Any corrections, disputations, or other comments from participants here, I welcome. In the last paragraph of this piece, I mention further discernments yet to be drawn out in the scope of this topic. These I am working on at present using works of a number of modern scholars on Aristotle, and of course, his own text. The work presented below is to become a portion of the book I’m writing (probably in a second chapter, following one on Nietzsche/Rand). My target audience for the book would be anyone with the ability and interest to read and absorb such a composition as Galt’s speech. Surely, additional explanation for the stretch of text below, such as the basics of syllogism, will be needed, at least in a note for the book version. In the end, I don’t want to suppose that all readers in the target audience have had a first course in logic. I realize that the citations would not be of interest to some such readers, but in this blog, as in the book, I expect scholarly readers as well. And anyway, I require that aspect for my own interest and roadmap.
On Logic, Aristotle and Rand
Rand set out:
To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of a specific nature made of specific attributes. Centuries ago, the man who was—no matter his errors—the greatest of your philosophers, has stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. You have never grasped the meaning of his statement. I am here to complete it: Existence is Identity, Consciousness is Identification. (AS 1016)
By “greatest of your philosophers,” Rand meant Aristotle. Unlike moderns such as Leibniz, Baumgarten, Kant, or Rand, Aristotle did not connect a “law of identity,” in so many words, with his principle of noncontradiction. Aristotle also did not connect the law of identity that speaks to the distinctive natures of things with a formula such as “A is A” or “A thing is itself.” Aristotle would say “A thing is itself” is nearly empty and useless, and he would not connect that proposition to “A thing is something specifically,” which he thought substantive and important.
Aristotle observed that saying “Man is man” or “The musical is the musical” and so forth are all occasions of affirming that a thing is itself. Someone who had said “Each thing is itself” might have meant “Each thing is inseparable from itself; and its being one just meant this” (Metaph. 1041a1). This meaning in A is A states a truth of all existing things—an existing thing is one, one with itself—and that is, I’d say, sufficient for some tare weight of objective meaningfulness in the statement. That much of A is A is a background assumption in all other meaningful statements.
In mathematics if we can show that an equation can be reduced to the equation 1=1 or 2=2 or sinq=sinq, and so forth, we have proven that the initial equation (apart from any physical application) is true. That is a usefulness of “A thing is itself.” In science one aim (and thrill) is discovery of A is A sleepers. This has been accomplished through the join of observation, mathematics, and induction. Examples are the discovery that the evening star is the morning star and that light is electromagnetic radiation (within a certain range of radiation frequency).
For Leibniz “the primary impossibility is this: A is not A; just as the primary necessity in propositions is this: A is A” (1678, 187). The identity of which Leibniz speaks as a basis of logical necessity is the identity of sameness. A demonstration establishes a sameness between the subject and predicate in the conclusion. It shows that the conclusion’s predicate is contained in the conclusion’s subject. Among the premises could be observations or intellectual truths. The demonstration proceeds by recognizing definitions and by substitution. For effective use in proofs, definitions must not contain contradictions, manifest or concealed. It is not enough that we understand what we say in a definition, for it can still be the case that our definition is of something impossible. Natures of things are implicated in deductive proofs by the observations, intellectual truths, and definitions employed in the demonstration.
Loemker writes of Leibniz: “Contradiction, . . . or the principle of impossibility, is implied in identity, and the two are opposite aspects of the same law, which Leibniz sometimes calls the basic law of being” (1969, 24). In Leibniz’ view, the law of identity entails that predicates of affirmative propositions are contained in their subjects. As with Aristotle, with Leibniz the primary form of being is substance. Identity-containments by subjects of their predicates record the relation of substance to its modifications. Such identity-containments look rather like Rand’s identity of character, or nature.
Rand did not continue with Aristotle’s central concept of substance, rather, she made existence most fundamental and made natured entity the primary form of existence. Entity, not substance, takes the role of bearing attributes and actions. Rand’s conception that “logic is the art of non-contradictory identification” and that “logic rests on the axiom existence exists” embed logic in her fundamental metaphysics: Existence exists and is identity; consciousness is of existence and is identification. In amplification of her compact statement “Existence is identity,” Rand goes on to say that the law of identity (and lack of contradiction) applies to objects, to attributes, to actions, and to their compositions into larger wholes. In Rand’s metaphysics, identity as to nature is tied at the most basic level to identity as self-sameness. For Leibniz identity as self-sameness is the deeper reality of the two. Not so for Rand.
