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  1. . Normativity of Logic – Kant v. Rand Stephen Boydstun 2009 In the perspective of Immanuel Kant, reasoning in accordance with logic can falter due to various empirical circumstances of the reasoning mind. Knowing those pitfalls and how to avoid them is what Kant would call applied logic. Principles of applied logic are partly from empirical principles. As for the principles of pure logic itself, logic apart from such applications, “it has no empirical principles” (B78 A54). The principles of logic are not principles of empirical psychology, and their ultimate authority stems from something deeper than empirical necessities of thought. Logic for Kant was Aristotelian logic. [Or so Kant thought. Stoic logic had been mixed into what he took for simply logic and credited to Aristotle.] He thought this discipline to have been set out completely by Aristotle, and he thought such finality of the discipline was due to the distinctive character of the discipline that is logic. “Logic is a science that provides nothing but a comprehensive exposition and strict proof of the formal rules of all thought” (Bxiii). The office of logic is “to abstract from all objects of cognition and their differences; hence in logic the understanding deals with nothing more than itself and its form” (Bix; B170 A131). Logic is “vestibule” of the sciences in which we acquire knowledge. Logic is presupposed in all judgments constituting knowledge (Bix). Knowledge requires the joint operation of a receptivity of the mind and a spontaneity of the mind. In our receptivity, sensible objects are given to us. In our spontaneity of conceptualization and judgment, those objects are thought (B29 A15). Sensory presentations are givens. The spontaneity of cognition is the ability to produce presentations ourselves. Kant calls understanding the faculty for bringing given sensible objects under concepts and therewith thinking those objects (B74–75 A50–51). Logic is “the science of the rules of the understanding as such” (B76 A52). These are “the absolutely necessary rules of thought without which the understanding cannot be used at all” (B76 A52). Kant distinguishes the faculty of understanding from its superintendent, the faculty of reason. The understanding can arrive at universal propositions by induction. Correct syllogistic inferences among propositions are from reason (B169 A130; B359–60 A303–4). By its formal principles, reason provides unity to the rules of understanding (B359 A302). I should mention that it is not the role of reason (or of understanding) in logic that Kant tries to curb in his Critique of Pure Reason (B=1787 A=1781). This role Kant takes as within the proper jurisdiction of reason. Kant regards logic as “a canon of understanding and of reason” (B77 A53; B170 A131). A canon is a standard or rule to be followed. How can rules of logic be rules to be followed by the understanding if they are the rules that characterize what is the form of all thought? How can the rules prescribe for X if they are descriptive of what X is? Let X be alternatively the faculty of understanding or the faculty of reason, the question arises. Kant calls such logic general logic, and this he takes as abstracting away “from all reference of cognition to its object” (B79 A55). This conception of logic is significantly different from that of Rand: Logic is an art of identification, regimented by and towards the fact of existence and the fact that existence is identity. Over a period of forty years, Kant taught logic at least thirty-two times. Syllogistic inference and non-contradiction were the rules for formal logic. Kant took these rules to concern some of the requirements for truth. They do not amount to all of the requirements for truth, “for even if a cognition accorded completely with logical form, i.e., even if it did not contradict itself, it could still contradict its object” (B84 A59). That much is correct, and Kant is correct too in saying that “whatever contradicts these rules is false” (B84 A59). Why? “Because the understanding is then in conflict with its own universal rules of thought, and hence with itself” (B84 A59). How can the normativity of logic be accounted for if its principles are taken for correct independently of any relations they might have to existence and any of the most general structure of existence? Kant needs to explain how general logical norms for our thinking can be norms without taking their standard from the world and how such norms can be rules restricting what is possibly true in the world. Might the source of norms for the construction of concepts be the source of norms for inferences when concepts are working in judgments? Can the normativity of forms of inference among judgments be tied to normativity in forms of judgments and normativity in the general forms of concepts composing those forms of judgment? What requirements must concepts meet if they are to be concepts comprehending particulars in true ways? From the side of the understanding itself, the fundamental forms concepts may take are required to be systematically interconnected to satisfy the circumstance that the understanding “is an absolute unity” (B92 A67). Considered apart from their content, concepts rest on functions. “By function I mean the unity of the act of arranging various presentations under one