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  1. . You’ll have to do the study and make your own informed discernments. (Record your sources and page numbers in your notes and drafts; it saves you time later and helps you make real progress over the years.) Before Kant what criticisms of Locke’s realism were made by Berkeley, Hume, and Reid? What criticisms were made by Kant of all those predecessors? Chapters 6-12 of Primary & Secondary Qualities – The Historical and Ongoing Debate (2011, Lawrence Nolan, editor) and see Kant’s Prolegomena and his Critique of Pure Reason (Pluhar translation, index). What empiricist rejoinders were promptly made against Kant? Kant’s Early Critics –The Empiricist Critique of the Theoretical Philosophy (2007, Brigitte Sassen, editor) Philosophy of perception continues alive and lively to this day, as in A. D. Smith’s The Problem of Perception. As for the Kant scholars, none find Kant either faultless or the last word worth saying on any of his topics.
  2. Here are the Abstracts. Beyond that, dive in for the swim. “Would Immortality Be Worth It” In this paper, one is invited into a carefully composed thought experiment about the meaning of life. In discussions touching on the meaning of life, one hears ordinary folk and beginning students of philosophy rather complacently assume that immortal life in heaven is the goal of life and that no more questions need be asked. The common contrary position is the view that since in reality we are not immortal, life is ultimately empty of value. Both positions rest on the premise that only immortality, and infinite life span, would make life worth living. This is the premise Hick’s thought experiment challenges. “Can Art Exist without Death” Reviews the currently envisioned [1993] theoretical biological limits on human life span; barriers to the human impulse to live effectively forever. Discusses the validity of the concept of infinity, distinguishing the metaphysically infinite from the physically infinite and from the mathematically infinite. Surveys carefully how and what Einstein's general theory of relativity, in its contemporary development, can tell us about the physical infinity of spacetime (in the large). Assimilates the possibility of effectively endless life with Rand's thesis that the concept of life—as we know it, vulnerable life—is what makes the concept of value possible. Elaborates and extends Rand's gedanken of the immortal, indestructible robot. Answers the question "Can art exist without death?"
  3. . Free online recent papers of high quality on Kant are available at Contemporary Studies in Kantian Philosophy.
  4. . Would Immortality Be Worth It? --Stephen Hicks (1992) Can Art Exist without Death? --Kathleen Touchstone (1993)
  5. . There you have it.
  6. . Peikoff's Dissertation Prep Plato Aristotle I To be continued.
  7. . On sensation for Kant: KANT'S THEORY OF FORM --Robert Pippin (1984) On sensation and perception: KANT'S INTUITIONISM --Lorne Falkenstein (1995) On sensation, perception, and definition: Follow Index of Werner Pluhar's translation (1996) of CRITIQUE OF PURE REASON. On definition, see especially A727-32 B755-60.
  8. . No, Budd. We do not have or even enter the discipline of geometry, such as that of Euclid without grasp of language stating axioms, postulates, definitions, and permitted constructions and remarking on the lettered diagrams. Prior to having language and any discursive concept, we have action- and image-schemata which of course entails some knowledge of geometrical forms (round, rollable ball / shape and motions of the dog); and without those attainments, an infant nearing its first word, its onset of first discursive concept, could not engage in the co-reference with caretakers by joint gaze or by finger pointing, which are necessary to attainment of first word. But that is not geometry in the sense of the structure Euclid lays before us, extensively and deeply illuminating character of space. Euclid, by the way, should be a prerequisite for study of philosophy in its epistemological and metaphysical wings. Both of those wings today, of course, should also be informed by assimilation of the results of our modern science of cognitive developmental psychology* and our physics. The absolute prerequisites for approach of philosophy in its theoretical parts are an elementary course in logic and a course working through Euclid's plane geometry. (With a serious interest, one can learn those two things in one's own study, without taking a course. That geometry is offered in high school, and what a divine joy it was and is for me. I had elementary logic in college. Then on my own I was able to learn whatever more advanced geometry [synthetic, like Euclid and later, or analytic, like Descartes and later] and more advanced logic.) Not knowing Euclid's geometry is not knowing really much of what Plato or Aristotle or Kant or Peikoff (dissertation) or I are talking about in epistemology or metaphysics. Not knowing both Euclid and the syllogistic logic of Aristotle's from elementary logic is like having a flat tire when turing Aristotle's thought in theory of science, definition, and metaphysics. There is no substitute for opening Euclid and just doing it. Euclid’s axioms (or common notions) are part of the starting points for the system and are not argued for. One is “things which are equal to the same thing are also equal to one another.” That is a relationship rather far beyond something one was simply presented in perception. It may fairly count as an intuitive induction, but we need to learn more about what that process was thought to be and what have been the problems with it. Work for the sequel of this study on LP’s dissertation.