Rand shared with Leibniz the view that the principle of noncontradiction rests on the law of identity. In the 1960’s lectures Basic Principles of Objectivism, Nathaniel Branden held forth and explained Rand’s idea that the law of identity is the basic principle of metaphysics and of epistemology.
The three . . . laws of logic are: The Law of Identity, the Law of Contradiction, and the Law of Excluded Middle. The last two are merely corollaries or restatements of the first.
[The law of identity] is the link between the two sciences, the bridge between existence and consciousness, between reality and knowledge.
As a principle of metaphysics, the Law of Identity tells us that everything which is, is what it is. As a principle of epistemology, it tells us that contradictions cannot exist, that a thing cannot be A and not-A. (Branden c. 1968, 66–67)
Those relations on identity and noncontradiction were also presented by Leonard Peikoff in his 1972 lectures on the history of philosophy, where he indicated historical philosophic puzzles resolved by these Randian conceptions. In Objectivism: The Philosophy of Ayn Rand, Peikoff writes:
The law of identity acts as a bridge linking existence and consciousness, or metaphysics and epistemology. The law acts as a bridge in a second respect also. The law defines the basic rule of method required for a conceptual consciousness to achieve its task. In this regard, the law tells man: identifications must be noncontradictory.
. . . Aristotle’s law of contradiction states . . . nothing can be A and non-A at the same time and in the same respect. This is not a different fact from the law of identity. It is a corollary of the latter, a restatement of it for the purpose of guiding human cognition. (1991, 118–19)
Rand’s sense of identity basing noncontradiction goes beyond Leibniz to include natures at the most fundamental level of identity. Identities of nature or character are not modifications of existence. Existence is identity, not only identity of sameness, but identity of character. There are no existents without both of those aspects of identity.
There are occasions in which one could say “Man is man” by way of stressing that some stunning actions of man are among human capabilities, parts of human nature. Seeing the first man walk on the moon, one might say “Man is man.” Seeing Romeo take his life, one might say “Man is man.” The reader of Atlas Shrugged finds Ayn Rand proclaiming “Man is man” with a meaning along these lines. Her proclamation was to stress that, notwithstanding his freedom of mind, man has a definite nature, that he is nothing but man, and that he is one.
In Rand’s fundamental Existence is identity, the identity of an existent includes its that/which and its what. Rand states her finer structure for the law of identity as follows:
Whatever you choose to consider, be it an object, an attribute, or an action, the law of identity remains the same. A leaf cannot be a stone at the same time, it cannot be all red and all green at the same time, it cannot freeze and burn at the same time. A is A.
. . .
A contradiction cannot exist. An atom is itself, and so is the universe; neither can contradict its own identity; nor can a part contradict the whole. (AS 1016)
Aristotle was the founder of logic, and his great contribution thereto was his theory of correct inference, which is largely his theory of the syllogism. Though he did not realize it, the formula “A is A” in the form “Every A is A” can be used to extend the kingdom of the syllogism. By about 1240, Robert Kilwardly was using “Every A is A” to show conversions such as the inference “No A is B” from the premise “No B is A” can be licensed by syllogism. Aristotle had taken these conversions, like the first-figure syllogistic inferences, to be obviously valid and not derivable. Aristotle takes first-figure syllogisms to be obviously valid and the paragons of necessary consequence. The mere statement of these syllogisms makes evident their necessary consequents. Using conversions as additional premises, Aristotle shows that all syllogisms not first-figure can be reduced to first-figure ones. Their validity is thereby established, by the obvious validity of the first-figure ones and by (what he took to be) the irreducible obvious validity of the conversions.
We find Leibniz, four centuries after Kilwardly, illustrating the utility of Some A is A for concluding Some A is B from All A is B via a syllogism, third mood of the first figure. “I offer these examples . . . to show that identities do indeed have a use and that no truth, however slight it may seem, is completely barren; on the contrary, . . . these identities contain the foundations for all the rest” (Leibniz 1679, 226; see also 1705, 362–63).
There are places in which Aristotle connects “A thing is something specifically” or “A thing is what it is” with the principle of noncontradiction: “The same attribute cannot at the same time belong and not belong to the same subject in the same respect” (Metaph. 1005b19–20). Though not given the pride of place given it by Rand, there is some recognition that Existence is identity in Aristotle: “If all contradictories are true of the same subject at the same time, evidently all things will be one . . . . And thus we get the doctrine of Anaxagoras, that all things are mixed together; so that nothing exists” (1007b19–26). Aristotle realized too that any existent not only is, but is a what.
