, Aria, Media, and among the Sakas, but also in non-Iranian lands like Samaria, Ethiopia, and Egypt. Their influence was also widespread throughout Asia Minor. It is, therefore, quite likely that the sacerdotal caste of the Magi was distinct from the Median tribe of the same name."

As early as the 5th century BC, Greek magos had spawned mageia and magike to describe the activity of a magus, that is, it was his or her art and practice. But almost from the outset the noun for the action and the noun for the actor parted company. Thereafter, mageia was used not for what actual magi did, but for something related to the word 'magic' in the modern sense, i.e. using supernatural means to achieve an effect in the natural world, or the appearance of achieving these effects through trickery or sleight of hand. The early Greek texts typically have the pejorative meaning, which in turn influenced the meaning of magos to denote a conjurer and a charlatan. Already in the mid-5th century BC, Herodotus identifies the magi as interpreters of omens and dreams (Histories 7.19, 7.37, 1.107, 1.108, 1.120, 1.128).

Other Greek sources from before the Hellenistic period include the gentleman-soldier Xenophon, who had first-hand experience at the Persian Achaemenid court. In his early 4th century BC Cyropaedia, Xenophon depicts the magians as authorities for all religious matters (8.3.11), and imagines the magians to be responsible for the education of the emperor-to-be. Apuleius, a Numidian Platonist philosopher, describes magus to be considered as a "sage and philosopher-king" based on its Platonic notion.

Roman period

Incised sarcophagus slab with the Adoration of the Magi from the Catacombs of Rome, 3rd century

Once the magi had been associated with "magic" – Greek magikos – it was but a natural progression that the Greeks' image of Zoroaster would metamorphose into a magician too. The first century Pliny the Elder names "Zoroaster" as the inventor of magic (Natural History xxx.2.3), but a "principle of the division of labor appears to have spared Zoroaster most of the responsibility for introducing the dark arts to the Greek and Roman worlds. That dubious honor went to another fabulous magus, Ostanes, to whom most of the pseudepigraphic magical literature was attributed." For Pliny, this magic was a "monstrous craft" that gave the Greeks not only a "lust" (aviditatem) for magic, but a downright "madness" (rabiem) for it, and Pliny supposed that Greek philosophers – among them Pythagoras, Empedocles, Democritus, and Plato – traveled abroad to study it, and then returned to teach it (xxx.2.8–10).

"Zoroaster" – or rather what the Greeks supposed him to be – was for the Hellenists the figurehead of the 'magi', and the founder of that order (or what the Greeks considered to be an order). He was further projected as the author of a vast compendium of "Zoroastrian" pseudepigrapha, composed in the main to discredit the texts of rivals. "The Greeks considered the best wisdom to be exotic wisdom" and "what better and more convenient authority than the distant – temporally and geographically – Zoroaster?" The subject of these texts, the authenticity of which was rarely challenged, ranged from treatises on nature to ones on necromancy. But the bulk of these texts dealt with astronomical speculations and magical lore.

One factor for the association with astrology was Zoroaster's name, or rather, what the Greeks made of it. His name was identified at first with star-worshiping (astrothytes "star sacrificer") and, with the Zo-, even as the living star. Later, an even more elaborate mytho-etymology evolved: Zoroaster died by the living (zo-) flux (-ro-) of fire from the star (-astr-) which he himself had invoked, and even that the stars killed him in revenge for having been restrained by him. The second, and "more serious" factor for the association with astrology was the notion that Zoroaster was a Chaldean. The alternate Greek name for Zoroaster was Zaratas / Zaradas / Zaratos (cf. Agathias 2.23–5, Clement Stromata I.15), which – according to Bidez and Cumont – derived from a Semitic form of his name. The Suda's chapter on astronomia notes that the Babylonians learned their astrology from Zoroaster. Lucian of Samosata (Mennipus 6) decides to journey to Babylon "to ask one of the magi, Zoroaster's disciples and successors", for their opinion.

Christian tradition

Main article: Biblical Magi

Byzantine depiction of the Three Magi in a 6th-century mosaic at Basilica of Sant'Apollinare Nuovo

Conventional post-12th century depiction of the Biblical magi (Adoração dos Magos by Vicente Gil). Balthasar, the youngest magus, bears frankincense and represents Africa. To the left stands Caspar, middle-aged, bearing gold and representing Asia. On his knees is Melchior, oldest, bearing myrrh and representing Europe.

