Sunday, February 21, 2016

Aquinas and Aristotle against Plato

Aquinas seated between Aristotle and Plato

The medieval synthesis of pagan philosophy and Christian theology in Albert and Aquinas may have drawn from five principal sources: (i) biblical scripture; (ii) Aristotle; (iii) Augustine; (iv) Pseudo-Dionysius; and (v) Avicenna. Although Platonic elements may be found in all of these sources, Aquinas consistently labours to distinguish his thought from its Platonic inheritance.  (See especially his Commentary on Pseusdo-Dionysius’ the Divine Names (17)) And although Aquinas has no full-length work on Plato and the Platonists, he consistently follows Aristotle in attacking the via Platonica for separating, duplicating, and reifying the logical intentions of the mind as universal forms in separated substances. R. J. Henle summarizes Saint Thomas’ objections:

“The Platonic theory [of Ideas] requires that we maintain that the Idea (1) is truly separated in being, (2) is truly one, (3) is the real formal cause of the particulars, (4) is truly related to them as a cause, a principle, a justification of knowledge, of predication and of being. If the separation is stressed, the theory tends towards pure extrinsecism; if the invasion of the particulars is stressed, the unity of the form drives towards entitative union and pantheism. These ambiguities and tensions are thus inherent in the pure Theory of Ideas. As we have seen, Saint Thomas himself recognizes these different pressures and their logical conclusions.” (Saint Thomas and Platonism,1970, p.378)

Aquinas’ central criticism is that Plato has externally reflected the ideas of the mind into separated substances that are meant to cause all particular phenomena. The result, Henle alleges, is either to cast the ideas of all possible cognition into extrinsic separation from phenomenal world, or to colonize the world with these concepts, until the creator-creation distinction is reduced to a pantheistic system of univocal concepts. Henle concludes:

“The Platonic argument thus doubles the ontological correlates for natural knowledge, but, by insisting that the separated form is what we truly know, it casts a shadow on the metaphysical structure of the material entity, obscuring the intrinsic form and rendering its status in being and knowledge extremely ambiguous.” (375)

Henle acknowledges (341) that Aquinas’ central criticism of separated substance is derived directly from Aristotle’s Metaphysics (Bk. I ch.4), where Aristotle summarizes:

“Plato accepted [Socrates’] teaching, but held that the problem applied not to sensible things but to entities of another kind-for this reason, that the common definition could not be a definition of any sensible thing, as they were always changing. Things of this other sort, then, he called Ideas, and sensible things, he said, were all named after these, and in virtue of a relation to these; for the many existed by participation in the Ideas that have the same name as they. Only the name 'participation' was new; for the Pythagoreans say that things exist by 'imitation' of numbers, and Plato says they exist by participation, changing the name. But what the participation or the imitation of the Forms could be they left an open question.  Yet what happens is the contrary; the theory is not a reasonable one. For they make many things out of the matter, and the form generates only once, but what we observe is that one table is made from one matter.”

Here Aristotle describes how, in response to the Heraclitean Flux of sensible things that ‘were always changing’, Plato recast Socrates’ definitions as unchanging supersensible  entities of reason, which he called Ideas. Later Aristotle represents these Ideas as separate substances:

“For it is evident that they are one in their intelligible expression, for one will express the same notion in speaking of each. Therefore, if there is a man-in-himself, who is a particular thing and is separate, the things of which he is composed, such as animal and two-footed, must also signify particular things and be separable and be substances.”  (Metaphysics 1039a)

Saint Thomas comments:

“[Aristotle] accordingly says, first, that it is evident that the animal present in man and that present in horse are one and the same in their intelligible expression… Hence, if, because of the fact that species are predicated of all individuals according to one intelligible expression, there is a common man, who is man-in-himself, existing by himself, “and who is a particular thing,” i.e., something subsistent which can be pointed to and is separable from sensible things, as the Platonists maintained…  [But] it is not possible for some one thing to be present in many things which exist separately. For you are present only in yourself, since you are not in many things which exist separately, as in flesh and bones, which are your parts. Therefore, if animal is one and the same, it will be incapable of existing in many species, as in man and in horse, since the separate Forms, according to the Platonists, are substances which are distinct from each other.”

