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  1. The distinguished linguist James McCawley wrote: “I know of no one in linguistics who accepts the idea that the structure of one’s native language imposes limits on what thoughts one can think.” For example, “all languages have simple ways of referring to the future, but they don’t necessarily use tenses of verbs for that purpose. Speakers of English are no better at thinking in terms of the future than are speakers of Chinese, which has no tense forms at all, nor any worse than speakers of Kikuyu, which has distinct near future and remote future tenses.” These are excerpts from a letter on page 6 here. ~~~~~~~~~~~~~~~~ Joseph Conrad and Ayn Rand were two excellent novelists in the English language, even though it was not their native language. Rand was also able to express philosophical ideas well in English. However, among people I've personally known, I've found that if English was not their native language, they have trouble understanding and expressing philosophical ideas with precision in English. So although grasp and expression of some ideas might be inherently more direct or more roundabout in one language or another as one navigates reality with it, I suggest that one's greatest competence for grasping reality is, for most of us, our own native language.
  2. PNC Ground Shifts to the Side of the Subject – Conventionalism II Logical empiricists rejected Kant’s synthetic a priori as a class of propositions, and they rejected as well Kant’s role of intuition in arithmetic and geometry. All a priori propositions were analytic for these twentieth century philosophers. Having taken that position, they took some modern philosophers before Kant, such as Leibniz or Hume, to have been on the right track; they saw Kant as a derailment. I should note that none of these twentieth century philosophers giving a significant nod to convention in logical principles, such as PNC, were epistemological skeptics. They found attractive Hume’s wall between abstract reasoning and matters of fact, which was similar to epistemological dipoles of their own. They could applaud his clipping wings of metaphysics. They treasured mathematics and modern empirical science, and they did not give an inch to religion. L. E. J. Brouwer threw a Kantian intuitionist spanner into the logical empiricist program in the late 1920’s. He formulated an intuitionist, constructivist, and finitary conception of mathematics which implied the invalidity of a significant portion of classical mathematics that had been developed by that time. Carnap proclaimed legitimate in broad perspective both the Brouwer system and classical mathematics by characterizing them as devoid of factual content and by leaving them to win the day according to which could best serve the formal deductive needs of empirical science.[1] The selection between Brouwer’s intuitionist mathematics and classical mathematics for the boosting of empirical science is not arbitrary. What is better suited or best suited to some end, such as boosting empirical science, is a matter of objective fact. The following, I notice, share nothing with the arbitrariness that enters convention (just as the need for a left-or-right-side driving rule shares nothing with the arbitrariness that enters the choice of which side): what is more rather than less convenient, what is more rather than less simple, and what is more rather than less practical. One slip into a subject-siding error in this neighborhood would be to say that because a model or a theory is more convenient or simple or practical, it is more likely to be true (or, stepping with Protagoras, it is what truth is). Within pure, unapplied geometry, it is false to say there is no correctness or incorrectness concerning hyperbolic geometry, elliptical geometry, and Euclidean geometry; all three are true within the discipline of pure mathematics. The impulse to consider these geometries as somehow not only distinct from, but as opposed to each other within pure geometry is wrong thinking. There is some truth to the conclusion of Poincaré and, later, the logical empiricists that question of which, between hyperbolic, elliptical, or Euclidean, within pure geometry is true (concerning their differences, not their commonalities) is a meaningless question. The context, I say, that makes such a question meaningless is a context in which there are facts, albeit facts not empirical. So Carnap was wrong to say additionally that purely formal disciplines and their systems are themselves devoid of factual content. It is misleading to confine usage of fact to empirical fact, just as it would be misleading to confine circumstance or form to empirical circumstance or empirical form. (My own view is that there are formal lays of the physical and ways of ours with the physical that are not empirical lays of the physical and not our empirical ways with the physical. Specifics are reserved for my book in progress.) Henri Poincaré died in 1912. He lived long enough to assimilate modern geometry and special relativity, and the Minkowskian geometric character of SR spacetime into his epistemological views on physics and on mathematics. Poincaré did not live to see the advent of general relativity (1915), with its condensations of the principle of inertia into spacetime geometry and gravitational force into inertial force, its spacetime structure affecting motions of mass-energy, and its distribution of mass-energy dictating spacetime structure, all at play in one super-fertile physical equation, Einstein’s field equation. Poincaré had over-extended the role of convention in both physical theory (kinematics and dynamics, including SR) and modern geometry. Those over-extensions have been soundly refuted, even without setting that much physics and physical geometry within general relativity. Those repudiations aside, general relativity was utterly devastating to the roles Poincaré had purported for conventions in physics and physical geometry.