  9. . Bravo to Tyler against the spoiling of 'begs the question'. Please say 'invites the question' or 'suggests the question'. Preserve the phrase 'begs the question' for our centuries-old informal logical fallacy of that name. I still mount an American flag once a year, for Independence Day, by the road, in our front woods. The republic for which it stands is still a great protector of individual rights, notwithstanding all its downfalls on that score. I recall once in college in the late '60's there was this black man, an older guy, who was a featured guest speaker sponsored by some left-socialist group (perhaps our SDS). He was speaking for socialism and telling of his recent international travels organizing and speaking in Africa. And then he mentioned that when he got back to America, he felt like kissing the ground, and he said there's nothing else this good. His hosts were extremely embarrassed, pretty sure. His vista was not entirely concordant with their own. In those days, we had the military draft, and an Administration with a big war need for our bodies, our lives. Over the arc of my life, that state aggression against our young men has been on hold, and that was some credit of our country in this interval (unfortunately, the recognition the draft's status as an aggression is cloudy in the view of most Americans, pretty sure). Over that arc, in a strand affecting me distinctively, our country legalized consensual adult gay sex throughout the land, got gays and lesbians openly and fully accepted into the armed forces, and recognized a legal power of same-sex couples to marry. We also mounted our flag in our Chicago years upon the attack of 9/11/01. And we mounted it here in Lynchburg on the day we got Bin Laden. I don't care what other people do to the American flag, and I certainly respect the diversity of feelings towards the flag and the republic, and the right to diverse expressions, including flag burning. But from me, respect and love of this flag and the now long line from Valley Forge to now of lives lain down for it and this country.
  10. . Peikoff's Dissertation Prep Plato Aristotle I To be continued. ~~~~~~~~~~~~~~~~ In the 'Aristotle I' post, I had written that “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). The translation I had quoted was by Ross. I made an error in my transcription. It should read ‘. . . so that nothing really exists.” That translation of 1007b26 very possibly should be otherwise. These other ways squash the suggestion that here Aristotle is virtually stating Rand’s “Existence is Identity.” The translations of Kirwan 1993 and of Reeve 2016 do not say “. . . so that nothing really exists.” Rather, they say “. . . so that nothing is truly one” and “. . . so that there is nothing that is truly one.” If these later translations are truer to Aristotle’s text here, then the connection between existence and identity is here rather more indirect, turning on rigid attachment of oneness to existence and depending on the fullness of Rand’s Identity being covered by the variety of Aristotle’s ways of oneness. New Reference Reeve, C. D. C., translator, 2016. Aristotle, METAPHYSICS. Hackett. http://ndpr.nd.edu/news/metaphysics/
  11. . Kant and Principia Space, Rotation, Relativity - Kant ~~~~~~~~~~~~~~~~ PS - In that second link, my essay was written in 1997. I'd like to mention two scholarly grand works appearing since then and pertinent to the topics in that essay: The volume Natural Science (2012) in the Cambridge edition of the works of Immanuel Kant. And by Michael Friedman, Kant's Construction of Nature (2013).
  12. . I’m pretty sure when I first learned the word “libertarian.” It was in a current issue of THE PERSONALIST at my university in around 1970. There was a debate in that issue wherein one side argued for government limited in the way I was familiar with from Rand, while the other side argued for anarchocapitalism. John Hospers was then the editor of that journal. I didn’t give the anarchocapitalist theory much thought until Nozick’s ASU came out (1974) and he made his case against that theory (especially those basing their position on individual rights) in consideration of issues of procedural justice. In 1971 Hosper’s book LIBERTARIANISM had been issued. Therein he defined libertarianism, “according to which the function of government should be limited to the protection of individuals against aggression by others or by government” (27). The last chapter of his book is titled “Is Government Necessary?” which I imagine set out the debate between limited-government libertarians and anarchocapitalist libertarians (his own side would have been the former, to be sure). Unfortunately, somewhere along the way, the latter portion of that book including that chapter in my paperback fell off and is lost. In 1972 I was old enough to vote for the first time, and I wrote in the name John Hospers, who was the Presidential candidate of the newly formed Libertarian Party. I was in the Party and worked pretty hard with it until 1984, when I left it. All of our Presidential candidates to that year were limited-government libertarians as I recall. It was at the national convention in New York in 1975 that I spotted and bought Tibor Machan’s HUMAN RIGHTS AND HUMAN LIBERTIES (1975). It was a systematic rights-based defense of limited-government libertarianism by another professional philosopher: “‘Libertarianism’ is the label that has been applied to the theory of society or political philosophy that identifies the initiation of force against others as the one form of human interaction that is impermissible in a human community under all circumstances. I have not used the label thus far because many libertarians base their acceptance of this basic prohibition on something other than a theory of human rights. Some take the principle to be self-evidently true. Others view it as an efficient device for social organization without giving it a foundation based on a moral point of view. But I will henceforth use the term ‘libertarianism’ to indicate the theory of human community proposed in this work” (147). We never thought of our rights-based limited-government libertarianism as some sort of poor stepsister to anarchocapitalist libertarianism. We did not concede the name “libertarianism” to them as most rightly theirs. I did read Murray Rothbard’s FOR A NEW LIBERTY (1974) and THE ETHICS OF LIBERTY (1982). Nice writing, but on his theory of property rights in land and their relations to enforcement institutions, the anarchocapitalist case collapses (again). (This was my comment in the link mentioned by William upstream.) Further, from my 1988 Right, Games, and Self-Realization.
