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  1. (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.
  2. . The Status of the Law of Contradiction in Classical Logical Ontologism Leonard Peikoff – Ph.D. Dissertation (NYU 1964) There are no true contradictions, and there cannot be any. That is the law of contradiction, or principle of noncontradition (PNC) as I shall call it. There is nothing and can be nothing that is both A and not-A at the same time and in the same respect. The last three decades, Graham Priest and others have argued specific exceptions to the law. These exceptions seem to be such that from them no possibility of observable, concrete true contradictions can be licensed. The debate over these circumscribed candidates for true contradictions continues. I shall in this study fence them off, without disposition, from our still very wide purview of PNC. There are reasons advanced in favor of these specific alleged exceptions to PNC, I should stress. It is not argued that we should just say true or false as we please of the contradiction reached in these cases. These are not situations for conventions such as the side of the road on which to regularly drive. (See Priest, Beall, and Armour-Garb 2004.) Under the term classical in his title, Peikoff includes not only the ancient, but the medieval and early modern. By logical ontologism, he means the view that laws of logic and other necessary truths are expressive of facts, expressive of relationships existing in Being as such. Peikoff delineates the alternative ways in which that general view of PNC has been elaborated in various classical accounts of how one can come to know PNC as a necessary truth and what the various positions on that issue imply in an affirmation that PNC is a law issuing from reality. The alternative positions within the ontology-based logical tradition stand on alternative views on how we can come to know self-evident truths and on the relation of PNC to the empirical world, which latter implicates alternative views on the status of essences and universals. Opposed to the classical logical ontologists are purportedly conventionalist approaches to logical truth in the first half of the twentieth century. Peikoff argues that infirmities in all the varieties of classical logical ontologism open the option of such conventionalism. Firstly, Peikoff examines the views of Plato (427­–347 B.C.E.) in their import for an explanation of our knowledge of PNC and its self-evident character and for the bases of PNC in reality. Peikoff then examines these imports in the views of Aristotle as well as in the views of the intellectual descendents of Plato and Aristotle to the time of Kant. Peikoff cites a number of passages in which Plato invokes varieties of PNC as a general principle of the character of things that must always be acknowledged in reasoning. “The same thing will not be willing to do or undergo opposites in the same part of itself, in relation to the same thing, at the same time” (Republic 436b). “Do you suppose it possible for any existing thing not to be what it is? / Heavens no, not I” (Euthydemus 293b). To citations given by Peikoff, I add Republic 534d where Plato speaks of some persons “as irrational as incommensurable lines.” The incommensurability of the length of the diagonal of a square to the length of its side had been discovered by the time of Plato, and its proof is by showing that on assumption of commensurability of those lines there follows the contradiction that whatever number of integral units composing the diagonal, the number is both even and odd. Peikoff rightly stresses that for Plato the perfect Forms are radically different from their empirical namesakes. Under the latter acquaintance, our knowing the Forms, so far as we do, is from memory of our full knowing of them in our existence before this life of perception, according to Plato: “Consider, he said, whether this is the case: we say that there is something that is equal. I do not mean a stick equal to a stick or a stone to a stone, or anything of that kind, but something else beyond all these, the Equal itself. Shall we say that exists or not? / . . . Most definitely / . . . / Whence have we acquired the knowledge of it? . . . Do not equal stones and sticks sometimes, while remaining the same, appear to one to be equal and to another to be unequal – Certainly they do. / But what of the equals themselves? Have they ever appeared unequal to you, or Equality to be Inequality? / Never, Socrates / . . . / Whenever someone, on seeing something, realizes that that which he now sees wants to be like some other reality but falls short and cannot be like that other since it is inferior, do we agree that the one who thinks this must have prior knowledge of that to which he says it is like, but differently so? / Definitely. / . . . / We must then possess knowledge of the Equal before that time when we first saw the equal objects and realized that all these objects strive to be like the Equal but are deficient in this” (Phaedra 74). Perceptibly equal things are deficient in that they can appear unequal in some occasions of perception. The Form Equal by contrast is always just that. Perceptibles “no more are than are not what we call them” (Rep. 479b). Plato does not clearly isolate PNC, but he was getting onto an ontological basis for it, so far as he did grasp PNC, by his characterizing what I should call his faux contradictions of empirical objects—faux because he fails to give square reality to situational and temporal determinates of objects and to our contexts of thought and speech about objects—as both being and not being, which is to say, deficient in being. It is fair enough to say, as Peikoff concludes, that for Plato PNC has the same standing in ontology and in our knowledge as such Forms as Being, Same, Other, Equal, and Inequal. Additional support, I notice, for that standing of PNC in Plato would obtain had Plato called out Identity as a Form, where Identity means what was said above at Euthd. 393b: an existing thing must be what it is. As later thinkers would observe, Identity in that sense entails PNC. Peikoff places Plato at the head of a sequence of philosophers who held PNC to be not learned from scratch by our experience in this world. They hold the principle to be in some sense innate and to be based on realities independent of the world we experience by the senses. In the innate-PNC sequence, Peikoff places later Stoicism (see Crivelli 2009, 393–94), Neoplatonism, early Christianity, Cambridge Platonism, and Continental Rationalism. Nearly all of these, I should note, are in a very different intellectual situation than Plato’s in that they have, directly or indirectly, Aristotle’s development of logic. The latter two certainly had as well his Posterior Analytics and Metaphysics. They had thereby Aristotle’s various formulations and accounts of PNC. They stand on the shoulders of both Plato (and Neoplatonism) and Aristotle, with innate-PNC being one of their leanings toward Plato along a line of difference with Aristotle. They had as well, unlike Plato or Aristotle, Euclid’s Elements, further mathematics beyond Euclid, and further developments in logic. By the time of Republic, Plato had evidently abandoned his view that we recognize Forms in our present life because we knew them well in a previous life free of the perceptual and variation spoilers of being (Tait 2005, 179). The recollection from a previous life is no longer mentioned. It remains for Plato that the Forms, such as are engaged in geometry, are accessed only by intellect, and not to be found in sensory experience nor abstracted from sensory experience. Peikoff was aware that some scholars had begun to question whether Plato had held on to his early express view that the realm of Forms was a world in which we had lived in a previous life and from which we now have some recollection of our previous knowing. Peikoff took Plato’s view as uniform on the recollection doctrine we saw in Phaedra. I’m persuaded to the contrary view. Peikoff rightly points out that through much of the history of philosophy the recollection view and the other-world-of-Forms view had been taken for Plato’s view, and Plato’s influence, pro or con, was under that picture. I think, however, that the separateness of a purely intelligible realm of Forms, a realm not also a prior world of life, Forms separate from empirical classes participating in them, is enough for saying Plato heads a line in which knowledge of necessary truths such as in geometry or in the rules of right reasoning (importantly PNC), even if their elicitation is by sensory experience, must be innate. That much, given Peikoff’s analysis of the significant senses of innate, is enough for sharp contrast with Aristotle and his line, and the dominance of the Good over all other Forms suffices, in a foggy way, for their normativity in the empirical world (Rep. 504d–11e, 533b-d; Philebus 20b–22e, 55d–60c, 64c–67a; Denyer 2007, 306–8). I mentioned the great difference, in Plato’s view, between the perfect Forms and their empirical namesakes. The bed one sleeps in is physically dependent on its materials and construction, but the bed constructed depends on the Idea or Form Bed, and the particular constructed bed is ontologically deficient in being when compared to the invariant full-being Bed, the Form on which the particular constructed bed’s being and name depends (Rep. 596–97). It is the rational, best part of the soul that measures and calculates, helping to rectify illusions in perceptual experience and to bring us nearer truth of being (Rep. 602c–603a). In geometry we employ diagrams, but our arguments and concern are for the Forms of these figures, not the particular constructed, material figures (Rep. 510b–511a; on the “mathematical intermediates” controversy, see Denyer 2007, 304–5; Tait 2002, 183–85). Even higher than our rational capability for geometry is our rational capability for proceeding from Forms to Form-Form relations to the first principle of all Being—and the necessary ultimate spring and harmony of all knowing—which for Plato is a Form, the Good. This purportedly highest process of knowing is called dialectic, a notch above thought even in geometry (Rep. 510b–511e; further, Denyer 2007, 306–8). Reviel Netz concludes “Greek mathematical form emerged in the period roughly corresponding to Plato’s lifetime” (1999, 311). He reports Hippocrates of Chios (not to be confused with the father of Greek medicine) as “first to leave writings on Euclidean subject matter,” say, around 440 B.C.E. (275). Hippocrates is credited with introducing the indirect method of proof into mathematics, which relies expressly on PNC. Netz concludes that “much of Greek mathematics was articulated in the Euclidean style” by around 360 B.C.E. (ibid.). Euclid’s Elements itself did not appear until about 300 B.C.E. Aristotle (384–322 B.C.E.) was attentive to this mature Greek mathematics, and he put it to some use in inference to and justification of the first principle that is PNC. Plato in his discussions of magnitudes and quantity (counts) stays rather distant from the systematization and rigor being given to mathematics in his day. Plato does make Form-hay from the circumstance that the idealized determinateness and exactitude supposed in geometry makes way for such knowledge as the relationships established in the Pythagorean Theorem (Meno 85–86), relationships that cannot be established so definitively by simply measuring sides of sensible triangles and squares, but require, rather, the operation of intellect on its own. Peikoff’s Platonic line of logical ontologists hold PNC to be innate knowledge, not learned from scratch from experience of the sensible world. Peikoff conceives this line to also consist in holding that essences provide what regularity there is in sensible nature. In Phaedo Plato has Socrates say: “I am speaking of all things such as