|Plato's Cratylus, by Nancy Rourke|
Aristotle is generally regarded as the founder of logic: he boasts that, before his formalization of logic, absolutely “nothing existed at all.” Yet a minority tradition has always recognized Plato as its founding genius. He can be read to have anticipated a response to Aristotle’s interchangeability thesis of subject and predicate terms when, in the Cratylus, Hermogenes claimed that “any name which you give, in my opinion, is the right one, and if you change that and give another, the new name is as correct as the old… For there is no name given to anything by nature; all is convention and habit of the users.” Since names are not given by nature, they can be freely substituted with any artificial linguistic convention. Socrates argues to the contrary that if we admit that there are true and false propositions; whole propositions are composed of particular words; and what is true of the whole is true of the parts; then we must also admit that there can be true and false words. The truth of words, which is prior to any composition in sentences, statements, and propositions, must then depend upon some correspondence between the appearance of the name and the essence of the thing named. Since the denial of this essential correspondence threatens to dissolve the true, fixed, enduring meaning of all names, Socrates claims that names must be “independent and maintain to their own essence the relation prescribed by nature.” Names are, thus, not merely artificially contrived, but are rather given by the most skilled poets and statesmen, who are said to have, through the art of dialectics, learnt how to distinguish and determine their intrinsic and essential relations. Before Aristotle had made propositions the basic truth evaluable units of logical analysis, Plato had already made names into the images of language that individually imitate the essential differences in and between the things named.
Plato once again examined this possibility of recognizing the falsity of language, difference, and negation in the Sophist. After dividing reality into five major kinds, or Arch-Ideas, including those of Existence, Identity and Difference, he argues that negative prefixes, such as ‘not-tall’, “do not mean something contrary to what exists but only something different.” Since the primary Arch-Idea of Existence is prior to those of Identity and Difference, the affirmation of some existing entity must always precedes its denial, negation, and differentiation. And since the names of terms are prior to their composition in propositions, term negation is also prior to propositional negation. The term negations that are meant to distinguish the meaning of names must thus correspond to the real structural differences in the essences of the things named. It is this essential correspondence of the difference of names to their named essences that ultimately allows Plato to affirm that the putative non-existence of negations and differences may be relationally present in and among things by participating in an identity at higher levels of existence. The decisive juncture in the development of ancient term logic thus occurs - at precisely this moment - when Plato describes how these real and essential differences uniquely admit for the possibility of the “blending of any one form with another.” Where previously all names had been individually affirmed to be indifferently and bivalently true or false, once the reality of these differences has been acknowledged, Plato can divide and combine the terms of speech into internally distinct but intrinsically related propositions. Plato even further elaborated the conditions for their truth and reference when he wrote: “Wherever there is a statement, it must be about something… And the true one states about you the things that are [or the facts] as they are… Whereas the false statements states about you things different from the things that are.” Plato rather than Aristotle may thus be recognized to have invented the first theory of how subject and predicate terms may be combined into propositions. Where Aristotle would later evacuate this intrinsic relation of names to essences between subject and predicate terms, Plato had already at the dawn of logic insisted on preserving it through a logic of propositions that imitated the fundamental and essential relations of metaphysics.
Aristotle afterwards developed a new logic of terms by widening this difference between the names and the essences of the things named until names could be isolated and interchangeably conjoined in the propositions of syllogisms. This widening difference allowed Aristotle to develop what was arguably the first formal logic of deductive inferences, in which rules of valid inferences could be defined prior to any consideration of the meaning of the words, as well as their various essential and metaphysical relations. This formalization was accomplished by reverting to a sophisticated adaptation of Hermogenes’ opinion, first proposed in the Cratylus, that the names of terms are conventional, artificial, and interchangeable. Aristotle thus distinguishes, in the Categories, between predicates that are ‘said of’ but not present and predicates that are present in the subject. He defines the presence of a predicate, not by the Platonic participation “as parts are present in a whole”, but by the separate subsistence of “being incapable of existence apart from the subject.” As an example of a predicate that is merely ‘said of’ but not ‘present in’ the subject, Aristotle writes: “‘man’ is predicable of an individual man, and is never present in the subject.” Where formerly Plato may have held the predicate ‘man’ to correspond to the Idea of man that could be instantiated in the inner essence of any individual man, Aristotle now suggests that it may be predicated independently from any further participative or essential relation. This relative indifference of ‘said of’ predicates crucially allows Aristotle to affirm an asymmetrical transitivity of predicates, in a cascading movement from predicate to subject. He writes: “When one thing is predicated of another, all that which is predicated of the predicate will be predicable also of the subject.” The meaning of the predicate can thus only be truthfully transferred from predicate to subject because the truth of a predicate is grounded in the subject, just as separable accidents are grounded in primary substances.