common presentation” (B93 A68). So far, so good, but then Kant’s account stumbles badly. Concepts are employed in the understanding to make judgments. In judgments, according to Kant, “a concept is never referred directly to an object” (B93 A68). Concepts, when not referring to other concepts, refer to sensory or otherwise given presentations (B177 A138–42). This is part of Kant’s systematic rejection of what he called intellectual intuition. That rejection is not entirely wrongheaded, but this facet of the rejection is one of Kant’s really bad errors. I say as follows: the fact that concepts relate perceptually given particulars does not mean that concepts do not refer directly to the particulars of which we have perceptual experience. It simply does not square with the phenomenology of thought to say that when we are using a concept we are not referring directly to the existents (or the possibility of them) falling under the concept. Kant will have cut himself off from an existential source of normativity in judgment through concepts, thence a possible source of normativity for inferences among judgments, unless that normativity can be gotten through his indirect reference for concepts to existents through given presentations of existents. For Kant, as for most every epistemologist, concepts are unities we contrive among diverse things according to their common characteristics (B39 A25, B377 A320). The problem for Kant is that the diverse things unified are diverse given presentations in consciousness that become objects of consciousness only at the moments of conceptualization and judgment themselves (A103–6, A113–14, A119–23, B519–25 A491–97, B141–46). (Kant’s empirical realism, in A367–77, B274–79, and B232–47 A189–202, is subordinate to his transcendental idealism; but see Abela 2002 and Westphal 2004.) The concept body can be used as a logical subject or in the predicate of a judgment. As subject in “Bodies are divisible,” body refers directly to certain given presentations of objects, but body does not refer to those objects unless in use in a judgment. In use for predicate in “Metals are bodies,” body refers to the subject concept metal, which in turn refers to certain given presentations of objects (B94 A69). “The only use that the understanding can make of . . . concepts is to judge by means of them” (B93 A68). According to Kant, we cannot begin to understand the concept body otherwise than as in judgments. Right understanding of body means only knowledge of its particular right uses as the logical subject or in the logical predicate. Kant observes that judgments, like concepts, are unities. It is the faculty of understanding that supplies those unities by its acts. The logical forms of judgment are not conformed to identity structures in the world or in given sensory presentations. Kant conceived those presentations as having their limitations set by relations of part to whole. He thought they could not also, in their state as givens, have relations of class inclusion (B39 A25, B377 A320). This is a facet of his overly sharp divide between sensibility and understanding. I have long held that relations of class inclusion are not concrete relations, unlike the relations of part-whole, containment, proximity, or perceptual similarity. That does not conflict, however, with the idea that what should be placed in which classes should be actively conformed to particular concrete relations found in the world. Kant thought that our receptivity of given sensory presentation is not cognitive and requires conceptualization in order to become experience (B74–75 A50–51). “All experience, besides containing the senses’ intuition through which something is given, does also contain a concept of an object that is given in intuition, or that appears. Accordingly, concepts of objects as such presumably underlie all experiential cognition as its a priori conditions” (B126 A93). The sensory given presentation contains particular and specific information about the object that can be thought in concepts and judgments concerning the object. But the most general and necessary forms of objects in experience is not information supplied by the sensory given presentations (sensory intuitions), but by the understanding itself for agreement with itself (B114–16, B133n). Without the general form of objects supplied by the understanding, there is no cognitive experience of an object. “Understanding is required for all experience and for its possibility. And the first thing that understanding does for these is not that of making the presentation of objects distinct, but that of making the presentation of an object possible at all” (B244 A199). Kant is concerned to show that there are general patterns of necessity found in experience that are seamless with logical necessities. He errs in supposing that that seamlessness comes about because the general forms for any possible experience of objects logically precedes any actual experience of objects. That a percipient subject must have organization capable of perception if it is to perceive is surely so. Consider, however, that a river needs channels in order to flow, yet that does not rule out the possibility (and actual truth) that the compatibility of a valley and a river was the result of the flow of water. According to Kant, we could have no experience of objects without invoking concepts