Size, Health, Strength and, in a word, the reality of all other things, that which each of them essentially is” (65d). In this dialogue, Plato invokes a notion of the contrary, within which can be read the contradictory, when he has Socrates invoke the principles (i) what one is explaining cannot have explanations giving the thing to be explained contrary qualities and (ii) an explanation must not itself consist in incompatible kinds of things (97a–b, 101a–b). Here Plato argues that the only adequate explanations are explanations by the regulative essences of things (e.g. the fineness of fine things), or we might also say, by the regulative Forms (e.g. the Fine) in which sensible and mathematical things participate, directly or indirectly (95e–102b; see Politus 2010.) I notice the implication in these parts of Phaedo that PNC, as within the prohibition of incompatibilities in explanations or in things explained, is a principle whose ultimate ground must lie in the realm of essence, or Form, not in the realm of the sensible world, lest explanation fall into the swamp of the sensible. Peikoff observes that in Plato’s view the eternal, necessary essences, or Forms, do not require mind for their existence, but for the Neoplatonists and from Augustine to Cudworth and Leibniz, these essences and all necessary truths, such as PNC, do require mind for their existence (cf. Peikoff 2012, 24–25). In the line of logical ontologism extending from Plato, necessary truths exist in the eternal mind of God, they are prescriptive for the created empirical world, and they hold in the nature of that world. Their ultimate source and residence is the divine mind. Peikoff draws out four arguments advanced in the Platonic line for why PNC cannot be learned from sensory experience. One of them is that PNC is a necessary truth. The principle states not only that there are no true contradictions, but that there cannot possibly be any true contradictions. In the Platonic line, let me add, such a necessity could no more be known merely from empirical induction than could be known in that way the necessary truth that any triangle in the Euclidean plane must have angles summing to exactly two right angles. These philosophers and theologians take such necessity to flow from the divine eternal mind, the permanent residence of such eternal, necessary truths. I observe, however, that their view that physical existence per se and in the whole of it is contingent because there are contingent things within this our world is an invalid inference. I say that ‘existence exists’ can be a necessity at least partly the ultimate base and reference of the truth and necessity of any necessary truths. On this corrective, Peikoff had things to say in his essay “The Analytic-Synthetic Dichotomy” in The Objectivist three years after completion of his dissertation (also Peikoff 2012, 12; further, Franklin 2014, 67–81). I should add that for Plato, the necessity of necessary truths does not descend from a divine mind, lord of existence, mathematical and empirical, but from the Good, lord of all Forms and their traces in our reasoning on the mathematical and physical world. The Good is the Form dependent on no others. It is self-sufficient and is self-evident in a general way to human reason. It is the necessity that is source of all orderly necessity (Rep. 505c, 508d–509a, 511b–d; Philebus 20d, 60c, 64b–65a; further, Demos 1939, 35, 106, 307, 335). In my view, from Rand, all good is set in the highly contingent organization that is life. Then, I add, since the good does not have the ontological standing given it in Plato’s view, it cannot of itself (only a necessary-for) be the base of the sort of necessity had in necessary truths, truths such as the principle that, necessarily, there are no true contradictions. To be continued. References Charles, D., editor, 2010. Definition in Greek Philosophy. Oxford. Crivelli, P. 2010. The Stoics on Definition. In Charles 2010. Demos, R. 1939. The Philosophy of Plato. Scribners. Denyer, N. 2007. Sun and Line: The Role of the Good. In The Cambridge Companion to Plato’s Republic. G. R. F. Ferrari, editor. Cambridge. Franklin, J. 2014. An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan. Netz, R. 1999. The Shaping of Deduction in Greek Mathematics. Cambridge. Peikoff, L. 1967. The Analytic-Synthetic Dichotomy. In Ayn Rand: Introduction to Objectivist Epistemology. Expanded 2nd edition. 1990. Meridian. ——. 2012. The DIM Hypothesis. New American Library. Plato [d. 347 B.C.E.] 1997. Plato – Complete Works. J. M. Cooper, editor. Hackett. Politus, Y. 2010. Explanation and Essence in Plato’s Phaedo. In Charles 2010. Priest, G., Beall, J. C., and B. Armour-Garb, editors, 2004. The Law of Non-Contradiction. Oxford. Tait, W. 1986. Plato’s Second-Best Method. In Tait 2005. ——. 2002. Noēsis: Plato on Exact Science. In Tait 2005. ——. 2005. The Provenance of Reason. Oxford. ~~~~~~~~~~~~~~~~ My remarks in this post concerned issues undertaken by Peikoff 1964 (the first two of his five chapters) on Platonist perspectives on the epistemological and the ontological standing of PNC. My next post will concern Peikoff’s third and fourth chapters, on Aristotelian perspectives on those standings. In a third post, I’ll address Peikoff’s fifth chapter, on the demise of classical logical ontologism and some alternatives to it that were adopted.
  3. Thanks! The sound in this production is a poem plus. I close my eyes to enjoy it best. Ode to a Nightingale
  4. . Religious Liberty or Religious License? Legal Schizophrenia and the Case against Exemptions Tara Smith – Journal of Law and Politics (25 April 2017) Abstract
  5. . Patrick, how would having a power of judgment capable of errors make one’s judgment anything but a judgment requiring a judging subject? Would requiring-a-subject additionally make an activity subjective in the sense of not tracking reality? Also, the sort of subjectivity I possess by my enjoyment of being in the woods alone is one sort. Wariness of wet stone in my hike requires my subjectivity in a very different sense.
  6. . ARISTOTLE RESURGENT – Allan Gotthelf Memorial Conference Series May 22–24, 2017, at the University of Pittsburgh. Anyone interested in these topics is welcome to attend.
  7. . "you people" <--- laziness on your part, Mr. Cunningham. There is no such monolithic thinking at this site. Rand's meaning of reason was express, and that was "the faculty that identifies and integrates the material provided by the human senses." In case you have some no-sloth interest in that concept of reason: this. My take on contemporary direct perceptual realism: A. D. Smith Contemporary direct perceptual realism from an Objectivist perspective: David Kelley
  8. New Anti-Kant František Příhonský S. Lapointe and C. Tolley, translators The full title is New Anti-Kant, or Examination of the Critique of Pure Reason according to the Concepts Laid Down in Bolzano’s Theory of Science. This book was published in 1850. Its author was a student and friend of Bernard Bolzano.* New Anti-Kant and Bolzano’s Theory of Science (Wissenschaftslehre, 1837) came into full English translation only last year. Until I read these books and recent works of contemporary scholars concerning Bolzano’s philosophy, I had known of Bolzano only slightly, by the brief remarks of Frederick Copleston in A History of Philosophy; and I had known the name Bolzano-Weierstrass Theorem* from a text on Real Analysis I had studied decades past. In recent years, a critical edition of the entire body of Bolzano’s works has been underway, and his major works are being translated into French and English. Bernard Bolzano has, at last, become recognized as one of the great philosophers of the nineteenth century. Not great in influence. Great in vista. My interest in Bolzano for my own book and philosophy caught fire when I noticed a certain closeness to Rand in his foundations of theoretical philosophy. I treat that logical kinship and its differences with Rand in my book. Of interest there is Bolzano’s conception of a general ground-consequence relation and its relations to deducibility and causality (and to Kant’s ground-consequence relation). I reform it for my own foundational work, closer to Rand’s. Of interest also for that project is Bolzano’s analysis, contra Kant, of the nature of concepts in relation to experience, the purely conceptual nature of pure mathematics, the nature of deduction, and the relations among logic, mathematics, and our empirical sciences. Logic and mathematics were known as science to Bolzano, and his monumental four-volume Theory of Science is importantly theory of logic in a broad sense. New Anti-Kant was written by Příhonský in close collaboration with Bolzano in the last years of Bolzano’s life. It was published two years after Bolzano’s death. It is called New to distinguish it from an earlier, then-known (and inept) work titled Anti-Kant (1788*) and to indicate that the case against Kant’s first Critique in Příhonský’s book is a fresh one. New Anti-Kant did not receive much comment from scholars at the time. For me it is a help for further grasp of Bolzano’s views. In the present note, I’d like to mention some remarks of Příhonský concerning influence of Kant’s philosophy which resemble some views of Rand on Kant’s influence, a topic that will not fit in my own book. In his Preface, Příhonský pauses to forestall the impression one might get from the book’s title that he and Bolzano (not idealists of any stripe) thought Kant had done nothing good by his philosophic writings. Příhonský’s corrective to that possible presumption provides a window into how Kant was being viewed, and lauded, by some of his well-versed opponents as of 1850 in German lands. One laudation from Příhonský concerned ethics: Rand wrote in 1960 “Kant’s expressly stated purpose was to save the morality of self-abnegation and self-sacrifice. He knew that it could not survive without a mystic base—and what it had to be saved from was reason” (FNI). The extent to which Kant was undermining reason in Rand’s meaning of the term needs to be detailed by consideration of how Kant had characterized perception and its relations to concepts and how he had characterized (partly affirming and partly limiting the) powers of understanding, reason, and judgment.* Where Rand wrote “expressly stated purpose,” she likely meant the Kant passage in the Introduction to the second edition of Critique of Pure Reason (KrV) at Bxxx about knowledge and faith.* She slides from faith to Judeo-Christian morality. That slide is not too wrong, considering what Kant did subsequently in moral theory. His is not altruism, to be sure. His is a partial self-sacrifice at base, but that sacrifice, so far as it is in the base, is not for the sake of others. His base shadows the First Commandment. Kant’s moral ideal entails of course only self-authored self-sacrifice. In his early formal education at Königsberg’s Collegium Fredericianum (from age 8 to 16), Kant would have memorized Luther’s Small Catechism and studied the Large. He would know Luther’s explication of the First Commandment. In the Lutheran doctrine, God is the source of goodness in the world. Every good in the world—health, wealth, and family—are gifts from God. Every right gift one might give to another or receive from another, must be seen as a gift from God. It is more than a pleasing coincidence that the words Gott and Güte are so similar. God commands that one’s heart and mind be set first and foremost on God. He will bring good things, temporal and eternal, to people who follow this commandment, and he will bring woe to people who put other goods in first place, higher than God. To keep the true God in first place, one must have the right heart and head, the right faith. Luther: “Believe in Christ and do your duty.” In his secular construction of morality, Kant would give to a good will the role Luther had given to a right faith. Kant wants to keep with individual necessary reward and penalty for individual condition of will, and he thinks he can find this necessary connection right here in the constitution of human will and reason. Beyond the sure sanctions for a good will is the hope of happiness in this life and hereafter.