  13. His Own Truth “While a wise man, as well as a just man and the rest, needs the necessaries of life, when they are sufficiently equipped with things of that sort the just man needs people towards whom and with whom he shall act justly, and the temperate man, the brave man, and each of the others is in the same case, but the wise man, even by himself, can contemplate truth, and the better the wiser he is; he can perhaps do so better if he has fellow-workers, but still he is the most self-sufficient.” (Aristotle, Nicomachean Ethics 1177a28–35, Ross/Urmson translation) By “the brave man” Aristotle had in mind a concept of bravery confined to the realm of social interactions, excluding the portion of our notion of bravery in humans engaged in risks with nature, such as in shooting the rapids. With bravery in his more narrow sense in this text, Aristotle is saying that in our thinking after truth we are more self-sufficient than in our occasions of being just, brave, and so forth. Self-sufficiency is a height. In this passage Aristotle is taking contemplation of truth as truth he conceives as nonpractical. Not that he has anything against practical thought, but here he is puffing up contemplation of truth not manifestly concerned with practical pursuits, contemplation of truth in metaphysics or geometry, for example. We can transfer Aristotle’s point, however, to a wider setting that includes thinking on practical things such as how to trim the shrubs oneself. It remains for this wider realm of thought that acts of thinking after truth are inherently less immediately social than one’s episodes of acting justly, acting independently, or telling the truth. In all of Rand’s novels, a natural human wholeness is prescribed, a way of human life that had been broken up by overblown conceptions of human social nature. Rand was not denying there is an important social goodness naturally in the life of an individual. That affirmation is an understatement, in my own view, which will be set out in my book in progress. Nonetheless Rand was right to contest the overly social conceptions of human being wrecking lives around the world. In this note, I’ll pull together some bits from my writings, which pertain to Rand’s binding of truth to individual agent and binding of beneficiary egoism to agency egoism.* Comrade Sonia says to Andrei Taganov: “I know—we know—what you think. But what I’d like you to answer is why you happen to think that you are entitled to your own thoughts? Against those of the majority of your Collective? Or is the majority’s will sufficient for you, Comrade Taganov? Or is Comrade Taganov turning individualistic?” (1936, 378). Early in the story, when he is courting Kira, the future love of his life, we are given the following picture of Andrei’s seamless character. Kira leads: “I thought that Communists never did anything except what they had to do . . . .” “That’s strange,” he smiled, “I must be a very poor Communist. I’ve always done only what I wanted to do.” “Your revolutionary duty?” “There is no such thing as duty. If you know a thing is right, you want to do it. If you don’t want to do it—it isn’t right. If it’s right and you don’t want to do it—you don’t know what right is—and you’re not a man.” “Haven’t you ever wanted a thing for no reason of right or wrong, for no reason at all, save one: that you wanted it?” “Certainly. That’s always been my only reason. I’ve never wanted things unless they could help my cause. For, you see, it is my cause.” “And your cause is to deny yourself for the sake of millions?” “No. To bring the millions up to where I want them—for my sake.” (92) Late in the novel, Andrei envisions (what is in the author’s view) an even greater seamlessness of character by setting his newly reached beneficiary egoism squarely in his life-long agency egoism. Addressing his Comrades: “You see, there are things in men, in the best of us, which are above all states and all collectives, things too precious, too sacred, things which no outside hand should dare touch. Look into yourself, honestly and fearlessly. Look and don’t tell me, don’t tell anyone, just tell yourself: what are you living for? Aren’t you living for yourself and only for yourself? For a higher truth which is your own? Call it your aim, your love, your cause—isn’t it still your cause? Give your life, die for your ideal—isn’t it still your ideal? Every honest man lives for himself. Every man worth calling a man lives for himself. The one who doesn’t—doesn’t live at all. You cannot change it. You cannot change it because that’s the way man is born, alone, complete, an end in himself.” (501) [1] Rand’s Prometheus declares, “I shall live my own truth” (1938, 