bearing, independently of experience, certain of the general forms had by any object whatsoever. The unity-act of the understanding that is the conceptual act, which gives a unified content, an object, to given sensory presentations is also the very unity-act that unifies the various concepts in a judgment (B104–5 A78–79). An additional power Kant gives to the understanding is the power of immediate inference. From a single premise, certain conclusions can be rightly drawn. “The proposition All human beings are mortal already contains the propositions that human beings are mortal, that some mortals are human beings, and that nothing that is immortal is a human being” (B360 A303). In these inferences, all of the material concepts, human being and mortal, appearing in conclusions were in the premise. Such inferences can be made out to be the mediate inferences of a syllogism, but only by adding a premise that is a tautology such as Some mortals are mortal (D-W Logic 769; J Logic 115). Mediate inferences require addition of a second judgment, a second premise, in order to bring about the conclusion from a given premise. The proposition All scholars are mortal is not contained in the basic judgment All men are mortal since the concept scholar does not appear in the latter. The intermediate judgment All scholars are men must be introduced to draw the conclusion (B360 A304). The basic judgment—the major premise of the syllogism—is thought by the understanding. This is the thinking of a rule. Under condition of that rule, the minor premise of the syllogism is subsumed, by the power of judgment. Lastly, reason makes determinate cognition by the predicate of the basic rule the new judgment, which is the conclusion (B360–61 A304). “What usually happens is that the conclusion has been assigned as a judgment in order to see whether it does not issue from judgments already given, viz., judgments through which a quite different object is thought. When this is the task set for me, then I locate the assertion of this conclusion in the understanding, in order to see whether it does not occur in it under certain conditions according to a universal rule. If I then find such a condition, and if the object of the conclusion can be subsumed under the given condition, then the conclusion is inferred from the rule which holds also for other objects of cognition. We see from this that reason in making inferences seeks to reduce the great manifoldness of understanding’s cognition to the smallest number of principles (universal conditions) and thereby to bring about the highest unity of this cognition.” (B361 A304–5) The faculty of reason, in contradistinction from understanding, does not deal with given sensory presentations, but with concepts and judgments. “Just as the understanding brings the manifold of intuition under concepts and thereby brings the intuition into connection,” so does reason “bring the understanding into thoroughgoing coherence with itself” (B362 A305–6). Reason provides cognition with logical form a priori, independently of experience. The principles of the understanding may be said to be immanent “because they have as their subject only the possibility of experience” (B365 A309). The principles of reason may be said to be transcendent in regard to all empirical givens. The spontaneity of thought is unifying activity, whether in conceiving, judging, or inferring. Readers here will have probably noticed in Kant the themes of integration and economy, which are major in Rand’s analyses of cognition. However, for Kant the unifying activity of the understanding and of reason is not “an insight into anything like the ‘intelligible’ structure of the world” (Pippin 1982, 93). Kant represents understanding and reason as working together as a purposive system. I maintain, in step with Rand, that all purposive systems are living systems or artifacts of those living systems. We hold that only life is an ultimate end in itself; life is the ultimate setter of all needs. The purposive system that is the human mind is the information-and-control system having its own dynamic needs derivative to serving the needs of the human individual and species for continued existence. Life has rules set by its needs for further life. Life requires not only coherent work among its subsystems, but fitness with its environment. Rules of life pertain to both. Rules of mind pertain to both (cf. Peikoff 1991, 117-19, 147-48). Rules of logic do indeed enable coherent work of the mind, but they also yield effective comprehension of the world. Identity and unity are structure in the world, and, in their organic elaboration, they are structure of the viable organism (cf. ibid., 125–26). The normativity of logic arises from the need of the human being for life in the world as it is. References Abela, P. 2002. Kant’s Empirical Realism. Oxford. Kant, I. 1992. Lectures on Logic. J. M. Young, translator and editor. Cambridge. ——. 1996. Critique of Pure Reason. W. S. Pluhar, translator. Hackett. Peikoff, L. 1991. Objectivism: The Philosophy of Ayn Rand. Dutton. Pippin, R. B. 1982. Kant’s Theory of Form. Yale. Westphal, K. R. 2004. Kant’s Transcendental Proof of Realism. Cambridge.
  2. . 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.
  3. . 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.
  4. . Avdiivka Is Being Evacuated by the Ukrainians Putin wins.