* Contradicting what Příhonský would say later, Schopenhauer (1839) had indicated a number of ways in which Kant’s ethics profoundly favors egoism, which Schopenhauer took to be a demerit of Kant’s theory. How much of this contradiction is surface and how much substantial, I’ll leave open in this remark. But I should enter a caution about Příhonský’s characterization of the condition of German ethical theory at mid-century. In his criticisms of the portions of Critique of Pure Reason outlining Kant’s ethics, we read some encouraging metaethical tenets of Bolzano-Příhonský. When common sense “determines the good nature or wickedness of an action to be performed, it usually weighs the advantages and disadvantages that can reasonably be expected from it, i.e. its influence on the welfare of the living” (Příhonský 1850, 128). Moreover: Those propositions combined with one conception of the nature of life give later in the century the moral theory of Jean Marie Guyau;*\* more recently, with another conception of life, the moral theory of Ayn Rand; and with yet another conception of life, the theory of Richard Kraut.* With Bolzano-Příhonský, we get a leap from those quoted propositions straight away to still another moral theory, again an anti-Kantian one: utilitarianism, which they rate excellent for its unselfishness. Many earlier thinkers, though not all, connected utilitarianism with conscious or unconscious psychological egoism (Windelband 1901, II.513–18). Příhonský’s picture of ethical egoism as a dead theory in his era in German lands might well be an exaggeration, an aim at death by reporting death, or it might be the true situation and the truth about Kant’s role in bringing it about. I speculate the truth is somewhere in between. Devotees of the subjective egoism of Max Stirner there may have been, quietly, secretly. Modest currents of egoism from Aristotle, from Judaism, Spinoza, and Heine, and from Christian personalism surely continued in the culture. But until the last decade or so of the century, until the entry of Nietzsche into the melieu, there was evidently no forthright ethical egoism (anti-ethical in some moments) publicly squaring off against Christian and Kantian self-sacrifice as moral virtue and gaining at least some popular following, if not academic following. At the end of the nineteenth century, Wilhelm Windelband writes: Of Kant and his first Critique, Rand writes: That sounds to me like someone who actually opened the book and gave it a try. Which translation would that have been? The best at that time in English would have been the one by Norman Kemp Smith. That was the translation of KrV in my hands 1971–1997. The book became a step less opaque with the new translations (plus copious notes and ample index), by Werner Pluhar in 1996 and by Paul Guyer in 1998. When I first read Rand’s remark that KrV rests on no definitions, I was taken aback a little. Kant defines analytic, concepts, contingency, empirical, experience, faith, freedom, happiness, and on and on through the alphabet. He has incorrect views, in my assessment, of empirical and philosophical definitions and conceptual change, views at odds with Rand’s, although these views held by Kant were perhaps unknown to her. Kant writes: “To define, as the term itself yields, is in fact intended to mean no more than to exhibit a thing’s comprehensive concept originally within its bounds” (A727 B755). To that statement, he attaches a footnote: In the case of empirical concepts, Kant argues that with the growth of knowledge of an object some characteristics in the object’s concept may need to be removed, or new characteristics may need to be added. Therefore, the concept is never securely bounded. For philosophical concepts, which Kant thinks of as a priori concepts, such as substance, cause, or right, he argues: Příhonský has important criticism of those views of Kant, starting with Kant’s notion of a priori concepts as independent of all experience (24–25). I’ll close with a lamentation of Příhonský over the effect of this section of KrV on German philosophy to the middle of the nineteenth century. References Bolzano, B. 1837. Theory of Science. P. Rusnock and R. George, translators. 2014. New York: Oxford University Press. Copleston, F. A History of Philosophy. Vol. 7, Pt. 2. Garden City: Image. Kant, I. 1781, 1787. Critique of Pure Reason. W. S. Pluhar, translator. 1996. Indianapolis: Hackett. Příhonský, F. 1850. New Anti-Kant. S. Lapointe and C. Tolley, translators. 2014. Basingstoke: Palgrave MacMillan. Rand, A. 1960. For the New Intellectual. In collection by that title. New York: Signet. ——. 1973. Untitled Letter. In Philosophy: Who Needs It? 1982. New York: Signet. Windelband, W. 1901. A History of Philosophy. Expanded edition. New York: Harper.
  9. Greg and Dennis, thanks for this discussion and information. I've not studied Campbell, but I've studied Galt's Speech, and that is squarely a message of salvation. It is a layout for one's liberation from false personally destructive doctrines that have saturated one's cultural setting all one's life. It tells how to break out of those doctrinal clutches, including those offering the fake salvations from death. It offers the salvation of having this life, this holy.
  10. . Korngold Marietta's Lied I Went to Him
  11. Seventh SB excerpt: "As an aside, I’d like to mention that the professor for that course would have been Aleksandr Ivanovich Vvdenskii, not Nikolai Onufrievich Losskii, whom Rand had later recalled to have been the professor. Chris Sciabarra wrote a rebuttal to Milgram’s conjecture in his second edition of Ayn Rand: The Russian Radical. I read Dr. Sciabarra’s rebuttal before reading Miligram’s own case, but upon reading the latter, I found it to be the more likely. I should mention, however, that even if Sciabarra were wrong about the identity of the professor, because Rand’s recall was in error, and hence about what was in the course, it could still be the case that ideas of Losskii influenced Rand in the facets proposed by Sciabarra (B. Branden did not buy this, and I'm doubtful myself). Beyond that, what is always more to my own interest and sense of importance, is the correct logical relation of the philosophy of philosopher A to philosophy of B, and that is something that can be worked through (well or poorly) quite apart from any historical influence. (Consider also the posts of Chris Sciabarra in this thread.)"
  12. . Here are some writings on seeing aspects of self by mirrors of self—particularly by mirrors of self in others—these writings being before Objectivist nonfiction writings on psychological visibility. Plato Alcibiades 1 132e–33c –Richard Sorabji, translator ~~~~~~~~~~~~~~~~ Shakespeare’s Julius Caesar Cassius: Tell me, good Brutus, can you see your face? Brutus: No, Cassius; for the eye sees not itself / But by reflection, by some other things. Cassius: ‘Tis just; / And it is very much lamented, Brutus, / That you have no such mirrors as will turn / Your hidden worthiness into your eye, / That you might see your shadow. . . . And, since you know you cannot see yourself / So well as by reflection, I, your glass, / Will modestly discover to yourself / That of yourself which you yet know not of. ~~~~~~~~~~~~~~~~ Herder’s Treatise on the Origin of Language (1772) If for human’s instinct must disappear, “then precisely thereby the human being receives ‘more clarity’. Since he does not fall blindly on one point and remain laying there blindly, he becomes free-standing, can seek for himself a sphere for self-mirroring, can mirror himself within himself” (82). ~~~~~~~~~~~~~~~~ Hölderlin’s Hyperion (1794) “Where is the being that knew her as mine did? in what mirror did the rays of this light converge as they did in me? was she not joyfully frightened by her own gloriousness when she first became aware of it in my joy?” “. . . when the dear being, more faithfully than a mirror, betrayed to me every change in my cheek . . . .” ~~~~~~~~~~~~~~~~ We the Living (1936 edition) In the first meeting of Kira and Leo: “Her face was a mirror for the beauty of his (58).” “He looked into her flaming eyes with eyes that were like mirrors which could reflect a flame no longer” (445). The setting is Kira urging Leo to continue the struggle for a free life, even though he no longer desires such life. The Fountainhead. (Page citations are from the 1943 first edition; all emphases are mine.) The steel frame of Howard Roark’s house for Austen Heller has been erected. On site the workers notice that Roark’s hands “reach out and run slowly down the beams and joints.” Workers say “‘That guy’s in love with the thing. He can’t keep his hands off’.” Absorbed in work at the site, Roark’s “own person vanished,” but “there were moments when something rose within him, not a thought nor a feeling, but a wave of some physical violence, and then he wanted to stop, to lean back, to feel the reality of his person heightened by the frame of steel that rose dimly about the bright, outstanding existence of his body at its center” (138). Of Roark the morning after first time with Dominique: “In some unstated way, last night had been what building was to him; is some quality of reaction within him, in what it gave to his consciousness of existence” (231–32). Of Dominique’s visits to Roark’s room and bed. “In his room, there was no necessity to . . . erase herself out of being. Here she was free to resist, to see her resistance welcomed by an adversary too strong to fear a contest, strong enough to need it; she found a will granting her the recognition of her own entity . . . . / . . . . It was an act of tension, as the great things on earth are things in tension. It was tense as electricity, the force fed on resistance . . .” (301). On their last time, before they are separated for years, Roark says “‘I love you, Dominique. As selfishly as the fact that I exist. . . . I’ve given you . . . my ego and my naked need. This is the only way you can wish to be loved. This is the only way I can want you to love me’” (400). Roark and Dominique are definite entities, definite selves, exposed to each other. Their tensed sexual occasions heighten awareness of their selves, awareness of each to own-self and to other-self. (Cf. Sartre’s Being and Nothingness 1943, 505–14 in the translation by Hazel Barnes.) In her marriage to Keating, Dominique is a non-entity. (No tension, strength, resistance, or ecstasy in bed.) Keating is a non-entity in most of his existence. Most all of his desires and candidate desires and most all of his opinions receive their value to him by their potential for impressing others. Dominique is a mirror to him, and she makes herself not more than a mirror (452–55). She says to Keating: “‘You wanted a mirror. People want nothing but mirrors around them. To reflect them while they’re reflecting too. You know, like the senseless infinity you get from two mirrors facing each other across a narrow passage. . . . Reflections of reflections . . . . No beginning and no end. No center and no purpose’”(455). Of Wynand and Dominique: “She sat at her dressing-table. He came in and stood leaning against the wall beside her. He looked at her hands, at her naked shoulders, but she felt as if he did not see her; he was looking at something greater than the beauty of her body, greater than his love for her; he was looking at himself—and this she knew, was the one incomparable tribute” (537–38). Atlas Shrugged (1957, page – first edition) “. . . her pride in herself and that it should be she whom he had chosen as his mirror, that it should be her body which was now giving him the sum of his existence, as his body was giving her the sum of hers” (957).