140). Rand gives him also these lines: “All things come to my judgment, and I weigh all things, and I seal upon them my ‘Yes’ or my ‘No’. Thus is truth born. Such is the root of all Truth and the leaf, such is the fount of all Truth and the ocean, such is the base of all Truth and the summit. I am the beginning of all Truth. I am its end” (128). There is echo here of the alpha and omega said of God in Revelations. However, Rand’s beginning and end of all truth in Anthem is no maker of all truth and value, as in the extreme voluntarist traditions of theology wherein God freely thinks and what he thinks becomes fact, there being no eternal truths, or any truths, independent of God’s choice. For Rand’s Prometheus, there is all the existence of the earth independent of his verdicts, and his is to find the earth and how to cultivate it. There is fact independent of mind, though there is no truth independent of mind. Rand is also affirming in that Anthem passage that all judgment of truth is individual and that all truth we render from the world is for our own final value. Those lines are preceded by these: “It is my eyes which see, and the sight of my eyes grants beauty to the earth. It is my ears which hear, and the hearing of my ears gives its song to the world” (A 128). Something is seen, and with the subject, it is rendered beautiful. Something is heard, and with the subject, it is rendered song of existence. Something is given, and with its recognition, it is rendered truth. Howard Roark says that a building’s integrity—its esthetic integrity, integral with its site, function, and physical integrity—“is to follow its own truth” (F PK I, 18). The architect Cameron, is said to have, through a succession of works, at last given shape “to the truth he had sought” (PK III, 41). In Fountainhead Rand works with an analogy between character of a building and character of a soul. A right building design has an individual truth and integrity; a right person has an individual truth and integrity. Furthermore, truth of the creator enters into truth of the creation, and responders to the latter truth hold it in ways unique to the unique constitution of their own souls. The concept Rand is forging with her building/soul analogy is integrity. One broad thesis of Fountainhead is that there is a type of egoistic individualism that is good and just; altruistic collectivism is evil and unjust. The argument focuses not so much on what is just as on what is good, purely of humans, purely of earth. Such are independence, reliance on reason (one’s own), honesty, creative achievement, love of one’s work, and courage. A concept of justice will make human life and happiness impossible if the concept ignores the uniqueness of individuals and the unity and self-sufficiency required by the preceding virtues. Integrity is the overarching virtue pronouncing this unity and self-sufficiency. Rand joins one’s integrity to one’s truth. “A building is alive, like a man. Its integrity is to follow its own truth, its one single theme, and to serve its own single purpose” (F PK I, 18). One’s truth in Fountainhead is the constitution of one’s self in the living and making of one’s self. In a creation, the creator had a truth for which he struggled. “His truth was his only motive. His own truth, and his own work to achieve it in his own way” (HR XVIII, 737). His creation was from and, in a fundamental sense, for his self. He lived for himself, for his own truth, for his own work. In Atlas Rand again connects integrity to truth, and both to agency egoism. Integrity entails unity “between body and mind, between acting and thought, between his life and his convictions” (1957, 1019). Integrity entails courage “of being true to existence, of being true to truth,” whatever public opinion and pressure might be. Integrity entails confidence “of being true to one’s consciousness.” Talk of one’s own truth is dropped. Devotion to existence and rationality and end-in-itself life, available alike to all, is the salvation of individual and society. ~~~~~~~~~~~~~~~~ [1] Rand’s contention that commitment to agency egoism—thinking for oneself—commits one, by some sort of consistency, to ethical beneficiary egoism continues through all her writings. This early attempt, in 1936, in which agency egoism together with psychological beneficiary egoism and the accepted virtues of honesty and courage yields ethical beneficiary egoism, is replaced by 1957 with denial of psychological beneficiary egoism, but with a constitution of human life set within an alleged basic character of any life, and from this situation Rand tries to pull a norm of ethical beneficiary egoism seamless with the life-goodness of agency egoism.