In On Interpretation, Aristotle further extends this difference between names and essences to radically re-assert the ontological dependence of both subject and predicate terms upon propositions. He writes: “Nouns and verbs, provided nothing is added, are like thoughts without combination or separation; ‘man’ and ‘white’, as isolated terms, are not yet either true or false.” Where Plato had preserved the truth value of names in correspondence to the essence of the things named, Aristotle claims that “there is no truth or falsity about [names], unless ‘is’ and ‘is not’ is added.” Once their truth is made entirely dependent upon the addition of the copula ‘is’ in the proposition, then the intrinsic and essential relation between subject and predicates can be made into an extrinsic and accidental relation of conjoining any two terms by a third copula. Aristotle’s extrinsic relation of two terms united by one copula may thus seem a fitting substitute for Plato’s intrinsic relation of many particular predicates united in one universal form. Yet Aristotle seems, in the Prior Analytics, to have recognized how any such substitution would produce paradoxes of relations: for if, according to the Third Man Argument, he is warranted in concluding that an infinite regress of universal forms must frustrate any hypothesis of one separate universal form of ‘man’ over many particular men, then he must similarly conclude that a no less vicious infinite regress of extrinsic relations would frustrate any hypothesis of one separate copula between two terms. And since the copula is essential to any proposition, such an infinite regress of extrinsic relations between terms would likely threaten to dissolve the essential bonds in all propositions. Thus, by the time of the Prior Analytics, Aristotle appears to have shifted from his old theory of two terms united by one copula to a new theory of two terms that are interchangeably applied to one another: where the propositions of On Interpretation had been formulated as ‘A is B’, the premises of the Prior Analytics are formulated as ‘B applies (hyparchei) to A.’ Although this immediate application of predicates seems to have been meant to obviate any requirement for the relations to be signified by the copula, it has only succeeded in delaying the paradox by virtually representing these copula relations in a sophisticated system of formalized syntax.
For the influence of Plato and Aristotle's logic on Trinitarian theology, see my essay:
 Aristotle. Prior Analytics, 185b34. Joseph Maria Bochenski expressed this general consensus when he wrote that it is “no exaggeration to say that Aristotle... was the first formal logician.” Cf. Bochenski, Joseph Maria. A History of Formal Logic, 1961: 40.
 Lutoslawski expressed the dissenting minority party opinion when he writes: “The first man whom we meet in the history of human thought as a logician… is Plato.” Cf. Lutoslawski, The Origin and Growth of Plato’s Logic, 1897: 3. Alcinous and some of the Middle Platonists seem to have regarded Plato’s dialectic as somehow methodologically superior to Aristotle’s syllogisms. Cf. Alcinous, Handbook of Platonism, 156.25-35. And Plethon even accused Aristotle of sophistry for not acknowledging his debt to Plato. Cf. Lutoslawski, The Origin and Growth of Plato’s Logic, 1897: 8-11.
 Plato. Cratylus, 384d.
 Plato. Cratylus, 385a. Socrates objects to the absurdity of absolute conventionalism when he comments: “Suppose I call a man a horse or a horse a man. You mean to say that a man will be rightly called a horse… and a horse again would be rightly called a man…?
 Plato. Cratylus, 385b-c. “[I]f propositions may be true and false, names may be true and false.” For modern logic, only propositions can be elevated as true or false. However, this restriction has resulted from the rejection of any Platonic participation of names with the paradigm of the things named.
 Plato. Cratylus, 386d-e. Plato clearly intends to associate Hermogenes’ linguistic conventionalism with sophistry when he contrasts the true dialectical way of distinguishing names with the untrue artifice of the Sophists, Callias, and Protagoras. Cf. Plato. Cratylus, 391b-c.
 Plato. Cratylus, 388c-391b. Before entering into a discussion about the Homeric origin of divine names, Socrates concludes that “the work of the legislator is to give names, and the dialectician must be his director if the names are to be rightly given… Cratylus is right in saying that things have names by nature, and that not every man is an artificer of names, but he only who looks to the name which each thing by nature has, and is able to express the true forms of things in letters and syllables.” Cf. Plato. Cratylus, 390d-e.
 Plato, Cratylus, 431a-b. Socrates comments: “For the name, like the picture, is an imitation… But if I can assign names, as well as pictures to objects, the right assignment of them we may call truth, and the wrong assignment of them falsehood.”
 Lutoslawski explains that the “question of error was left unsettled in the Cratylus (429d), and in the Theaetetus (187d, cf. 200d). It is only here [in the Sophist] that Plato explains error as a judgment about Not-Being, while in all earlier works the possibility of thinking and judging Not-Being was denied in agreement with Plato’s philosophical predecessors.” Cf. Lutoslawski, The Origin and Growth of Plato’s Logic, 1897: 429.