  13. . OCON 2017 - Pittsburgh
  14. . These Words These words we read from some desire . . that someone live . . the this entire. Read is our reach, . . our grasp, our be . . life that is know . . wings that are free. Copyright Stephen C. Boydstun 2016
  15. . Hi Ilya, thank you for all the thinking comments. No, I haven’t yet gotten to read Collin’s book. On Reid and Kant, the great help is Manfred Kuehn’s Scottish Commonsense in Germany 1768–1800. I wondered in what ways you think of Descartes as having a great influence on Kant. Is it because of Kant’s attraction to the a priori? But wouldn’t that be a long inheritance starting back at Plato, not at Descartes? Kant did not buy Descartes’ metaphysical scheme of extension and thought. And Kant did not seem to take the Cartesian form of skepticism seriously, unlike his seriousness with Humean skepticism. Leibniz had earlier shredded Descartes’ skeptical-doubting way to sure knowledge; perhaps that had an effect on Kant. I do recall some striking concord with Descartes' concept of motion (and significant deviations from Newton's dynamics) in Kant's Metaphysical Foundations of Natural Science. I’ve lately been studying Alcinous’ The Handbook of Platonism (c. 150). He’s got Aristotle and the Stoics as articulators of implicit systematic doctrine in the Dialogues of the perfect master Plato. Even the syllogistic, invented by Aristotle, is credited to Plato. Yes, Alcinous was a go for the negative way, among other ways more positive. From the negative spiel: “God is ineffable and graspable only by the intellect [intuitive intellect, I think], as we have said, since he is neither genus, nor species, nor differentia, nor does he possess any attributes, neither bad (for it is improper to utter such a thought), nor good (for he would be thus by participation in something, to wit, goodness), nor indifferent (for neither is this in accordance with the concept we have of him), nor yet qualified (for he is not endowed with quality, nor is his peculiar perfection due to qualification) nor unqualified (for he is not deprived of any quality which might accrue to him). Further, he is not a part of anything, nor is he in the position of being a whole which has parts, nor is he the same as anything or different from any thing; for no attribute is proper to him, in virtue of which he could be distinguished from other things. Also he neither moves anything, nor is he himself moved.” (165, 5–17) Translation of John Dillon (1993).
  16. . She saved my life.
  17. . Who Is Ayn Rand? Ayn Rand in Her Own Words
  18. Mysticism – Kant and Rand Reason Rand gives to Ellsworth Toohey the voice for some of her thinking on how certain false ideas compromise independent rational judgment, thereby making an individual ready for rule by the authority of others. Toohey speaks to Keating: When I was a youth, in high school, I was still religious. I had originated a saying: Logic in life is faith. I had not yet studied any logic, but of course one knows something about it before entering one’s first class or opening one’s first textbook on it. (I became an atheist at eighteen, shortly before reading Rand.) When Rand wrote The Fountainhead, published when she was thirty-eight, she knew quite a bit about logic and quite a bit about reason. Rand had some exposure to Kant by the time she wrote We the Living, for she refers to him in that work (1936). She uses the word transcendental in both Living and Fountainhead, although in these usages, the sense is as contrast with square perception and with immanent practicality. One definition of transcendental in American Heritage is “rising above common thought or ideas; exalted; mystical.” Rand joins the notions of saintliness and nobility more than once in Fountainhead. She expresses the radiant aspect of religion in what Toohey tells Stoddard to tell Roark in order to persuade Roark to build the Temple of the Human Spirit. She again expresses that radiant aspect in Dominique’s testimony at the court case over the temple. Dark aspects of religion are also not neglected in Fountainhead. The testimonies of Toohey and Keating at the trial express them, and the link between religion and socialism is remarked in several places in the novel. It is tempting to read Rand’s “just say that reason is limited” in Toohey’s technique as an allusion to Kant (see also 1961a, 18). Whether the statement is such an allusion or not, Rand certainly was speaking in the passage I quoted to anyone who was caught in the tension between reason and faith. In Atlas Shrugged the following is likely an allusion to Kant’s bifurcation of things as they are in themselves and things as they are in our sensory and rational cognition of them: “‘Things as they are’ are things as perceived by your mind; divorce them from reason and they become ‘things as perceived by your wishes’” (1957, 1036). A few paragraphs later, Rand tells the religionist: “Whenever you committed the evil of refusing to think and to see, of exempting from the absolute of reality some one small wish of yours, whenever you chose to say: Let me withdraw from the judgment of reason . . . the existence of God, let me have my one irrational whim and I will be a man of reason about all else—that was the act of subverting your consciousness, the act of corrupting your mind” (1037). Rand was not opposed to feelings. She was not against the idea of the human soul, provided it is thought of as naturally part of one’s living body and mortal as one’s body. In Fountainhead she has dialogue between Keating and his wife Dominique in which soul is given the expressly nonreligious meaning: that in one that is one’s genuine person—not only one’s body—one’s will and meaning, that in one which independently thinks, values, decides, and feels (GW II 454–55; cf. 1957, 1057). In Fountainhead religion that entails belief in the supernatural is taken to be false. It is not presented, however, as something needing to be abandoned for the sake of human independence and freedom. It is not expressly taken as subversive of those good things. That changes in Atlas, wherein all religion holding forth the supernatural is openly opposed as inimical to human life and freedom. There religion is proclaimed to be mysticism. I agree. (See also Peikoff 1991, 183–84; Underhill 1925.) In Fountainhead the classification mysticism had not been given directly to the Judeo-Christian belief in God. It was given to religion of the ancient Egyptians. It was maintained that such mysticism and atheistic dialectical materialism were only “‘superficially varied manifestations of the same thing’” (HR VI 600). Earlier in the novel, Rand had Toohey iterate and reiterate that the central moral teachings of Jesus and socialism were like peas in a pod. Rand had made clear that belief in God was mistaken and partly at odds with human life and achievement on earth (PK III 45). She had stopped short of pronouncing belief in God mystical. Early in Galt’s radio speech in Atlas, Rand attacks as mystical the common belief that there is a supernatural power called God, who issues moral commands based on whim, and to whom one must dedicate one’s life (1011). There are no ghosts in heaven (1012). There is no “mystic God with some incomprehensible design” (1025). Rand attacked the old conception of man as divided into two antagonists: soul, which “belongs to a supernatural realm,” and body, which is “an evil prison holding it [soul] in bondage to this earth” (1026). This division denies the reality of mind, the living self, as sovereign of human life. Without reason, man is left as a battleground of two monsters, “of a body moved by unaccountable instincts and of a soul moved by mystic revelations” (1026). Around this division are gathered two competing congregations against man’s life and happiness. These camps are known as spiritualists and materialists, which Rand characterized as the mystics of spirit and the mystics of muscle (1027). In reality, on earth, both mystical schools “want their consciousness to be an instrument not of perceiving but of creating existence, and existence to be not the object but the subject of their consciousness—they want to be that God they created in their image and likeness, who created a universe out of a void by means of arbitrary whim. . . . They want an omnipotent power over existence; instead, they lose the power of their consciousness” (1036–37). The underlying bond between religious mysticism and secular dialectical materialism in The Fountainhead has been expanded into a bond of spiritualism and materialism in Atlas Shrugged, which bond is called mysticism by Rand. She had introduced the latter two variants of mysticism by way of repudiating all dichotomies between soul and body. In 1961 Rand posed the opposition between reason and mysticism as underlying not only the soul-body dichotomy, but other false dichotomies as well: mind v. heart; liberty v. equality; and practical v. moral (1961b, 88). The fundamental opposition is between reason, “the faculty which perceives, identifies, and integrates the material provided by man’s senses,” and mysticism, “the claim to some non-sensory, non-rational, non-definable, supernatural means of knowledge” (1961b, 89; cf. Russell 1914, 6–7). Mysticism is the belief that “man’s mind is impotent” and that “man must be guided by some irrational ‘instinct’ or feeling or intuition or revelation, by some form of blind, unreasoning faith” (ibid., also 1960 62–63; cf. Russell 1914, 9–14). That definition of mysticism is close to one in American Heritage. One meaning of mysticism is “belief in the existence of realities beyond perceptual and intellectual apprehension, but central to being and directly accessible by intuition.” Another meaning of mysticism is “confused and groundless speculation; superstitious self-delusion.” Rand includes this second sense also with her concept of mysticism, for she writes that it is “the acceptance of allegations without evidence or proof, either apart from or against the evidence of one’s senses and one’s reason” (1960, 62). Certainly it is self-delusional to turn to supernatural dimensions through which simply wishing will make so (further, Rand 1957, 1035–36). In Atlas Rand had characterized mystics of spirit as believing in consciousness without existence (1027). She had characterized mystics of muscle as believing in existence without consciousness (1027; on this side of the coin, see also Efron 1968; Rand 1972; and Peikoff 1991, 33–35). In the context of those characterizations of the two kingdoms of mysticism, existence is preeminently material existence (1027). Schools of philosophy denying the reality of matter are called idealism. (Continued)