Rand acknowledges the greatness of Aristotle particularly for his laws of logic, as they are called in elementary logic texts of today and the last few centuries: the laws of noncontradiction, excluded middle, and identity. Those are important principles of logic, though, as we have seen, Aristotle was not securely on board with that last one. It is not clear that Rand was cognizant of the even greater importance for logic of the theory of correct inference that Aristotle invented with his theory of syllogism.
The tremendous importance of the laws of noncontradiction, excluded middle, and identity, in Aristotle’s sense of them or in Rand’s, is importance for metaphysics, thence all appropriate thinking on account of that metaphysical structure. Rand praised Aristotle also for his identification of “the means of human knowledge.” That was in a postscript to her Atlas Shrugged. Presumably, this point of praise refers not only to the role of the three laws of what may be called metaphysical logic, but to Aristotle’s general picture of how we obtain knowledge by reasoning on sensory experience, not by mentally contacting a transcendent platonic realm of forms. Rand writes also that Aristotle’s “incomparable achievement lay in the fact that he defined the basic principles of a rational view of existence and of man’s consciousness: that there is only one reality, the one which man perceives—that it exists as an objective absolute . . .” (1961, 22).
This particle has the set of properties A.
Particles having the set of properties A are electrons.
Therefore, this particle is an electron.
That is a case of a first-figure syllogism, or anyway, excluding singular terms from syllogisms, it is a close relative of that first-figure, third-mood syllogism: Some a’s are b, and all b’s are c; therefore, some a’s are c. On account of a syllogistic inference such as my electron one, Rand could sensibly say “the process of subsuming new instances under a known concept is, in essence, a process of deduction” (ITOE 28). This deduction looks every bit like a case of identification, based on Rand’s kind-sense of identity, though without reliance on the principle of noncontradiction. So I’d say Rand got the genus right, though the differentia wrong, when she defined logic as the art of noncontradictory identification. Perhaps “the art of perfectly truth-preserving inferential identification” would be a better definition of deductive logic devolving from Rand’s conception that logic is slave of existence, that existence is identity, and that consciousness is identification.
The inferences of first-figure syllogisms are, I maintain, licensed directly by identity alone, in Rand’s full sense of identity, and without recourse to noncontradiciton. Nathaniel Branden and Leonard Peikoff erred in trying to support Rand’s definition of logic, with its differentia of the noncontradictory, by appeal to noncontradiction rather than directly to identity as basis of the inference in a certain first-figure syllogism. It is the inference-form of my electron example, but in the familiar case: Socrates is a man, all men are mortal, and therefore, Socrates is mortal. They rightly point out that denial of this inference would lead to contradiction, but that is not to the point of first basis: One already knows that these first-figure inferences are valid, that their conclusions necessarily follow, just as Aristotle observed.
Rand took thinking and logical inference to be volitional cognitions. “To think is an act of choice. . . . The connections of logic are not made by instinct” (AS 1012). Logical inference is consciously directed, in Rand’s view, and that seems right to me in consideration of the process of bringing forward and latching onto logically relevant reasons for some target proposition and the process of finding implications of some target proposition.
Rand wrote further: “The pre-conceptual level of consciousness is nonvolitional; volition begins with the first syllogism” (1961, 15). I rather think volitional thinking, with action- and image-schemata, is in the repertoire before attaining first uttered word (at about one year), which word is co-referential and incorporated into schemata (and later into sentences). But the thing of present interest is Rand’s notion that volition begins with the first syllogism. That would be a deductive inference, whereas the abstractive process of getting one’s first worded concepts would really be, in her view, an induction. “The process of observing the facts of reality and integrating them into concepts is, in essence, a process of induction” (ITOE 28).
At times Rand seems to use syllogism in a super-broad, rather emblematic way to mean simply any logical inference, deductive or inductive. Pellegrin points out that at 92a28 of Post An. “the term syllogism is taken in a broad and non-technical sense” (2010, 131n15). In the Barnes translation of Post. An., the term syllogism does not appear in this line. Rather in Barnes, Aristotle’s allusion reads “if you produce a demonstration in this way.” In a translation appearing in Code 2010, the allusion reads “for this manner of syllogism” (78). Taking demonstration in an ordinary, nontechnical way, I suggest that the places in which Rand uses syllogism in a broad and nontechnical sense, she means demonstration (or validation) in a broad and nontechnical sense. That is, in a sense broad enough to include demonstrations by deductive inference (say, mortality of man from mortality of animals) as well as demonstrations by induction (say, from various sets of evidence to the mortality of all animals, to the roundness of the earth, or to the cause of the tides).