  5. . Eastern Ukraine Combat Resumes “The US and EU imposed sanctions on Russia in response to its actions in eastern Ukraine. Russia has denied backing the rebels. “The renewed violence coincided with President Donald Trump’s first phone-call with Russian President Vladimir Putin since he took office.” Putin wins.
  6. . Who needs Aristotle or Plato for realism at our present stage of science and philosophy, whether the realism is in philosophy of perception, philosophy of mathematics, theory of concepts, or philosophy of physics? I wasn’t sure SK to whom you wanted to address your question. Perhaps to each of the contributors so far to this thread. I’m also not sure to which of those areas of philosophy just named you wonder about some sort of realism perhaps on offer by me (or Budd or Grames). I hope, at any rate, you do not give Plato/Aristotle a corner on what may count as realism in any of those areas. That would not be true to the varieties of realisms on offer by the philosophy-profession leaders in those areas today. In philosophy of perception, I tend towards the realism of A. D. Smith. http://rebirthofreason.com/Forum/ArticleDiscussions/2141_2.shtml#49 In theory of concepts, Ayn Rand gets some favor from me. http://www.objectivistliving.com/forums/index.php?/topic/13542-thought-and-measurement/#comment-199701 My variety of realism in philosophy of mathematics and in philosophy of physics is still in development. But of note for the latter would be my essay “Space, Rotation, Relativity.” http://www.objectivity-archive.com/abstracts.html Like most philosophers today (me too), Rand and her leading expositors, reject Aristotle’s mechanics; method of science; overextension of teleology; overdone substance, essence, and formal causation; matter-form hylomorphism; as well as his version of moderate realism in universals. In his Ph.D. dissertation (1964), Leonard Peikoff argued for the inadequacy of Aristotle’s ontological rendition (and Plato’s, of course) of the principle of non-contradiction.
  7. . I earned a B.S. degree in Physics (minor in Philosophy) and did some grad school in Physics. I then earned a B.S. degree in Mechanical Engineering, from which I made money. Cross-sectional area of a beam is a physical thing and has the magnitude it has regardless of whether we measure it and regardless of our method of measuring it or our units of measure or whether we use base 8 or base 10 in the numerical expression of the area magnitude. Set theory we employ (at least implicitly) in our measurement scales are abstract, not concrete and therefore not physical. Similarly, the choices of coordinate systems available in an engineering mathematics text do not yield different physical magnitude results of the calculations we perform with those various coordinate systems. Which coordinate system for calculation we use is a free choice not affecting the concrete magnitude, and we select a coordinate system that will be most convenient for us. Physical magnitudes exist independently of our measurement of them. The span of my hand has a certain ratio to my height. That ratio is nothing depending on our choice of scales or our undertaking to ascertain what the ratio is. That ratio is a concrete existent, specifically a concrete relation, not an abstract one. Similarly it goes with the relation of geometry as in Euclid, where we use no scales, to Descartes' analytic correspondence set over that geometry. It is what we call synthetic geometry (as in Euclid) that is physical structure independently of us. Descartes' analytic geometry uses (at least implicitly) set-membership relations, which is abstract not concrete. Analytic geometry depends on our special facility with abstract sets, but it also depends on the synthetic geometric structure to which it is being overlain and which makes it useful to us in engineering or in physics. Force and its degree is physical and independent of us; force per unit area and its degree, such as a torsional shearing stress and its degree, is physical and independent of our coming to those appropriate concepts and our discernments of the existence and magnitudes of those physical referents. Coming up with widest distinctions such as abstract v. concrete and refining more and more what is that distinction and which depends on which in what ways are good work for theoretical philosophy, and results there will have ramifications for theory of practical value, such as moral value, as well as have the loveliness of its own wide vista assimilating all science, mathematics, common experience, everyday knowledge, and the having and making of life.