 Plato. Sophist, 254d-257b.
 The Eleatic Stranger affirms the asymmetrical priority of positive existence to negative difference when he comments: “[W]e say that two of the three will not blend with one another… Whereas existence can be blended with both, for they both exist.” Cf. Plato. Sophist, 254d; Horn, Lawrence. A Natural History of Negation, 2001: 19.
 The Eleatic Stranger highlights this isomorphic correspondence when he comments that “the nature of the different appears to be parcelled out, in the same way as knowledge.” Cf. Plato. Sophist, 257c.
 Plato. Sophist, 258b-d. The Eleatic stranger concludes “‘that which is not’ unquestionably is a thing that has a nature of its own.” Cf. Bäck, Allan. Aristotle’s Theory of Predication,2000: 40-41.
 Plato. Sophist, 260a-c. Plato more emphatically suggests that the atomic division all names into interchangeable parts threatens to annihilate the possibility of discourse, dialectic, and philosophy itself when the Eleatic Stranger describes how “the attempt to separate every thing from every other thing not only strikes a discordant note but amounts to a crude defiance of the philosophical muse… This isolation of everything from everything else means a complete abolition of all discourse, for any discourse we can have owes its existence to the weaving together of forms.” Cf. Plato. Sophist, 259e-260a; Parmenides 135c.
 Plato sketches of how noun and verb terms may be mixed to form complex propositions when he concludes: “Neither in this example nor in the other do the sounds uttered signify any action performed or not performed or nature of anything that exists or does not exist until you combine verbs with names… Because now it gives information about facts or events in the present or past or future; it does not merely name something but gets you somewhere by weaving together verbs with names. Hence we say it ‘states’ something, not merely ‘names’ something, and in fact it is this complex that we mean by the word ‘statement’ [i.e. proposition].” Cf. Plato. Sophist, 262b-d.
 Plato. Sophist, 262d-263b. For a contemporary examination and defence of Plato’s theory of truth and reference, see Berman, Scott. “A Platonic Theory of Truthmaking,” Metaphysica 14 (2013): 109-25.
 Lutoslawski, The Origin and Growth of Plato’s Logic, 1897: 430.
 Plato suggests the metaphysic al subordination of linguistic discourse, including all names, terms, and propositions, to dialectical thinking when he writes: “thinking and discourse are the same thing, except that what we call thinking is, precisely, the inward dialogue carried on by the mind with itself without spoken sound…. Whereas the stream which flows from the mind through the lips with sound is called discourse.” Cf. Plato. Sophist, 263e. Plato also seems to reaffirm the divine origin of the possibility of thinking and discourse when he writes: “Must we not attribute the coming-into-being of these things out of not-being to divine craftsmanship and nothing else… from a cause which, working with reason and art, is divine and proceeds from divinity?” Cf. Plato. Sophist, 265c. This reference to the creative cause of mixed forms seems to be a clear reference to the Demiurge, or divine craftsman, of the Timaeus (28a) which Plato elsewhere describes as the formal cause of order in the World-Soul (26e, 27b, 273b, 530a, 265c, 28a, 28c) and the king (basileus) of the world (274e, 28c, 28d, 272e), who gives order to heaven and earth (28d, 30c, 97c, 98a, 30c, 97c, 28e, 966e, 967b) for the highest good (30a, 37d). Cf. Menn, Stephen. Plato on God As Nous, 1995: 4-7.
 Bochenski, Joseph Maria. A History of Formal Logic, 1961: 40.
 Plato. Cratylus, 384d.
 Aristotle. Categories, 2b-c, 20-25.
 Gerson notes that this ‘said of’ and ‘present in’ predicate distinction seems like the “smoking gun of antiharmonization” between Plato and Aristotle, but he responds that this distinction is alone insufficient to warrant the conclusion that ‘said of’ predicates may not also remain essentially related to the ‘present in’ predicates of Plato. Cf. Gerson, Lloyd. Aristotle and Other Platonists, 2005: 83. However, Aristotle’s example of the predicate ‘man’ seems to have been deliberately chosen to emphasize this precise discontinuity and disharmony, for ‘man’ is also the predicate that Aristotle deploys against Plato’s theory of the Ideas in the famous Third Man Argument. Cf. Fine, Gail. On Ideas, 1993: 203.
 Aristotle. Categories, 3a, 10-15.
 Aristotle. On Interpretation, 16a, 1.10-15.
 Aristotle. On Interpretation, 16a, 1.15-20.
 Geach, Peter. “History of the Corruption of Logic”, 1968: 48-49. Cf. Aristotle. Prior Analytics, 24a15,25.