  14. (I’m going to be talking more Rand in this segment, and I want the reader to keep in mind that Peikoff managed to hammer out his dissertation without any mention of Rand or her ideas, though her frame was also his in the years he was writing his dissertation.) Aristotle I Peikoff scrutinizes the broadly empiricist thinkers Aristotle, Aquinas, and Locke in their aspect of opposition to the Platonic views that necessary truths, such as the impossibility of contradictions in reality, are (i) innate in the human mind and (ii) features of essences accessible only by intellect and objectified beyond the particulars accessible by sensory perception. Aristotle recognized that the precise knowledge by demonstrations we make from true precise premises require principles constraining inference that are themselves true and precise and not themselves demonstrable.[1] Like all knowledge, in Aristotle’s view, these indemonstrable, necessarily true principles, such as PNC, must somehow derive from sensory experience. This somehow Aristotle sketched is a process begun in perception and capped by what has long been called intuitive induction.[2] In the decades I lived in Chicago, there were university libraries that allowed the general public, if well behaved, to come in and read and xerox. The one with the most generous access was DePaul, which happened to be only an L-stop away from where I lived. One day I was there perusing bound volumes of The New Scholasticism, and I came across therein an article by Leonard Peikoff titled “Aristotle’s ‘Intuitive Induction’.” I knew what went by the name intuitive induction, that it was also known as abstractive induction, that it was a genre among other genre of induction, and that it “exhibited the universal as implicit in the clearly known particular” (APo 71a8).[3] Peikoff’s published article was composed from portions of his dissertation.[4] My quotation from Posterior Analytics (APo) just now was from the translation in the Oxford volumes edited by Ross (1910–52), which Peikoff had relied on in his dissertation and article.[5] In 1984 a Revised Oxford Translation of Aristotle was completed in which three of Aristotle’s books—Categories, de Interpretatione, and Posterior Analytics—unlike all the other books, were not mild emendations to the earlier translations into English, but were entirely new translations into English. The new translation of APo is by Jonathan Barnes. Some years after that translation, he thought he could do a little better, and he made a second translation. His translation of the familiar old-time Oxford “exhibiting the universal as implicit in the clearly known particular” becomes (i) a class of inductive arguments “proving the universal through the particular’s being clear” and (ii) “proving something universal by way of the fact that the particular cases are plain.” Richard McKirahan paraphrases APo 71a8–9 on the sort of inductive arguments at issue as revealing the universal “through the fact that the particular is obvious” (1992, 237). The obvious example, I say, would be from geometry, such as proving of any and every triangle that its interior angles sum to two right angles. Some proof of that result was known to Aristotle, and hopefully, any modern reader of philosophy knows the Euclidean proof.[6] I should mention that any three stars (not all in a single straight line) in a portion of the clear night sky reflected in still water determine a triangle in a Euclidean plane. The figure triangle exists in the world, whether by nature alone or by our constructions indicating that figure.[7] And for all such triangles, it is a fact that if they lie in a Euclidean plane their interior angles sum to two right angles. (Refer to this fact as 2R.) A triangle is a particular—one clear, plain, and obvious—and we can prove the fact 2R about triangles, a character of triangles holding necessarily for all of them. Is the principle of noncontradiction a fact of the world in the way the sum of angles in a triangle is a fact in the world? Not exactly, I should say. That my right hand has five appendages is part of the character of the hand itself. That five fingers are not seventeen fingers is a fact, although one dependent not only on the character of five-fingered hands, but on auxiliary relations of five-fingered hands to something pretty far afield. Cases of noncontradiction run arbitrarily far afield: a five-fingered hand is not an opera, not an empty region of space, and so forth. A malformed human hand might lie on gradations between a typical hand and other natural or artificial instruments for grasping, but there is no such gradation between a typical hand and an opera. Full-scope noncontradiction depends for its existence in part on thought of negations arbitrarily far afield, negations untied from unities of real physical organization. PNC has some existential dependency on thought. 