Rand’s broad use of syllogism is a bit grating in speaking of the right way of changing adult minds, authentically changing them, coordinate with their autonomy and with objective facts. Logic would have been better, reason better still. Her use of syllogism in connection with acquisition of one’s first concepts is grating to the point of a jam. Some sort of abstractive induction is prize principle of that day, and even demonstration (or validation) would seem out of order as characterization of what is happening in that day of the child’s development: (i) personal grasp and naming of some class of items grouped by similarity facts and (ii) boost in personal power of communication by that acquisition.
Notwithstanding such fumbling, I incline to think Rand has proposed worthwhile extension and reform of Aristotle in philosophy of logic; with her conception of logic and all cognition as identification; with existence (ever with identity) supplanting being; with entity supplanting substance; with identity supplanting form; and with essential characteristic(s), as relative to a context of knowledge, supplanting absolute essence. I expect all these shifts imply further differences, yet to be discerned, between logic in Aristotle and logic as it should stand in the metaphysics and epistemology of Rand.
 Cf. Avicenna 1027: “It is evident that each thing has a reality proper to it—namely, its quiddity” (I.5.10). I shall use what or whatness in place of the traditional quiddity (quidditas); see e.g. Gilson 1939, 199.
 Leibniz 1678; Baumgarten 1757 , §11; Kant 1755, 1:389; 1764, 2:294. Rand, in the “About the Author” postscript to AS, and N. Branden, in Basic Principles of Objectivism, erroneously thought Aristotle held the tight bond of identity and noncontradiction that had actually come to be recognized only with Leibniz and his wake.
 Aristotle, Metaph. 1030a20–24, 1041a10–24.
 Intellectual truths such as “Nothing is greater or less than itself.”
 Leibniz 1684, 293.
 AS 1015–16.
 Cf. Peikoff:
Aristotelians seem committed, in spite of themselves, to the view that particulars qua particulars are unknowable by man. Every determinate characteristic of a particular, and thus everything knowable about it, is placed ultimately on the side of Form; Matter in itself is the unorganized, the indeterminate, the nothing-in-particular; it is, as . . . Aristotle put it, “unknowable.” But if all we can ultimately know of a particular is Form; if the individualizing element, the principle of individuation, is in itself unknowable; does this not suggest that the individuality of things is in itself unknowable, i.e., that particulars qua particulars are unknowable? (1964, 214)
 First mood of the second figure; Kneale and Kneale 1962, 235–36; see also Kant 1800, §44n2.
 Lear 1980, 3–5.
 Lear 1980, 1–14.
 See also Aristotle, Metaph. 1006b26–27, 1007a26–27. Let EI designate Rand’s “Existence is Identity.”Aristotle, Avicenna, Henry of Ghent, John Duns Scotus, Francis Suárez, Spinoza, Leibniz, Baumgarten, Kant, and Bolzano also reached principles close to (EI), though not the Randian rank of (EI) or near-(EI) among other metaphysical principles. A Thomist text Rand read had included: “What exists is that which it is” (Gilson 1937, 253). That is a neighbor of Rand’s “Existence is identity.” Neighbor Baumgarten: “Whatever is entirely undetermined does not exist” (1757, §53).
 Metaph. 1030a20–24; Post. An. 83a25–34.
 De Int. 17a33–35; Metaph. 1011b26–27; Plato, Rep. 436b.
 De Int. 17b27–29; Metaph. 996b26–30.
 Cf. Bolzano: “The name of laws of thought is justified to a certain extent because laws of things as such are also laws of our thinking of those things” (1837, §45).
 Cf. Rödl 2012, 22, 39–43.
 Aristotle, Post. An. 99b35–100b5; Salmieri 2008; 2010.
 AS 1016.
 “Logic rests on the axiom that existence exists” (AS 1016). That does not imply that logic is not a tool of right inference concerning propositions containing only terms referring only to nonexistent things (specified by mention of existent things).
 Branden c.1968, 67; Peikoff 1991, 119. Leibniz errs in this way as well; 1678, 187. But on another occasion, Leibniz writes, after listing some “Propositions true of themselves” (such as A is A), writes “Consequentia true of itself: A is B and B is C, therefore A is C” (quoted in Kneale and Kneale 1962, 338).
 See further Buridan 1335, 119–20.
 The first definition of syllogism in my American Heritage Dictionary is as in any elementary logic text. The second definition is: “Reasoning from the general to the specific; deduction.” The definitions are very like these in my Webster’s Unabridged.
 AS 1022–23.
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© Stephen C. Boydstun 2015