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Boydstun

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Everything posted by Boydstun

  1. Gravity Probe B A drag-free satellite equipped with exquisite monitoring of spin axis of superconducting gyroscopes brings confirmation of two effects of GR. More on final results of the experiment will be posted soon here at the Stanford site.
  2. . The Journal of Ayn Rand Studies is planning to publish this paper of mine next year. The paper is 63 journal pages. I’ve shown its subsections on the wall back there. No walls suffered graffiti in the production of this notice. This photo reflects only what I looked like 22 years ago. This is the most extensive study ever made comparing these two philosophies in their contrasting foundational approaches. Leads to my own philosophy in my book in progress are found in this paper in its alignments with Rand against Descartes, in its amplifications of those oppositions, and in the charges I bring against Rand and Descartes in common. (No, not the usual, ignorant charges brought against them in common.) This kind of sustained examination of individual philosophers such as Descartes will not be feasible to include in my book. There, the parts of Rand I adopt and extend, the parts I reject and replace, and my own systematic, integrated replacement philosophy is the main work. The pertinent ideas from the history of philosophy to our contemporaries will be noticed and addressed, however, all along the way. ~~~~~~~~~~~~~~~~ By the way, I do indeed intend to complete the installments here at Objectivism Online on Leonard Peikoff’s dissertation and its subsequent tributaries into Objectivist writings. It has continued slowly this year because his topics are also among mine in my book, and as I study the pertinent contemporary literature in these areas, I give priority to their assimilation into my book. I hope their assimilation into the concluding portions of my Peikoff series can be concluded this year.
  3. I've recently had an informative exchange with a Facebook friend who is a serious student of philosophy. I need to keep that person's identity anonymous, so I'll just here name him Fellow. He posed the following question. I'll try to post installments of our exchanges in the next few minutes in this thread. Some digging has gone into this. And perhaps participants here will have some further thoughts. FELLOW - Stephen, I am contacting you with a question regarding an important idea that, as far as I am aware, is the product of Ayn Rand: floating abstractions. I chose to reach out to you specifically because I have run across some of your work (e.g. “Universals and Measurement”) and I judged that you might be able assist me given your knowledge of philosophy, and in particular Rand’s philosophy. I am interested in reading something relatively comprehensive on the subject of floating abstractions, and I was hoping you might be able to direct me to a resource which deals with floating abstractions in some detail. There is a section in Peikoff’s Objectivism: The Philosophy of Ayn Rand (p. 96) which describes what a floating abstraction is; yet, while it does bring some clarity to the subject, I still find the notion of a floating abstraction a bit murky and difficult to apply. For example, what about certain concepts in mathematics that seem to have some sort of use (e.g. transfinite cardinal numbers, or geometric points)? They seem to meet Peikoff’s description of floating abstractions as “concepts detached from existents”. STEPHEN - I'm inclined to think that in pure mathematics there is always connection to reality in that we reach a concept such as transfinite numbers and accept it only by it satisfying the requirements mathematicians have over centuries refined to qualify as a legitimate mathematical concept, with its connections to more elementary mathematical concepts and its emerging connections to other areas of mathematics. That is, for my part, there are binds of accepted mathematical concepts to reality and to our abstractive and inferential processes themselves other than the binds of such concepts when we do find them appropriate for application to empirical situations. Another thing I think good to remember is that there are apparently things concretely real that we access only by abstraction. Such would be an electron or a geometric point. That is not to say every validly established concept or theorem in mathematics having physical instance will have causal powers, such as an electron has. But things such as geometrical points might be also instanced physically (which Euclid, Descartes, and Newton inclined to take them to be), themselves be part of physical process and part of our empirical experience, yet not themselves possess causal powers. / I imagine my conceptions expressed in this note have some deviation from the picture Rand had so far as she got and some variance from the pictures reached by others who are intellectually indebted to her.
  4. Boydstun

    About Those 'Floating Abstractions'

    There is an example of feeble thinking Rand gives that seems to me to be an excellent case of what she called ‘floating abstraction’ though she doesn’t call that out in her presentation of this case. That example is a use of the abstraction ‘truth’. I want to quote three paragraphs before that truth-paragraph too. I think her concern expressed here fits the weight of attention Objectivist writers, including Rand, have tended to give to everyday trip-ups by floating abstraction, in comparison to diagnoses of floating abstraction in the ‘castles-in-the-air’ of Rationalist philosophers. “There is an old fable which I read in Russian . . . . A pig comes upon an oak tree, devours the acorns strewn on the ground and, when his belly is full, starts digging the soil to undercut the oak tree’s roots. A bird perched on a high branch upbraids him, saying: ‘If you could lift your snoot, you would discover that the acorns grow on this tree’. “In order to avoid that pig’s role in the forest of the intellect, one must know and protect the metaphysical-epistemological tree that produces the acorns of one’s convictions, goals and desires. And, conversely, one must not gobble up any brightly colored fruit one finds, without bothering to discover that it comes from a deadly yew tree. If laymen did no more than learn to identify the nature of such fruit and stop munching it or passing it around, they would stop being the victims and the unwary transmission belts of philosophical poison. But a minimal grasp of philosophy is required in order to do it. “If an intelligent and honest layman were to translate his implicit, common-sense rationality (which he takes for granted) into explicit philosophical premises, he would hold that the world he perceives is real (existence exists), that things are what they are (the Law of Identity), that reason is the only means of gaining knowledge and logic is the method of using reason. Assuming this base, let me give you an example of what a philosophical detective would do with some . . . catch phrases. “‘It may be true for you, but it’s not true for me’. What is the meaning of the concept ‘truth’: Truth is the recognition of reality. . . . The same thing cannot be true and untrue at the same time and in the same respect. That catch phrase, therefore, means: a. that the Law of Identity is invalid; b. that there is no objectively perceivable reality, only some indeterminate flux which is nothing in particular, i.e., that there is no reality (in which case there is no such thing as truth); or c. that the two debaters perceive two different universes (in which case no debate is possible).” (“Philosophical Detection” – 1974) Harry Binswanger points out in How We Know that definitions are the main help in remembering what is the hierarchy of one's concepts which though validly structured in the past, may have faded (214). Rand invokes definitions in the preceding detection.
  5. Boydstun

    About Those 'Floating Abstractions'

    ET, I agree about the deceit in that example used by B. Branden. It came up very prominently again this year, with the big spending bill following on the tax cuts. It would be often claimed that, well, the tax cuts (and regulation removals) would be so tremendous, the economy would boom so much, and the income tax receipts would be so great that there won’t be a deficit. It sounded to me very much like a sop thrown to those really concerned with a balanced budget, a smokescreen for what had really been decided: the interest in a balanced budget lost to other interests, and more debt is the reality. My inclination on your closing question would be: both. By the time I was a senior in high school, I’d become a Christian Socialist. That was for the simple reason that I’d concluded that private property should be abolished because it allowed people to be selfish, and selfishness was wrong. Altruism was right, and it was the focus of what moral virtue consisted of. But if such a young man were willing to really begin to cash out all those ideas and ideals in terms of practical reality and practical connection to other ideals also held (such as individual liberty), they begin to wither as ideals.
  6. Boydstun

    About Those 'Floating Abstractions'

    Invictus, where you say “random associations” wouldn’t it be enough to just say “associations”? If I understand you correctly, your contrast is with rational derivations and cognitive connections to reality, especially concrete perceptual reality, and that sort of derivation and connection is in contrast to associations even if we can see the association is not random. I mean our most basic meaning of the concept ‘breakfast’ could sensibly be “meal following pretty closely a pretty full sleep.” One could have associations with ‘breakfast’ such as what kinds of foods are typical at that meal or the association of ‘breakfast’ with its typically being in the morning. We can see why those associations get attached, they’re not random, and it’s enough to contrast associative connections with reasoned ones. I take it that when you talk of adopting a concept from others, you mean adopting it without understanding it very far. I can get a square concept of ‘mineral’ from geology class. Your analysis strikes me as landing pretty well on Rand’s concept of a ‘floating abstraction’. I mention Rand because this error and its name were formulated by her. She gets a monopoly on it, so to speak. Similarly, with Whitehead and the fallacy of ‘misplaced concreteness’. With the general, long-standard fallacies and their names, such as the fallacy of ‘hasty generalization’, there too, it’s good to stay fixed on the exact concept defined and not simply presume what it is that the name is suggesting without official definition. I mention this for all of us.
  7. Boydstun

    About Those 'Floating Abstractions'

    STEPHEN - Yes, the Berkeley idea seems the same, but in other terms. And a lot of Objectivist types when thinking about the nature of mathematics come down rather like Berkeley. I disagree with them both on the mathematical situation. We do have physical applications of complex numbers. But we did not have any such applications (i.e., physical structures known to coincide with the structure of complex numbers) at the time complex numbers were first thought up. They were never ungrounded in rationally grasped realities, even before physical application was found for them. And there are other things mathematically sensible that to this day we’ve found no physical instantiation of, and perhaps there is no such instantiation. Rand wrote against the idea of a system of free-market private protective agencies replacing government in the primary functions of the latter: “Nor can one call it a floating abstraction, since it is devoid of any contact with or reference to reality and cannot be concretized at all, not even roughly or approximately.” Here she seemed to think of floating abstractions as having some weak connection to reality. Although, presumably, that could still leave them of limited use and even detrimental for knowledge. On the NOT side, it occurs to me that I’ve NOT noticed any Objectivist writings taking Platonic Ideas as floating abstractions. The fact that such Ideas have regular relations to concretes may perhaps be enough to save them from being the sleaze of floating abstractions, even though we do not obtain them by abstraction from concretes perceived by the senses. In the 1960’s while articulating Objectivism, together with Rand and others, Barbara Branden gave a lecture series called “Principles of Efficient Thinking.” Therein she spoke in a kind of psychological-type way of persons who characteristically think in terms of floating abstractions. She said they don’t see the trees for the forest. There’s “nothing in his head but floating abstractions—that is, abstractions which he’s unable to concretize, which he believes, without any idea of what they would actually mean in reality. / An example of this kind of thinking is a meeting at which a political candidate declares that he stands for a balanced budget, decreased taxes, and increased government spending; and his audience bursts into applause. No one who understood concretely what these abstractions meant could possibly applaud. / A man who holds floating abstractions understands words not in terms of what they denote, but in terms of what they connote. Words connote things to him. They call up pleasant or unpleasant emotions, associations, memories. They suggest; they do not denote. His abstractions float in space, untied to meanings, to facts, to reality.” (Transcribed on p. 178 of the book THE VISION OF AYN RAND.) In the 1980’s Leonard Peikoff gave a lecture series called “Understanding Objectivism.” I notice there that he thought of Leibniz, and presumably Rationalists more generally as dealing in floating abstractions (which is rather the idea you get of Rand’s view of Rationalism in her “For the New Intellectual” even though she doesn’t use the name ‘floating abstraction’ there so far as I’ve found). Peikoff mentions a type of psychosis “which has some elements of being concrete-bound, and has some elements of floating abstractions (certain schizophrenics will build castles in the air), but still they are crazy, and Leibniz wasn’t.” (Transcribed on p. 265 of the book UNDERSTANDING OBJECTIVISM.) The quotation on floating abstractions you found in Peikoff’s OPAR is helpful. Thanks. There he seems to be back to thinking about persons not very philosophical in their thinking. (Cf. Rand’s ITOE 75-76; also p. 214 of Harry Binswanger’s HOW WE KNOW.) Gregory Salmieri maintains that floating abstractions are one possible result of not taking the dependency relations of concepts into one’s thinking. He seemed to have in mind the dependency chain of concepts ultimately to “first-level concepts” (presumably elementary concepts of kinds of concretes ordinary in perception). “A floating abstraction is a concept that has become detached in one’s mind from its basis in perception and has therefore lost its meaning (Peikoff 1991, 96).” (p. 71 in CONCEPTS AND THEIR ROLE IN KNOWLEDGE – REFLECTIONS ON OBJECTIVIST EPISTEMOLOGY.)
  8. Boydstun

    About Those 'Floating Abstractions'

    FELLOW - Do you think that, without God to ground these other ways the world could have been, that such conjecture would be reduced to floating abstractions? / That said, if we could return more specifically to the topic of floating abstractions, I still suspect that I do not have a firm grasp on what they are. Peikoff, in OPAR, defines a floating abstraction specifically as "['Floating abstraction'] is Ayn Rand's term for concepts detached from existents, concepts that a person takes over from other men without knowing what specific units the concepts denote. A floating abstraction is not an integration of factual data; it is a memorized linguistic custom representing in the person's mind a hash made of random concretes, habits, and feelings that blend imperceptibly into other hashes which are the content of other, similarly floating abstractions. The 'concepts' of such a mind are not cognitive devices. They are parrotlike imitations of language backed in essence by patches of fog" (96). With this in mind, I take it that floating abstractions are not cognitively meaningless, since they will derive meaning from “random concretes, habits, and feelings” (perhaps use as well?) even though they have no objective referent. So, a floating abstraction does not have an objective referent, I gather—which I might put in other terms by saying that the concept does not refer to anything with ontic status. Peikoff seems to want to say that these are concepts in name only—inauthentic concepts—which cannot be put to any use in attaining knowledge. A system of floating abstractions might then be said to constitute a mere game of language. I am reminded of Bishop Berkeley’s remarks about theoretical mathematics, as opposed to applied, “The Theories therefore in Arithmetic, if they are abstracted from the Names and Figures, as likewise from all Use and Practice, as well as from the particular things numbered, can be supposed to have nothing at all for their Object. Hence we may see, how entirely the Science of Numbers is subordinate to Practice, and how jejune and trifling it becomes, when considered as a matter of mere Speculation” (Principles, §120)—regardless of whether you think he is correct, he seems to me to speak of floating abstractions, just in his own terms.
  9. Boydstun

    About Those 'Floating Abstractions'

    FELLOW - I gathered as much; considered as formalisms, or even as eternal abstracta, the actual-potential distinction simply doesn't seem to apply. You wrote that “the experts would know far better whether it was yet specified enough to be truly a grounded possibility.” If we are discussing the point at which actuality had its genesis, then I worry that whatever grounded possibility there might be, it will not itself be grounded in anything actual, but will merely be a logical possibility that is grounded insofar as it is not self-contradictory. Did Newton discuss what grounds the possibility of such forces being different than they actually are? I am not familiar with Newton, but I conjecture it would be grounded in the will of God to bring forth a world with different physical laws. STEPHEN - Newton first established his bare mechanics, like what we call now his three laws of motion. He then argued the nature of central force in general within that framework for the orbits of bodies and showed that different dependence of the strength of force from the central area (such as falling off from the inverse cube versus falling off from the inverse square) leads to specific different shapes of orbits of bodies about such candidate centers. Then he can use Kepler et al. observations to say, well since the actual orbits of the planets about the sun have the shape of ellipses, the attracting force must be strong inversely to the inverse square separation. That candidate is the winner in the real world. That is then part of his formula for the force we call gravitation. It must have power of accelerating distant bodies with a strength falling off with inverse square. That then, is one specific form of force that he can fit into his second law of mechanics. So on the left of our equation, we put his expression for force in general (say, mass times acceleration, be a little too simplistic) and on the right we put the formula of the specific kind of force we are concerned with, such as the gravity force. Those are differential equations, and the solutions satisfying the equations give us the time course of the bodies in their paths in space. / In Newton's larger theological and metaphysical picture, he had space as co-eternal with God. As I recall, he had time beginning with God's creation of the material world in space, and in that part his was the usual view. PS - That space was 3D and Euclidean of course. Also, I meant to include that I'd wager he'd think God could have chosen inverse cube, say, rather than inverse square for the character of gravitation. For that matter, I don't know as he would have a reason for thinking God had to make a material world such that it had such a thing as gravitational force. Although without something like that, it becomes hard to imagine what humans, with their material character would be like. [Pretty floaty now I think of it.]
  10. Boydstun

    About Those 'Floating Abstractions'

    FELLOW - To be clear about your view, you are saying that for something to be a genuine possibility, rather than a floating abstraction, it must be realizable through the potential contained in actual existents. So, rather than a groundless ontological ensemble of possible beings awaiting actualization, the possibilia are always contained in, as potential, actual beings and, in that way, await actualization. Prima facie, I have some sympathy for your view. What do you make of claims that the initial conditions of the world/universe/existence (though not the fundamental axioms) could have been otherwise than they were? The idea, I gather, is that many different sets of initial conditions were logically possible, though only ours was actualized. If those counterfactual claims can be assessed as true, it would seem that there would be no actual objects in which their possibility could have been grounded as potential. STEPHEN - Before addressing that, let me add a further point I forgot mention in the previous note. My conception about actuals, potentials, and possibilities does not pertain to purely formal realities such as pure mathematics. I mean that the actual-potential concepts do not pertain to them. Possibilities of course are entertained in mathematics based on previously established results shown to be true or false (or undecidable) with an aim to establishing new results. / But to your present question, possibilities of characteristics of those alternative to those that obtained at the initial singularity would seem grounded and cognitive provided they are specific and tied to established other physics. The physicists are talking specifics and have guide rails from other established physics in their papers on such alternatives. They have reasons (hard-won reasons) for saying that at the initial singularity its mass-energy, charge, and total angular momentum were the same as they are now. It would seem to me a sensible question to then ask What if the value of total mass-energy of the universe were not constant but instead oscillated in a simple harmonic way? The experts would know far better whether it was yet specified enough to be truly a grounded possibility. (Oh, I should have mentioned that the initial singularity is not no object.) / That sort of reasoning about alternatives was important in Newton's PRINCIPIA. He was able to show that if a central force had strength falling off as the inverse square of separation distance, a freely orbiting body would have and elliptical orbit; whereas, if the strength fell off as the inverse cube of separation distance, a freely orbiting body would have another perfectly specific shape of orbit, not an ellipse; and so forth. His physical assumptions and the mathematics for these conditionals are very specific and explicit. And there was light.
  11. Boydstun

    About Those 'Floating Abstractions'

    FELLOW - That seems like a reasonable way to understand such concepts as geometric points. What do you think about something even more abstract, like merely possible objects? They might be said to exist, in the broadest sense (some philosophers have used the term 'subsist' to account for such things), but not in a narrower sense of the term 'exist' which only covers actual things. I'm trying to pin down just what sorts of things are ruled out as floating abstractions and which are not. STEPHEN - I do not myself allow as cognitive possibilities alleged possibilities that have nothing to suggest how they could be realized from the potentials of existing things. To be a cognitive possibility in my book, an idea has to do more than be merely not self-contradictory. There are other kinds of possibilities such as for our entertainment in fiction. But possibilities aiming to be cognitive, such philosophical reflections, yet which are not specifically grounded in potentials of actuals, are floating abstractions.
  12. Boydstun

    My Verses

    . These Words These words we read from some desire . . that someone live . . the this entire. Read is our reach, . . our grasp, our be . . life that is know . . wings that are free. Copyright Stephen C. Boydstun 2016
  13. Boydstun

    My Verses

  14. Boydstun

    Ayn Rand and the French

    . Oh, I was just interested what is your impression for the parallel question to yours: What do the French today think of Guyau? I was just curious, since I have an interest in this French philosopher. By the way, I thought your English was fine. Concerning a related question “What do Americans think of Ayn Rand?” my impressions are these: The egoism she brought on the scene, beginning to get some notice in the 1940’s due to her book and film The Fountainhead, was foreign to America. Individualism, fine; egoism, hell’s bells. There were traces of egoism in Emerson, but nothing like this. By egoism, I mean the idea of having self-interest as the ultimate justification for every right action and the throwing out of any old virtues that cannot be justified on that basis. Her championing of reason and her jettison of faith and the supernatural is, as you know, perfectly normal for those in American academia. But the egoism and the attendant pure capitalism of her ethical and political philosophy mean that she is pretty roundly shut out of serious development by philosophers who have won a place in academia. Outside of academia, in the wider literate public, her view upholding full reason, including her dismissal of the supernatural, and her view of morality based purely on self-interest are anathema. Though we are not a significant percentage of the American population, some of us read Rand and benefitted from her thought and productions in building our own wide understanding of things and in making a life for ourselves.
  15. Boydstun

    Here I Stand

    . This October 31 will be 500 years since Martin Luther nailed his 95 Theses to a church door in Wittenberg. Ideas move the world. October 31 is Halloween, and Luther had his reasons for selecting that day to launch what would become the Reformation. That day came to be known also as Reformation Day. I was born on that day in 1948, a Sunday in that year. I was born before dawn, and I’ve found that is my right time for starting each day. Ideas move the world. Ein Feste Burg
  16. Boydstun

    Here I Stand

    . Finding Morality and Happiness without God
  17. Boydstun

    Ayn Rand and the French

    Gio, Do you hear in France today anything of the French philosopher Jean-Marie Guyau? Especially, do you know anything of his book Esquisse d'une Morale sans Obligation, ni Sanction? Nietzsche got the first edition hot off the press in 1885. I like some of Guyau's ideas in that book. Nietzsche, Guyau, and Rand all made moral theories based on biological human nature, they were all moral individualists, opposed to utilitarianism and to Kantian ethics and to Schopenhauer's pessimism. All three were completely secular, not theistic. The three had different conceptions of what was the basic nature of life per se, and this was harmonious with their three different moral conceptions. Guyau's moral theory was not an egoistic one. I like his theory better than Nietzsche's predominant congealing view from about 1883 forward. Rand's moral view is more developed and systematic than either of those other two. Guyau was more friendly towards modern capitalistic society than was Nietzsche. Rand had read some Nietzsche in Russia before coming to the US, but those were not good translations into Russian. One of her biographers here has mentioned to me that a course on Guyau was offered at Rand's university in Russia during her college years, but that she did not take that course. This book of Guyau's was translated into English by an American near the end of the 19th Century. Guyau died young. As I recall, he had some influence on Bergson (and perhaps a bit on Nietzsche), but my impression has been that he was known best in late 19th and early 20th century. There is an American philosopher of that era named Josiah Royce who had some appreciation of Guyau. --S
  18. Tony, Definitely draining the security of my country by massive continued deficit spending. All President Trump had to do was veto that spending bill, send it back to the House, and promise to sign a bill with the exact same internal proportions and with the total amount allocated reduced to expected revenue. That would drain a swamp, or more precisely, a real definite threat to our country (USA). That would be serious leadership. Time to stop so many metaphors, other words of vagueness, and name-calling, and replace this President with someone not anti-intellectual. Politically, this is not a great time for our country, due to the anti-intellectuality riding so high.
  19. Boydstun

    Greetings from New York

    Welcome to the forum. Thanks for your inputs.
  20. Boydstun

    The Logical Leap by David Harriman

    I got mixed up, Ninth. What I had come across was this little bit of posting, but I see that this too was at Objectivist Living, only under a different user name. I'll link this one here. It gives a link to his own personal blog, which shows some of his range of his interests.
  21. Boydstun

    The Logical Leap by David Harriman

    . Some readers here may have known Ted Keer, at least as a poster. He posted a while at Objectivism Online. I have learned from his Facebook page that he died on 5 March 2018. He died in his sleep of natural causes. Ted once quipped of my paper Universals and Measurement: "At last, metaphysics that stays crispy in milk." Here is a comment of Ted's on The Logical Leap.
  22. . The Status of the Law of Contradiction in Classical Logical Ontologism Leonard Peikoff – Ph.D. Dissertation (NYU 1964) There are no true contradictions, and there cannot be any. That is the law of contradiction, or principle of noncontradition (PNC) as I shall call it. There is nothing and can be nothing that is both A and not-A at the same time and in the same respect. The last three decades, Graham Priest and others have argued specific exceptions to the law. These exceptions seem to be such that from them no possibility of observable, concrete true contradictions can be licensed. The debate over these circumscribed candidates for true contradictions continues. I shall in this study fence them off, without disposition, from our still very wide purview of PNC. There are reasons advanced in favor of these specific alleged exceptions to PNC, I should stress. It is not argued that we should just say true or false as we please of the contradiction reached in these cases. These are not situations for conventions such as the side of the road on which to regularly drive. (See Priest, Beall, and Armour-Garb 2004.) Under the term classical in his title, Peikoff includes not only the ancient, but the medieval and early modern. By logical ontologism, he means the view that laws of logic and other necessary truths are expressive of facts, expressive of relationships existing in Being as such. Peikoff delineates the alternative ways in which that general view of PNC has been elaborated in various classical accounts of how one can come to know PNC as a necessary truth and what the various positions on that issue imply in an affirmation that PNC is a law issuing from reality. The alternative positions within the ontology-based logical tradition stand on alternative views on how we can come to know self-evident truths and on the relation of PNC to the empirical world, which latter implicates alternative views on the status of essences and universals. Opposed to the classical logical ontologists are purportedly conventionalist approaches to logical truth in the first half of the twentieth century. Peikoff argues that infirmities in all the varieties of classical logical ontologism open the option of such conventionalism. Firstly, Peikoff examines the views of Plato (427­–347 B.C.E.) in their import for an explanation of our knowledge of PNC and its self-evident character and for the bases of PNC in reality. Peikoff then examines these imports in the views of Aristotle as well as in the views of the intellectual descendents of Plato and Aristotle to the time of Kant. Peikoff cites a number of passages in which Plato invokes varieties of PNC as a general principle of the character of things that must always be acknowledged in reasoning. “The same thing will not be willing to do or undergo opposites in the same part of itself, in relation to the same thing, at the same time” (Republic 436b). “Do you suppose it possible for any existing thing not to be what it is? / Heavens no, not I” (Euthydemus 293b). To citations given by Peikoff, I add Republic 534d where Plato speaks of some persons “as irrational as incommensurable lines.” The incommensurability of the length of the diagonal of a square to the length of its side had been discovered by the time of Plato, and its proof is by showing that on assumption of commensurability of those lines there follows the contradiction that whatever number of integral units composing the diagonal, the number is both even and odd. Peikoff rightly stresses that for Plato the perfect Forms are radically different from their empirical namesakes. Under the latter acquaintance, our knowing the Forms, so far as we do, is from memory of our full knowing of them in our existence before this life of perception, according to Plato: “Consider, he said, whether this is the case: we say that there is something that is equal. I do not mean a stick equal to a stick or a stone to a stone, or anything of that kind, but something else beyond all these, the Equal itself. Shall we say that exists or not? / . . . Most definitely / . . . / Whence have we acquired the knowledge of it? . . . Do not equal stones and sticks sometimes, while remaining the same, appear to one to be equal and to another to be unequal – Certainly they do. / But what of the equals themselves? Have they ever appeared unequal to you, or Equality to be Inequality? / Never, Socrates / . . . / Whenever someone, on seeing something, realizes that that which he now sees wants to be like some other reality but falls short and cannot be like that other since it is inferior, do we agree that the one who thinks this must have prior knowledge of that to which he says it is like, but differently so? / Definitely. / . . . / We must then possess knowledge of the Equal before that time when we first saw the equal objects and realized that all these objects strive to be like the Equal but are deficient in this” (Phaedra 74). Perceptibly equal things are deficient in that they can appear unequal in some occasions of perception. The Form Equal by contrast is always just that. Perceptibles “no more are than are not what we call them” (Rep. 479b). Plato does not clearly isolate PNC, but he was getting onto an ontological basis for it, so far as he did grasp PNC, by his characterizing what I should call his faux contradictions of empirical objects—faux because he fails to give square reality to situational and temporal determinates of objects and to our contexts of thought and speech about objects—as both being and not being, which is to say, deficient in being. It is fair enough to say, as Peikoff concludes, that for Plato PNC has the same standing in ontology and in our knowledge as such Forms as Being, Same, Other, Equal, and Inequal. Additional support, I notice, for that standing of PNC in Plato would obtain had Plato called out Identity as a Form, where Identity means what was said above at Euthd. 393b: an existing thing must be what it is. As later thinkers would observe, Identity in that sense entails PNC. Peikoff places Plato at the head of a sequence of philosophers who held PNC to be not learned from scratch by our experience in this world. They hold the principle to be in some sense innate and to be based on realities independent of the world we experience by the senses. In the innate-PNC sequence, Peikoff places later Stoicism (see Crivelli 2009, 393–94), Neoplatonism, early Christianity, Cambridge Platonism, and Continental Rationalism. Nearly all of these, I should note, are in a very different intellectual situation than Plato’s in that they have, directly or indirectly, Aristotle’s development of logic. The latter two certainly had as well his Posterior Analytics and Metaphysics. They had thereby Aristotle’s various formulations and accounts of PNC. They stand on the shoulders of both Plato (and Neoplatonism) and Aristotle, with innate-PNC being one of their leanings toward Plato along a line of difference with Aristotle. They had as well, unlike Plato or Aristotle, Euclid’s Elements, further mathematics beyond Euclid, and further developments in logic. By the time of Republic, Plato had evidently abandoned his view that we recognize Forms in our present life because we knew them well in a previous life free of the perceptual and variation spoilers of being (Tait 2005, 179). The recollection from a previous life is no longer mentioned. It remains for Plato that the Forms, such as are engaged in geometry, are accessed only by intellect, and not to be found in sensory experience nor abstracted from sensory experience. Peikoff was aware that some scholars had begun to question whether Plato had held on to his early express view that the realm of Forms was a world in which we had lived in a previous life and from which we now have some recollection of our previous knowing. Peikoff took Plato’s view as uniform on the recollection doctrine we saw in Phaedra. I’m persuaded to the contrary view. Peikoff rightly points out that through much of the history of philosophy the recollection view and the other-world-of-Forms view had been taken for Plato’s view, and Plato’s influence, pro or con, was under that picture. I think, however, that the separateness of a purely intelligible realm of Forms, a realm not also a prior world of life, Forms separate from empirical classes participating in them, is enough for saying Plato heads a line in which knowledge of necessary truths such as in geometry or in the rules of right reasoning (importantly PNC), even if their elicitation is by sensory experience, must be innate. That much, given Peikoff’s analysis of the significant senses of innate, is enough for sharp contrast with Aristotle and his line, and the dominance of the Good over all other Forms suffices, in a foggy way, for their normativity in the empirical world (Rep. 504d–11e, 533b-d; Philebus 20b–22e, 55d–60c, 64c–67a; Denyer 2007, 306–8). I mentioned the great difference, in Plato’s view, between the perfect Forms and their empirical namesakes. The bed one sleeps in is physically dependent on its materials and construction, but the bed constructed depends on the Idea or Form Bed, and the particular constructed bed is ontologically deficient in being when compared to the invariant full-being Bed, the Form on which the particular constructed bed’s being and name depends (Rep. 596–97). It is the rational, best part of the soul that measures and calculates, helping to rectify illusions in perceptual experience and to bring us nearer truth of being (Rep. 602c–603a). In geometry we employ diagrams, but our arguments and concern are for the Forms of these figures, not the particular constructed, material figures (Rep. 510b–511a; on the “mathematical intermediates” controversy, see Denyer 2007, 304–5; Tait 2002, 183–85). Even higher than our rational capability for geometry is our rational capability for proceeding from Forms to Form-Form relations to the first principle of all Being—and the necessary ultimate spring and harmony of all knowing—which for Plato is a Form, the Good. This purportedly highest process of knowing is called dialectic, a notch above thought even in geometry (Rep. 510b–511e; further, Denyer 2007, 306–8). Reviel Netz concludes “Greek mathematical form emerged in the period roughly corresponding to Plato’s lifetime” (1999, 311). He reports Hippocrates of Chios (not to be confused with the father of Greek medicine) as “first to leave writings on Euclidean subject matter,” say, around 440 B.C.E. (275). Hippocrates is credited with introducing the indirect method of proof into mathematics, which relies expressly on PNC. Netz concludes that “much of Greek mathematics was articulated in the Euclidean style” by around 360 B.C.E. (ibid.). Euclid’s Elements itself did not appear until about 300 B.C.E. Aristotle (384–322 B.C.E.) was attentive to this mature Greek mathematics, and he put it to some use in inference to and justification of the first principle that is PNC. Plato in his discussions of magnitudes and quantity (counts) stays rather distant from the systematization and rigor being given to mathematics in his day. Plato does make Form-hay from the circumstance that the idealized determinateness and exactitude supposed in geometry makes way for such knowledge as the relationships established in the Pythagorean Theorem (Meno 85–86), relationships that cannot be established so definitively by simply measuring sides of sensible triangles and squares, but require, rather, the operation of intellect on its own. Peikoff’s Platonic line of logical ontologists hold PNC to be innate knowledge, not learned from scratch from experience of the sensible world. Peikoff conceives this line to also consist in holding that essences provide what regularity there is in sensible nature. In Phaedo Plato has Socrates say: “I am speaking of all things such as Size, Health, Strength and, in a word, the reality of all other things, that which each of them essentially is” (65d). In this dialogue, Plato invokes a notion of the contrary, within which can be read the contradictory, when he has Socrates invoke the principles (i) what one is explaining cannot have explanations giving the thing to be explained contrary qualities and (ii) an explanation must not itself consist in incompatible kinds of things (97a–b, 101a–b). Here Plato argues that the only adequate explanations are explanations by the regulative essences of things (e.g. the fineness of fine things), or we might also say, by the regulative Forms (e.g. the Fine) in which sensible and mathematical things participate, directly or indirectly (95e–102b; see Politus 2010.) I notice the implication in these parts of Phaedo that PNC, as within the prohibition of incompatibilities in explanations or in things explained, is a principle whose ultimate ground must lie in the realm of essence, or Form, not in the realm of the sensible world, lest explanation fall into the swamp of the sensible. Peikoff observes that in Plato’s view the eternal, necessary essences, or Forms, do not require mind for their existence, but for the Neoplatonists and from Augustine to Cudworth and Leibniz, these essences and all necessary truths, such as PNC, do require mind for their existence (cf. Peikoff 2012, 24–25). In the line of logical ontologism extending from Plato, necessary truths exist in the eternal mind of God, they are prescriptive for the created empirical world, and they hold in the nature of that world. Their ultimate source and residence is the divine mind. Peikoff draws out four arguments advanced in the Platonic line for why PNC cannot be learned from sensory experience. One of them is that PNC is a necessary truth. The principle states not only that there are no true contradictions, but that there cannot possibly be any true contradictions. In the Platonic line, let me add, such a necessity could no more be known merely from empirical induction than could be known in that way the necessary truth that any triangle in the Euclidean plane must have angles summing to exactly two right angles. These philosophers and theologians take such necessity to flow from the divine eternal mind, the permanent residence of such eternal, necessary truths. I observe, however, that their view that physical existence per se and in the whole of it is contingent because there are contingent things within this our world is an invalid inference. I say that ‘existence exists’ can be a necessity at least partly the ultimate base and reference of the truth and necessity of any necessary truths. On this corrective, Peikoff had things to say in his essay “The Analytic-Synthetic Dichotomy” in The Objectivist three years after completion of his dissertation (also Peikoff 2012, 12; further, Franklin 2014, 67–81). I should add that for Plato, the necessity of necessary truths does not descend from a divine mind, lord of existence, mathematical and empirical, but from the Good, lord of all Forms and their traces in our reasoning on the mathematical and physical world. The Good is the Form dependent on no others. It is self-sufficient and is self-evident in a general way to human reason. It is the necessity that is source of all orderly necessity (Rep. 505c, 508d–509a, 511b–d; Philebus 20d, 60c, 64b–65a; further, Demos 1939, 35, 106, 307, 335). In my view, from Rand, all good is set in the highly contingent organization that is life. Then, I add, since the good does not have the ontological standing given it in Plato’s view, it cannot of itself (only a necessary-for) be the base of the sort of necessity had in necessary truths, truths such as the principle that, necessarily, there are no true contradictions. To be continued. References Charles, D., editor, 2010. Definition in Greek Philosophy. Oxford. Crivelli, P. 2010. The Stoics on Definition. In Charles 2010. Demos, R. 1939. The Philosophy of Plato. Scribners. Denyer, N. 2007. Sun and Line: The Role of the Good. In The Cambridge Companion to Plato’s Republic. G. R. F. Ferrari, editor. Cambridge. Franklin, J. 2014. An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan. Netz, R. 1999. The Shaping of Deduction in Greek Mathematics. Cambridge. Peikoff, L. 1967. The Analytic-Synthetic Dichotomy. In Ayn Rand: Introduction to Objectivist Epistemology. Expanded 2nd edition. 1990. Meridian. ——. 2012. The DIM Hypothesis. New American Library. Plato [d. 347 B.C.E.] 1997. Plato – Complete Works. J. M. Cooper, editor. Hackett. Politus, Y. 2010. Explanation and Essence in Plato’s Phaedo. In Charles 2010. Priest, G., Beall, J. C., and B. Armour-Garb, editors, 2004. The Law of Non-Contradiction. Oxford. Tait, W. 1986. Plato’s Second-Best Method. In Tait 2005. ——. 2002. Noēsis: Plato on Exact Science. In Tait 2005. ——. 2005. The Provenance of Reason. Oxford. ~~~~~~~~~~~~~~~~ My remarks in this post concerned issues undertaken by Peikoff 1964 (the first two of his five chapters) on Platonist perspectives on the epistemological and the ontological standing of PNC. My next post will concern Peikoff’s third and fourth chapters, on Aristotelian perspectives on those standings. In a third post, I’ll address Peikoff’s fifth chapter, on the demise of classical logical ontologism and some alternatives to it that were adopted.
  23. Boydstun

    Peikoff's Dissertation

    . Plato “Firstly, Peikoff examines the views of Plato in their import for an explanation of our knowledge of PNC and its self-evident character and for the bases of PNC in reality. . . .” Aristotle I “Peikoff scrutinizes the broadly empiricist thinkers Aristotle, Aquinas, and Locke in the aspect of opposition to the Platonic views that necessary truths, such as the impossibility of contradictions in reality, are (i) innate in the human mind and (ii) features of essences accessible only by intellect and objectified beyond the particulars accessible by sensory perception. . . .” Aristotle II “Marco Sgarbi 2013 shows that highly empiricist Aristotelian logic texts flourished in Britain in the 16th and 17th centuries. Frances Bacon criticized the strain therein subordinating the world to the mind and the mind to its concepts. Insofar as Locke took concepts as tightly bound to the mind-independent world, he is located, as Peikoff locates him, in the tradition of logical ontologism, specifically in its Aristotelian wing. . . .” Kant I “We have seen the weaknesses of the classical accounts of how PNC is grounded in the nature of objects apart from their subjects. Platonic and Aristotelian accounts of form and essence fell off the center stage of philosophy in the modern era. With them fell the accounts of the necessity and normativity of the principle of noncontradiction (PNC) utilizing them. . . .” Kant II “I mentioned that Kant’s own logic lecture notes compiled by Jäsche were always available to German readers from 1800. We have seen that Kant therein, in his introduction to the discipline of logic, made an analogy between logic and grammar. . . .” Kant III “Having acknowledged the tension between having logical principles such as PNC be at once absolutely necessary laws of human mind, yet crossable by that mind, Kant in the Jäsche LOGIC addresses how such error is possible. . . .” To be continued.
  24. Boydstun

    Peikoff's Dissertation

    . PNC Ground Shifts to the Side of the Subject – Kant III I’d like to pause, before answering that question, to mention that a reasonably complete theory of the rules of elementary formal logic, how we come to know them and their character of absolute necessity, and how it is possible to violate them would need to cover not only PNC. It should include in its scope also the fallacies of affirming the consequent (AC) and the fallacy of denying the antecedent (DA). (“If someone recently sat in this chair, then it will be warm; and it is warm, so someone recently sat in this chair.” “If it’s raining, then the sky is not entirely clear; but it’s not raining, so the sky is entirely clear.”) All adult interlocutors, however meager their formal education, know in practice that they should not violate PNC in their reasoning. But the unschooled seem oblivious to those other rules for their right reasoning and keeping to reality. This is especially so when the reasoning is not about such concrete matters as in my examples, but about more abstract matters as come up in disputations in politics and religion in which they mainly want the conclusion and are not keenly interested in whether a particular reasoning to it is valid. They generally take care to avoid PNC even in heated argument. Its invalidating character is ever close with them, and they know it’s ever close to all the participants or observers. I suggest that PNC is more obviously mandated (than AC and DA are mandated) by the metaphysical principle of identity as to the which and the what in reality and that PNC is more obviously required for keeping hold of those identities and for communication concerning them. Although avoiding the fallacies of AC and DA also rests on those aims and on those aspects of identity in reality, they are less primitive and less fundamental for discursive cognition than the logical principle of noncontradiction. Nevertheless, the principles of barring AC and barring DA have the same absolute, perfectly general necessity and normativity as PNC. Having acknowledged the tension between having logical principles such as PNC be at once absolutely necessary laws of human mind, yet crossable by that mind, Kant in the Jäsche Logic addresses how such error is possible. The faculty of understanding would make no errors were its judgments never under illusions it forms in its commerce with the faculties of sense (also KrV A293–94 B350–51). The sensory inputs themselves are not erroneous, for only judgments can be true or false. Kant is in keeping with Descartes’ view that errors all arise from allowing our will to outrun our understanding. We alone are responsible for all our errors. That analysis of error is fine for a wide class of errors, but not, I say, for the class into which contradictions fall. Formal contradictions are judgment against judgment, and the rather obvious sources of contradictions in one’s judgments are limitations of memory and not drawing out all the implications of one’s various judgments. The latter source can range from evasion to plain economics of mental reflections in the course of a human day or life. Like most any philosopher before him, Kant can dig into our motives for the willful portions of such errors. He cannot explain and seems reluctant to admit the existence of one’s contradictions not willful. Might Kant’s analogy help here, his analogy between logic and grammar, each discovered and become explicit by reflection on their natural employment, consisting of rules descriptively necessary yet normative? No. The problem is that when Kant speaks of the necessity of the rules of grammar being contingent rather than absolutely necessary, he does not mean that rules of grammar are probabilistic rules. He means they might have been otherwise, and that makes the analogy converge on congruence in the crucial respect. The grammar is as necessary within a language or range of languages as PNC is necessary in any possible setting. He cannot explain (or even acknowledge?) an error of grammar not willful any more than he can explain a contradiction not willful. Peikoff 1964 does not attempt to delve into these various doctrines of Kant concerning the character and sources of error. He takes it, like some other contemporary philosophers, that one cannot succeed in holding onto the absolutism of logical rules while saying also that we can violate them and that they are due only to the constitution of the mind. So far, my mining of Kant on error confirms that estimation of Kant’s effort on his conundrum. What about the kind of error Kant mentioned in the Anthropology in the preceding post? That was the error of mistaking linguistic signs for things they signify and vice versa. Such signs, Kant calls artificial, in contrast to natural indicators such as smoke for fire. Kant observed that people having common language can yet signify in their vocabulary concepts quite different one person to the next. He implies that this variance is due to infirmities in the faculty of signification, which rather suggests that if we were all working correctly in our linguistic significations, we should have no variance among persons in concepts signified by a word. I seriously doubt that, given the variance in individual backgrounds of experience and education and given the creativity in thought, especially in more abstract thought. Were Kant’s rigid connection between vocabulary and right concept correct, infirmity of word-concept powers would yet not explain how errors of logic or grammar are possible. The same goes under my denial of the word-concept complete rigidity of right signification, for then there is utter incommensurability between the would-be explanation and the thing to be explained, since the rules of logic and grammar are fixed, in Kant’s view, in all the heads talking and thinking to themselves and with others. Error of signification and its source (source pretty vague in Kant) does not help to explain error in logic or grammar. The sort of error to which Kant draws attention most famously is the one that is mood lighting for his Critical philosophy. That is the error of letting reason run off into speculations about things as they are in themselves, things as they are beyond the bounds of possible experience. Kant’s advertisement for his critique of reason by reason is that all fundamental contradictory positions on metaphysical questions before his 1781 are resolvable once we realize that opposing answers are addressing the question in different senses. One side is addressing a question about a thing as it is in itself; the other side, as that thing is an object of possible experience (A395, Bxxvii). This error is an extrapolation from the kind of error Descartes and others had cautioned against: making judgments on things for which we are not in a position to judge. Rather, we should withhold judgment and not let our will outrun our understanding. Kant’s casting as error reason overstepping the so-called phenomenal district, reason stepping into the so-called noumenal district, relies on correctness of PNC. This overstepping error, Kant’s sweetheart, provides no help to resolving his problem of how absolute necessity of PNC is on account of the way the mind operates yet that mind is able to commit contradictions. So I concur with the conclusion of Peikoff and others he cites that once Kant had the constitution of the subject the sole source of the purely formal and purely a priori, he was not able to stably maintain an absolute necessity of PNC and other principles of logic together with their normativity, which latter entails our ability to not adhere to such principles. I add that this same irresolvable mess arises for every other sort of cognition purely formal and purely a priori, whether analytic or synthetic, once Kant has squarely located their source purely in the constitution of mind, in its fundamental dynamics, not at all in the constitution of the world. (In the next installment, I’ll cover Peikoff’s story of the shift of PNC ground to the side of the subject beyond Kant and the role of Kant in that further development to 1964. I’ll assess his account of Kant’s role and carry the story of the ground shift away from logical ontologism to the present.)
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