The word mágos (Greek) and its variants appear in both the Old and New Testaments. Ordinarily this word is translated "magician" or "sorcerer" in the sense of illusionist or fortune-teller, and this is how it is translated in all of its occurrences (e.g. Acts 13:6) except for the Gospel of Matthew, where, depending on translation, it is rendered "wise man" (KJV, RSV) or left untranslated as Magi, typically with an explanatory note (NIV). However, early church fathers, such as St. Justin, Origen, St. Augustine and St. Jerome, did not make an exception for the Gospel, and translated the word in its ordinary sense, i.e. as "magician". The Gospel of Matthew states that magi visited the infant Jesus to do him homage shortly after his birth (2:1–2:12). The gospel describes how magi from the east were notified of the birth of a king in Judaea by the appearance of his star. Upon their arrival in Jerusalem, they visited King Herod to determine the location of the king of the Jews's birthplace. Herod, disturbed, told them that he had not heard of the child, but informed them of a prophecy that the Messiah would be born in Bethlehem. He then asked the magi to inform him when they find the child so that he himself may also pay homage to the child. Guided by the Star of Bethlehem, the wise men found the child Jesus in a house. They paid homage to him, and presented him with "gifts of gold and of frankincense and of myrrh." (2.11) In a dream they are warned not to return to Herod, and therefore return to their homes by taking another route. Since its composition in the late 1st century, numerous apocryphal stories have embellished the gospel's account. Matthew 2:16 implies that Herod learned from the wise men that up to two years had passed since the birth, which is why all male children two years or younger were slaughtered.

In addition to the more famous story of Simon Magus found in chapter 8, the Book of Acts (13:6–11) also describes another magus who acted as an advisor of Sergius Paulus, the Roman proconsul at Paphos on the island of Cyprus. He was a Jew named Bar-Jesus (son of Jesus), or alternatively Elymas. (Another Cypriot magus named Atomos is referenced by Josephus, working at the court of Felix at Caesarea.)

One of the non-canonical Christian sources, the Syriac Infancy Gospel, provides, in its third chapter, a story of the wise men of the East which is very similar to much of the story in Matthew. This account cites Zoradascht (Zoroaster) as the source of the prophecy that motivated the wise men to seek the infant Jesus. 

Jewish tradition

In the Talmud, instances of dialogue between the Jewish sages and various magi are recorded. The Talmud depicts the Magi as sorcerers and in several descriptions, they are negatively described as obstructing Jewish religious practices. Several references include the sages criticizing practices performed by various magi. One instance is a description of the Zoroastrian priests exhuming corpses for their burial practices which directly interfered with the Jewish burial rites. Another instance is a sage forbidding learning from the magi.

Islamic tradition

Main article: Majus

In Arabic, "Magians" (majus) is the term for Zoroastrians. The term is mentioned in the Quran, in sura 22 verse 17, where the "Magians" are mentioned alongside the Jews, the Sabians and the Christians in a list of religions who will be judged on the Day of Resurrection.

In the 1980s, Saddam Hussein's Ba'ath Party used the term majus during the Iran–Iraq War as a generalization of all modern-day Iranians. "By referring to the Iranians in these documents as majus, the security apparatus [implied] that the Iranians [were] not sincere Muslims, but rather covertly practice their pre-Islamic beliefs. Thus, in their eyes, Iraq's war took on the dimensions of not only a struggle for Arab nationalism, but also a campaign in the name of Islam."

Indian tradition

Brihat Samhita of Varahamihira, 1279 CE palm leaf manuscript, Pratima lakshana, Sanskrit

In India, the Sakaldwipiya Brahmins are considered to be the descendants of the ten Maga (Sanskrit मग) priests who were invited to conduct worship of Mitra (Surya) at Mitravana (Multan), as described in the Samba Purana, Bhavishya Purana and the Mahabharata. Their original home was a mythological region called Śākadvīpa. According to Varahamihira (c. 505 – c. 587), the statue of the Sun god (Mitra), is represented as wearing the "northern" (Central Asian) dress, specifically with horse riding boots. Some Brahmin communities of India trace their descent from the Magas. Some classical astronomers and mathematicians of India such are Varahamihira are considered to be the descendants of the Magas.

Varahamihira specifies that installation and consecration of the Sun images should be done by the Magas. al-Biruni mentions that the priests of the Sun Temple at Multan were Magas. The Magas had colonies in a number of places in India, and were the priests at Konark, Martanda and other sun temples.

Possible loan into Chinese

Main article: Wu (shaman) § Etymologies

Chinese Bronzeware script for wu 巫 "shaman"

Victor H. Mair (1990) suggested that Chinese wū (巫 "shaman; witch, wizard; magician") may originate as a loanword from Old Persian *maguš "magician; magi". Mair reconstructs an Old Chinese *m^yag. The reconstruction of Old Chinese forms is somewhat speculative. The velar final -g in Mair's *m^yag (巫) is evident in several Old Chinese reconstructions (Dong Tonghe's *m^ywag, Zhou Fagao's *mjwaγ, and Li Fanggui's *mjag), but not all (Bernhard Karlgren's *m^ywo and Axel Schuessler's *ma).

Mair adduces the discovery of two figurines with unmistakably Caucasoid or Europoid features dated to the 8th century BC, found in a 1980 excavation of a Zhou dynasty palace in Fufeng County, Shaanxi Province. One of the figurines is marked on the top of its head with an incised ☩ graph.

Mair's suggestion is based on a proposal by Jao Tsung-I (1990), which connects the "cross potent" bronzeware script glyph for wu 巫 with the same shape found in Neolithic West Asia, specifically a cross potent carved in the shoulder of a goddess figure of the Halaf period.