Aquinas, following Aristotle, infers that Plato’s argument from science (Rep. 477b) implies that the ideas must be necessary, immutable, and separate substances from mutable material world. Since everything in the world consists in matter in motion, the immateriality and immobility of the Ideas seems to place them beyond the world. Since Ideas are supersensible, they must also be super-substantial separated substances. Plato’s separate substances are thus alleged to have illegitimately hypostatized logical intentions into a duplicate parallel reality. This duplicated reality of Ideas is considered to be illegitimate because, contrary to its scientific purpose, it cannot begin to explain the sensible world. Henle thus summarizes (343) six arguments that Aquinas made against Plato:

“1. The Ideas cannot be causes of motion or transmutation precisely because they were set up to explain the immobility of science and are therefore principles of immobility rather than of change.

2. They cannot serve to explain knowledge of the sensibilia because they are separated from them.

3. They cannot be exemplar principles because – aside from the metaphorical character of this assertion – (a) as separated exemplars they would render the obvious agency of immediate natural causes superfluous.

4. The Ideas cannot be the formal intrinsic causes of material individuals since they are separated.

5. They cannot explain becoming.

6. Moreover, the Platonists are inconsistent, for they do not posit Ideas of artefacts.”

Henle’s six arguments, from beginning to end, each depend upon the contention that Platonic Ideas are separated substances: for Ideas may only be considered immobile, supersensible, non-natural, extrinsic, and natural beings once they have been separated from the mobile, sensible, natural, and intrinsic productivity of the world that is becoming. It may come as a surprise, then, that, not only did Plato never describe Ideas as separate substances, but he even insisted that the Ideas can never be so separated from the world: Plato criticizes the spurious separation of the Ideas from the world in his criticism of the idealist ‘friends of the gods’ (Sophist 246a-249d); the separation of the universals forms from particulars instances in the Greatest Difficulty Argument (Parmenides 133a-134a); and even represents the forms as constituted of the elemental building blocks of the world in the Timaeus. (28a-31b) Although Thomas Aquinas could have had access to Calcidus’ early Latin translation of Plato’s Timaeus, Henle acknowledges that he overlooked this important later development. (325) 

Aristotle, who was in the best position to know Plato’s doctrines, seems to have represented Platonic Ideas as separated forms for the purpose of distinguishing himself from and reformulating Plato’s forms. He indicates that because the sensible things of the world are “always changing”, and Plato’s Ideas are supersensible entities of reason, the Ideas must be separated from the sensible things of the world. Yet Plato’s insistence on the supersensibility is not meant to imply an ontic separation of forms from substances, but rather an even more intimate ontological bond between the Ideas and the word: for since the perfect paradigms of all predicate-properties (e.g. largeness) are the onto-noetic condition for the intelligibility and being of every imperfect instance (e.g. something large), there is an immediate ontological continuity between the paradigms and their instances that is only logically distinguished by their universal and particular scope. The impartation of the intelligibility and being of perfect paradigms into imperfect instances thus constitutes a kind of hyper-dynamic ontological motion beyond the observable dynamics of physical motion. And since these paradigms may only be thought as the universal predicates of sensible properties, even the most abstract paradigms must be thought through a kind of hyper-intuition beyond sensible intuition.