2R does not. Objectivists could put it this way: Noncontradiction is a ramification of identity. The latter is not per se dependent on thought, I say, as they say. Fundamentally, identity is a fact like 2R, notwithstanding the circumstance that 2R is a demonstrable fact, whereas identity and noncontradiction are primitive principles (presumed, even if unstated) of demonstration (i.e., discursive demonstration, such as demonstration of 2R). An intuitive induction from sensory perception to the principles of identity and noncontradiction is not the same as intuitive induction cum demonstration from sensory experience with triangles to 2R. An intuitive induction from experience to the principle of noncontradiction cannot be a demonstrative proof, though it must be as precise and settled as demonstrations that rely on it. Intuitive induction to principles of identity and noncontradiction are more like proof-lacking inductions to “any three points not colinear determine a plane” and “nothing comes from nothing.” Although, those two facts grasped by intuitive induction do not depend at all on the cognitive power(s), the intuitive induction, under which they are cognized. In that they are like 2R or identity and unlike PNC. We should notice with Netz that, whether or not they are made explicit, certain intuitive propositions—intuitive in the sense of being obviously and necessarily true—are employed in the starting points and inferences of Greek mathematical proofs.[8] Objectivists and some other moderns (e.g. Leibniz, Baumgarten, and Kant) have thought of noncontradiction as ontologically dependent on identity. Aristotle in Prior Analytics shows he knew that not all valid deductions exercise noncontradiction. Rather, the most perfect syllogistic forms of deduction exercise merely universal instantiation or transitivity of identity. Yet he says in Metaphysics: One can, I say, think of a belief (or anything else) and its contradictory at the same time, where “same time” has a small, but nonzero duration. That would be on the duration-order of working memory. But only a mentally defective person could believe a thing and its contradictory within that scale of duration. Peikoff interpreted Aristotle in this passage to be arriving at the proposition, that one cannot believe a thing and its contradictory at the same time, by instantiation of the principle of noncontradiction in application to all existents, in this case the existent human mind.[9] That seems a shaky interpretation and a shaky conception of the human mind unless we have passed on from mere description to proper functioning of human mind. Peikoff’s 1964 position on this point, as straight description of mind, though it was in error, does not affect his characterization of logical ontologism or his contrast between its Platonic and Aristotelian wings. Aristotle’s claim that “all who carry out a demonstration refer it to this [PNC] as an ultimate belief; for this is naturally the starting-point even for all other axioms” is close-but-no-cigar. The ultimate recognition for demonstration (which for Aristotle is a genre of syllogism), I say, is recognition of a principle of identity as rich as Rand’s or approximately that rich. Rand wrote in 1957: The distinction of existence and identity is independent of consciousness, independent of identification. The distinction between existence and identity, as well as the inseparability of the former from the latter, are fundamental facts of the world.[11] Existence in its identity shows the elements of that identity to be without contradiction or self-contrariety.[12] The Law of Identity in Rand’s usage of the title encompassed: A is A, a thing is itself, a thing is what it is, and existence is identity. 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.[13] 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.[14] In Topics he holds that each and every thing is predicable of itself, predicable essentially and necessarily. Specifically, this predication is the thing’s definition. In this he means only that a thing and its definition refer to the same thing.[15] He does not convey the further thought that a thing is necessarily and nothing but the instanced definition together with all other instanced specific identity of the thing, along with any particularities of the thing, such as location. He does not convey that further thought from Rand I think right: that all those together compose the existence of the thing without remainder. 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 consolidate 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.[16] Aristotle had taken these conversions, like he had taken the first-figure syllogistic inferences, to be obviously valid and not derivable.[17] Aristotle takes first-figure syllogisms to be obviously valid and the paragons of necessary consequence. The mere statement of these syllogisms makes evident their conclusion as following necessarily. 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 the irreducible obvious validity of the conversions.[18] In this program, which is in Prior Analytics, Aristotle uses also the principle of noncontradiction; for some of his reductions of second- and third-figure syllogisms to first-figure employ indirect proof, specifically proof per impossibile. However, the per impossibile steps only establish a premise that can then be employed in a direct proof of reduction to first figure.[19] The principle of noncontradiction, like the first-figure inferences and the logical conversions, is self-evident. The principle of noncontradiction is not the entire or main base of valid logical inference, I observe. Rather, I maintain, identity is directly the main base, and indirectly identity is base when noncontradiction is base, for the former is base of the latter. Notice also: That the logical conversions were centuries later shown to be derivable from first-figure syllogisms by using A is A as a premise does not imply that the conversions are not also self-evident.