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

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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.

Ultimate Boeing 747 gambit

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Ultimate_Boeing_747_gambit

The Ultimate Boeing 747 gambit is a counter-argument to modern versions of the argument from design for the existence of God. It was introduced by Richard Dawkins in chapter 4 of his 2006 book The God Delusion, "Why there almost certainly is no God".

The argument is a play on the notion of a "tornado sweeping through a junkyard to assemble a Boeing 747" employed to decry abiogenesis and evolution as vastly unlikely and better explained by the existence of a creator god (although this quote is first attributed to Fred Hoyle, who used it to argue for panspermia, not creationism). According to Dawkins, this logic is self-defeating as the theist must now account for the god's existence and explain whether or how the god was created. In his view, if the existence of highly complex life on Earth is the equivalent of the implausible junkyard Boeing 747, the existence of a highly complex god is the "ultimate Boeing 747" that truly does require the seemingly impossible to explain its existence.

Context and history

The "ultimate Boeing 747 gambit" was originally proposed by Richard Dawkins in his 2006 book The God Delusion.

Richard Dawkins begins The God Delusion by making it clear that the God he talks about is the Abrahamic concept of a personal god who is susceptible to worship. He considers the existence of such an entity to be a scientific question, because a universe with such a god would be significantly different from a universe without one, and he says that the difference would be empirically discernible. Therefore, Dawkins concludes, the same kind of reasoning can be applied to the God hypothesis as to any other scientific question.

After discussing some of the most common arguments for the existence of God in chapter 3, Dawkins concludes that the argument from design is the most convincing. The extreme improbability of life and a universe capable of hosting it requires explanation, but Dawkins considers the God hypothesis inferior to evolution by natural selection as an explanation for the complexity of life. As part of his efforts to refute intelligent design, he redirects the argument from complexity in order to show that God must have been designed by a superintelligent designer, then presents his argument for the improbability of God's existence.

Dawkins' name for the statistical demonstration that God almost certainly does not exist is the "Ultimate Boeing 747 gambit". This is an allusion to the junkyard tornado. Astrophysicist Fred Hoyle, who was an atheist, anti-theist and advocate of the panspermia theory of life, is reported as having stated that the "probability of life originating on Earth is no greater than the chance that a hurricane, sweeping through a scrapyard, would have the luck to assemble a Boeing 747."

Arguments against empirically based theism date back at least as far as the eighteenth-century philosopher David Hume, whose objection can be paraphrased as the question "Who designed the designer?" According to philosopher Daniel Dennett, however – one of Dawkins' fellow "brights" – the innovation in Dawkins' argument is twofold: to show that where design fails to explain complexity, evolution by natural selection succeeds as the only workable solution; and to argue how this should illuminate the confusion surrounding the anthropic principle.

Dawkins's statement

Dawkins summarizes his argument as follows; the references to "crane" and "skyhook" are two notions from Daniel Dennett's book Darwin's Dangerous Idea.

1. One of the greatest challenges to the human intellect, over the centuries, has been to explain how the complex, improbable appearance of design in the universe arises.
2. The natural temptation is to attribute the appearance of design to actual design itself. In the case of a man-made artefact such as a watch, the designer really was an intelligent engineer. It is tempting to apply the same logic to an eye or a wing, a spider or a person.
3. The temptation is a false one, because the designer hypothesis immediately raises the larger problem of who designed the designer. The whole problem we started out with was the problem of explaining statistical improbability. It is obviously no solution to postulate something even more improbable. We need a "crane", not a "skyhook"; for only a crane can do the business of working up gradually and plausibly from simplicity to otherwise improbable complexity.
4. The most ingenious and powerful crane so far discovered is Darwinian evolution by natural selection. Darwin and his successors have shown how living creatures, with their spectacular statistical improbability and appearance of design, have evolved by slow, gradual degrees from simple beginnings. We can now safely say that the illusion of design in living creatures is just that – an illusion.
5. We don't yet have an equivalent crane for physics. Some kind of multiverse theory could in principle do for physics the same explanatory work as Darwinism does for biology. This kind of explanation is superficially less satisfying than the biological version of Darwinism, because it makes heavier demands on luck. But the anthropic principle entitles us to postulate far more luck than our limited human intuition is comfortable with.
6. We should not give up hope of a better crane arising in physics, something as powerful as Darwinism is for biology. But even in the absence of a strongly satisfying crane to match the biological one, the relatively weak cranes we have at present are, when abetted by the anthropic principle, self-evidently better than the self-defeating skyhook hypothesis of an intelligent designer.