[2] The logical empiricists sometimes situated conventions in logical truths in ways self-consciously similar to ways Poincaré had (mistakenly) thought he found sturdy niches for convention in physics and geometry. That does not mean that every such mimic of Poincaré mistaken. I should say only beware, for separating what is conventional and what is not is not always easy, within one’s present context of knowledge. But the more important point I want to make for our present examination of possible connection of PNC ontological and epistemological character from Kant to conventionalism is that Poincaré held a generalized version of Kant’s synthetic a priori status for arithmetic, geometry, and fundamental mechanics. This generalized version with its niches for convention possessed those niches only due to advances in mathematics and science since the time of Kant. No shifting of ontology to the side of the subject nor deflation of ontology by Kant, in his specific ways, seems to be required for Poincaré to have made his conventionalist moves. And the logical empiricists made their conventionalist moves on logical truths, including PNC, without any reliance on, indeed in flat denial of the Kantian class of the a priori that is also synthetic. Kant’s critical philosophy further sealed the tomb of logical ontologism, but in my assessment thus far, Kant prepared no ground and planted no seeds for the spring of twentieth-century conventionalisms in the character of logic or its applications. But what about Kant via tributaries from neo-Kantians (viz., Marburg ones) into logical empiricism? (To be continued.) [1] Friedman 2010, 669–76. [2] Ben-Menahem 2006, 40–68; Friedman 2010, 642–64; Gray 2013, 525–33. ~~~~ Ben-Menahem, Y. 2006. Conventionalism. Cambridge. Friedman, M. 2010. Synthetic History Reconsidered. In Discourse on a New Method. M. Domski and M. Dickson, editors. Open Court. Gray, J. 2013. Henri Poincaré – A Scientific Biography. Princeton.
  3. SL, I don’t think that Rand’s character of categories requires that all concrete existents belong to one of those four categories and not to the other three. Those four are entity, action, attribute, and relationship. Firstly, one could take angular momentum, for example, to be truly an action but also an attribute, and a relation. Her way with categories is simply different than Aristotle’s way of absolutely unique categorization of a thing. (Please, anyone, correct me if I’m wrong about that point on Aristotle.) But secondly, and pertinent to the spacetime/mass-energy characterizations into Rand’s categories, it has seemed to me that anytime a concrete existent is understood as a system, one can rightly take it as an entity. For example, in AS 1016, Rand takes the solar system to be an entity. One could also take it as “this particular matter with such-and-such orbital angular momentum about the sun, also this other particular matter with such-and-such other orbital angular momentum about the sun, also . . .” Then we’ve a summation of actions of entities, not an entity. I’m comfortable with that sort of multiple categorization of a thing where it is true to a thing. So I’d think it fine to take spacetime in its global structures to be an entity even if locally it were not an entity, but a relationship. And in GR we’d take this room I’m in to be, over very short, shorter, . . . periods of time, as asymptotically an inertial frame of motion. I’m fine with taking the space contained by these walls and containing me as not only an entity containing other sorts of entities, and the spacetime entity I’ve here as asymptotically of zero curvature; but as well, as a collection of a certain kind of relationships between other sorts of entities. Probably the most important multiplicity of category that Rand employed was the ontological status of mind. As an operating system, an instrumentation and control system, it’s an entity. But it’s also a process and activity, that is, it falls in the category action. The utility of Rand’s categories seem somewhat like the utility of a certain easy network understanding of a thing, a hand-over-hand sort of comprehension of a thing (although this easy network is an alternation staying outside entity): “A pear is a kind of fruit which is a part of a pear tree which is a kind of plant which (with others) is a part of the biosphere.” (30) None of this entails, I should mention, that entity is a category not having primacy over other categories of existents, primacy in acquisition of language, in conceptual dependencies, and in ontological relations. [I notice that Kant's categories do seem to require no dual memberships. Perhaps that is because they are lifted from distinct logical forms of judgment. The latter could reflect basic ontological standings (contrary to Kant's conception of their ultimate source and justification). Kant's categories seem, however, less readily useful than a freer and more accessible set of categories such as Rand's.]