  19. . The Status of the Law of Contradiction in Classical Logical Ontologism Leonard Peikoff – Ph.D. Dissertation (NYU 1964) Leonard Peikoff first met Ayn Rand when he was seventeen. That was in 1951. His cousin Barbara Wiedman (later Branden) had become a friend of Rand’s in the preceding year. The young friends of Rand had read and been greatly moved by her novel The Fountainhead, and they were greatly impressed with Rand and her philosophical ideas as conveyed to them in conversation with her. In 1953 Peikoff moved to New York from his native Canada (where he had completed a pre-med program) and entered New York University to study philosophy, which was his passion. He was able to read Atlas Shrugged in manuscript form prior to its publication and to converse with its author. He continued at NYU for his Ph.D. in Philosophy, which he completed in 1964. That was the year Allan Gotthelf entered graduate school in Philosophy. Ayn Rand and her distinctive ideas on metaphysics and logic, as published in 1957 in Atlas Shrugged, do not appear in Peikoff’s dissertation. Except for one modest point, his treatment of his topic is consistent with Rand’s views on metaphysics and logic, as well as with her thought on universals (ITOE 1966–67) and her broad-brush arc of the history of philosophy. His dissertation is worthy of study, certainly by me, for what have been many of the positions and arguments concerning the ontological status and epistemological origin of the Principle of Noncontradiction (PNC) in Western philosophy from Plato to mid-twentieth century. It is valuable as well for a picture of what Peikoff could bring to the discussions with Rand and her close circle, as well as to their recorded lectures and published essays (including his own “Analytic-Synthetic Dichotomy” published by Rand as an immediate follow-on to her ITOE) in the ten years or so after 1957. A speculative sidebar: Beyond Rand’s philosophy, I doubt that Leonard Peikoff ever had anything to learn from Nathaniel Branden in philosophy. The flow of learning in philosophy not Objectivism was likely entirely the other way. That goes for the flow of reliable information in that domain as well between Peikoff and Rand. By the late ‘60’s, Peikoff, and Rand too, could of course learn from the studies of Gotthelf in Greek philosophy. I’ll sketch and comment on the course of the intellectual adventure that is Peikoff’s dissertation in a separate thread in Books to Mind. I’ll do that shortly. In the present thread, I want to just state his broad thesis (i–viii, 239–49), then turn (i) to the Kant resources Peikoff had available and relied upon in his story and (ii) to setting out from my own available resources, these decades later, what were Kant’s views and teachings on logic, what was always available in German, and what now in English. Under the term classical in his title, Peikoff includes not only the ancient, but the medieval and early modern. By logical ontologism, he means the view that laws of logic and other necessary truths are expressive of facts, expressive of relationships existing in Being as such. Peikoff delineates the alternative ways in which that general view of PNC has been elaborated in various classical accounts of how one can come to know PNC as a necessary truth and what the various positions on that issue imply in an affirmation that PNC is a law issuing from reality. The alternative positions within the ontology-based logical tradition stand on alternative views on how we can come to know self-evident truths and on the relation of PNC to the empirical world, which latter implicates alternative views on the status of essences and universals. Opposed to the classical logical ontologists are contemporary conventionalist approaches to logical truth. Peikoff argues that infirmities in all the varieties of classical logical ontologism open the option of conventionalism. He mentions that his own sympathies are with logical ontologism. Alas, repair of its failures lies beyond the inquiry of his dissertation.
  20. . Peikoff’s squarely secondary source on Kant (d. 1804), relied upon in his dissertation, is Prolegomena Logica: An Inquiry into the Psychological Character of Logical Processes (1860, 2nd ed.). The author is Henry Longueville Mansel (1820–1871), an English philosopher, theologian, and priest. In philosophy he esteemed and followed broadly the Scottish thinker Sir William Hamilton (1788–1856). That is not the Sir William Hamilton we adore today. Our hero, the bringer of Hamiltonian Mechanics and inventor of quaternions was not from Edinburgh, but Dublin (1805–1865). William Hamilton of Edinburgh was a barrister, but with interest in research in formal logic and interest in German philosophy. He introduced Kant to English readers and tried to show harmony between Kant and the Scottish philosophers of Common Sense, such as Thomas Reid. In Prolegomena to any Future Metaphysics (1783, 4:257–60, 369–71), Kant had cut down the possibility of success of Reid, Oswald, and Beattie in their appeals, however popular, to common sense for answer to Hume’s request for a warranty of thinking there to be any necessary connection between distinct events. Common sense, necessary and welcome as it is in the domain of its natural function, can only sensibly bear on that domain of perceptually manifest patterns (including applied mathematics), and it cannot be used to warrant any a priori principles, such as causality, contained in those patterns. Common sense cannot sensibly run on beyond its right domain and answer metaphysical questions. To the considerable fortune of our time, I should note the scholarship of Manfred Kuehn (1987) in tracking down the many ingresses of Scottish Common Sense philosophy to German lights, including Kant, in Scottish Common Sense in Germany 1768–1800. Henry Mansel tells us in Prolegomena Logica that his own views are greatly indebted to Kant and to William Hamilton of Edinburgh, although, his own views do not coincide perfectly with either of theirs. One shared aim of Hamilton and Mansel was to concoct a bound to confound secular reason in its all-too-common vistas of materialism, atheism, and clockmaker deism. In 1858 Mansel gave a controversial lecture “The Limits of Religious Thoughts” plotting the old line that because we have no positive notions of God, the unconditioned, or the absolute (absolute in the senses: free from any relation as a condition of its existence or [ii] out of any relation to human knowledge), reason must be supplemented with faith, and no criticisms of theology based on human conceptions are valid. Follow-on treatises were lobed between J. S. Mill and Mansel. C. S. Peirce (b.1839) was very familiar with the writings of William Hamilton of Edinburgh and the writings of Henry Mansel. In a personal manuscript of 1864: “I hold the Doctrine of Common Sense to be well fitted to Reid’s philosophical caliber and about as effective against any of the honored systems of philosophy as a potato-pop-gun’s contents might be against Gibraltar” (I.153). Peirce criticized Hamilton’s organization of syllogistic, with Hamilton’s quantification over predicates, in an 1865 lecture at Harvard (I.294–98). In 1886 Peirce would write: “The quantification of the predicate, an idea originating with the botanist George Bentham, was for some years in vogue in this country and in England. It was developed with a singular defect of clear thought by Sir William Hamilton, and more ably by Stanley Jevons. . . . If the theory of the syllogism had been extended to relative terms, the quantification of the predicate might have been useful; but in the hands of Sir William Hamilton it only led to a complicated syllogistic, full of blunders; in the hands of Jevons, it stood in the way of a better development of a meritorious system of formal logic.” (V.352–53). Peirce was not impressed with Hamilton’s efforts of innovation in formal logic, which were a dim prospect anyway for Hamilton, who was short on mathematics. The spring of formal logic with reaches far beyond its medieval spring would first sing, in 1847, in George Boole. I shall be returning to this nineteenth-century chorus in my other thread of straight-off survey and discussion of Peikoff’s dissertation. Peirce wrote a paragraph during the winter of 1869–70 remarking on Henry Mansel’s Prolegomena Logica: “Now if you examine Hamilton’s logic or any of those logics which are the immediate product of pure Kantianism as his was (—not his [Hamilton’s] peculiar system but his lectures in which his system does not appear as it was worked up later) you will find logic defined as the Science of Thought as Thought—or something of that sort. . . . Take for example Mr. Mansel’s admirable Prolegomena Logica where the Kantian conception of logic is developed in the most consistent and beautiful manner.” (II.349) I’ll just see about that. We are ready now for the Peikoff dissertation itself, for that other thread. ~~~~~~~~~~~~~~~ The citations for Peirce in the preceding are from Writings of Charles S. Peirce – A Chronological Edition (Indiana). By the way, Hamilton’s Lectures on Logic and Metaphysics [1859], an entry in Peikoff’s bibliography, is available for free online at archive.org.