  8. [This post is not on a book I’ve studied in composing my own, but a window into the latter in progress.] Entities and Other Categories, Concrete and Abstract Philosophers often use the term entity to mean any item whatever. That is one customary usage and perfectly all right. Rand decided to take entity into her technical vocabulary as something more restricted. She went on to name some fundamental categories that cannot exist without connection to entities: action, attributes, and relationships.[1] In Rand’s view, mine too, all of those categories have some instances in concrete existents. Actions, attributes, and relationships are not entities in Rand’s sense. To qualify as an entity, I say and think Rand could have been brought around to say, an entity has to do more than be able to stand as the subject of predication (or as the argument of a propositional function). Running or oscillation can be the subjects of predicates, but they can do so as actions, not entities. Fraction and containment can be the subjects of predicates, but they can do so as relations, not entities. Twill and vesicular quality can be subjects of predicates, but they can do so as attributes, not entities. One could include the category relationship under the category attribute.[2] Rand 1966 instead called out relationship as a fourth category, adding to entity, action, and attribute of 1957. Action of course could be subsumed under attribute and relationship in their ordinary scope. Actions of a body such as its angular momentum or its internal kinetic energy could be said to be attributes of that body. Actions of a body such as its translational motion or its infrared emissions from its heat or its interference potentials denominated by its DeBroglie wavelength could be said to be relationships to other things. Rand highlights action by setting it as a category alongside the other three. In the category action, I should say, include the phenomena dealt with in kinematics, dynamics, and kinetics. Include also the phenomena of statics and strength of materials. Include the formation of stars, planets, oceans, and organisms. Include chemical reactions and phase changes. Include as actions, also, organic growth, locomotion and the activities that are consciousness. Rand’s categories of entity, action, attribute, and relationship are her broadest categories of existents articulating her broad circumstance Existence is Identity. Though consciousness is one of her axiomatic concepts, its ontology is under action and attribute, and as a concrete operating system, under entity. Rand specified a relation of entity to material substance: in specific amount, which always it is,[3] material substance is an entity. For example, an ounce-coin of gold or the earth’s atmosphere would be entities.[4] Departing from Rand, in my ontology, I take as an Entity not only particular amount of material, but the material itself regardless of amount. Material such as wood bears properties such as temperature, tensile strength, flammability, and thermal conductivity. The dimensions of the wood are irrelevant to the bearing of such characteristics.[5] A material bears some attributes independently of the material’s extent, and those attributes are factors in specific causal interactions. Such material, independently of its particular spatial dimensions, I classify as Entity, a concrete Entity. Not only matter, but physical fields too, I include under Entity. I’ll capitalize the term to indicate when I’m speaking of entity in my sense broader than Rand’s entity.[6] Notice that on my broader concept, (i) the mass-energy of the universe and (ii) spacetime are Entities whether they are found by our modern physics to be finite or infinite, constant or variable. The axis of the earth’s rotation, though it has no causal powers, is also a concrete Entity, existing in physical spacetime and having determination from material factors. (The fundamental categories in my ontology beyond Entity are three, though not the three selected by Rand. Either set of three can be distributed exhaustively among the other set. My set and the reasons for their selection are lain out in my book in progress, and I’ll not show them here.) Once in Fountainhead Rand used the phrase “concrete reality,” and this was in one of its usual senses: as a contrast to abstraction.[7] There the sort of abstraction spoken of was long-term goals with understanding of principles behind them. The concrete reality there spoken of was actual behaviors of people, at odds with their own poorly understood long-term objectives. Rand’s usage of concrete there exercised two of the specific definitions of the term in my American Heritage Dictionary: “Existing in reality or in real experience; perceptible by the senses; real.” “Designating a thing or group of things as opposed to an abstraction.” Also under those meanings, Rand used concrete in Atlas as specifics and particulars about a character’s actions and responsibilities in contrast to evasive, stale generalities people stated about him.