[20] 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).[21] Aristotle acknowledges on occasion that any existent not only is, but is a what.[22] He contradicts that principle, however, when he says: “That which is primarily and is simply (not is something) must be substance” (Metaph. 1028a30). The art of noncontradictory identification is logic, in Rand’s conception of it. I take some issue with that definition, for avoidance of contradiction is not the main rule of deductive inference. That main rule is directly identity itself. Mathematical induction, also, does not rest on noncontradiction, but is a variety of identity. Then too, the rule of noncontradiction itself rests on the fact(s) of identity. This asymmetric dependence was evidently recognized in Rand 1957, wherein she had it that existence exists and is identity and that “existence exists” is the basis of logic. She took consciousness to be fundamentally identification and took logic to be the genre of consciousness-endeavor noncontradictory identification. That differentia noncontradictory is an inadequate span of the modes of inference in the discipline of logic. I suspect Rand was led astray by Aristotle’s “all who are carrying out a demonstration refer it to this [PNC] as an ultimate belief; for this is naturally the starting-point even for all other axioms” which is only a few lines of Aristotle beyond the lines she quotes in the closing scene of 1957. The inferences of first-figure syllogisms are, I maintain, licensed directly by identity alone, in Rand’s ample sense of identity, and without recourse to noncontradiction. Nathaniel Branden and Leonard Peikoff in their Objectivist writings 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.[23] That certain one is the inference-form of the familiar case: Socrates is a man, all men are mortal, and therefore, Socrates is mortal. Peikoff 1991 and Branden c.1968 rightly point out that denial of this inference would lead to contradiction,[24] but that is not to the point of first, most direct basis.[25] One already knows that these first-figure inferences are valid, that their conclusions necessarily follow, without invoking PNC, just as Aristotle had rightly observed in Prior Analytics and had messed up in Metaphysics. Another class of deductions not fitting Rand’s definition is the direct proof of mathematical identities, such as the trigonometric identities. All such proofs conclude 1=1, showing the initial proposed identity true. No appeal to noncontradiction is made; identity is invoked directly and is the entire basis of proofs of mathematical identities. That identity in a broad Randian sense of the term is more fundamental than and is ground of PNC, though underground in Peikoff’s dissertation, does not undermine his characterization of Aristotle’s logical ontologism. Then too, characterization of PNC as being not only a fact of the world but a fact partly dependent on operation of thought in the world—my own added characterization—does not degrade Peikoff’s characterization of Aristotle’s logical ontologism, though my ontology of PNC may in the end suggest reformation in Peikoff’s divisions of schools of thought in the history of philosophy of logic. In the next installment, I’ll continue with Aristotle and with Peikoff’s treatment of him, beginning with intuitive inductions to necessary truths including PNC. I want to close the present installment by noting the change in translation of APo. II 19 by Barnes concerning the traditional intuition in intuitive induction. The older translation relied upon by Peikoff 1964, 66, reads: “From these considerations it follows that there will be no scientific [i.e. deductive] knowledge of the primary premises, and since except intuition nothing can be truer than scientific knowledge, it will be intuition that apprehends the primary premises” (APo. 100b10–12). Barnes final translation reads: “Hence there will not be understanding of the principles; and since nothing apart from comprehension can be truer than understanding, there will be comprehension of the principles” (APo. 100b10–12). In the Barnes translation, scientific knowledge has become understanding; primary principles have become principles; and intuition has become comprehension. Each of these differences is significant, and Barnes argues for them. On the last of those three alterations in translation, Barnes argues against the traditional English of nous into intuition. He remarks in part: Barnes argues that induction factors into Aristotle’s answers on whether we have innate knowledge of indemonstrable principles that are starting-points of demonstrations and, if not, how knowledge of such principles is acquired. He argues that nous is answer to a different question of Aristotle’s: what is our state that knows those principles? Under Barnes picture, Aristotle has us in the state Barnes calls understanding when we know theorems and has us in the state nous, which Barnes calls comprehension, in our knowledge of indemonstrable principles. “Understanding is not a means of acquiring knowledge. Nor, then, is nous. / . . . ‘Intuition’ will not do as a translation for nous; for intuition is precisely a faculty or means of gaining knowledge. Hence in my translation I abandon ‘intuition’ and use instead the colourless word ‘comprehension’ (268). We can be sure that such issues of translation of Aristotle, and consequent divergent characterizations of Aristotle’s views, have been acute not only in translations into modern languages, but into Arabic and into Latin centuries ago. To be continued. Notes [1] APo. 72b19–24, 99b20–21. [2] APo. 99b35–100b5. [3] Boydstun 1991, 36. [4] Mainly pages 63–79 of his dissertation. [5] The translations in Richard McKeon’s The Basic Works of Aristotle are from the Ross edition. [6] APo. 71a19–29, 85b5–15, 91a3–4; Metaph. 