  21. . Normativity of Logic – Kant v. Rand Stephen Boydstun 2009 In the perspective of Immanuel Kant, reasoning in accordance with logic can falter due to various empirical circumstances of the reasoning mind. Knowing those pitfalls and how to avoid them is what Kant would call applied logic. Principles of applied logic are partly from empirical principles. As for the principles of pure logic itself, logic apart from such applications, “it has no empirical principles” (B78 A54). The principles of logic are not principles of empirical psychology, and their ultimate authority stems from something deeper than empirical necessities of thought. Logic for Kant was Aristotelian logic. [Or so Kant thought. Stoic logic had been mixed into what he took for simply logic and credited to Aristotle.] He thought this discipline to have been set out completely by Aristotle, and he thought such finality of the discipline was due to the distinctive character of the discipline that is logic. “Logic is a science that provides nothing but a comprehensive exposition and strict proof of the formal rules of all thought” (Bxiii). The office of logic is “to abstract from all objects of cognition and their differences; hence in logic the understanding deals with nothing more than itself and its form” (Bix; B170 A131). Logic is “vestibule” of the sciences in which we acquire knowledge. Logic is presupposed in all judgments constituting knowledge (Bix). Knowledge requires the joint operation of a receptivity of the mind and a spontaneity of the mind. In our receptivity, sensible objects are given to us. In our spontaneity of conceptualization and judgment, those objects are thought (B29 A15). Sensory presentations are givens. The spontaneity of cognition is the ability to produce presentations ourselves. Kant calls understanding the faculty for bringing given sensible objects under concepts and therewith thinking those objects (B74–75 A50–51). Logic is “the science of the rules of the understanding as such” (B76 A52). These are “the absolutely necessary rules of thought without which the understanding cannot be used at all” (B76 A52). Kant distinguishes the faculty of understanding from its superintendent, the faculty of reason. The understanding can arrive at universal propositions by induction. Correct syllogistic inferences among propositions are from reason (B169 A130; B359–60 A303–4). By its formal principles, reason provides unity to the rules of understanding (B359 A302). I should mention that it is not the role of reason (or of understanding) in logic that Kant tries to curb in his Critique of Pure Reason (B=1787 A=1781). This role Kant takes as within the proper jurisdiction of reason. Kant regards logic as “a canon of understanding and of reason” (B77 A53; B170 A131). A canon is a standard or rule to be followed. How can rules of logic be rules to be followed by the understanding if they are the rules that characterize what is the form of all thought? How can the rules prescribe for X if they are descriptive of what X is? Let X be alternatively the faculty of understanding or the faculty of reason, the question arises. Kant calls such logic general logic, and this he takes as abstracting away “from all reference of cognition to its object” (B79 A55). This conception of logic is significantly different from that of Rand: Logic is an art of identification, regimented by and towards the fact of existence and the fact that existence is identity. Over a period of forty years, Kant taught logic at least thirty-two times. Syllogistic inference and non-contradiction were the rules for formal logic. Kant took these rules to concern some of the requirements for truth. They do not amount to all of the requirements for truth, “for even if a cognition accorded completely with logical form, i.e., even if it did not contradict itself, it could still contradict its object” (B84 A59). That much is correct, and Kant is correct too in saying that “whatever contradicts these rules is false” (B84 A59). Why? “Because the understanding is then in conflict with its own universal rules of thought, and hence with itself” (B84 A59). How can the normativity of logic be accounted for if its principles are taken for correct independently of any relations they might have to existence and any of the most general structure of existence? Kant needs to explain how general logical norms for our thinking can be norms without taking their standard from the world and how such norms can be rules restricting what is possibly true in the world. Might the source of norms for the construction of concepts be the source of norms for inferences when concepts are working in judgments? Can the normativity of forms of inference among judgments be tied to normativity in forms of judgments and normativity in the general forms of concepts composing those forms of judgment? What requirements must concepts meet if they are to be concepts comprehending particulars in true ways? From the side of the understanding itself, the fundamental forms concepts may take are required to be systematically interconnected to satisfy the circumstance that the understanding “is an absolute unity” (B92 A67). Considered apart from their content, concepts rest on functions. “By function I mean the unity of the act of arranging various presentations under one common presentation” (B93 A68). So far, so good, but then Kant’s account stumbles badly. Concepts are employed in the understanding to make judgments. In judgments, according to Kant, “a concept is never referred directly to an object” (B93 A68). Concepts, when not referring to other concepts, refer to sensory or otherwise given presentations (B177 A138–42). This is part of Kant’s systematic rejection of what he called intellectual intuition. That rejection is not entirely wrongheaded, but this facet of the rejection is one of Kant’s really bad errors. I say as follows: the fact that concepts relate perceptually given particulars does not mean that concepts do not refer directly to the particulars of which we have perceptual experience. It simply does not square with the phenomenology of thought to say that when we are using a concept we are not referring directly to the existents (or the possibility of them) falling under the concept. Kant will have cut himself off from an existential source of normativity in judgment through concepts, thence a possible source of normativity for inferences among judgments, unless that normativity can be gotten through his indirect reference for concepts to existents through given presentations of existents. For Kant, as for most every epistemologist, concepts are unities we contrive among diverse things according to their common characteristics (B39 A25, B377 A320). The problem for Kant is that the diverse things unified are diverse given presentations in consciousness that become objects of consciousness only at the moments of conceptualization and judgment themselves (A103–6, A113–14, A119–23, B519–25 A491–97, B141–46). (Kant’s empirical realism, in A367–77, B274–79, and B232–47 A189–202, is subordinate to his transcendental idealism; but see Abela 2002 and Westphal 2004.) The concept body can be used as a logical subject or in the predicate of a judgment. As subject in “Bodies are divisible,” body refers directly to certain given presentations of objects, but body does not refer to those objects unless in use in a judgment. In use for predicate in “Metals are bodies,” body refers to the subject concept metal, which in turn refers to certain given presentations of objects (B94 A69). “The only use that the understanding can make of . . . concepts is to judge by means of them” (B93 A68). According to Kant, we cannot begin to understand the concept body otherwise than as in judgments. Right understanding of body means only knowledge of its particular right uses as the logical subject or in the logical predicate. Kant observes that judgments, like concepts, are unities. It is the faculty of understanding that supplies those unities by its acts. The logical forms of judgment are not conformed to identity structures in the world or in given sensory presentations. Kant conceived those presentations as having their limitations set by relations of part to whole. He thought they could not also, in their state as givens, have relations of class inclusion (B39 A25, B377 A320). This is a facet of his overly sharp divide between sensibility and understanding. I have long held that relations of class inclusion are not concrete relations, unlike the relations of part-whole, containment, proximity, or perceptual similarity. That does not conflict, however, with the idea that what should be placed in which classes should be actively conformed to particular concrete relations found in the world. Kant thought that our receptivity of given sensory presentation is not cognitive and requires conceptualization in order to become experience (B74–75 A50–51). “All experience, besides containing the senses’ intuition through which something is given, does also contain a concept of an object that is given in intuition, or that appears. Accordingly, concepts of objects as such presumably underlie all experiential cognition as its a priori conditions” (B126 A93). The sensory given presentation contains particular and specific information about the object that can be thought in concepts and judgments concerning the object. But the most general and necessary forms of objects in experience is not information supplied by the sensory given presentations (sensory intuitions), but by the understanding itself for agreement with itself (B114–16, B133n). Without the general form of objects supplied by the understanding, there is no cognitive experience of an object. “Understanding is required for all experience and for its possibility. And the first thing that understanding does for these is not that of making the presentation of objects distinct, but that of making the presentation of an object possible at all” (B244 A199). Kant is concerned to show that there are general patterns of necessity found in experience that are seamless with logical necessities. He errs in supposing that that seamlessness comes about because the general forms for any possible experience of objects logically precedes any actual experience of objects. That a percipient subject must have organization capable of perception if it is to perceive is surely so. Consider, however, that a river needs channels in order to flow, yet that does not rule out the possibility (and actual truth) that the compatibility of a valley and a river was the result of the flow of water. According to Kant, we could have no experience of objects without invoking concepts bearing, independently of experience, certain of the general forms had by any object whatsoever. The unity-act of the understanding that is the conceptual act, which gives a unified content, an object, to given sensory presentations is also the very unity-act that unifies the various concepts in a judgment (B104–5 A78–79). An additional power Kant gives to the understanding is the power of immediate inference. From a single premise, certain conclusions can be rightly drawn. “The proposition All human beings are mortal already contains the propositions that human beings are mortal, that some mortals are human beings, and that nothing that is immortal is a human being” (B360 A303). In these inferences, all of the material concepts, human being and mortal, appearing in conclusions were in the premise. Such inferences can be made out to be the mediate inferences of a syllogism, but only by adding a premise that is a tautology such as Some mortals are mortal (D-W Logic 769; J Logic 115). Mediate inferences require addition of a second judgment, a second premise, in order to bring about the conclusion from a given premise. The proposition All scholars are mortal is not contained in the basic judgment All men are mortal since the concept scholar does not appear in the latter. The intermediate judgment All scholars are men must be introduced to draw the conclusion (B360 A304). The basic judgment—the major premise of the syllogism—is thought by the understanding. This is the thinking of a rule. Under condition of that rule, the minor premise of the syllogism is subsumed, by the power of judgment. Lastly, reason makes determinate cognition by the predicate of the basic rule the new judgment, which is the conclusion (B360–61 A304). “What usually happens is that the conclusion has been assigned as a judgment in order to see whether it does not issue from judgments already given, viz., judgments through which a quite different object is thought. When this is the task set for me, then I locate the assertion of this conclusion in the understanding, in order to see whether it does not occur in it under certain conditions according to a universal rule. If I then find such a condition, and if the object of the conclusion can be subsumed under the given condition, then the conclusion is inferred from the rule which holds also for other objects of cognition. We see from this that reason in making inferences seeks to reduce the great manifoldness of understanding’s cognition to the smallest number of principles (universal conditions) and thereby to bring about the highest unity of this cognition.” (B361 A304–5) The faculty of reason, in contradistinction from understanding, does not deal with given sensory presentations, but with concepts and judgments. “Just as the understanding brings the manifold of intuition under concepts and thereby brings the intuition into connection,” so does reason “bring the understanding into thoroughgoing coherence with itself” (B362 A305–6). Reason provides cognition with logical form a priori, independently of experience. The principles of the understanding may be said to be immanent “because they have as their subject only the possibility of experience” (B365 A309). The principles of reason may be said to be transcendent in regard to all empirical givens. The spontaneity of thought is unifying activity, whether in conceiving, judging, or inferring. Readers here will have probably noticed in Kant the themes of integration and economy, which are major in Rand’s analyses of cognition. However, for Kant the unifying activity of the understanding and of reason is not “an insight into anything like the ‘intelligible’ structure of the world” (Pippin 1982, 93). Kant represents understanding and reason as working together as a purposive system. I maintain, in step with Rand, that all purposive systems are living systems or artifacts of those living systems. We hold that only life is an ultimate end in itself; life is the ultimate setter of all needs. The purposive system that is the human mind is the information-and-control system having its own dynamic needs derivative to serving the needs of the human individual and species for continued existence. Life has rules set by its needs for further life. Life requires not only coherent work among its subsystems, but fitness with its environment. Rules of life pertain to both. Rules of mind pertain to both (cf. Peikoff 1991, 117-19, 147-48). Rules of logic do indeed enable coherent work of the mind, but they also yield effective comprehension of the world. Identity and unity are structure in the world, and, in their organic elaboration, they are structure of the viable organism (cf. ibid., 125–26). The normativity of logic arises from the need of the human being for life in the world as it is. References Abela, P. 2002. Kant’s Empirical Realism. Oxford. Kant, I. 1992. Lectures on Logic. J. M. Young, translator and editor. Cambridge. ——. 1996. Critique of Pure Reason. W. S. Pluhar, translator. Hackett. Peikoff, L. 1991. Objectivism: The Philosophy of Ayn Rand. Dutton. Pippin, R. B. 1982. Kant’s Theory of Form. Yale. Westphal, K. R. 2004. Kant’s Transcendental Proof of Realism. Cambridge.