  4. First Earth-Based Radio-Wave Image of Galactic Black Hole (4/10/19) In general relativity, including in its combine with quantum field theory at the event horizon of a black hole (Hawking radiation), mass-energy is one thing and spacetime with all its curvatures is another thing. Mass-energy is an entity. Distribution of mass-energy in spacetime determines how spacetime will curve. A thing susceptible to such a dynamics is an entity, I'd say, or at least it is some sort of concrete existent. So I think of spacetime---even empty spacetime, i.e., even spacetime if it had no vacuum energy---as an entity. Spacetime curvature is a causal factor in how mass-energy moves. This too supports the classification of physical spacetime as an entity. In talking of entity and of concrete existent, I'm talking of some philosophical, metaphysical categories, specifically some categories in Ayn Rand's metaphysical scheme. That sort of broad framework is useful for assimilating and keeping somewhat unified all the areas of one's experience and learning. Methods of successful science are in part from rational philosophy (rational epistemology) down the ages as the discipline of philosophy assimilated and analyzed such success in science and mathematics as had been attained. However, in the mature sciences such as modern relativity physics, astrophysics, and astronomy, additional methods for success have also been forged by some scientists themselves (under their epistemology thinking cap, we might say) as they hunted what is in nature. .
  5. The Stoics were the first to develop an explicit theory of propositional connectives. An example they used of what now we call modus ponens: If it is day, then it is light. It is day. Therefore, it is light. The basic unit of Stoic logic is not the term, as in Aristotle, but the proposition. Modus ponens is a form of valid argument that students in a first logic course say Yes to right off. They see its validity, and it’s as if one had already known it was a valid form of reasoning before seeing it in the course. Not so with material implication, which is a more contrived creature of modern logic. William O, John Stuart Mills is the one most famous for giving an empiricist answer to how we come to know logical principles such as modus ponens. The logical empiricists (also called logical positivists) thought such principles are somehow gotten from experience, though it could not be gotten as Mills proposed. Aristotle and Rand/Peikoff also suppose learning of basic logical principles must come from experience (in the present life of an individual), but not in the empiricist way of Mills or in the experiential ways we learn unsupported bodies fall or learn that we have receptors in the skin that guage coolness or warmth by rate and direction of heat transfer. I do not think that questions of origins of any of the various sorts of knowledge that individuals attain, from infancy to a first course in geometry, can be answered in the finest way without assimilation of the pertinent results of cognitive developmental psychology of the last 70 years.
  6. “If p, then q” is taken in logic texts to be identically equivalent to “Not (p and not-q).” “Not (there is a naturally evolved bird with talons, and it is not a bird of prey)” is identically equivalent to “If there is a naturally evolved bird with talons, then it is a bird of prey.” It seems that we know up front that this “identically equivalent” relation holds however much our knowledge of birds increases; it cannot be found false. Whether there are presently unknown conditions under which this particular “If p, then q” can be found false is open, though until specific prima facie plausible conditions of that sort are proposed (at least in a sketchy way), that open possibility is a vacuous possibility, a degenerate, impotent sort of possibility, whether the if-then concerns nature or mathematics. The nature of birds is a matter of identity, but it seems a wider sort of identity than that in the “identically equivalent” relation. And the latter would seem to be something one learns about later than the former, although maybe the latter is already present in a precursor way in prelinguistic action schemata (eg. there’s more than one way to get attention, more than one form under the schema get attention). In his book How We Know, Harry Binswanger takes syllogistic inference to be a case in which what is already implicit in the premises is drawn out and made explicit in the conclusion. That is a common perspective on deductive inference. The syllogism is a form of “If p, then q” in which p is a conjunction of two propositions: “If r and s, then q.” For r and s to be true and to bear implicit truths, of course, r and s both have to express awareness of facts (254–55). This viewpoint is smooth with the views of Rand that logic is a form of identification and that existence is identity. In his book Objectivism: The Philosophy of Ayn Rand, Leonard Peikoff remarked: “The method of logic . . . does reflect the nature and needs of consciousness. It also reflects the other factor essential to a proper method: the facts of external reality. The principle which logic provides to guide man’s mental steps is the fundamental law of reality” (120–21). There are no contradictory facts in reality, I should add, to be thought in conjunction if thought is aimed at fact. To put forth without evidence or design for evidence the thesis that there are naturally evolved birds with talons that are not birds of prey contradicts evident facts without resolving the purported contradiction with other (not-adduced) evident facts. I suggest that denials of modus ponens should be understood as that sort of denial under the basic conception of logic in Objectivism. Logical validities are never independent of all facts of reality. Some excerpts from Nathaniel Branden’s lectures The Basic Principles of Objectivism: “Logic is the tool of reason. Logic is based on facts, on the fact that that which is, is; but it is not a science of facts. It is a science of method (75).” “One proves a proposition by demonstrating that it is logically necessitated, that its denial would contradict facts already known to exist. . . . . “Until one has grasped that A is A, and that contradictions cannot exist, there can be neither proof nor the concept of ‘proof’. . . . “The Law of Identity is a genetic root of the concept of ‘proof’. . . . (73, transcription in The Vision of Ayn Rand)
  7. 2046, I’ll hold off remarking on pragmatism until we get to Dewey and Lewis. Concerning the classical ontologists, “they regarded the laws of logic as themselves matters of fact (i.e. ontological in character, not ‘mere’ matters of fact)” (Peikoff 1964, 13). The classical philosophers basing logic in ontology (such as Plato, Aristotle, Aquinas, and Leibniz) would want to have PNC both as an ontological fact of the world and as a norm, a consciously followed constraint, for ascertaining any fact, whether itself or other facts, whether facts empirical or mathematical. With the variations in ontology between various theories basing logic in ontology are variations in what is ontological form. I think it is always what philosophers say about the ontology of form that is key to their ontology of PNC and their account of how PNC is also a norm. Below is Peikoff’s representation of Aristotle’s ontology at work in a syllogistic inference. I should like to mention that this text is my personal favorite in Peikoff’s dissertation. Also, I’d like to mention that, as Jonathan Lear showed from Prior Analytics, the certitude of the validity of the syllogism below, and the other first-figure ones, is the base certitude of validity by which Aristotle, using some self-evident logical conversions, certified validity of the syllogisms of the other figures. Lastly, in their lectures and writings concerted with Rand; Branden and Peikoff point to contradictions that occur if one denies the conclusion of this syllogism below while affirming its premises. It is a good assignment for the future to work out the moments of Aristotelian form in rendering those contradictions. Under Aristotle’s account, we learn the truth of PNC by observing instances of it and performing an intuitive induction to it (also called an abstractive induction). PNC has to be a law prior to the operation of thought in order to be discovered by such observation and abstraction. The normativity of PNC in Aristotle’s account is from the purpose of thought, which is the comprehension of existence. To serve as guide to that purpose in the way PNC serves, PNC must, in Aristotle’s view, be a first principle in existence. We must not think a thing has and has not a certain character at the same time because, as Joseph puts it, “we see that a thing cannot have and not have at once the same character; and the so-called necessity of thought is really the apprehension of a necessity in the being of things’” (Peikoff 1964, 162). I’ll be looking at Dewey’s expansive notion of logic in turn when we come to it in this series. Looking also at Lewis and at Peikoff’s extractions from both of them. I don’t expect to take up Wittgenstein, and Peikoff also did not. But I thought I’d mention just now a book from Penelope Maddy The Logical Must – Wittgenstein on Logic (2014).
  8. PNC Ground Shifts to the Side of the Subject – Conventionalism I Peikoff addressed logical conventionalism in a sense broad enough to include the various approaches to logical truth within what he took to be the most influential movements of Anglo-American philosophy in the twentieth century to the time of his dissertation (1964, 165n). Those would be pragmatism, logical empiricism, and the analytic movement. For exemplification of philosophies upholding conventionalism in fundamental character of logical truths, Peikoff delves into Dewey’s Logic: The Theory of Inquiry (1938); C. I. Lewis’ Mind and the World Order (1929) and An Analysis of Knowledge and Evaluation (1946); A. J. Ayer’s Language, Truth, and Logic (1946 [1936]); and E. Nagel’s Logic without Metaphysics (1956). There had been an analogue of conventionalism in logical and mathematical principles within a minority of earlier thinkers who, wanting to guard doctrine of the omnipotence of God and taking the truth and necessity of formal principles to emanate from divine selection of them, endowed formal principles with an ultimate arbitrariness. Those principles would be perfectly unchanging, however, as far as human thought is concerned. Anyway, such an ultimate situation was from a brew of theology with an extra-heavy dose of vacuum imagination. The conventionalisms Peikoff addressed took shape and took hold in part and in some sense due to inadequacies of the various forms of logical ontologism that had been on offer (186–87, 210–11, 235–36, 239). The rejection of those logical ontologisms was reasonable, as Peikoff illustrated, even if we consider them only from within the discipline of classical philosophy from Plato to Kant. The conventionalist replacements for logical ontologism were presaged by (i) nominalist strands in epistemology,* and (ii) substantial additions to logic itself and to geometry in the latter part of the nineteenth century. To those two in the vista of Peikoff 1964, I should add (iii) the spectacular empirical success—from Maxwell to Einstein (GR) and Schrodinger (wave QM) / Heisenberg (matrix QM)—won by casting physical relations in terms of portions of modern analytic mathematics. In my own assessment, it is (ii) and (iii), against the background of (i) and inadequacy of old-time logical ontologism that are the main and sufficient preparations for the crop of conventionalist characterizations of logical truth by logical empiricists to mid-twentieth century. “My concern has not, of course, been to maintain a primarily causal thesis; it has not been my intention to argue, for instance, that Cudworth’s difficulties with God or Locke’s problems with Aristotle’s forms were the causal factors centrally responsible for the dominance in our century of the conventionalist approach to logical truth. Such a thesis would hardly be tenable; the creation of non-Euclidean geometries, to cite just one example, was undoubtedly more influential in this connection than the sort of difficulties I have discussed. . . . My concern has been rather, by considering a few aspects of the question, to suggest that, as a matter of fact, the seeds of conventionalism were implicitly present in the formulations of the classical logical ontologists, and that there was a logic to this presence.” (Peikoff 1964, 240) Peikoff took Kant to be “the philosopher most responsible for the demise of logical ontologism in the history of philosophy” (165). In a roundabout way, I concur. The demise of ontological essences, Platonic forms, and Aristotelian forms and formal causes had transpired before Kant, as far as the modern stream of philosophy was concerned. In that fall was also the fall of logical ontologism. Kant’s weight on the demise was through his own imposing, positive system of theoretical philosophy replacing Aristotle’s (and replacing modern systems such as the system of Leibniz). Kant weight on that demise and Kant shadows on the future saliently include: His success in bringing to much attention a philosophical division of sense and understanding and of the synthetic and the analytic (not what we mean by synthetic/analytic in geometry); his subject-rooted theory of how geometry is possible; his replacement of Aristotle’s categories as in the world with categories as belonging to human understanding in its approach to sensory experience of the world; lastly and most profoundly, in my estimation, his particular replacement of Aristotelian ontological form with subject-side form.** “Although many—but not all—classic philosophers subscribed to the necessary-contingent or rational-empirical dichotomies in their classification of propositions, this was not for them the equivalent of the logical-factual dichotomy; to this latter the vast majority did not subscribe, nor could they have, since they regarded the laws of logic as themselves matters of fact (i.e., ontological in character, not ‘mere’ matters of fact).” (13) The philosophers Peikoff examines in their conventionality of logical principles do not regard these salutary principles as arbitrarily selected, although, as with Kant, their basis is not some fact(s) holding independently of human existence and consciousness. Peikoff quotes logical empiricist Ayer denying that analytic propositions “provide any information about any matter of fact. In other words, they are entirely devoid of factual content” (Ayer 79; Peikoff 170). Ayer does not follow Kant’s proposal that analytic patterns are from invariant organization of the human mind. Rather, granted various linguistic conventions, “the laws of logic which flow from them are necessary and incontestable truths” (Peikoff 174).*** From what we have seen of Kant in previous segments of this essay, he would take conditioning truth and necessity of logical principles such as PNC on any conventional structure of language as inadequate to deliver the necessity logical truths possess. Any indebtedness of logic to structure of language cannot be indebtedness to anything conventional in language, because conventionality is contingency, not absolute necessity, not the necessity Kant attached to the a priori. Ayer and Kant agree that logical truths are a priori and analytic. An example of an analytic statement from Ayer is: “Either some ants are parasitic or none are” (79). “Either some are or none are” is so no matter what facts of the world it is being applied to. And no observation in experience could refute this logical truth. On that much Kant and Ayer could agree. Kant famously did not think that analytic truths are the only sort of a priori truths. The other sort of a priori truths, he called synthetic. He took the analytic and the synthetic to exhaust the sorts of a priori truth. The exemplar of synthetic a priori truths was geometry of Euclidean space, the only structure of physical space known until Einstein’s general relativity (1916). That space (spatial slices of the four-dimensional [semi-] Riemannian spacetime manifold of variable curvature) is not intuitive in the ready-to-hand way that Euclidean space is intuitive (in carpentry or, differently, in Euclid), thus not congenial to Kant’s conception of space as pure form of outer, sensory intuition (in Kant’s technical sense of intuition). Logical empiricism arose in an intellectual scene in which Kant’s exemplar of synthetic a priori truth lay in shambles. Moreover, by that time, David Hilbert had staked pure geometry as purely abstract and independent of any physical application or sensory experience. Hans Reichenbach in 1920 correctly observed that Kant had held a priori truth to be not only necessary and unrevisable, but constitutive of the concept of the object as object of knowledge. That last character of the a priori was not toppled by Einstein’s revolution. At least it was not toppled in the obvious way that universality and unrevisability were toppled with respect to physical Euclidean geometry. At first Reichenbach thought such constitutive principles were at hand in modern application of mathematics to physics, but he soon became persuaded that those principles of application were neither true nor false. They were simplicity- and tractability-based conventions. By the 1920’s, the last toeholds of Kant’s intuitive, synthetic a priori in geometry and in geometry’s physical exemplification had been dissolved by Reichenbach, Schlick, and Carnap.**** (To be continued.) ~~~~~~~~~~~~~~~~ * In the installment “Aristotle II”, I conveyed Peikoff 1964 on inadequacies of nominalism in provisioning a theory of logic. See also Paul Forster’s Peirce and the Threat of Nominalism (2011, 24–28, 38). ** On transformation of Aristotle’s matter-form distinction from Leibniz to Kant, see Marco Sgarbi’s Kant and Aristotle – Epistemology, Logic, and Method (2016, 79–94). *** Cf. Herder c.1767 and 1772 in Michael Forster’s Johann Gottfried von Herder – Philosophical Writings (2002, 48, 100). **** Michael Friedman’s “The Evolution of the A Priori in Logical Empiricism” in The Cambridge Companion to Logical Empiricism, Richardson and Uebel, editors (2007, 95–108).
  9. . Hi Nell, If I recall Roe correctly, the 6-month mark was taken as significant not because at that point the fetus passed into being a human, but because of your other feature of that time: the fetus will have reached a development such that it could live outside the womb, live independently of its mother if supported by modern medicine and whomever pays for that. Roe’s mark there had two built-in considerations making the 6-month time not exact and not fixed against future contraction: (i) when a particular fetus might be viable outside the womb (judgment of viability in the case being made by attending physicians), with present technology, can vary somewhat from one fetus to another, though around 6 months was typical and (ii) with medical technological progress, the typical time at which viability outside the womb is reached could be pulled in to earlier and earlier times. I suppose that if entirely “test-tube babies” become a reality in the future, then any fetus or conceptus could be removed and grown to infancy independently of further support from the mother’s body. I’ve always supported Roe. It looks like the opponents have finally gotten enough anti-abortionists on the Court to overturn it, that is, to let each State determine the question within its own State boundaries. Here are a law professor’s brief and informative remarks on the recent moves on third trimester and their connection to preparations from the freedom-of-the-mother-to-abort side for the post-Roe legal situation in States in which abortions are not made illegal throughout pregnancy. https://www.pbs.org/newshour/show/state-battles-over-abortion-policy-anticipate-a-post-roe-world
  10. PNC Ground Shifts to Side of the Subject – On to Conventionalism Peikoff laid out the varieties of logical ontologism, these being the various ways in which it had been thought that principles of logic, such as PNC, are general ways the world is. The principle of noncontradiction (PNC) is a guide for us to adhere to in thinking, and under ontology-based theories of logic—Plato to Leibniz—PNC is right to follow in one’s thought because it is a fact of the world independently of human mind, an everywhere fact of the world. If our aim in thought is grasp of the world, PNC is a fact of the world we must hold onto for success in that aim. Let us notice that in claiming (not-A and B ) both the not and the and can be in the world. An object not having support and that object’s falling to the floor is a fact of the world. If our aim is keeping objects from falling, we must see to it that they are adequately supported. For that A and B, in usual household life, do not (not-A and B). In the formula (not-A and A), we move to what Peikoff called a formal aspect of the world. Logical ontologism would have it: do not (not-A and A) in thought if our pursuit is getting and keeping a grip on the world, because [not (not-A and A)] is an everywhere formal fact of the world, a necessity given, regardless of our aims. I had written in “Aristotle I” that for my own part I thought that, notwithstanding its objectivity, PNC has some dependency on thought which 2R (the fact that the angles of a triangle in the Euclidean plane sum to two right angles) does not have. That was because cases of noncontradiction run arbitrarily far afield, as far as our free imaginations: a five-fingered hand is not an opera, and so forth for anything at all not a five-fingered hand. That composition was nearly two years ago, and I’ve changed my mind. PNC is not partly dependent at root on operations of mind, notwithstanding PNC’s unlimited scenes of pertinence. Peikoff’s 1964 dissertation talk of formal aspects to the empirical world, without embrace of Aristotelian or Kantian schemes of form, is talk and conception that has proven valuable to me in development of my own metaphysics in my book in progress. Independently of Peikoff 1964, it is also talk and conception now taking hold and developing in philosophy of logic and mathematics by Gila Sher, as in Epistemic Friction (2016). As of mid-20th Century, however, as Peikoff 1964 observed, principles of logic in modern philosophy had become sourced no longer in the world, but in the subject. (To be continued right away.)
  11. I took this evening photo a little after writing this poem, written lying on the living room floor beneath her. -2/4/19The 'he' is Jerry (d. 1990).
  12. NC, I liked Neal and Massey the best. But linked below is a scene in which Cooper as Roark is landing the book true (though he has the drawback of age). There is a Cooper scene I especially liked (no link) in which Roark says to Keating that men able to do something are his kind of man. Cooper seemed to really get that. Neal and Massey https://www.youtube.com/watch?v=kCMarRkVRk4 Neal and Cooper https://www.youtube.com/watch?v=vC5yxqKedTk
  13. Boydstun

    Which Eternity?

    . Possibilities are cognitive/epistemological (or entertainments in the case of fictions). Potentials are existential/metaphysical things belonging to concrete actualities. Possibilities are run over actualities with their potentials (or they are run over formalities such as in mathematics). I’ve some significant overlap with pre-modern philosophies in these partitions. Additionally, I’ll mention again for ease of reference for interested readers the book arguing in the contemporary vernacular to the vicinity of my partition, the book by Barbara Vetter: Potentiality – From Dispositions to Modality (2015). One book I’ve found helpful in tracing the rise, the variations, and the fall of the actual/potential partition in the history of philosophy (from Aristotle to early modern), as well as occurrences of the actual/potential distinction in contemporary science is Handbook of Potentiality (Engeland and Quante, editors, 2018). There is an excellent chapter “Potentiality in Physics” by Max Kistler in the Handbook. He sorts out what is and is not an occasion of metaphysical potentiality in the various modern physics concepts, classical and quantum, going under such names as potentials and capacities. Thanks to you all for sharing your conceptual organizations concerning these fundamentals.
  14. Boydstun

    Which Eternity?

    . SL, our quickest perceptions of objects or events is one or two hundred milliseconds in duration. We have some quicker processes of perceptual discriminations occurring (requiring) only about ten milliseconds. There is nothing physically significant in the demarcation of past and future existence about those particular intervals of “the present” of our experience. In our “instant” of perceptual consciousness (or of any consciousness) of a physical object, there are atomic transitions taking place in the object down at the level of 10-to-the-minus-18 seconds and nuclear transitions taking place in those atoms down at the level of 10-to-the-minus-23 seconds. In an instant of observation is an ocean of objective time. Transitions, actions, and processes are part of existence. They are existents, and the entities to which they pertain are existents. An episode of alterations is part of existence no matter the rate of its transition or epoch of its occurrence. I'd not confine existence or Existence to a particular point or particular limited interval in its duration. No dividing line of past and future existents should be treated as containing all that exists. And if we say only that that dividing line is all that exists at that dividing time, that's true, but it does not preclude existence at all times being included in the all that is Existence.
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