Aquinas’ criticisms of Plato are thus directly derived from Aristotle’s misrepresentation of Plato’s ontology for the purpose of advancing his own competing substance-metaphysics. In fact, it is Aristotle’s substance-metaphysics rather than Plato’s ontology that is most responsible for introducing so many sharp philosophic divisions between form and matter, intention and existence, logic and nature. Once it is recognized that Plato’s Ideas were never conceived as separate substances, it becomes possible to respond to Aquinas’ criticisms of Plato:

1. Ideas can impart motion because each of perfect paradigm imparts a hyper-dynamic motion into the imperfect instances.

2. Ideas can explain sensibilia because each of the paradigms is the hyper-intuited exemplar of sensible exemplifications.

3. Since the Principles, Ideas, and forms are the originary onto-noetic source of all intelligibility and being, there is no originary division of the mythical, metaphoric, linguistic or logical from the real entities of nature. Hence, natural causes should be explained, along with all other orders of causation, through the formal relations of Ideas emanating from the supreme Principle of the Good.

4. Since there is an immediate ontological continuity between paradigms and exemplifications, the Ideas are never extrinsic to material substances.

5. The Ideas are, not only not static, but are indeed the originary hyper-dynamic source of ‘becoming’ in logic, nature, and society.

6. The hyper-dynamic ‘becoming’ of the Ideas in human society implies that the Ideas can be continually reconstructed into artefacts, such as mathematical objects and even an Idea of a bed. (Rep. 596b)

Aquinas seems to have followed Aristotle in making two critical mistakes: first, he adopts Aristotle’s distinction of form and matter, in which the material world is distinguished from its forms; and then, on the basis of this first distinction, he concludes that the necessity, immutability, and separation of the Platonic forms are incompatible with materiality, mobility, and interpenetration. These mistakes did not originate with Plato, nor even with Aquinas who did not possess all of Plato's texts, but rather in Aristotle’s own substance metaphysics, which he afterwards interpolated into his interpretation of Plato when he characterized the Ideas as ‘separated substances’. For Plato, to the contrary, the Ideas are not separated but connected to all ‘substances’ through an unbreakable ontological continuum that hyper-dynamically imparts the intelligibility and being of perfect paradigms to imperfect exemplifications; and the ‘matter’ (from ‘hyle’ meaning ‘wood’) is merely a metonym for the passive matrix into which all forms are plastically received to take shape. Aristotle’s suggestion that Plato’s supersensible Ideas must be separate substances, in which universal forms are cast beyond the mobile and material world, can thus be nothing less than a deliberate misrepresentation of Plato’s authentic doctrines.

See also my lecture Plato, Logic, and Ontology:

Friday, February 19, 2016

Contra Aristotle on Contradiction

Aristotle Contemplating Homer, by Rembrandt
Aristotle advertises the Principle of Non-Contradiction, in the Metaphysics (Bk. IV, ch.3-6), as the first, most certain, and unhypothetical principle upon which all demonstration depends. He writes: “[T]he most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known… and non-hypothetical.” In contrast to hypotheses, unhypothetical principles are not conjectured as merely possible, but are rather meant to be known immediately and necessarily through some direct noetic intuition: Aristotle’s allusion to unhypothetical principles at Metaphysics 1005b14 plausibly alludes to Plato’s unhypothetical principles of knowledge prescinding from the supreme principle of the Good at Republic 510b7-511b7. Where hypotheses are only possibly true and must be discursively demonstrated from some higher and prior conditions, unhypothetical principles are - by definition - fundamental, indemonstrable, and discursively incontrovertible. The incontrovertibility of these unhypothetical principles might suggest that Aristotle, no less than Plato, has quite dogmatically demanded that we accept an indefensible assertion.  Aristotle’s indirect argument for the Principle of Non-Contradiction, however, crucially relies upon classical Platonic principles of dialectic, noesis, and emanation.