  22. . Over a period of forty years (1756–96), Kant taught logic at least thirty-two times. Lecturers at the University of Konigsberg at that time were required to proceed upon a textbook recognized by the Prussian authorities. For his classes on logic, Kant used George Friedrich Meier’s Excerpt from the Doctrine of Reason (1752). The term excerpt (Auszug) here means that it treats its subject briefly, in contrast to a larger treatment. It does not mean the shorter treatment is a snippet from a larger work. Meier was a leading figure in the German Enlightenment. He had been a student of Christian Wolff and of Alexander Baumgarten. He studied John Locke in depth and helped introduce English philosophy in German lands. He straddled the rationalist and empiricist traditions. Auszug is not a text in formal logic, though it enters what we should be learning in an elementary logic text today by Meier’s bits on concepts, judgments, good definitions, proper inferences, and informal fallacies. Auszug touches on of all sorts of things that make the various types of human knowledge possible and the expression of knowledge excellent. I set down here some sections from Auszug: §§109–11 (which bear on Peikoff’s remarks on p. 185) and §§43, 98, 103 referred to in the 109–11 stretch. The translation is by Aaron Bunch (Bloomsbury 2016). §43. The ignorance of a human being is (1) an absolutely necessary and unavoidable ignorance, which he cannot avoid owing to the bounds of his power of cognition; and (2) a voluntary ignorance, whose contrary cognition he could attain if he wanted to. §98. We must not assume: (1) that a cognition is true, just because we are aware of no internal impossibility in it; (2) that it is false, just because we are aware of no internal possibility in it; (3) that a cognition is true, the groundlessness and false grounds and consequences of which we are unaware; (4) that a cognition is false, of which we cognize no correct grounds and consequences. For we human beings are not all-knowing. §103. Learned cognition can be false in a threefold way: (1) if the cognition of the things is false, although the cognition of the grounds is correct; (2) if the cognition of the grounds is false, although the cognition of the things is correct; (3) if the representation of the connection between the true grounds and consequences is incorrect . . . . Thus, a true learned cognition must be at the same time a correct cognition of the things, of the grounds, and of their connection . . . . §109. Error consists in our taking false cognition to be true, and true cognition to be false. Consequently, (1) every erroneous cognition is false . . . (2) not every false cognition is erroneous, namely if we cognize that it is false; (3) error arises from false cognition. Had we no false cognition at all, we could also have no errors. Error is worse than merely false cognition, for error is a secret poison. Learned cognition can therefore be erroneous in a threefold way §103. §110. Error arises §109 if we break the rules of the 98th paragraph. The first source or all errors is thus ignorance . . . , if it is accompanied by haste, whereby we deny that of which we have no cognition. §111. Error is either avoidable or unavoidable. The former arises from an avoidable ignorance, and the latter from an unavoidable ignorance §43. The former is nothing but a blameworthy disgrace to learned cognition, but the latter cannot and may not be avoided. It’s safe to wake up now. I should make two points concerning §110. The focus on haste in the production of error is likely simply a Cartesian hand-me-down analysis of error: human will outrunning human understanding. The focus on denials concerning things of which we have no cognition (also in §98) is mainly a bowing of the head to religious mysteries. Sealing obeisance to mysticism into theories of rational cognition was not an innovation of Immanuel Kant. Kant lectured for his logic classes, cued from Meier’s Auszug, but Kant was allowed to register and did register objections and to use points in this approved text as springboards to state his own views concerning those points and their neighborhoods. We have a few sets of class notes taken by students in Kant’s logic lectures. One set was taken in the early 1770’s, so that would be after his Inaugural Dissertation (1770) and during the period in which he was turning his thinking around to full vista of his Critical philosophy, as would be brought to press in 1781 in Critique of Pure Reason (KrV). A couple of sets of logic-lectures student notes are from around 1780, when Kant was completing KrV. Another set is from the early 1790’s. We have English translations of all these sets of class notes, issued by Cambridge in 1992. It is interesting to follow the student notes from the Kant lectures corresponding to §§109–11 across those different years of notes. (Any one of them is more interesting than Auszug itself.) One of Kant’s students was Gottlob Benjamin Jäsche. He had courses under Kant in 1791, and by end of the century, he had become a professor at Königsberg and an exponent of Kant’s philosophy. At Kant’s request, Jäsche composed a manual. It was issued in 1800, and it is titled Immanuel Kant’s Logic – A Manual for Lectures. Kant gave his lecture copy of Auszug, with all its margin notes and interleaved papers with notes that Kant had relied on at some time or other across his forty years of teaching logic. Jäsche tried to decipher the notes and include in the manual the notes he estimated to be in the later portion of Kant’s career. Kant never saw or approved the finished product. This manual remained available continuously in its original German to this day. It is given some wary weight by scholars trying to represent Kant’s views on logic. Today, Anglophone scholars know this work as The Jäsche Logic, and it is included with the other sets of student notes of Kant’s logic lectures translated into English in Immanual Kant – Lectures on Logic (Cambridge 1992). In his dissertation, Peikoff had to rely on the portion of The Jäsche Logic that had been translated by T. K. Abbott into English in 1885 under the title Kant’s Introduction to Logic. The contemporary translator for the Cambridge collection mentions that “Abbott’s translation, though not bad, is so loose and so old-fashioned in its terminology that I have not made any use of it.” Peikoff cites the Abbott translation of the Jäsche production as simply Kant, not Jäsche. That seems to have been customary in the era of Peikoff’s dissertation. William and Martha Kneale’s monumental The Development of Logic issued in 1962. They too cite the Jäsche production as Kant, not Jäsche. Incidentally, Peikoff in his dissertation does not mention anything from this book. Perhaps he had not studied it in time. Information in this text sometimes improved on points advanced by Peikoff from his older resources, and I shall mention some of these (not related to Kant) in the next thread. Writings of Kant himself would be the primary source in any representation of his view (which of course does not have any fog of translation for the German reader or scholar). I’d rate the original, German version of Jäsche’s manual as somewhere between a primary and a secondary source, and I’d rate that portion translated by Abbott (“not bad”) still between primary and secondary. It was unfortunate for Peikoff 1964 that Abbott did not include in his translation the Preface to the Jäsche Logic, that Abbott also did not include the logic-proper portion of the Jäsche Logic, and that Peikoff did not have, apparently, the placement of Kant in the history of logic lain out by Kneale and Kneale (1962). Peikoff relied also on a squarely secondary source for Kant’s picture, a source originating in English in 1860. I’ll look at that source in another post on this thread another day, hopefully soon. In my next post today in this thread, I’ll copy from an earlier study of mine, what one can say of Kant’s views on logic drawing simply from KrV. I wrote that piece years before I had gotten hold of Peikoff’s dissertation, and my contrast therein to Kant is not anyone among predecessors of Kant, but to me and to my contemporary Ayn Rand. Peikoff had KrV in hand, in English, back in his dissertation days, but he makes no mention with citation of these elements of KrV in his dissertation. What can be gleaned from KrV should be posted in this thread as part of the orienting preparation for the next thread which will tackle Peikoff’s dissertation and its offspring square on and which will engage many philosophers besides Kant.
