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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.

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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.

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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.



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.

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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.

Edited by Boydstun
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  • 10 months later...


The installments (in the other thread “Peikoff’s Dissertation”) of my representation of and commentary on Peikoff’s dissertation that I have completed and posted are:  

Plato – 3/17/17

Aristotle I – 5/14/17 

Aristotle II – 11/2/17 

Due to a stretch of writing my book, in some Aristotle areas, I’ve only just now resumed studies required for my next installment on Peikoff’s dissertation. In this continuation, I want to convey and assess Peikoff’s account of Kant’s contribution to the transition to conventionality in philosophy of PNC. I hope to touch on not only conventionalist theories to the time of Peikoff’s dissertation, but on those flourishing today and their historical setting. I plan to add a coda that is an inventory of the elements and the cited works in Peikoff’s dissertation that plainly contributed to things addressed in the early ’60’s in the Rand/Branden journals, points in Rand’s epistemology (1966–67), and points, with morphisms, in Peikoff’s own writings from his “Analytic-Synthetic Dichotomy” (1967) to The DIM Hypothesis (2012).

Here is the Table of Contents for Peikoff’s dissertation. The three installments I mentioned of my series concerned the first 4 chapters of the dissertation. I’ll include here the detail Contents for the remaining, final chapter.

The Status of the Law of Contradiction in Classical Logical Ontologism

Table of Contents

I. Platonism: The Law’s Epistemological Status

II. Platonism: The Law’s Ontological Status

III. Aristotelianism: The Law’s Epistemological Status

IV. Aristotelianism: The Law’s Ontological Status

V. The Demise of Logical Ontologism

—Some central features of non-ontologism in logic, whether Kantian or conventionalist.

—Kantianism as intermediate between ontologism and conventionalism; some difficulties it has faced in the attempt to sustain such a position.

—Some problems for the theory of the Law of Contradiction suggested by the later Platonist view of essences as Divine thoughts.

—How the attempt to resolve such problems pointed toward a Kantian account of the Law; some signs of this in Cudworth.

—Some difficulties in the Aristotelian Form-Matter ontology; the effects of Locke’s rejection of it on his ability to defend logical ontologism.

—Suggestions of conventionalism in Locke; the relation between these and his rejection of realism in the theory of universals.


I’d like to indicate here the book with which I resume my studies for treatment of the issues in the remainder of Peikoff’s dissertation. The summary information here about this book is an addition to all my report on Kant’s ideas on logic in earlier posts in the present thread “Peikoff’s Dissertation – Prep.”

Kant and Aristotle – Epistemology, Logic, and Method

Marco Sgarbi (2016)

From the back cover:

Kant and Aristotle reassesses the prevailing understanding of Kant as an anti-Aristotelian philosopher. Taking epistemology, logic, and methodology to be the key disciplines through which Kant’s transcendental philosophy stood as an independent form of philosophy, Marco Sgarbi shows that Kant drew important elements of his logic and metaphysical doctrines from Aristotelian ideas that were absent in other philosophical traditions, such as the distinction of matter and form of knowledge, the division of transcendental logic into analytic and dialectic, the theory of categories and schema, and the methodological issues of the architectonic. Drawing from unpublished documents including lectures, catalogues, academic programs, and the Aristotelian-Scholastic handbooks that were officially adopted at Königsberg University where Kant taught, Sgarbi further demonstrates the historical and philosophical importance of Aristotle and Aristotelianism to these disciplines from the late sixteenth century to the first half of the eighteenth century.” 


Here are excerpts from the author’s prospectus for 1 and 2:

Chapter 1 – “I contextualize Kant’s facultative logic within the Aristotelian tradition. Kant denies that facultative logic can be based on the philosophical attempts of John Locke and Nicolas Malebranche, who were more concerned with psychology or metaphysics. . . . I examine facultative logic in Aristotle and the Aristotelian tradition with particular reference to Zabarella and the rise of gnostology [science concerning the mental habit that has to do with the cognizable as cognizable, i.e, the mode of knowing the object in general] and noology [study of the mind’s operation of forming subject-predicate propositions and study of the principles and axioms issuing from such propositions]. . . . I show that Kant can be considered as a part of this philosophical Aristotelian tradition from the time of his early writings up to the Critique of Pure Reason. . . . I examine Kant’s relation to the so-called discipline of physiology, characterizing his Kantian categories as a habit of the mind characteristic of the Aristotelian tradition. . . . Characterize the origin of Kant’s notion of pure concepts of understanding as acquired concepts. I compare Kant’s ideas with those of Locke and Leibniz on the polemic against innatism . . . .”

Chapter 2 – “Deals with two fundamental concepts of Kantian epistemology, namely the matter and form of knowledge, and outlines their Aristotelian origin. . . . Philosophical significance of this conception in Kant’s precritical philosophy and in the transcendental aesthetic and logic of his later years. . . . Kant’s appropriation of the Aristotelian syllogism and doctrine of categories. . . . I suggest that Kant’s reawakening from a dogmatic slumber is connected with his rediscovery of Aristotelian categories. Once having established the nature of the categories, I argue that Kant’s conception of categories and schema comes from the nominalistic interpretation of categories elaborated by Königsberg Aristotelianism, and in particular by Rabe [Paul Rabe, c.1700]. . . . I emphasize the epistemological value of analytic and dialectic for Aristotle. Then I suggest the hypothesis that, in the slipstream of the Königsberg Aristotelian tradition, the analytic of concepts corresponds to gnostology, while the analytic of principles corresponds to noology. More specifically, I demonstrate Rabe’s influence on Kant’s conception of analytic and dialectic in conceiving the former as the logic of concepts and principles and the latter as the logic of probability, or logic of illusion.”



“In the conclusion, I show how the failure of the precritical logical and metaphysical projects prompted Kant to develop the Critique of Pure Reason. I then summarize briefly the result of my research, thereby providing justification for my thesis that Kant’s work must be included within the Aristotelian tradition.” –M. Sgarbi

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  • 9 months later...


Here is some work related to Peikoff’s treatment of Locke on philosophy of logic in his 1964 dissertation. The Peikoff 1985 cited herein is a bit of his dissertation. I wrote this paper in 2012.

Contradiction and Red/Green – Locke 

Recall Ayn Rand’s law of identity in application to attributes, such as color. “Existence is Identity, Consciousness is Identification. / Whatever you choose to consider, be it an object, an attribute or an action, the law of identity remains the same. A leaf cannot be . . . all red and all green at the same time . . .”(1957, 1016).

The logical character of the proposition that a particular surface cannot be all red and all green at the same time has been controversial. In Book 1 of his Essay concerning Human Understanding (EU), John Locke held “principles of demonstration ‘Whatever is, is’ and ‘It is impossible for the same thing to be and not be’” (EU 1.1.4) as unnecessary for the acquisition of all knowledge. “These maxims are not in the mind so early as the use of reason . . . . How many instances of the use of reason may we observe in children, a long time before they have any knowledge of this maxim, ‘That it is impossible for the same thing to be and not be’?” (EU 1.1.12).

In Locke’s view of development, one first gets ideas of particular things through sense impressions, then general ideas by abstraction from the particular ideas. Before one has learned that it is impossible for the same thing to be and not be, indeed, before one has learned to speak, one has learned that bitter is not sweet, white is not black, and red is not blue. Upon that and upon coming to speech, one learns that wormwood and sugarplums are not the same thing, that a rod and a cherry are not the same thing, that a square is not a circle, and so forth. Upon the same grounds that one came to know those differences, one later comes to know that it is impossible for the same thing to be and not be (EU 1.1.15-20; 1.3.3–4; 2.1.6, 22–26; 4.7.9–10).

Turning from development of knowledge to its structure, Locke goes on to say in Book 4 that in apprehending that white is not black or that a circle is not a triangle we do so directly. Knowledge that our ideas of these things are mutually exclusive is not known by demonstration, hence they require no principles of demonstration such as the principle of noncontradiction. We grasp the exclusivity of black and white in a self-evident perception, which Locke calls intuition. Like Plotinus, Anselm and many others before him, Locke thinks of all other knowledge as dependent on intuitive knowledge. The latter is the ultimate source of all certainty in knowledge. “A man cannot conceive himself capable of a greater certainty than to know that any idea in his mind is such as he perceives it to be; and that two ideas, wherein he perceives a difference, are different and not precisely the same” (EU 4.2.1; see also 3.8.1; 4.7.4, 19).

Is the sum of the angles of a triangle the same or variable from one triangle to another? Seeing the sameness of that sum and the sameness of that sum to the angle of a half-circle for all triangles in the Euclidean plane is not self-evident, but requires demonstration (EU 4.2.2). Each step of a demonstration, in Locke’s view, requires intuitive knowledge (EU 4.2.6). The mind can perceive immediately the agreement or disagreement of each step in the demonstration just as the eye can immediately perceive that black and white are distinct and whether a white paper is entirely so or contains some black marks (EU 4.2.5).