Aristotle vehemently repudiates his ‘uneducated’ critics, who ask for the principle of non-contradiction to be demonstrated, for failing to realize that not every principle can be proven, for the simple reason that any attempt to demonstrate everything would produce an infinite regress of demonstrations. (For a critical discussion of Aristotle’s abhorrence of infinity, see my Theological History of Infinity) Although he declines to elaborate what this education is meant to consist in, judging by the introduction of unhypothetical principles in the Republic, we may guess that Aristotle intends it to resemble something of what Plato had described in the Republic, consisting in a dialectical ascent, from less to more certain hypotheses through, up the ladder of discursive reasoning until it can recognize the first unhypothetical principle of non-contradiction. Although Aristotle admits that unhypothetical principles cannot be demonstrated by any direct deduction from premises to conclusion, he nonetheless contends that these first principles of philosophy can only be corroborated by an indirect argument, in which Platonic dialectic is formalized for the purpose of refuting any contrary denial of the principle of non-contradiction. However, under closer scrutiny it appears that without the hypothetical and discursive construction of the cosmos through Platonic dialectics, Aristotle’s indirect argument quickly collapses into ampliative circularity.

Aristotle first argues that the principle of non-contradiction is held to be the most certain of all principles, that “answers to the definition” of a hypothetical principle, because “it is impossible for anyone” to affirm and deny the same thing. He suggests that the Principle of Non-Contradiction is meant to be indirectly proven from the impossibility of affirmative and negative opinions in Heraclitean flux: for if Heraclitean flux were extended to all opinions, and all opinions were simultaneously affirmed and denied, then any and all opinions would be both true and false; true by default; and no determination could ever be made between truth and falsity. To preserve the possibility of determining truth, Aristotle rejects this kind of ‘pan-inconsistency’ of all opinions. But this rejection of paninconsistency, in which all opinions are inconsistently true and false, does not immediately also imply the rejection of paraconsistency, in which the truth and falsity of some opinions does not produce an explosive inconsistency of all opinions, triviality, or trivialism.  Indeed, Paulla Gottlieb has indicated that Aristotle even appears to endorse at least some paraconsistent syllogistic conclusion at Prior Analytics II 15 64a15 when he writes: “Consequently it is possible that opposites may lead to a conclusion, though not always or in every mood, but only if the terms subordinate to the middle are such that they are either identical or related as whole to part.”

Aristotle’s most famous indirect argument is from the impossibility of meaningfully denying the Principle of Non-Contradiction: for if a sceptic of the Principle of Non-Contradiction makes any significant statement, then the critic must have, in the very act of making this statement, already presupposed the principle of non-contradiction. There are two stages to this argument: analytic and hypothetical. First, if every meaningful statement possesses some determinate shape of signification, then, in the very act of making a meaningful statement, even the sceptic must analytically presuppose the possibility of some determination. Second, such a determination is only possible on the hypothesis that some determination is true and its contrary determination is false. But since this truth and falsity of contrary determinations is only possible on the further hypothesis that for any determination that is true, its contrary cannot be true but must be false, it seems that for every act of determinate signification we must presuppose the lawful prohibition of the coincidence of contrary determinations.

The first analytic stage of the argument is undoubtedly true, but the second hypothetical stage of the argument is problematic for three reasons: first, because it surreptitiously deploys discursive and hypothetical arguments to indirectly demonstrate what is advertised as a non-discursive and explicitly unhypothetical principle; second, because it neglects any explanation of the source, scope, and specificity of its determinations; and third because this entire hypothetical inference remains ampliative. An argument is ampliative if its premises and rules are insufficient for the necessary demonstration of its conclusions. Hypothetical inferences are always ampliative, and insufficiently demonstrative, for the simple reason that there could always be alternative hypotheses that remain to be considered. Plato deliberately deploys hypothetical arguments to produce contrary theses and motivate his dialectic, but Aristotle’s didactic demonstrations are meant to be necessary, and which have neglected to consider alternative formulations for the scope of non-contradiction: specifically whether non-contradiction implies the rejection all inconsistencies (i.e. paninconsistency) or merely some instances of inconcistency that do not entail triviality (i.e. paraconsistency).