  23. [This post is not on a book I’ve studied in composing my own, but a window into the latter in progress.] Entities and Other Categories, Concrete and Abstract Philosophers often use the term entity to mean any item whatever. That is one customary usage and perfectly all right. Rand decided to take entity into her technical vocabulary as something more restricted. She went on to name some fundamental categories that cannot exist without connection to entities: action, attributes, and relationships.[1] In Rand’s view, mine too, all of those categories have some instances in concrete existents. Actions, attributes, and relationships are not entities in Rand’s sense. To qualify as an entity, I say and think Rand could have been brought around to say, an entity has to do more than be able to stand as the subject of predication (or as the argument of a propositional function). Running or oscillation can be the subjects of predicates, but they can do so as actions, not entities. Fraction and containment can be the subjects of predicates, but they can do so as relations, not entities. Twill and vesicular quality can be subjects of predicates, but they can do so as attributes, not entities. One could include the category relationship under the category attribute.[2] Rand 1966 instead called out relationship as a fourth category, adding to entity, action, and attribute of 1957. Action of course could be subsumed under attribute and relationship in their ordinary scope. Actions of a body such as its angular momentum or its internal kinetic energy could be said to be attributes of that body. Actions of a body such as its translational motion or its infrared emissions from its heat or its interference potentials denominated by its DeBroglie wavelength could be said to be relationships to other things. Rand highlights action by setting it as a category alongside the other three. In the category action, I should say, include the phenomena dealt with in kinematics, dynamics, and kinetics. Include also the phenomena of statics and strength of materials. Include the formation of stars, planets, oceans, and organisms. Include chemical reactions and phase changes. Include as actions, also, organic growth, locomotion and the activities that are consciousness. Rand’s categories of entity, action, attribute, and relationship are her broadest categories of existents articulating her broad circumstance Existence is Identity. Though consciousness is one of her axiomatic concepts, its ontology is under action and attribute, and as a concrete operating system, under entity. Rand specified a relation of entity to material substance: in specific amount, which always it is,[3] material substance is an entity. For example, an ounce-coin of gold or the earth’s atmosphere would be entities.[4] Departing from Rand, in my ontology, I take as an Entity not only particular amount of material, but the material itself regardless of amount. Material such as wood bears properties such as temperature, tensile strength, flammability, and thermal conductivity. The dimensions of the wood are irrelevant to the bearing of such characteristics.[5] A material bears some attributes independently of the material’s extent, and those attributes are factors in specific causal interactions. Such material, independently of its particular spatial dimensions, I classify as Entity, a concrete Entity. Not only matter, but physical fields too, I include under Entity. I’ll capitalize the term to indicate when I’m speaking of entity in my sense broader than Rand’s entity.[6] Notice that on my broader concept, (i) the mass-energy of the universe and (ii) spacetime are Entities whether they are found by our modern physics to be finite or infinite, constant or variable. The axis of the earth’s rotation, though it has no causal powers, is also a concrete Entity, existing in physical spacetime and having determination from material factors. (The fundamental categories in my ontology beyond Entity are three, though not the three selected by Rand. Either set of three can be distributed exhaustively among the other set. My set and the reasons for their selection are lain out in my book in progress, and I’ll not show them here.) Once in Fountainhead Rand used the phrase “concrete reality,” and this was in one of its usual senses: as a contrast to abstraction.[7] There the sort of abstraction spoken of was long-term goals with understanding of principles behind them. The concrete reality there spoken of was actual behaviors of people, at odds with their own poorly understood long-term objectives. Rand’s usage of concrete there exercised two of the specific definitions of the term in my American Heritage Dictionary: “Existing in reality or in real experience; perceptible by the senses; real.” “Designating a thing or group of things as opposed to an abstraction.” Also under those meanings, Rand used concrete in Atlas as specifics and particulars about a character’s actions and responsibilities in contrast to evasive, stale generalities people stated about him.[8] And in the “About the Author” of Atlas, she wrote that concretes differ between (i) her characters’ lives lived by her philosophy and (ii) her own life lived by that philosophy. “The abstractions are the same.” There is another, closely related sense of concrete set out in my dictionary: “Relation to an actual specific thing or instance; not general, particular.” Do not neglect that word instance. Rand began to use concrete in her public writings under this third meaning—instanced particular of an abstraction—in “The Objectivist Ethics” (1961), in which she began to expose some of her view of the character of concepts. There she spoke of “perceptual concretes” being isolated from other particulars by abstraction which can then be integrated into the mental unity that is a concept. She most fully worked out her theory on the instance-relation of concretes to abstractions in Introduction to Objectivist Epistemology (1966–67). She remarked in oral exchange, around 1970: “Abstractions as such do not exist. Only concretes exist” (ITOE App., 173). I should not go along with that, at least at face value. Potentials, as well as actuals, are part of existence in my own view. My recipe for brownies exists not only in cookbook text and in thoughts and in occasions of past makings of brownies, but in potential makings. Even if I could not get Rand to go along with my placement of potentials as such in existence together with my mixing of potentials into all abstractions, she could easily go along with adding the qualification “apart from thought” to her two statements, yielding: “Abstractions as such do not exist apart from thought. Only concretes exist apart from thought.” Leonard Peikoff writes in 1991 that abstraction “is the power of selective focus and treatment; it is the power to separate mentally and make cognitive use of an aspect of reality that cannot exist apart from thought” (OPAR 78).[9] I shall take it as the Objectivist view, as well as the fact of the matter, that only concretes exist apart from thought. Additionally, I maintain that potentials apart from thought, like actuals apart from thought, are only concrete. Peikoff continues, however, by saying that integration of a group of items similar in an aspect grasped in abstraction results in a concept, which he calls “a mental entity.” Perhaps he means only “a mental item,” which is what I should say of that what. Perhaps he means there are not only concrete entities, but abstract entities, abstractions having the ontological standing entity. It is tempting to think of mathematical items, such as a complex number, a right triangle, or a vector space, as abstract entities (or abstract Entities). And if not physically, concretely instantiated, then purely abstract entities. The complex number (3 +7i) would be a purely abstract particular entity, purely a possibility for exemplification in concretes. The purely abstract entity has its mathematical characteristic suite of possibilities, which, if the abstract entity is also exemplified concretely, are also concrete potentials. That picture is mine, not expressly Rand’s, but mine fully only if we replace abstract entity with abstract item (or with something better yet to come). The status of mathematical items as abstract is not merely on account of requiring a process of abstraction to be comprehended. After all, there are concretes that also require abstraction to grasp. Such would be neutrinos, electromagnetic fields, physical spacetime, and economic demand at a price. Mathematical items are abstract fundamentally (i) because they consist of set-membership relations or other relations that are only abstract and (ii) because of their temporal standing and their relation to concretes in their very different temporal standing. I restrict entity or Entity to ontology of only concrete existence. Purely mathematical existence, Yes. Purely mathematical entities, No. Rather, purely mathematical items. We prove that on certain suppositions certain mathematical items, attributes, or relations exist and that certain others do not exist. Mathematical existence per se is only an obtaining, a certain fitness in an abstract scheme. That is why mathematical existence requires deductive proof and why deductive proof suffices. We have two roads, developed from the world in two different ways and affording access to the world and its aspects in two different ways. One is the empirical road, the other the purely mathematical. On the first, we continue to measure ever more finely whether there is any difference in magnitude of the inertial and the gravitational mass of a body. On the second, we do not measure squares and their diagonals to gain further assurance that a diagonal is incommensurable with the sides of the perfect square. Existence (or non-existence) of mathematical items and their attributes and relations are creatively discovered, although not created in a radically originative way by the human intellect attaining them. Kant was correct in rejecting as a human intellectual power any such radically originative intellect (intellectual intuition, in his parlance). However, we should go further than Kant on this point and recognize that no such power could exist for any sort of intellect whatever, call it divine intellect or what you will. The notion of intellectual intuition with that creative sense is only a chimera, a slip into the falsehood of the primacy of consciousness over existence. We should reject as well Kant’s notion of any human faculty at all that is radically originative of Euclidean space in the concrete, physical world. That too, had been a slip into the primacy of consciousness over existence. [1] AS 1016; ITOE 7, 264–79. [2] Bolzano did that. [3] Cf. Aristotle, Phy. 188b9–20; Metaph. 1033a5–22. [4] ITOE 15; Aristotle, Metaph. 1003b16–19, 1028b3–5, 1043b13–14. [5] Among such characteristics are the intensive variables of classical statistical mechanics. [6] Heidegger’s technical sense of entity, descendent of Kant’s object, far from Rand’s entity or my Entity, is pulled together by Béatrice Han-Pile in “Early Heidegger’s Appropriation of Kant” in Blackwell’s A Companion to Heidegger (2005). [7] ET XII, 369. [8] AS 879. [9] See further, David Kelley (1984), “A Theory of Abstraction” in Cognition and Brain Theory 7:329–57; David Kelley and Janet Krueger (1984), “The Psychology of Abstraction” in Journal for the Theory of Social Behaviour 14(1):43–67.
  24. . Avdiivka Is Being Evacuated by the Ukrainians Putin wins.