A central thesis of the argument is that compared to supernatural abiogenesis, evolution by natural selection requires the supposition of fewer hypothetical processes; according to Occam's razor, therefore, it is a better explanation. Dawkins cites a paragraph where Richard Swinburne agrees that a simpler explanation is better but reasons that theism is simpler because it only invokes a single substance (God) as a cause and maintainer of every other object. This cause is seen as omnipotent, omniscient and totally "free". Dawkins argues that an entity that monitors and controls every particle in the universe and listens to all thoughts and prayers cannot be simple. Its existence would require a "mammoth explanation" of its own. The theory of natural selection is much simpler – and thus preferable – than a theory of the existence of such a complex being.

Dawkins then turns to a discussion of Keith Ward's views on divine simplicity to show the difficulty "the theological mind has in grasping where the complexity of life comes from." Dawkins writes that Ward is sceptical of Arthur Peacocke's ideas that evolution is directed by other forces than only natural selection and that these processes may have a propensity toward increasing complexity. Dawkins says that this scepticism is justified, because complexity does not come from biased mutations. Dawkins writes:

[Natural selection], as far as we know, is the only process ultimately capable of generating complexity out of simplicity. The theory of natural selection is genuinely simple. So is the origin from which it starts. That which it explains, on the other hand, is complex almost beyond telling: more complex than anything we can imagine, save a God capable of designing it.

Assessment and criticism

Theist authors have presented extensive opposition, most notably by theologian Alister McGrath (in The Dawkins Delusion?) and philosophers Alvin Plantinga and Richard Swinburne. Another negative review, by biologist H. Allen Orr, sparked heated debate, prompting, for example, the mathematician Norman Levitt to ask why theologians are assumed to have the exclusive right to write about who "rules" the universe. Daniel Dennett also took exception to Orr's review, leading to an exchange of open letters between himself and Orr. The philosopher Sir Anthony Kenny also considers this argument to be flawed. Cosmologist Stephen Barr responded as follows: "Paley finds a watch and asks how such a thing could have come to be there by chance. Dawkins finds an immense automated factory that blindly constructs watches, and feels that he has completely answered Paley's point."

Simplicity of God and materialist assumptions

Both Alvin Plantinga and Richard Swinburne raise the objection that God is not complex. Swinburne gives two reasons why a God that controls every particle can be simple: first, a person, as indicated by phenomena such as split-brains, is not the same as their highly complex brain but "is something simpler" that can "control" that brain; and second, simplicity is a quality that is intrinsic to a hypothesis, not related to its empirical consequences.

Plantinga writes:

So first, according to classical theology, God is simple, not complex. More remarkable, perhaps, is that according to Dawkins's own definition of complexity, God is not complex. According to his definition (set out in The Blind Watchmaker), something is complex if it has parts that are "arranged in a way that is unlikely to have arisen by chance alone." But of course God is a spirit, not a material object at all, and hence has no parts. A fortiori (as philosophers like to say) God doesn't have parts arranged in ways unlikely to have arisen by chance. Therefore, given the definition of complexity Dawkins himself proposes, God is not complex."

He continues:

"But second, suppose we concede, at least for purposes of argument, that God is complex. Perhaps we think the more a being knows, the more complex it is; God, being omniscient, would then be highly complex. Given materialism and the idea that the ultimate objects in our universe are the elementary particles of physics, perhaps a being that knew a great deal would be improbable – how could those particles get arranged in such a way as to constitute a being with all that knowledge? Of course we aren't given materialism.

In other words, Plantinga concludes that this argument, to be valid, would require materialism to be true; but, as materialism is not compatible with traditional theology, the argument begs the question by requiring its premise to assume God's non-existence.