It is intuitive knowledge alone, in Locke’s sense of the concept, that is at the base of human knowledge, certain or probable (EU 4.2.8; 4.2.19). It enables the certain demonstrations in geometry, demonstrations with the ideas of “extension, figure, number, and their modes” (EU 4.2.9; a triangle is a relatively simple mode: 2.12.4; 2.31.3; 3.3.18; 3.9.19; 4.4.6; 4.7.9). 

We enjoy accuracy in making and discerning differences in our simple ideas of extension, figure, and number because they are quantitative. (On simple ideas, see EU 2.2.1; 2.3.1; 2.5; 2.7.7-9; 2.30.2; 2.31.2, 12; 2.32.9, 14–16; 3.4.11, 14; 3.8.2; 4.1–2; 4.3.1–21; 4.4.4.) Those ideas are of the primary qualities of things such as Rand’s leaf. Secondary qualities apparently of things, such qualities as colors, are ideas produced in us by the impingement of particles endowed with only primary qualities. In Locke’s day, there were no ways of measuring relations of sameness and difference in the degree of a secondary quality, though he ventures to suppose that greater intensities of primary qualities produce greater degrees of a secondary quality. There are presumably degrees of differences in whiteness that we cannot discern, degrees corresponding to fine degrees of differences in primary qualities that could produce them.

All the same, there are degrees of difference in secondary qualities we do perceive, and such intuitions suffice to found inferential knowledge beyond subjects such as geometry or mechanics. Where the difference in discerned difference in a secondary quality “is so great as to produce in the mind clearly distinct ideas, whose differences can be perfectly retained, there these ideas or colors, as we see in different kinds, as blue and red, are as capable of demonstration as ideas of number and extension” (EU 4.2.13). Where Locke has written “as capable of demonstration,” I think he means “as capable of use in demonstration” (though he could mean additionally what he argues elsewhere in the treatise: there is equally zero capability of any of these different kinds being discerned by demonstration).

Is a sheet of paper before Locke, a paper waiting for the first impression of his pen, all white? Even if it is everywhere white, is it anywhere also red (yet not pink) or black (yet not gray)? We have no direct verdict below our visual thresholds. How does Locke have us know for sure that if the sheet is all white, it is in no part also red or black?

Leaving rather faint the issue of how we know secondary qualities are always produced by primary qualities (cf. Ayers 2011, 146–51), Locke sinks intuitive knowledge concerning imperceptible secondary qualities into the bedrock of intuitive knowledge of primary qualities (EU 4.2.11–12; 4.3.11–13, 15; cf. Descartes 1632, 3–6; 1647–48, 255–56; on Locke’s distinction of primary-secondary, see EU 2.8.9–23; 2.30.2). Locke maintains that for any particular object whatsoever, at a particular time, its extension will be a particular extension, excluding all other particular extensions; its figure will be a particular figure, excluding all others; its motion will be a particular motion, excluding all others. He maintains furthermore that particles of light reflected from a definite part of an object to a particular place of a viewer cannot appear both yellow and azure. “For it is as impossible that the very same particle of any body should at the same time differently modify or reflect the rays of light, as that it should have two different figures and textures at the same time” (EU 4.3.15; see also 2.32.14; unique awareness from unique physical inputs had been embraced also by Descartes, supra; Des Chene 2001, 139–40). Locke generalizes these various sorts of particular exclusion: an object cannot have two exclusive degrees of a given quality simultaneously.

Locke realizes that the impossibility of a leaf being all red and all green is a case of the principle that it is impossible to be both A and non-A. After all, he takes the latter principle to be a generalization of such exclusions encountered in leaf color, fortified by underlying exclusivities in the characters of primary qualities (cf. EU 2.27.1, 4). To say the impossibility of a leaf being at once all red and all green is a case of the logical impossibility of being both A and non-A is not to say the impossibility of the former case derives from the impossibility of the latter general principle. That redness of entire leaf and greenness of entire same leaf are mutually exclusive is not shown by the general principle there are mutually exclusive attributes of entities in existence. Locke correctly recognizes that. “These particular instances, when well reflected on, are no less self-evident to the understanding than the general maxims [superfluously] brought to confirm them: and it was in those particular instances that the first discoverer found the truth, without the help of the general maxims: and so may any one else do, who with attention considers them” (EU 4.7.11[3]).

One weakness in Locke’s sensualist tendency to inductively warrant the necessity of noncontradiction by necessity of exclusions one encounters in sensory qualities is noted by Leonard Peikoff. Leaving the necessity of the principle of noncontradiction as only a necessity encountered in sensory qualities “seems to invite an immediate Humian type of refutation” (Peikoff 1985, 199). Locke’s theory of abstraction is inadequate to the task of delivering from perceptual bases the principle of noncontradiction, noncontradiction in particular and specific identity, noncontradiction in natured entities, their actions, and their attributes. In Locke’s view, we do not attain certain knowledge of the essential natures of physical entities, unlike the situations of our knowledge of simple sensory qualities (primary and secondary) and of mathematical entities. Staying within his view, there is no possibility of arriving at Rand’s absolute principles of identity and noncontradiction through the objects of the senses (EU 2.1.3–9, 22–26; 2.8.7–8; 2.10.6; 2.11.1–9; 2.18.6–7; 2.22.4–5; 2.25.9; 3.3.6–20, 28–38, 49; 4.4.1–6; 4.6.4–16; 4.7.4, 9–10, 16–19; 4.8; 4.11.13–14). 

It is a defect of Locke’s view of color qualities that it is set on difference and sameness in sensed qualities as secondary and their tie to qualities as primary. According to Locke’s scheme, the former, such as the qualities red and green, are in us; they are modifications of our sense organs, thence appearing in our minds, wrought by impinging primary qualities. Rand is set, rather, on the leaf and its color nature. Yes, red and green are different things. Yes, part of the story of how we attain express understanding of the principle of noncontradiction is by prior learning of sameness, difference, and exclusivity encountered in experience. But the sense of noncontradiction Rand is deploying—the sense of identity and exclusion Rand is deploying—is of natured entities. One does not need to know anything about the travel of light to the eye, the physical nature of light, the physiology of the eye, or perceptual thresholds in order to know that it is of the nature, the identity, of leaves and our visual power that no leaf can be at once all red and all green (cf. EU 4.11.2).

Thanks to a presentation of Paul Churchland’s, I have experienced afterimages that seem to be entirely of two distinct colors at once. That experience has now become available to me (more tenuously) in Churchland’s chapter on chimerical colors in Neurophilosophy at Work (2007). I follow the viewing procedure, and in figure 9.11, I get to see fading afterimage discs that are at once mauve and black or at once blue and black and so forth. The point of constructing this figure is for the experience of what Churchland calls “impossibly dark” afterimage colors (the scare quotes are his), not to show patches of afterimages that are two colors at once. I leave it for the reader to dig into this important book’s purposes and their fulfillment.

Afterimages are always fading. What I am experiencing as mauve and black “at once” is occurs while mauve is turning to black. Whether this experience is rightly a case of seeing a portion of surface, screen or page, as two colors could be reasonably disputed. Suppose it qualifies as such a case. It can be taken under wing in Rand’s picture by saying that leaves have their color nature, afterimages have theirs. The same sort of assimilation could be taken were it the case in the future we learn (i) that canonical reflectance profiles of a surface (Churchland 2007, Ch. 10) can be made two canonicals at once by some treatment of the surface and (ii) our visual system can be made to discern them distinctly when artificially and appropriately altered by, say, an electronic apparatus. Were leaves susceptible to said treatment giving them two canonical reflectance profiles, then in Rand’s conception of noncontradiction in attributes, we should say untreated leaves have their color nature, treated leaves have theirs.

In the experience of Rand or Locke, it was not only the surfaces of leaves that were not anywhere at once both red and green. The same was found of any physical surface whatever. It was found likewise for volumetric color. Locke, and Rand too, might recall a certain liquid which when poured into another produces two colors; but the orange and azure produced are regional in the volume, not both simultaneously throughout (EU 2.11.3). 

Locke, like all of us, would want to look into the particulars of the physiology that make afterimage “impossibly dark” colors possible. Understanding of this physiology indeed enabled prediction of this previously unknown effect (Churchland 2007, Ch. 9). Locke could be pleased to see that afterimage colors have their bases in some primary qualities. These colors, like all experienced colors so far as we know, are patterns of nervous activities transforming retinal patterns of activity. Afterimage effects are artifacts of a visual system adaptive in its evolution to color perception of the world. The exclusion character of different canonical surface-reflectance profiles is present in the exclusions of the pattern of nervous activities that are color. But the particulars of this transport of exclusivity shows that Locke’s reasoning from exclusions among primary qualities to exclusions among secondary qualities was spurious.