[8] And in the “About the Author” of Atlas, she wrote that concretes differ between (i) her characters’ lives lived by her philosophy and (ii) her own life lived by that philosophy. “The abstractions are the same.” There is another, closely related sense of concrete set out in my dictionary: “Relation to an actual specific thing or instance; not general, particular.” Do not neglect that word instance. Rand began to use concrete in her public writings under this third meaning—instanced particular of an abstraction—in “The Objectivist Ethics” (1961), in which she began to expose some of her view of the character of concepts. There she spoke of “perceptual concretes” being isolated from other particulars by abstraction which can then be integrated into the mental unity that is a concept. She most fully worked out her theory on the instance-relation of concretes to abstractions in Introduction to Objectivist Epistemology (1966–67). She remarked in oral exchange, around 1970: “Abstractions as such do not exist. Only concretes exist” (ITOE App., 173). I should not go along with that, at least at face value. Potentials, as well as actuals, are part of existence in my own view. My recipe for brownies exists not only in cookbook text and in thoughts and in occasions of past makings of brownies, but in potential makings. Even if I could not get Rand to go along with my placement of potentials as such in existence together with my mixing of potentials into all abstractions, she could easily go along with adding the qualification “apart from thought” to her two statements, yielding: “Abstractions as such do not exist apart from thought. Only concretes exist apart from thought.” Leonard Peikoff writes in 1991 that abstraction “is the power of selective focus and treatment; it is the power to separate mentally and make cognitive use of an aspect of reality that cannot exist apart from thought” (OPAR 78).[9] I shall take it as the Objectivist view, as well as the fact of the matter, that only concretes exist apart from thought. Additionally, I maintain that potentials apart from thought, like actuals apart from thought, are only concrete. Peikoff continues, however, by saying that integration of a group of items similar in an aspect grasped in abstraction results in a concept, which he calls “a mental entity.” Perhaps he means only “a mental item,” which is what I should say of that what. Perhaps he means there are not only concrete entities, but abstract entities, abstractions having the ontological standing entity. It is tempting to think of mathematical items, such as a complex number, a right triangle, or a vector space, as abstract entities (or abstract Entities). And if not physically, concretely instantiated, then purely abstract entities. The complex number (3 +7i) would be a purely abstract particular entity, purely a possibility for exemplification in concretes. The purely abstract entity has its mathematical characteristic suite of possibilities, which, if the abstract entity is also exemplified concretely, are also concrete potentials. That picture is mine, not expressly Rand’s, but mine fully only if we replace abstract entity with abstract item (or with something better yet to come). The status of mathematical items as abstract is not merely on account of requiring a process of abstraction to be comprehended. After all, there are concretes that also require abstraction to grasp. Such would be neutrinos, electromagnetic fields, physical spacetime, and economic demand at a price. Mathematical items are abstract fundamentally (i) because they consist of set-membership relations or other relations that are only abstract and (ii) because of their temporal standing and their relation to concretes in their very different temporal standing. I restrict entity or Entity to ontology of only concrete existence. Purely mathematical existence, Yes. Purely mathematical entities, No. Rather, purely mathematical items. We prove that on certain suppositions certain mathematical items, attributes, or relations exist and that certain others do not exist. Mathematical existence per se is only an obtaining, a certain fitness in an abstract scheme. That is why mathematical existence requires deductive proof and why deductive proof suffices. We have two roads, developed from the world in two different ways and affording access to the world and its aspects in two different ways. One is the empirical road, the other the purely mathematical. On the first, we continue to measure ever more finely whether there is any difference in magnitude of the inertial and the gravitational mass of a body. On the second, we do not measure squares and their diagonals to gain further assurance that a diagonal is incommensurable with the sides of the perfect square. Existence (or non-existence) of mathematical items and their attributes and relations are creatively discovered, although not created in a radically originative way by the human intellect attaining them. Kant was correct in rejecting as a human intellectual power any such radically originative intellect (intellectual intuition, in his parlance). However, we should go further than Kant on this point and recognize that no such power could exist for any sort of intellect whatever, call it divine intellect or what you will. The notion of intellectual intuition with that creative sense is only a chimera, a slip into the falsehood of the primacy of consciousness over existence. We should reject as well Kant’s notion of any human faculty at all that is radically originative of Euclidean space in the concrete, physical world. That too, had been a slip into the primacy of consciousness over existence. [1] AS 1016; ITOE 7, 264–79. [2] Bolzano did that. [3] Cf. Aristotle, Phy. 188b9–20; Metaph. 1033a5–22. [4] ITOE 15; Aristotle, Metaph. 1003b16–19, 1028b3–5, 1043b13–14. [5] Among such characteristics are the intensive variables of classical statistical mechanics. [6] Heidegger’s technical sense of entity, descendent of Kant’s object, far from Rand’s entity or my Entity, is pulled together by Béatrice Han-Pile in “Early Heidegger’s Appropriation of Kant” in Blackwell’s A Companion to Heidegger (2005). [7] ET XII, 369. [8] AS 879. [9] See further, David Kelley (1984), “A Theory of Abstraction” in Cognition and Brain Theory 7:329–57; David Kelley and Janet Krueger (1984), “The Psychology of Abstraction” in Journal for the Theory of Social Behaviour 14(1):43–67.