1051a24–27; Euclid’s Elements I.32. [7] On Memory 450a1–4; Metaph. 1089a25–26. [8] Netz 1999, 182–85,189–98. [9] Peikoff 1964, 156–57. See further, the translation and commentary of Kirwan 1993. [10] Cf. Avicenna 1027: “It is evident that each thing has a reality proper to it—namely, its quiddity” (I.5.10). Think whatness for the traditional quiddity (quidditas, tinotiz); see e.g. Gilson 1939, 199. [11] Cf. Heidegger’s ontological articulation and disclosedness in Haugeland 2013, 197–98, notes 6 and 7. [12] AS 1016; ITOE App. 240, 286–88. [13] Leibniz 1678; Baumgarten 1757 [1739], §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. [14] Metaph. 1030a20–24, 1041a10–24. [15] Top. 103a25–29, 135a9–12. [16] First mood of the second figure; Kneale and Kneale 1962, 235–36; see also Kant 1800, §44n2. It was through Kneale and Kneale 1962 that I learned of Kilwardly’s recognition of the logical serviceability of “A is A” in the form “Every A is A.” In his 1964 dissertation, Peikoff did not make use of this book by the Kneales. Relying on older books on the history of logic, Peikoff noted in the Introduction to his dissertation that the law of identity specifically formulated as such was apparently not in play until end of the thirteenth century (works of Antonius Andreas). Placing first recognition of the law of identity a century or so earlier by more recent historical studies of logic, such as by the Kneales, still locates inception of the law’s recognition in the medieval era, as alleged in Peikoff’s older histories. [17] Lear 1980, 3–5. [18] Lear 1980, 1–14. [19] Lear 1980, 34–53; Bonevac 2012, 68–72. [20] On Aristotle’s alternative method ecthesis for reducing second- and third-figure syllogisms to first-figure, see Malink 2013, 86–97. This method rests directly on identity, not indirectly via noncontradiction. [21] See also 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). [22] Metaph. 999a28; 1030a20–24; APo. 83a25–34. [23] Branden c. 1968, 67–69; Peikoff 1991, 119, though Peikoff had not made this error in explicating this syllogism in his dissertation 1964, 134. 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). [24] See further, Buridan 1335, 119–20. [25] See also Kneale and Kneale 1962, 357, and their conclusion that “the principle of noncontradiction is not a sufficient foundation for all [syllogistic] logic.” References Aristotle c. 348–322 B.C.E. The Complete Works of Aristotle. J. Barnes, ed. 1984. Princeton. Avicenna 1027. The Metaphysics of The Healing. M. E. Marmura, trans. 2005. Brigham Young. Barnes, J., trans. and comm., 1992. Aristotle – Posterior Analytics. 2nd ed. Oxford. Baumgarten, A. 1757 [1739]. Metaphysics. 4th ed. C. D. Fugate and J. Hymers, trans. 2013. Bloomsbury. Bonevac, D. 2012. A History of Quantification. In Logic: A History of Its Central Concepts. D. M. Gabbay, F. J. Pelletier, and J. Woods, ed. Elsevier. Boydstun, S. 1991. Induction on Identity. Pt. 1. Objectivity 1(2):33–46. Branden, N. c. 1968. The Basic Principles of Objectivism Lectures. Transcribed in The Vision of Ayn Rand. 2009. Cobden. Buridan, J. 1335. Treatise on Consequences. S. Read, trans. 2015. Fordam. Euclid c. 300 B.C.E. The Elements. T. L. Heath, trans. and comm. 2nd ed. 1925. Dover. Gilson, E. 1937. The Unity of Philosophical Experience. Ignatius. ——. 1939. Thomist Realism and the Critique of Knowledge. M. A. Wauk, trans. 1986. Ignatius. Haugeland, J. 2013. Dasein Disclosed – John Haugeland’s Heidegger. J. Rouse, ed. Harvard. Kant, I. 1755. A New Elucidation of the First Principles of Metaphysical Cognition. D. Walford and R. Meerbote, trans. In Immanuel Kant – Theoretical Philosophy, 1755–1770. 1992. Cambridge. ——. 1764. Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality. D. Walford and R. Meerbote, trans. In Immanuel Kant – Theoretical Philosophy, 1755–1770. 1992. Cambridge. ——. 1800. The Jäsche Logic. J. M. Young, trans. In Immanuel Kant – Lectures on Logic. 1992. Cambridge. Kirwan, C., trans. and comm., 1993. Aristotle – Metaphysics, Books G, D, and E. Oxford. Kneale, W., and M. Kneale 1962. The Development of Logic. Oxford. Lear, J. 1980. Aristotle and Logical Theory. Cambridge. Leibniz, G. W. 1678. Letter to Herman Conring – March 19. In Gottfried Wilhelm Leibniz: Philosophical Papers and Letters. L. E. Loemker, trans. 2nd ed. 1969. Kluwer. Malink, M. 2013. Aristotle’s Modal Syllogistic. Harvard. McKirahan, R. D. 1992. Principles and Proofs – Aristotle’s Theory of Demonstrative Science. Princeton. Netz, R. 1999. The Shaping of Deduction in Greek Mathematics. Cambridge. Peikoff, L. 1964. The Status of the Law of Contradiction in Classical Logical Ontologism. Ph.D. dissertation. ——. 1985. Aristotle’s “Intuitive Induction.” The New Scholasticism 59(2):185–99. ——. 1991. Objectivism: The Philosophy of Ayn Rand. Dutton. Rand, A. 1957. Atlas Shrugged. Random House. ——. 1990. Introduction to Objectivist Epistemology. Expanded 2nd ed. Meridian.
  15. Thanks! The sound in this production is a poem plus. I close my eyes to enjoy it best. Ode to a Nightingale