Returning to Locke’s sensualist epistemology more generally, afterimage experience of two colors everywhere in a region and my futuristic technological scenario quake Locke’s claim that we know the essence of colors just by knowing red is not green and not blue and so forth. Our knowing distinct simple ideas of qualities, secondary or primary, and our putting distinct names on these distinct ideas is insufficient to capture their exclusionary character, their essential natures as attributes of entities. Let the quake shake off that pretension of closure. It remains for Locke and everyone that “red is green” is a contradiction of experience or a contradiction of correct labels. Experience supporting “red is not green” can still support a principle of noncontradiction that recognizes there are distinct items in the world and distinct names to keep them straight. These remains are, however, not distinctive of attributes. They fall short of recognizing the radical general dependence of attributes on their entities and recognizing the full structure of noncontradiction as it applies to attributes.

There is more trouble for Locke. We have seen he held we grasp the exclusivity of red and green by self-evident perception, which he called intuition. Though we become ready to grasp the general exclusivity of A and non-A by such previous sensory experiences of exclusivity, the former is self-evident and self-evident in the same way as the latter (EU 4.7.9–10). If the intuition that nothing can be at once all red and all green were self-evident in the same way as red not being green is self-evident, then fallibility of self-evidence in the proposition that nothing is at once red and green all over shows fallibility of self-evidence for the principle that nothing is at once A and non-A. My afterimage experience and my futuristic, scientifically informed scenario indicate fallibility in the “self-evidence” of the proposition that nothing is at once red and green all over. Time to check premises, for the result that contradictions are not perfectly self-evidently false is patently false.

We may have also some trouble for Rand, but as suggested already, it can be skirted without significant alteration of her metaphysics. In saying a leaf cannot be at once all red and all green, she may have been relying on an Aristotelian sort of dynamical contrariety among colors themselves. Then regardless of what surface or medium may sport colors, the colors dynamically exclude each other at a given place. Her language is pretty strongly against this interpretation, for she speaks of leaf color, though that could by slim chance indicate merely that the dynamical contrariety of colors holds for all surfaces, including leaf surface. Any such line of thought about attributes can be omitted from Rand’s metaphysics. There remain more than enough riches of identity to get beyond Locke.



Ayers, M. 2011. Primary and Secondary Qualities in Locke’s Essay. In Primary and Secondary Qualities. L. Nolan, editor. Oxford.

Churchland, P. 2007. Neurophilosophy at Work. Cambridge.

Descartes, R. 1632. Treatise on Light. In Gaukroger 1998.

——. 1647–48. Description of the Human Body. In Gaukroger 1998. 

De Chene, D. 2001. Spirits & Clocks – Machine & Organism in Descartes. Cornell.

Gaukroger, S., editor, 1998. Descartes – The World and Other Writings. Cambridge.

Locke, J. 1690. An Essay concerning Human Understanding. A. C. Fraser, editor. 1894. Dover.

Peikoff, L. 1985. Aristotle’s “Intuitive Induction.” The New Scholasticism 59(2):185–99.

Rand, A. 1957. Atlas Shrugged. Random House.

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  • 11 months later...

This is taken from a work posted at OL in 2013. It will be good to have this much available right here.

Objectivist Concept of Truth

Rand wrote in 1966: “Truth is the product of the recognition (i.e., identification) of the facts of reality. Man identifies and integrates the facts of reality by means of concepts. He retains concepts in his mind by means of definitions. He organizes concepts into propositions—and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts, but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsehood of his designations of essential characteristics.” (ITOE 48)

Brand Blanshard’s book Reason and Analysis appeared in 1962. (Leonard Peikoff made some use of that book and an earlier one by Blanshard The Nature of Thought in his dissertation completed in 1964.) It was reviewed favorably by Nathaniel Branden the following year in The Objectivist Newsletter. Branden understood that Blanshard was some sort of absolute idealist, but the book offered access to contemporary positivist and analytic philosophy (including the analytic-synthetic distinction), and it offered criticisms of them, which Objectivists might join.

In Rand’s view, Branden said, in his Basic Principles of Objectivism lectures (c. 1968): “All knowledge is contextual, which means: has to be integrated, has to form a logical, consistent, non-contradictory whole. / ‘All thinking’, states Galt, 'is a process of identification and integration’. All logic, then, is a process of context-keeping. No conclusion of a formal logical argument can be considered true out-of-context. Only a full context can determine its truth or falsehood.” (Branden 2009, 75)

Peikoff wrote “Logical processing of an idea within a specific context of knowledge is necessary and sufficient to establish the idea’s truth” (OPAR 171). Peikoff maintained that unless his proposition is true, the fact that we don’t know everything can be turned into the skeptical result that we don’t know anything. If we have no means of possessing any limited knowledge not susceptible to being shown false in the future, no means of knowledge sufficient for truth, then the skeptic can say “for all we know, all of our limited knowledge is false.”

“Logical processing” in Rand’s philosophy, as is well known, includes a lot and is essential to truth and objectivity. To know the number of oval-head #4 five-eighths-inch brass screws I have remaining in their box, I need to count them. That process and result will require not only correspondence, but the right connections among the parts of the process of counting. Moreover, the process of counting is not only necessary; counting, with all my counting crosschecks, is sufficient for truth about the number of screws.

Truth at a conceptual level of cognition is necessarily an integration, and if it were entirely free of any misidentifications in all its network, it would necessarily be true. That is, in this limit of cognitive performance, the cognitive conditions are sufficient for truth. That is Rand's picture. I say Peikoff's establish should stand between verify or confirm, on the one hand, and constitute, on the other; therewith he was not saying something beyond Rand’s picture of ’57 and ’66–’67.

I take issue with Rand’s philosophy on the issue neatly captured in Peikoff’s statement. To start, the “an idea” and the “the idea” will usually have evolved with the advance of knowledge. That all animals are mortal was a truth with the Greeks as with us, but what we mean by animal and mortal have been considerably revised and improved over what it meant to them. The reference class of what is meant by animal has broadened and understanding of what is living process and its cessation has expanded tremendously. But Peikoff’s statement can likely be elaborated so as to take all that into account without substantive retreat.

I attended Lecture 6 in Peikoff’s 1992 series The Art of Thinking. Peikoff remarked there, allowing for inaccuracy in my notes, that he does not see the preface “in the present context of knowledge” as sensible for: (i) perceptions or memory, (ii) automated conceptual identifications (table in contrast with hostility or pneumonia), and (iii) axioms (philosophical [very delimited; widest framework] and mathematical [very delimited subjects]). Saying “in the present context” in the cases where it is sensible is not proof against error. One can have been fully rational to have held views based on errors one later sees. However, error is not inevitable for the methodologically conscious adult. That is what I have in my notes.

Suppose one’s knowledge were based on perceptual observation and correct reasoning upon them, including correct use of mathematics in application to them. Then it would seem fair to say that “Logical processing of an idea within a specific context of knowledge is necessary and sufficient to establish the idea’s truth” (OPAR 171). Perfect conceptual identifications, even though not all the identity of their referents are known, if perfect in all presently known connections with observations and with all other perfect conceptual identifications, are sufficient to establish the conceptual identification’s truth.

Leaving aside the three categories of knowledge set aside in Lecture 6, there remains much in our knowledge that is also virtually perfect knowledge, because it has been so thoroughly tested for contradiction in its many connections, and because these durable propositions have been given ever more exact delimitation with the advance of science. “All animals are mortal” or “I must breathe to live” are examples.

Even for a given context of knowledge, our integration and checking for contradictions is an incomplete work in progress. Meanwhile, we are adding new information, more context for knowledge, and beginning its integration and checking for contradiction. For all conceptual identifications in a condition of significantly incomplete integration and checking, correct logical processing is insufficient to establish truth (cf. Peikoff in Berliner 2012, 303–4). At first blush, this is no problem for the Rand-Peikoff view, for that just means that the knowledge is not to be rightly taken as certain knowledge.

Rand’s picture in Peikoff’s bold statement is significantly incorrect in my view because as one’s (scientific) knowledge grows one’s knowledge of what was one’s previous context of knowledge also grows. One continues to learn what were the ways in which one's previous generalizations were over-generalizations (and in what ways they were inexplicit, indefinite, or vague). There was no reason to suppose that the Galilean rule for addition of velocities was only a close approximation to the low-velocity portion of a different rule for addition of velocities more generally, no reason until the electrodynamical results in the nineteenth century. There was no reason to post a specific caveat before then, along the lines of "for all velocities we've experienced so far."  It remains that in present truth there is past truth and so forth to the future. We cannot know entirely which elements of scientific truth today will stand in a hundred more years of advance nor how those elements will have been transformed and connected with new concepts. Our repeatable experiments will still be repeatable (notwithstanding the unfounded imaginings of the Hume set), whatever new understanding we bring to them.

Peikoff is correct when he writes “No matter what the study of optics discovers, it will never affect the distinction between red and green. The same applies to all observed facts, including the fact of life” (1991, 192).

Peikoff’s sufficiency clause—its application to all cases for which the proviso of delimited truth-context pertains—is not necessary to foil skeptical maneuver. That rational thinkers sometimes have very reasonably taken something for true that is later shown to be false does not justify skepticism. Every such showing of falsehood is a showing of truth and a showing that skepticism concerning the type of knowledge at hand is false. Neither does the skeptic, nor the relativist, have justification for skipping to the contradictions of earlier science with later science, skipping, that is, the context of non-contradiction as a norm, the everywhere-context of things as they are and our ability to know them.

Rand read John Hosper’s book An Introduction to Philosophical Analysis in 1960–61. Rand’s firm anchor of truth in correspondence and the primacy of existence comes through in her marginalia on truth, on propositions, on definitions and tautology, and on logical possibility (Mayhew 1995, 68–70, 75–80). Rand objected to shuffling the question “What is truth?” into “What are true propositions?”. She jotted: “Truth cannot be a matter of propositions, because it is a matter of context” (Mayhew 1995, 68).

Like Aristotle’s, Rand’s is a substantial theory of truth. It pertains to the real, the cognitive agent, and the right relation between them. It declines linguistic stances as well as deconstructionist and relativistic stances towards truth. Aristotle’s writings “present truth in the context of a multifaceted account of knowledge that includes epistemological and psychological dimensions and in which truth directly pertains to issues of meaning, reference, intentionality, justification, and evidence . . .” (Pritzl 2010, 17). Rand can agree with Aristotle that being is the single constant context of truth. She can agree with Aristotle in holding truth to be not only saying of what is that it is, but saying of what is what it is (Metaphysics IX.10). However, she should deny Aristotle’s views that intellectual truth is an irreducible type of being and that “cognition is an identity of knower and known” (Pritzl 2010, 17).

Rand’s has an integration element in her correspondence theory of truth (Peikoff 2012, 12–15).  Integration is essential for truth in Rand’s theory. Fact is interconnected and multilayered in Rand's picture. Fact caught in mind will be truth, and truths will not be isolated in their facts nor in their relations to other truths.

In Rand’s metaphysics, every existent stands in relationships to the rest of the universe. Every existent affects and is affected (ITOE 39). Rand does not go so far as the coherence theorist who would hold that relations to other things is what constitutes what something is.

Concerning the historical roots of the integration element in Rand’s theory of truth, I think the main root is not the coherence views of absolute idealists, nor of Spinoza before them, but the views of Aristotle.

“Truth is the product of the recognition (i.e., identification) of the facts of reality. . . . The truth or falsehood of [man’s] propositions rests, not only on their relation to the facts he asserts, but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsehood of his designations of essential characteristics.” (ITOE 48)

Rand’s conception of the connectivity of facts for truth and her requirement of definitions designating essential characteristics for concepts in assertions are among the integration elements in Rand’s theory. Her theory is revised Aristotle.

Aristotle wrote that "a definition is a phrase signifying a thing's essence" (Topics 101b37). Fundamentally, "the essence of each thing is what it is said to be in virtue of itself. For being you is not being musical; for you are not musical in virtue of yourself. What, then, you are in virtue of yourself is your essence" (Metaph. 1029b14-16). For Aristotle the essential predicates of a thing say what it is, what it is to be it. To say that man is musical does not say what man is. It says something truly of man, but it does not say what is man. 

Thus far, Rand concurs. "A definition must identify the nature of the units [subsumed under the concept being defined], i.e., the essential characteristics without which the units would not be the kind of existents they are" (ITOE 42). Moreover, the essential characteristic of a kind under a concept is "the fundamental characteristic without which the others would not be possible. . . . Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others" (ITOE 45).

Aristotle held that all natural bodies are a composite of matter and form. He took form, rather than matter, to be what makes a thing the kind of thing it is. Essence is a form (Gill 2010, 120; Peikoff 1985; Witt 1989, 116–19; Bolton 2010, 40–46).

Rand rejected this component of Aristotle’s metaphysics (ITOE Appendix, 286). "Aristotle held that definitions refer to metaphysical essences, which exist in concretes as a special element or formative power. . . . Aristotle regarded 'essence' as metaphysical; Objectivism regards it as epistemological" (ITOE 52). For Aristotle what makes gold gold or an animal cell an animal cell is a metaphysical essence, a metaphysical form. Metaphysical essential forms in Aristotle’s account are traditionally seen as universals; Charlotte Witt argues they are particulars (1989, chap. 5).

In our modern view, the essence of the chemical element gold, that in virtue of which it is gold, is: having such-and-such numbers of protons and neutrons bound in a nucleus and the electrons about it. That is what makes its further distinctive properties possible. The essence of a living animal cell is that it offsets the potentially catastrophic drive of water inward through its wall by pumping sodium ions out through its wall. That is what makes possible its further distinctive properties (distinctive, say, from a living plant cell). These essences are physical. The essence of a human being—rational animality—is physical and mental. These are all essences in Rand's sense. They are physical or mental, but not metaphysical in the form-sense of Aristotle's essences.

For Rand "an essential characteristic is factual, in the sense that it does exist, does determine other characteristics, and does distinguish a group of existents from all others; it is epistemological in the sense that the classification of 'essential characteristic' is a device of man's method of cognition" (ITOE 52). Proper essential characteristics in Rand’s theory of definitions required for truth use factual characteristics about a thing to state what it is. Aristotle, in contrast, did not take the essence of a thing to be one of its characteristics among others. He did not take it to be a characteristic of a thing. The form that is the essence of a thing, the form that makes it what it is, is prior in every way to the individual thing it makes possible (Witt 1989, 123–26).

In Rand’s metaphysics, entity, not substance, is the primary existent. Though characteristics and relationships presuppose entities, an entity is nothing but its characteristics and relationships, for entities, like all existents, are nothing but identity. Rand’s realism of definition and essence reaches rock bottom of reality, while dropping some Aristotelian doctrines of substance, essence, and form.

Rand contended that one must never form any convictions “apart from or against the total, integrated sum of one’s knowledge” (1961, 26). That integrated sum is one’s entire cognitive context, “the entire field of a mind’s awareness or knowledge” (ITOE 43).

We have noted Rand’s statement “No concept man forms is valid unless he integrates it without contradiction into the sum total of his knowledge” (AS 1016). To the extent that his mind deals with valid concepts, “the content of his concepts is determined and dictated by the cognitive content of his mind, i.e., by his grasp of the facts of reality” (ITOE 43).

It is not the integration that makes the content true, though the integration is necessary to truth, necessary to the grasp of fact. Peikoff writes “If one drops context, one drops the means of distinguishing between truth and fantasy” (OPAR 124). That is partly due to the nature of facts. The context of knowledge is the context of grasped fact, which is a context of fact. Facts have contexts, independently of our grasp of them (cf. OPAR 123).

The contextual character of truth in an Objectivist account should be hands-on-world, rather as Rand’s essential characteristics of concepts are hand-on-world. Recall that in Rand’s theory of definition, the fundamental characteristic serving as the essential characteristic of a concept is both metaphysical and epistemological; it tells relations of dependency in the world and relations of explanation in the mind. The relations of context in the world will naturally include more than relations of dependency, and relations of context in the mind will include more than relations of explanation.

My contention that the essential characteristic(s) of a concept, in Rand’s epistemology, is not only epistemological, but metaphysical, is consistent with Rand’s text saying that an essential characteristic is factual and does determine other characteristics, its being fundamental being a metaphysical fact. However, on the face of it, my contention contradicts Rand’s statement “Aristotle regarded ‘essence’ as metaphysical; Objectivism regards it as epistemological” (ITOE 52).

In Rand’s view, “the metaphysical referent of man’s concepts is not a special, separate metaphysical essence, but the total of the facts of reality he has observed, and this total determines which characteristics of a given group of existents he designates as essential” (ITOE 52). She goes on immediately to say in what sense an essential characteristic is factual and in what sense it is epistemological. Rand is excluding from her concept of an essential characteristic the overblown sort of metaphysics Aristotle gives to essence, and she is introducing epistemological factors that bear on correct identification of an essential characteristic. She is not excluding metaphysics as a crucial, determining factor in the identification of essential characteristic(s).

I concur with Rand. Essence as in her conception of an essential characteristic is not metaphysical in the full sense of the metaphysical that Aristotle gives to essence. However, in a less ponderous sense of the metaphysical, Randian essential characteristics are both metaphysical and epistemological. Rand requires a metaphysical basis for the designation of essential characteristics for our concepts of things. Furthermore, an essential characteristic should be not only a fact distinguishing a group of existents from all others within the present context of human knowledge; the essential characteristic of items under a concept should be additionally a fundamental one, the fundamental one on which the greatest number of the items’ other species-differentiating characteristics depend. This is metaphysical structure.

Rand should agree with Aristotle that capability for learning grammar would be an improper distinction among animals for capturing the essence of that which is man (Top. 102a18–30; ITOE 49). This is due to facts of dependency. This is metaphysical structure.

It would not do in Rand’s epistemology to follow Descartes in his idea that the primitive essence of matter is extension. That is a good distinguishing and logically necessary characteristic of matter (provided we take extension to stand for all aspects of spatiality). But it ignores the ontological primacy of entities among existents. And space is an existent. Concrete relationships are existents. A proper definition of matter must set it correctly in its relation of non-containment to consciousness (ITOE Appendix 247–50), and it must situate matter in relation to entities. Matter can be rightly defined in that second aspect partly by finding a fundamental distinctive commonality—say mass-energy—for all materials, but the standing of materials in relation to entities must also be captured in a proper definition of matter. There is much metaphysical structure in Randian definition according to essentials.

Consider too a definition of solidity. I like to define it as a state of matter in which there is resistance to shearing stresses, or more exactly, in which there is an elastic zone of resistance to shearing stresses. This definition states physical relationships. It reflects metaphysical structure and physical structure within that metaphysical frame (assuming a proper concept matter). It reflects also context of cognition (and of potential vital action). That is to say, it reflects also the present state of knowledge of matter, an epistemological circumstance.

Rand allows that with further understanding of matter I may have to expand my definition of solidity. Expanding “does not mean negating, abrogating or contradicting; it means demonstrating that some other characteristics are more distinctive” of solidity (ITOE 47). The qualification of a characteristic to be taken for essential continues to rest on the identities given to our consciousness so far—including relations of difference, similarity, and dependency—identities basing the economical scope of cognition and effective action we attain by rightly recognizing them.

I have spoken of relations of context in the world and relations of context in the mind. The membership relation is one relation among contents of mind that is not that relation among the mind-independent, concrete objects corresponding to those contents. That is entailed when philosophers say with Aristotle that what-such depends on this-such, but not vice-versa, or when one says with Rand that only concretes exist in reality.

The binding of membership relations to concrete factual relations, though necessarily not by complete identity with the latter relations, is surely a major impetus for integration in abstract knowledge and integration of abstract knowledge with experience. Rand’s cast of concept-class membership relations as analyzable in terms of suspension of particular values in mathematically scaled relations—relations that can express concrete magnitude relations in the world—is a grand structure for integration beyond non-contradiction. It makes the meaning of correspondence in “truth as correspondence with facts” more specific, and it accords with the success of science in improving correspondence by use of mathematics.



Aristotle c. 348–322 B.C. The Complete Works of Aristotle. J. Barnes, editor. 1983. Princeton.

Berliner, M., editor, 2012. Understanding Objectivism, Leonard Peikoff’s Lectures. NAL.

Blanshard, B. 1962. Reason and Analysis. Open Court.

Bolton, R. 2010. Biology and Metaphysics in Aristotle. In Lennox and Bolton 2010.

Branden, N. 2009. The Vision of Ayn Rand. Cobden.

Gill, M. L. 2010. Unity of Definition in Metaphysics H.6 and Z.12. In Lennox and Bolton 2010.

Hospers, J. 1953. An Introduction to Philosophical Analysis. Prentice-Hall.

Lennox, J. G., and R. Bolton, editors, 2010. Being, Nature, and Life in Aristotle. Cambridge.

Mayhew, R. 1995. Ayn Rand’s Marginalia. ARI.

Peikoff, L. 1985. Aristotle’s “Intuitive Induction.” The New Scholasticism 59(2):185–99.

——. 1991. Objectivism: The Philosophy of Ayn Rand. Dutton.

——. 1992. The Art of Thinking. Lecture.

——. 2012. The DIM Hypothesis. NAL.

Pritzl, K. 2010. Aristotle’s Door. In Truth – Studies of a Robust Presence. Catholic University of America.

Rand, A. 1957. Atlas Shrugged. Random House.

——. 1961. The Objectivist Ethics. In The Virtue of Selfishness. 1964. Signet.

——. 1966–67. Introduction to Objectivist Epistemology. Expanded 2nd edition. 1990. Meridian.

Witt, C. 1989. Substance and Essence in Aristotle. Cornell.

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I learned only today of a book out in 2018 on Kant's thinking about logic. It is titled Kant and the Science of Logic: A Historical and Philosophical Reconstruction. The author is Huaping Lu-Adler, and the press is Oxford. I've ordered this book for myself, I don't expect to say more about it online. I want however to share a very good window into the book at the Notre Dame Philosophical Reviews here.

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Quine’s “Two Dogmas”

It was Quine's essay "Two Dogmas of Empiricism" (TD), published in 1951, that brought his debate with Carnap over the analytic-synthetic distinction to widespread attention among philosophers. In this essay, Quine argues against the validity of the distinction. Carnap wanted to maintain a sharp distinction between analytic statements depending entirely on the meanings being used and synthetic statements making assertions about the empirical world. Quine's alternative view had it that all statements face the world as part of a corporate body of statements. On this view, experience bears the same kind of evidential relation to the theoretical parts of natural science as it does to mathematics and logic (see also Quine 1954).

One of Quine’s aims in “Two Dogmas” is to argue that no sharp distinction can be drawn between analytic statements and synthetic statements. Analytic statements are ones alleged to be “true by virtue of meaning and independently of fact” (TD 21). Truths grounded in fact are known as synthetic truths; statements of such truths are called synthetic statements.

Quine reminds the reader that meaning “is not to be identified with naming” (TD 21). My height and my stature (under one of its definitions) name the same thing and mean the same thing. Likewise for three and drei. In general, however, concepts with different meanings can name the same thing, as my right hand and my writing hand.

Quine writes of terms, but these are terms working in a certain way, terms employed in statements admitting of truth or falsity. Quine’s “terms in statements” would seem not far from “concepts in propositions” which is the technical vocabulary adopted by Rand.

Turning to general terms like right hand, Quine observes that we must distinguish between the meaning of the term and the extension (the referents) of the term. Think of the essence of right hands. Instead of thinking of the essence in the Aristotelian way—as inhering in those hands (actual and possible)—let it inhere in the term. That thought is the meaning of a general term, and, like Aristotelian essence, it is not one and the same as the thing signified (TD 21–22).

I better hit the gavel for Rand at this point. We speak of the meanings of words, but words are only markers for concepts, “and the meaning of a concept consists of its units.” We define concepts “by specifying their referents.” Concepts and definitions are certain ways of specifying referents (ITOE 44).

I look up the word derelict in my dictionary and find one of its meanings: abandoned property; especially, a ship abandoned at sea. Knowing how to apply the latter term (grammatically, a phrase), I might now use this sense of the word derelict. The word being defined and its definition have the same meaning. They are cognitively synonymous.

Quine thought that the useful conceptions of meanings come down to (i) giving synonyms or (ii) making significant utterances (1948, 11). Rand held that when we make significant utterances that engage concepts, or general terms, those concepts have definitions specifying their referents. (Prior to being able to state propositions in which concepts figure, a concept like ball is [marked by a word and] nested in image and action schemata [ITOE 13, 20, 43]. Presumably, this rudimentary mentation, alternative to explicit propositions and definitions, informs them.)

Quine notices that there are definitions of a sort that are not simply the giving of synonyms, and he calls these sorts of definitions explications.

“In explication the purpose is not merely to paraphrase the definiendum [the term being defined] into an outright synonym, but actually to improve upon the definiendum by refining or supplementing its meaning. But even explication, though not merely reporting a preexisting synonymy between definiendum and definiens [the definition], does rest nevertheless on other preexisting synonymies. . . . Any word worth explicating has some contexts which, as wholes, are clear and precise enough to be useful; and the purpose of explication is to preserve the usage of these favored contexts while sharpening the usage of other contexts. In order that a given definition be suitable for purposes of explication, therefore, what is required is not that the definiendum in its antecedent usage be synonymous with the definiens, but just that each of these favored contexts of the definiendum, taken as a whole in its antecedent usage, be synonymous with the corresponding context of the definiens.

“Two alternative definientia may be equally appropriate for the purposes of a given task of explication and yet not be synonymous with each other; for they may serve interchangeably within the favored contexts but diverge elsewhere. By cleaving to one of these definientia rather than the other, a definition of explicative kind generates, by fiat, a relation of synonymy between definiendum and definiens which did not hold before. But such a definition still owes its explicative function, as seen, to preexisting synonymies.” (TD 25)

When philosophers lay out theories of good definition, they are theories of an explicative kind of definition (see Kelley 1988, chapter 3). Consider Rand’s definition of reason as the faculty that identifies and integrates the evidence of the senses. In my dictionary, I find reason defined as the capacity for rational thought, rational inference, or rational discrimination. The terms rational and thought go to already familiar synonymies with reason. The differentia within the rational, in this dictionary definition, are the discriminatory and the inferential.

Rand’s definition stays close to the common usage reflected by the dictionary, but it replaces discrimination and inference by their kin identification and integration, it eliminates the non-explicative rational, and it adds a base for the activities of reason, specifically, deliverances of the senses. Rand’s definition is explanatory of the common usage found in the dictionary, and it is tailored to tie neatly to a particular wider philosophical view.

Quine could say this is a fine explicative type of definition. Rand has given the term reason a new synonymy. The various contexts in which reason under the dictionary definition is properly used remain contexts in which reason under the new, explicative definition is properly used. The new definition covers the processes of drawing distinctions and making inferences. The new definition also applies to the wider processes of identification and integration of sensory evidence, processes in which the narrower processes are embedded. Quine would stress that, nonetheless, “such a definition still owes its explicative function . . . to preexisting synonymies” (TD 25). Quine is being too short here.

Quine’s argument against the idea that there are clearly statements true purely by virtue of meanings, and true independently of fact, hangs on his conception of meaning. We have joined Quine in saying that meaning is distinct from reference. We have not allowed that meaning can be independent of reference. The meanings of my right hand and my writing hand differ, but both meanings are specifications of a referent. Similarly, the meanings of right hand and writing hand differ, but both are specifications of the extensions (the referents) under those concepts.

Quine’s conception of meaning is shriveled into “synonymy of linguistic forms” (TD 22). He allows that a logical truth such as “Every tall man is a man” has a guarantee of truth that rests on more than one’s experiences of facts about men. He realizes that logical truths are sometimes called analytic, but his target is other statements taken for analytic: statements reducible to logical truths by synonymies, statements reducible to logical truths by meaning.

Quine shares with defenders of analyticities the conviction that logical truths are true, and true regardless of particular facts to which they are applied. If there are statements reducible to logical truths by virtue of meaning and independently of fact, then their truth would be guaranteed by virtue of meaning and independently of fact. A candidate analytic statement from Kant would be “Bodies have location.” (A contrasting synthetic statement would be “Orbiting bodies are weightless.”) One who has the concept body knows that having location is part of the meaning of the concept. Substituting “Things having location (and . . .)” for body yields the logical truth “Things having location (and . . .) have location.”

Now, we know “Necessarily, things having location (and . . .) have location.” Does only that sense of necessity attach when we claim “Necessarily, bodies have location”? Quine disputes the idea that purported analyticity of a statement can be adequately explained by cognitive synonymies and logical truth (TD 29–31). Analyticity cannot be explained by a sensible conception of meaning joined with logical truth. An adequate way of distinguishing analytic from synthetic statements has not been produced.

Quine uncovered a narrow, but serious, problem for the analytic-synthetic distinction. It would seem that there are wider problems for the distinction that he passes over because of his cramped conceptions of meaning, definition, and essential characteristics.


Kelley, D. 1988. The Art of Reasoning. W. W. Norton.

Rand, A. 1990 [1966–67]. Introduction to Objectivist Epistemology. Expanded 2nd edition. Meridian.

Quine, W. V. O. 1948. On What There Is. In Quine 1953.

——. 1951. Two Dogmas of Empiricism. In Quine 1953.

——. 1953. From a Logical Point of View. Harvard.

——. 1954. Carnap and Logical Truth. In The Ways of Paradox and Other Essays. 2nd edition. 1976. Harvard.

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I wrote this several years ago, and I want to post it here in the Prep thread in order to refer to it in the Dissertation thread, where I'll be assimilating the work of Lu-Adler mentioned in the post before last after all).

Normativity of Logic – Robert Hanna

Robert Hanna does not accept Kant’s idealism. His account of the normativity of logic in Rationality and Logic (RL) is nonetheless sensibly characterized as a quasi-Kantian account. Professor Hanna proposes that we have a faculty of logic in which dwells a protologic—a set of schematic logical structures—upon which any formal logic, classical or nonclassical, is constructed. This protologic Hanna argues to be presupposed, constructively and epistemologically, by any formal logical system.

Standard modern logic, which is an enlargement (and some correction) of logic beyond its development by Aristotle, is called classical to distinguish it from its further extensions and from its rivals. Logics that only extend classical logic will have modified some of “the classical logical constants, interpretation rules, axioms, or inference rules such that all the tautologies, theorems, valid inferences and laws of elementary logic still hold, along with some additional ones” (RL 40–41). Such are modern modal logics (Garson 2006; Priest 2001). The rivals of classical logic make modifications to “logical   operators [constants], interpretation rules, axioms, or inference rules such that not all the tautologies, theorems, valid inferences, and laws of classical or elementary logic still hold” (RL 41). Such is relevance logic (Mares 2004; Priest 2001) or paraconsistent logic (Priest 2006).

The logics in rivalry with classical logic are contestants on the field of specifying which inferences, among our inferences in the vernacular, are valid. One inference certified in classical logic that many students find repugnant is the taking as valid any inference from false premises to a true conclusion. Paraconsistent logics and relevance logics are systematic formulations of logic in which such inferences come out as invalid. I should mention, too, that various informal fallacies of classical logic come to be formal fallacies within various nonclassical logics (RL 218).

All systems of logic are systematic formulations of “the necessary relation of consequence” (RL 43). Examples from classical logic would be “if p and q, then p” and “if both (i) if p then q and (ii) p, then q” and “if both (i) if p then q and (ii) not-q, then not-p.” Hanna is proposing that behind all logical systems, whether classical or not, there must be a single set of schematic logical structures which determine what will count as a possible logical system; there is a single protologic epistemologically presupposed by every logical system. This protologic is used in justifying assertions about any classical or nonclassical logic; the protologic is constructively presupposed by every logical system (RL 44).

In justifying claims about logic, we are invoking conscious logical beliefs about protologic. Having such a role, there is no way the protologic set of schematic structures could be revised. Moreover, they must be a priori.

Kant took a priori to mean necessarily so (B3–4, B119–24, A87–92); true independently of all experience, not having its source in experience (B2, B117–19 A84–87, B163); but true of the experienced world and needed for any empirical cognition (B5–6, B121–27 A89–94, B163–65, B196–97 A157–58). (Further, see Robinson 1969 and Tait 1992.)

For his own concept a priori, Hanna defines its cognitive facet as cognition not entirely determined by “inner, proprioceptive or outer sensory experiences even though it is always actually accompanied by such sensory experiences” (RL 273n25). He defines the semantic facet of the a priori as sentence meaning wherein the truth conditions of the sentence are not entirely determined by its verification conditions. He defines the epistemic facet of the a priori as belief wherein its justification is not entirely determined by sensory evidence.

No system of logic rejects all of classical logic. Hanna conjectures that the metalogical principles in the protologic might consist of weak versions of four basic principles in classical logic. One would be that “an argument is valid if it is impossible for all of its premises to be true and its conclusion false” (RL 45). Another would be that “not every sentence is both true and false” (RL 45). Cognitive psychology can contribute to the further specification of principles such as these, principles a priori and not revisable, in our repertoire. Our faculty of language epistemologically presupposes our faculty of protologic.

The protologic faculty of logic is sensitive to external experiential stimuli, but not entirely determined by such stimuli. It is an essential aspect of the mind of a rational animal, and it is an a priori aspect of such a mind. “It is not modally controlled by the empirical world, although it inevitably tracks the empirical world” (RL 83). “The logic faculty is a central and informationally promiscuous faculty of the human mind (and apparently the only one), whose role it is to mediate between the peripheral faculties and the central processes of theory-formation, judgment, belief, desire, and volition” (RL 109). That we have innate logical powers does not entail that we have any innate ideas (RL 135).

Hanna is a realist about logic and logical necessity. Any explanation and justification of logic must presuppose logic. No explanatory reduction of logic to other things is possible. The thesis that we are endowed with a logical faculty offers not an explanatory reduction, but a connection for logic of a nonreductive, yet realist nature: “(i) logic is cognitively constructed by rational animals, and (ii) logic is objectively real via language, and consequently logical necessity is an objectively real property or fact in a world that objectively and really contains linguistic structures” (RL 158; also 80–81).

Hanna argues that the innate logical faculty includes a capability for logical intuition. This is an act in which we grasp logical rules, and grasp them as justified and necessary, in a noninferential, a priori, yet fallible way (RL 167–82).

To say that formal logic is normative is to say “humans ought to reason soundly or validly (more generally, cogently). Otherwise put, the normativity of logic consists in the fact . . . that the justification of human beliefs or intentional actions depends on our ability to reason cogently” (RL 203).

Hanna maintains that logic is categorically normative, not hypothetically normative. Logic enjoins one to hold a certain belief or take a certain action under all circumstances and primarily because of logic alone. A view of logic as hypothetically normative would say that logic enjoins one to hold a certain belief or take a certain action because of logic, but only in certain circumstances and primarily because of something extralogical (RL 203).

Mill held that logic is intrinsically normative (necessarily normative) and that logic is explanatorily reducible to empirical psychology. This implies that logic is intrinsically but hypothetically normative, not categorically normative. Then conditions from particular human interests or conditions from natural facts could constrain the scope of the applicability of logical obligation. Hanna maintains to the contrary that logical norms apply in all possible contexts.

Hanna constructs a logical argument, which leans on elements of modal logic, to refute the thesis that logic is reducible to empirical psychology (RL 20–21, 27). That is not to say that there is no essential connection between the logical and the psychological. Hanna argues for such an essential connection: logic is cognitively constructed by rational animals who are essentially logical animals (RL 25). The logical in the phrase “essentially logical animals” is to be understood as primarily normative (RL 215–16). Although we obey the protologic perfectly whenever we reason, we shall adhere only imperfectly to normative mental principles that we construct from the protologic, and only imperfectly to formal logical norms we construct from the protologic (RL 149–53).

Hanna elects the path of Kant, Boole, and Frege. “Logic is the universal, topic-neutral, a priori science of the necessary laws of truth, and also a pure normative science based directly on rationality itself” (RL 204). He calls this the moral science conception of logic. Logic is a moral science (RL 205). It is “an integral part of human morality, namely the part that consists in justifying moral judgments and decisions, including direct moral arguments and reflective equilibrium” (RL 206).

Hanna rejects the idea, put forth by Otto Weininger of virtually identifying logic with ethics (RL 205–6). To the contrary, “moral wrongdoing is not necessarily or even usually connected with wrong logical reasoning; and on the other hand, wrong logical reasoning is not necessarily or even usually sinful” (RL 217). Weininger’s idea was that “logic and ethics are fundamentally the same, they are no more than duty to oneself” (1903).

Hanna rejects the idea that morality is entirely a system of hypothetical imperatives. Kant’s categorical imperative of ethics is not “an all-purpose practical decision procedure or algorithm. . . . Negatively described, the categorical imperative is a filter for screening out bad maxims; positively described, it is a constructive protocol for correctly generating maxims, given the multifarious array of concrete input-materials to practical reasoning . . .” (RL 212). In parallel with the role of an ethical categorical imperative, Hanna alleges a logical categorical imperative. Specifically, that imperative would be: “Think only according to those processes of reasoning that satisfy the protologic” (RL 213).

From this perspective, Hanna would have us see through the errors of radically conventionalist theories of logic (RL 210–11) and skeptical, even nihilistic, attacks on the objectivity of the norms of logic (RL 206, 223–30). Good for Robert Hanna.

To Hanna’s logical imperative, I should add this prior one: think. And we should supplement Hanna’s theory with the circumstance that the choice to think is the choice to live, that the categorical demands of logic are vested by the categorical structure of existence and the hypothetical standing of human life.*

*See also the review by Gila Sher, especially her criticisms 2 and 5.


Garson, J. W. 2006. Modal Logic for Philosophers. Cambridge.

Hanna, R. 2006. Rationality and Logic. MIT.

Kant, I. 1996 [1787]. Critique of Pure Reason. W. S. Pluhar, translator. Hackett.

Mares, E. D. 2004. Relevant Logic: A Philosophic Interpretation. Oxford.

Priest, G. 2001. An Introduction to Non-Classical Logic. Cambridge.

——. 2006. Doubt Truth to Be a Liar. Oxford.

Robinson, R. 1969 [1958]. Necessary Propositions. In The First Critique. T. Penelhum and J. J. MacIntosh, editors. Wadsworth.

Tait, W. W. 1992. Reflections on the Concept of A Priori Truth and Its Corruption by Kant. In Proof and Knowledge in Mathematics. Routledge.

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Kant and the Foundations of Analytic Philosophy - Robert Hanna (Oxford 2001)

Robert Hanna (Oxford 2001)

From the publisher:

“The rise of analytic philosophy decisively marked the end of the hundred-year dominance of Kant’s philosophy in Europe. But Hanna shows that the analytic tradition also emerged from Kant’s philosophy in the sense that its members were able to define and legitimate their ideas only by means of an intensive, extended engagement with, and a partial or complete rejection of, the Critical Philosophy. Hanna’s book therefore comprises both an interpretative study of Kant’s massive and seminal Critique of Pure Reason, and a critical essay on the historical foundations of analytic philosophy from Frege to Quine. Hanna considers Kant’s key doctrines in the Critique in the light of their reception and transmission by the leading figures of the analytic tradition—Frege, Moore, Russell, Wittgenstein, Carnap, and Quine. But this is not just a study in the history of philosophy, for out of this emerges Hanna’s original approach to two much-contested theories that remain at the heart of contemporary philosophy. Hanna puts forward a new ‘cognitive-semantic’ interpretation of transcendental idealism, and a vigorous defense of Kant’s theory of analytic and synthetic necessary truth.”

Discussion by Hanna at 1:15 of Quine's A/S attack.

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Further Contrast of Quine and Rand/Peikoff – A

In the post before the last two in this “Preparation” thread, I conveyed some of Quine’s case against a sharp divide between types of proposition designated by Logical Empiricists as analytic and those designated as synthetic. Additional elements in Quine’s case and comparison with Peikoff’s Objectivist case were conveyed in the thread "Peikoff's Dissertation" in the two posts Conventionalism VII and VIII. In the present post and and at least one following it, I’ll add to the comparison of Quine’s case for no analytic-synthetic bifurcation (NAS) with the case for NAS made by Peikoff in his 1967 paper, which was cast within the Objectivist epistemology and metaphysics. (The notation NAS is from Sher 2016, 100.) I’ll propose specific differences in conceptions of the relations of mind to world that are further factors in the difference of NAS argued by Quine and of NAS argued by Rand and Peikoff. Rand and Quine were both empiricists in the broad sense that they grounded concepts and propositions in sensory experience, but their differences in specifying what this amounts to are large. (For differences in the empiricisms of Aristotle, Locke, and Rand, see Salmieri 2016, 277–78.)

Rand had expressed in Atlas Shrugged (1957) how she thought about the beginning of the infant’s mind in his first days after delivery. She interpreted the baby as having not yet grasped that A is A, meaning having not yet grasped it with Rand’s entailment by “A is A” that things have distinct specific natures. This is the stage “when a consciousness acquires its initial sensory perceptions and has not learned to distinguish solid objects.” To a baby at this stage, “the world appears as a blur of motion, without things that move—and the birth of his mind is the day when he grasps that the streak that keeps flickering past him is his mother and the whirl beyond her is the curtain, that the two are solid entities and neither can turn into the other . . .” (1040–41).

She wrote also in the 1957 exposition: “The task of [man’s] senses is to give him the evidence of existence, but the task of identifying it belongs to his reason, his senses tell him only that something is, but what it is must be learned by his mind.” She defined man’s reason as “the faculty that perceives, identifies and integrates the material provided by his senses.” (Rand was still using that definition in her 1960.)

She took human knowledge to run part-and-sum “from the first ray of light you perceive at the start of your life to the widest erudition you might acquire at its end” (1016). “Sensations are . . . an automatic form of knowledge” (1961a, 18). A sensation is “a sensation of something, as distinguished from the nothing of the preceding and succeeding moments” (1966–67). Rand took knowledge broadly enough at times such that sensation, which informs perceivers only that something exists, not what exists, counts as some knowledge. Knowledge for humans would be, in full, “a mental grasp of a fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation” (1966–67, 45; further, 1970, 84–87).

Rand had taken all consciousness to be identification (1957, 1016). So all perception, even perception of a first ray light in infancy, would be an identification. It is therefore not surprising that in her later articulation of Objectivism she would contract her definition of reason to simply “the faculty that identifies and integrates the material provided by man’s senses” (1961a, 20) in place of “perceives, identifies and integrates . . . .”

Rand had it that “sensations are integrated into perceptions automatically by the brain of a man or of an animal” (1961b, 14). Those perceptions in humans are volitionally integrated into conceptual comprehension by reason. Sensations are transitory identifications, not identifying what, only that. Unless a sensation is itself focused upon—say, in neuropsychology—it is not, in Rand’s meaning of the concept sensation, retained in memory, which I cash to mean specifically not retained in working memory or in episodic or semantic memory.

Conceptualization, conjecture, and inference come under the name reason for Rand by falling under the volitional identification and integration of material from the senses. In Rand’s view, as in Reid and Peirce, the conscious uptake from the senses for the makings of reason is sensory information already automatically integrated into percepts. (See further, Kelley 1986, 31,  44–51, 141–74. The term percept is from Peirce and his contemporaries; see Moore 1961, cited in Rand 1966–67, 2; further, Wilson 2016, 190–95, 204–5). 

“A percept is a group of sensations automatically retained and integrated by the brain. It is in the form of percepts that man grasps the evidence of his senses and apprehends reality. . . . Percept, not sensations, are the given, the self-evident” (1966–67, 5). Animals capable of percepts, perceive entities, in Rand’s narrow sense of that term. Percepts and their objects are susceptible to retention in memory. 

Once Rand had taken on percept and its position in cognition from sensation to reason, I think she really needed to do a little refinement on her 1957 statement that it is only by reason that we discern what an existent is. Animals capable of percepts have some of what a perceived thing is and what actions a thing affords right there. So do we. With reason we grasp more, much more, of what a perceived thing is.

There is some refinement in Rand’s thought in this period. In her 1966–67, she added: “The (implicit) concept ‘existent’ undergoes three stages of development in man’s mind. The first stage is a child’s awareness of objects, of things—which represents the (implicit) concept ‘entity’. The second and closely allied stage is the awareness of specific, particular things which he can distinguish from the rest of his perceptual field—which represents the (implicit) concept ‘identity’”(6). Only at a third stage are concepts attained, in Rand’s cameo portrait. 

The ability to regard entities as units is man’s distinctive method of cognition, which other living species are unable to follow.

“A unit is an existent regarded as a separate member of a group of two or more similar members. (Two stones are two units; so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground.) Note that the concept unit involves an act of consciousness (a selective focus, a certain way of regarding things), but that it is not an arbitrary creation of consciousness: it is a method of identification or classification according to the attributes which a consciousness observes in reality. . . . The criterion of classification is not invented, it is perceived in reality. Thus the concept “unit” is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships.” (1966–67, 6–7).

Leonard Peikoff renders Rand’s idea of an existence-identity sequence in early development on page 12 of his Objectivism: The Philosophy of Ayn Rand (1991). He refers to this idea of Rand’s as something of a suggestion, and I think that is fair enough.

“The three axioms [axiomatic concepts] are not [implicitly] learned by the developing child simultaneously. ‘Existence’, Miss Rand suggests, is implicit from the start; it is given in the first sensation. . . .

“Before a child can distinguish this object from that one, and thus reach the implicit concept of ‘identity’, he must first come to perceive that objects exist. This requires that he move beyond the chaos of disparate, fleeting sensations with which his conscious life begins; it requires that he integrate his sensations into the percepts of things or objects. . . . At this point, the child has reached, in implicit form, the concept of ‘entity’.” 

I think Peikoff’s piecing together of Rand’s existence-identity sequence has a certain neatness. He has identity wait for entity, where entity is in the form object (all these notions being only implicitly held, once they are held at all). However, I do not think it is reasonable to have the identity that is at hand with this versus that wait on grasp of object. There are other existents with their this-versus-that assimilated by the infant mind sooner than that. There are layers of identity grasped that precede grasp of some whatness identity that arrives with the entry of percepts.

I should add it seems reasonable to amend Rand’s suggestion—amendment from me—that with the earliest sensation there is only existence, not identity, with acknowledgment of a lowest-level sort of identity, namely, the identity of existing as distinct from not existing. In this way, at all stages, “existence is identity” is the rule. There is an internal discord between Rand’s fundamental metaphysics and her suggestion that would absent identity from existence in cognition at the earliest stage; my amendment resolves that conflict.

From developmental cognitive psychological research, as of today: through the third week, it appears the infant has not yet had a percept. By three weeks, she has attained expectation for the reappearance of visual objects that have been gradually occluded by a moving screen, provided the occlusion time is short. She is not yet able to engage in explorations sufficiently controlled, and with enough memory, to have what might be plausibly regarded as a percept. Sensory experience, discriminations, detections, responses—but no percepts. If we go with Rand’s concept of percept, its debut (in implicit form) would land at two-to-four months of age, when the infant has evidently gotten some mental grip on solid objects, enduring when not perceived (Carey 2009, 40–46).

Rand thought that young children acquire some concepts before acquiring language. These concepts, she surmised, take a visual form. (See further Boydstun 1990, 16–18.) That is correct I’d say. I should add to Rand (with which she could smoothly concur) that the infant, at about one year, getting her first word such as ball—holding the ball in her hands, saying the word (“ba”), then doing with it what infants do—has the notion of that entity set in actions suited to that sort of entity. So even though the infant at this stage cannot verbally connect that labeled concept of a ball with other labeled concepts, she has the concept ball enmeshed in other known things, visual, auditory, and motoric. In latter development, that enmeshment can be supplemented by joining labeled concepts into sentences and organization of concepts by definitional sentences (see Enright 1991, 56–57; Jetton 1991, 81; Touchstone 1993, 108–9, 118; Bissell 1997, 40–43).

The course of speech development suggests that concepts of entities are formed before concepts of attributes. One need not have already formed concepts of the attributes and affordances of an entity to discern those attributes and affordances and to use them in forming similarity groups of entities. “Common nouns are the first conceptual words we learn (Macnamara 1986, 144–45), and they evidently cue us to think of similarity groups (Bauer and Mandler 1989; see also Premack 1989, 52–53).” (Boydstun 1990, 29; further, 34–38)

(To be continued.)


Bauer, P. and J. M. Mandler 1989. Taxonomies and Triads: Conceptual Organization in One- and Two-Year-Olds. Cognitive Psychology 21:156–84.

Bissell, R. E. 1997. The Essence of Art. Objectivity 2(5):33–65.

Boydstun, S. 1990. Capturing Concepts. Objectivity 1(1):13–41.

Carey, S. 2009. The Origin of Concepts. Oxford.

Enright, J. 1991. Ascent to Volitional Consciousness. Objectivity 1(2):47–65.

Gotthelf, A. and G. Salmieri, editors, 2016. A Companion to Ayn Rand. Wiley Blackwell.

Jetton, M. 1991. Imagination and Cognition. Objectivity 1(3):57–92.

Kelley, D. 1986. The Evidence of the Senses – A Realist Theory of Perception. Louisiana State University.

Macnamara, J. 1986. A Border Dispute: The Place of Logic in Psychology. MIT.

Moore, E. C. 1961. American Pragmatism: Peirce, James, and Dewey. Columbia.

Peikoff, L. 1967. The Analytic-Synthetic Dichotomy. In Rand 1990.

——. 1991. Objectivism: The Philosophy of Ayn Rand. Dutton.

Premack, D. 1989. Minds with and without Language. In Weiskrantz 1989.

Rand, A. 1957. Atlas Shrugged. Random House.

——. 1960. Faith and Force. In Rand 1982.

——. 1961a. The Objectivist Ethics. In Rand 1964.

——. 1961b. For the New Intellectual. Signet.

——. 1964. The Virtue of Selfishness – A New Concept of Egoism. Signet.

——. 1966–67. Introduction to Objectivist Epistemology. In Rand 1990.

——. 1970. Kant versus Sullivan. In Rand 1982.

——. 1982. Philosophy: Who Needs It. Signet.

——. 1990. Introduction to Objectivist Epistemology. Expanded 2nd edition. H. Binswanger and L. Peikoff, editors. Meridian.

Salmieri, G. 2016. The Objectivist Epistemology. In Gotthelf and Salmieri 2016.

Sher, G. 2016. Epistemic Friction – An Essay on Knowledge, Truth, and Logic. Oxford.

Touchstone, K. 1993. Intuition, the Subconscious, and the Acquisition of Knowledge. Objectivity 1(6):47–136.

Weiskrantz, L., editor, 1989. Thought without Language. Oxford.

Wilson, A. B. 2016. Peirce’s Empiricism – Its Roots and Its Originality. Lexington Books.

Edited by Boydstun
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On 2/25/2017 at 10:16 AM, Boydstun said:

.. . .

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.

Webster’s Unabridged has: Ontologism - the philosophical doctrine that the knowledge of God is immediate and intuitive and that all other knowledge springs from it.

Specifics of ontologism in this regular way it originally was used in philosophy can be found in the entry for the term at New Advent, i.e., Catholic Encyclopedia.

And from John Dewey’s entry for that term in James Mark Baldwin’s Dictionary of Philosophy and Psychology (1902), we have:

Ontologism -

  1. The philosophical (ontological) method which proceeds from logical categories directly to reality: it is applied to the great speculative systems of which the ontological postulates are not grounded in experience.
  2. The theory of the school founded by Gioberti in Italy (1801-52). The doctrine, namely, that the method and principles of philosophy should be sought for in the object, not in the subject. The theory is a reaction from the supposed subjectivism of modern thought. Gioberti held that Descartes had substituted a psychologic method . . . for the true ontological, and that modern philosophy, in so far as it proceeded from an examination either of consciousness or of the process of knowing, had put philosophy further off the right track, and had logically ended in sensualism, Protestantism, and atheism. We must begin [instead] with the supreme and objective intuition of the mind: Ens creat existentias [Being creates existences].

Peikoff 1964 uses the term ontologism in a broad sense. He uses it to mean only a basing in facts independent of mind, an expressing of relationships existing in non-mental existence itself. What Peikoff had termed Platonic ontologism, with its bases in Forms, and Aristotelian ontologism, with bases in hylomorphism and essences in the forms in that metaphysical partition, are close to the meaning (1). His speaking of ontologism in his broad sense (under which a basing of logic and concepts offered by Rand could be included, by the way) seems likely a use of the term descendent from (2) which along its evolution had dropped the excess baggage of intuition and conception of Being. The newer, broader sense was not a novelty of Peikoff 1964. I see it being used by Milton Munitz of NYU in his 1958 philosophy of physics paper “The Relativity of Determinism” in his characterization of Einstein’s philosophy of modern physics in contrast to philosophy of modern physics from others, such as Bohr, who were its Founders.

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