In an extensive analysis published in Science and Christian Belief, Patrick Richmond suggests that "Dawkins is right to object to unexplained organised complexity in God" but that God is simply specified and lacks the sort of composition and limitations found in [physical] creatures; hence the theist can explain why nature exists without granting unexplained organised complexity or the extreme improbability of God.

Some respondents, such as Stephen Law, have suggested that God is or would indeed be complex if responsible for creating and sustaining the universe; According to Law, God's omniscience would require the retention of and ability to use all knowledge. Richard Carrier also argued that God's mind is extremely complex.

Necessity of external explanations

There are many variations on how to express this objection. William F. Vallicella holds that organized complexity as such does not need explanation, because when in search of an ultimate explanation, one must in the end accept an entity whose complexity has no external explanation. Dawkins has stated that we should search for simple beginnings for explanations, like in evolution which moves from simple to complex, and so what we ultimately accept with no external explanation must be simple for it to be a good explanation. And Plantinga writes that when not in search for an ultimate explanation of organized complexity, it is perfectly fine to explain one kind of complexity, that of terrestrial life, in terms of another kind of complexity, namely divine activity. Dawkins addresses this point in his debate with John Lennox over The God Delusion, saying that it would be perfectly reasonable to infer from artifacts on earth or another planet that an intelligence existed, but that you would still need to explain that intelligence, which evolution does, while for God's existence there is no such explanation.

Alister McGrath suggests that the leap from the recognition of complexity to the assertion of improbability is problematic, as a theory of everything would be more complex than the theories it would replace, yet one would not conclude that it is less probable. Dawkins has responded to this point in his debate with Lennox and at other times, saying that while physics is hard to understand, fundamentally, unlike biology, it is simple. McGrath then argues that probability is not relevant to the question of existence: life on earth is highly improbable and yet we exist. The important question in his view is not whether God is probable, but whether God is actual. In interviewing McGrath for The Root of All Evil, Dawkins responds that the existence of life on Earth is indeed highly improbable, but this is exactly why a theory such as evolution is required to explain that improbability. In the case of God, Dawkins says, there is no such satisfactory explanation.

On the point of probability, Alvin Plantinga claims that if God is a necessary being, as argued by classical theism, God is, by definition, maximally probable; thus an argument that there is no necessary being with the qualities attributed to God is required to demonstrate God's improbability. Eric MacDonald has pointed out that theists assume the coherence of their position when they make arguments for God when, by Plantinga's standards, they would have to present an argument that the concept of God is not logically incoherent before discussing other arguments. Plantinga's objection would seem to apply to all atheist arguments that contend that God is improbable, such as evidential arguments about the problem of evil and the argument from nonbelief. But the reason why theists and atheists do not usually address this prior to making their arguments is because they want to go beyond merely discussing whether God is maximally probable or impossible.

Dawkins's response to criticism in The God Delusion

Dawkins writes about his attendance at a conference in Cambridge sponsored by the Templeton Foundation, where he challenged the theologians present to respond to the argument that a creator of a complex universe would have to be complex and improbable. He reports the strongest response as the claim he was imposing a scientific epistemology on a question that lies beyond the realm of science. When theologians hold God to be simple, who is a scientist like Dawkins "to dictate to theologians that their God had to be complex?" Dawkins writes that he did not feel that those employing this "evasive" defence were being "wilfully dishonest", but that they were "defining themselves into an epistemological safe-zone where rational argument could not reach them because they had declared by fiat that it could not."

Theologians, Dawkins writes, demand that there be a first cause named "God". Dawkins responds that it must have been a simple cause and contends that unless "God" is divested of its normal associations, it is not an appropriate name. Postulating a prime mover that is capable of indulging in intelligent design is, in Dawkins's opinion, "a total abdication of the responsibility to find an explanation"; instead, he seeks a "self-bootstrapping crane" (see above) that can "lift" the universe into more complex states. This, he states, does not necessitate a scientific explanation, but does require a "crane" rather than a "skyhook" (ibid.) if it is to account for the complexity of the natural world.