  9. . Also of possible interest for Phylo or others would be Objectivism in One Lesson – An Introduction to the Philosophy of Ayn Rand (Andrew Bernstein, 2008). From the Preface: “This book . . . assumes that the reader has some familiarity with Ayn Rand’s novels—especially Anthem, The Fountainhead, and/or Atlas Shrugged—and now seeks to further explore Ayn Rand’s distinctive ideas.” “Ayn Rand wrote many non-fiction books and essays, as well, but no comprehensive theoretical presentation of her philosophy. The definitive treatment of her thought is Leonard Peikoff’s Objectivism: The Philosophy of Ayn Rand (OPAR). . . . , an in-depth work . . . [although] never intended as an introduction to Objectivism. Consequently, a bridge is needed, an introductory text for the millions of readers who love Ayn Rand’s novels and who want to take the next step in understanding her philosophy . . . . / Objectivism in One Lesson is that text.”
  10. . Policy of Truth Check Your Premises Correspondence and Coherence
  11. . Welcome to OBJECTIVISM ONLINE, Phylo! In ATLAS SHRUGGED, did you read through all of Galt's radio speech? Was that pretty much all of interest to you? Do you have areas within the topics that come up in Rand's fiction that are especially of interest to you? A lot of Rand's readers have found her ideas helpful in making a life and finding happiness. Some of us additionally just really love some areas of philosophy, and pursue them with great passion and enjoyment. I like the big picture of philosophy for one thing, and I like making my own big picture ever more full and precise. I think the presentation of Rand's philosophy in a systematic way by Leonard Peikoff in his OBJECTIVISM: THE PHILOSOPHY OF AYN RAND is excellent. It is not more technical or difficult than the presentation in Galt's Speech. It does round out what was in the Speech with further issues that Rand and associates refined in the years from ATLAS to the end of her life. That Peikoff book, known by the acronym OPAR, was based very much on Peikoff's 1976 lectures laying out Rand's philosophy, and Rand was present at those lectures, and anyway knew what was to be in them, and she proclaimed them to be an accurate representation of her philosophy. One nice thing about his book is that he has citations to Rand's own writings pretty much all along the way. I have some formal training in physics and in mathematics and in philosophy. I study many sorts and areas of philosophy from ancient to now. I advise, for serious study of the major figures in philosophy, not only study of elementary logic, as Dallas recommended, but the study of Euclid's geometry. But it depends on your interests and life situation whether you would want to study philosophers much besides Rand. One does understand hers better in some ways (endless additional ways, really) by studying others' and comparing to hers. You can see some of my own writings resulting from such studies in my 'Books to Mind' sector at this site and at the 'Stephen Boydstun Corner' over here (I am the author who accidentally ended up with the name Guyau there): http://www.objectivistliving.com/forums/index.php?/forum/126-stephen-boydstun-corner/ .
  12. . Roderick Long has lately tracked down the song “John Gray” that Rand employed in We the Living. He reports it was written in 1923 by Matvei Blanter (1903–1990). The lyrics coincide with those translated by Rand. They are by Vladimir Mass (1876–1979). https://www.youtube.com/watch?v=LX7bF5mEBnA “Petrograd had known sweeping epidemics of cholera; it had known epidemics of typhus, which were worse; the worst of its epidemics was that of ‘John Gray’. “Men stood in line at the co-operatives—and whistled ‘John Gray’. At recreation hour in schools, young couples danced in the big hall, and an obliging pupil played ‘John Gray’. Men hung on the steps of speeding tramways, humming desperately ‘John Gray’. Workers’ clubs listened attentively to a lecture on Marxism, then relaxed while a comrade showed his skill on a piano out of tune, playing ‘John Gray’." (1936, 178)
  13. The preceding painting by JMB is titled 'The Kingdom of Earth' (1972). Below is her drawing 'The Possessor'.
  14. .