The greatest difficulty for Aristotle is that his entire indirect argument seems to have circuitously presupposed the very possibility of a determinate disjunction that it has been developed demonstrate. For every indirect argument involves a disjunctive syllogism (i.e. A v B; ¬ B, TF: A); the function of disjunction (i.e. A v B) already involves at least two determinate disjuncta (i.e. A & B); and these disjuncta are each, in turn, meant to be determined as distinct disjuncts by the Principle of Excluded Middle (i.e. Ex(Fx v ¬Fx)). But if Aristotle maintains that the Principle of Excluded middle presupposes determination, and determination presupposes the Principle of Non-Contradiction, then he has circuitously presupposed this very principle for the purposes of demonstrating it. Where Plato’s supreme unhypothetical principle of the Good is meant to be virtuously circular, because it is the emanative beginning and assimilative end of all discursive reasoning, the circularity of Aristotle’s indirect demonstration for the fundamental unhypothetical Principle of Non-Contradiction surely compromises its purely formal status as a first principle of reason.

For the purpose of distancing himself from any dialectical ascent towards the Good, Aristotle transposes the question of contradiction from polysemous words to putatively unambiguous and punctiliar facts. Any finite number of meanings can be reduced to individual meanings, and individual meanings can be self-identically represented as an abstract variable according to a formal notation convention. Where Plato had formalized Socratic dialectic into a written dialogue, Aristotle formalized Plato’s dialogue into didactic instruction. Since, however, even the words used in didactic instruction can be ambiguous, and liable to contradiction, Aristotle adopts a formalized language with symbols that appear simply identical to themselves. This formal notation is meant to prevent contradictions between terms, but inadvertently engenders an even broader conflict between formality and physicality: for once all terms have been formulated into a consistent system, then this formal system remains distinct and indifferent to the physical world.

Aristotle points to the true purpose of his indirect argument when he contends that the ultimate implication of rejecting the Principle of Non-Contradiction must be to reject all determination, individuation, and definition, and thus to entirely “do away with substance and essence.” His purpose, in defending the principle of non-contradiction, is thus, not merely to preserve the possibility of any determinatively significant statements, but rather, and more metaphysically, to preserve the real definition of essences and the very determinate shape of all substances. For if significant statements did not presuppose determination, and determination did not presuppose non-contradiction, then there could be neither determinations, nor essences, nor substances, and all essences would be reduced to a swamp of accidental attributes, wherein nothing could ever endure and never be known.

Aristotle’s Principle of Non-Contradiction is thus meant to preserve the determinacy of signs, substances and essences. The indirect argument declines to specify whether the principle applies to all instances of contradiction, i.e. paninconsistency, or only some instances of contradiction, i.e. paraconsistency. Aristotle can only prohibit any possibility of contradiction by making the further assumption that a prohibition on the totality of all inconsistencies also implies a prohibition on any particular inconsistency. However, this assumption requires the principles that obtain in every part to be identified with those of the whole and vice versa, so that the whole cosmos may be lawfully regulated, or nomologically constrained, by one self-identical and supreme principle.

The self-identity of forms is, moreover, only possible by the imposition of some superior paradigm of identity, unicity, and individuality. The Principle of Non-Contradiction thus requires that we hypothesize a supreme principle of identity, unicity, and individuality to nomologically constrain the parts by the whole. However, Aristotle cannot admit this hypothetical presupposition without compromising its status as an unhypothetical first principle of reason. Once Aristotle has formalized dialectics into didactic instruction, and further formalized this didactic instruction into various formulae, he can no longer ascend the dialectical ladder from hypotheses, to refutation, to the supreme principles, and his indirect argument for the Principle of Non-Contradiction ineluctably collapses into ampliative circularity. Were the Principle of Non-Contradiction to have, more Platonically emanated from the first principle of the Good through the second principle of Intellect (Nous), then Aristotle might more plausibly preserve all determinations in the virtuous circle of Platonic emanation and assimilation.

See also my lecture Plato, Logic, and Ontology: