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  1. Hi William. I have a shelf of books on physics and philosophy of time in my personal library, but so far, the time has not been right for taking a deep plunge into their contents. Three seem most closely related to your interests in this post: McTaggart’s Paradox (2016) by R. D. Ingthorsson, a philosopher. NOW – The Physics of Time (2016) by R. A. Muller, a physicist. (clip) The Order of Time (2018) by Carlo Rovelli, a physicist. Rovelli thinks twentieth-century physics show that an objective global present does not exist. Presentism, the view that there is an objective global present, is false. He thinks that simply from special relativity, in which he rightly takes reference frames, relative velocities between them, clocks, and light beams to be objective things in terms of which SR is cast and tested. He moves from objective frame-relativity of simultaneity of distant events with local events to lack of any such thing as an objective global present without explanation for that move. Perhaps that move can be made smooth, perhaps not. His conclusion is that presentism is false and “the world should not be thought of as a succession of presents. / What alternatives do we have?” [Unger and Smolin pose an additional alternative “inclusive time” in their book The Singular Universe and the Reality of Time (2015), which seems unnecessarily extravagant to me, at least in all they try to hitch up to it.] “Philosophers call ‘eternalism’ the idea that flow and change are illusory: present, past, and future are all equally real and equally existent. Eternalism is the idea that the whole of spacetime, as outlined in the above [SR] diagrams, exists all together without anything changing. Nothing really flows.* –p. 108 ((* “In the terminology of a celebrated article by John McTaggart (1908), this is equivalent to denying the reality of the A-series (the organization of time into ‘past-present-future’) The meaning of temporal determinations would then be reduced to only the B-series (the organization of time into ‘before-it, after-it’). For McTaggart, this implies denying the reality of time. To my mind, McTaggart is too inflexible: the fact that my car works differently from how I’d imagined it and how I’d originally defined it in my head does not mean that my car is not real”.)) –pp. 221–22 “The distinction between past, present, and future is not an illusion. It is the temporal structure of the world. But the temporal structure of the world is not that of presentism. The temporal relations between events are more complex than we previously thought, but they do not cease to exist on account of this. The relations of filiations do not establish a global order [linear sequence of presents self-same across all material frames, i.e., for all bits of non-zero rest mass]), but this does not make them illusory. If we are not all in single file, it does not follow that there are no relations between us. Change, what happens—this is not an illusion. What we have discovered is that it does not follow a global order.” –p. 110 So Rovelli has it that even though A-series is shown false, as objective structure, by SR, the relation past-present-future remains objective temporal structure, just not the A-series one presumed before SR. William, I don't know how many physicists follow along Rovelli's lines in this area of philosophical wider view taking in SR spacetime and kinematics. However, I doubt that any of them who have thought about it so much as the authors I've mentioned in this post have needed or relied on any particular schools of philosophy in their quest for wider understanding.
  2. Addendum of mine to my article on Descartes/Rand Kant argued against Descartes’ view that the existence of one’s mind is more immediately and more certainly known than the existence of one’s body.[1] Kant cast out Descartes’ view that the mind is a thinking substance.[2] Because Kant rejected also Descartes’ ontological proof for the existence of God,[3] Descartes’ first philosophy collapses. Metaphysical arguments to rational necessity of the existence of God or immortality of the soul are all cases of reason flapping its wings in a vacuum, by the lights of Kant. The THE CRITIQUE OF PURE REASON (KrV) contains Kant’s case for a more limited scope for effective theoretical reason: stay within the bounds of possible sensory experience. Kant accepted, as had Descartes and Aquinas before him, some notion that ‘I think’ entails ‘I am’. Then again, with Rand’s mature philosophy, acknowledgment that ‘Existence exists’ entails existence of one who acknowledges. For Kant, contra Descartes, ‘I think’ does not mean I think with a mental substance,[4] radically distinct from body; and thinking of my body and of bodies outside me is as certain as the circumstance that I think and that I exist as a thinking thing.[5] Kant had a role for ‘I think’ basic to his transcendental idealism, and such is not the role it had in the first philosophy of Descartes. Let me call Kant’s the “company-role” of ‘I think’. “The ‘I think’ must be capable of accompanying all my presentations; for otherwise something would be presented to me that could not be thought at all—which is equivalent to saying that the presentation either would be impossible, or at least would be nothing to me.”[6] (B131–32) Kant’s ‘I think’ is utterly dependent on there being rational judgments it attends. ‘I think’ is not premier of knowing, contra Descartes. Neither it nor the ‘cogito sum’ containing it nor join of the ‘cogito sum’ to the premise of divine, absolute perfection amount to an adequate foundation of all human cognition.[7] We might object, however, to Kant’s reasoning in the quoted passage. In early development we each had been perceiving and investigating and coordinating without any ability to reflect and realize of those episodes ‘I am having’ or ‘I am doing’, let alone ‘I am thinking’. It might be countered for Kant, in our current context of cognitive developmental psychology, that to each such episode adults around the infant or toddler can attach ‘He is having’ or ‘She is doing’ and that grown older the former little one could say of filmed early episodes ‘I was seeing’, ‘I was searching’, and so forth. The objection remains, for those remarks would be merely as from outside and pronounced on the little person, not by that person as he or she perceived, investigated, and coordinated. That such episodes occur without first-person capability to reflect and realize ‘I am having’ or ‘I am doing’ means that, notwithstanding the important fact of the company-role of ‘I think’ for all mature, discursive human cognition, it is not a necessary condition for the possibility of all human cognition in the apriori way Kant argued at B131–32. Kant’s argument there ignores the existential fact that discursive thought has a genesis from and an alliance with prelinguistic thought in early development. When Kant does discuss the pertinent infant development, in his anthropology lectures,[8] he foists the necessity argued in B131–32 off on all that development. The company-role of ‘I think’ (as well as ‘I am having’ and ‘I am doing’) is a necessity for adult human cognition, though not for the ultimate reason and not with the type of ultimate necessity given it by Kant. And self-reflection is not a necessity for one’s earliest stage of cognition. The necessity of the company-role of ‘I think’ and its precursors ‘I am having’ and ‘I am doing’ is most basically biological, not transcendental. Without adult capability for some self-reflection, and its precursors in development, there will have been no capability for language, thence not yet human cognition in such a species. Conceptual necessities are from the life of mind situated in larger life situated in the world. Conceptual necessities do not require Kant’s conceit of generative mind as ultimate origin of temporal and spatial organization in sensory experience and objective world nor Kant’s conceit of generative mind as base origin of its own fundamental concepts as forms with which the world as known shall be. Necessary conditions on the possibility of experience and cognition are in my view rightly seen as situated within biological necessities, not within Kant’s supposed, wider transcendental necessities.[9] Organicism in human consciousness—with its unities, roles, interdependencies, and self-generations—is offspring of and sign of the biological nature of consciousness. Kant saw it rather the other way around.[10] As with any other body, the body of a physical organism is in his view an object standing in spatial, temporal, and causal connections whose source of necessity is the transcendental synthetic unity of apperception.[11] Organic unities of organisms, according to Kant, are to be seen as if they were designed by a cosmic intelligence, keeping in mind that those unities are projections of the unities of our own reason, which is to say organic unities of organisms are to be understood as if sourced (and as in fact divinely sourced) in organic unities of intelligence.[12] ~~~~~~~~ The ‘I’ of Kant’s company-role ‘I think’ is a unified conceptual maker of coherence from variety in the ‘I’s world of perception.[13] As Béatrice Longuenesse observes: Because the causal relation is among the organizing principles constituting the coherence-making self that must be able to accompany any sensory experience it has, we have in Kant’s company-role ‘I think’ a post in Kant’s fence against Hume’s skepticism concerning necessary connection between distinct perceived events.[14] ~~~~~~~~ NOTES [1] Kant 1781(A) and 1787(B): A366–80, B274–79. [2] A343–47 B401–6, A348–51, B407–8, B416–22. Rand, and I with her, replace substance of Aristotle or of Descartes with entity, and we would count the mind and the self as an entity, notwithstanding the special ways in which one knows one’s own mind and self. [3] A592–603, B620–31. [4] But see Heidegger 1953, 318–21/304–7. [5] Kant, KrV B270–79. [6] Also B137–39, B157–-58n, A341–43, B399–401, A347 B405, A354–55, A397- 402, B422–23n, B428–32, A848 B876; 1798, 7:127–28. [7] Kitcher 2011, 57–62, 116–17, 193–97. [8] Kant 1798, 7:128-29. [9] Cf. Criticism of Kant, on possible origins of necessity in synthetic apriori judgments, by Gottlob Ernst Schulze 1792, 142–45. [10] Mensch 2013, 99–109, 113–24, 130–45, 153–54. [11] Kant, KrV A22–36 B37–53, B131–69, B232–34, A189–211 B235–56. [12] A317–18 B374, B425, A686–704 B714–32. [13] A67 B92, A107–8, A113–14, A119, A124–25, B129–39, A199–202 B244–47, A214–18 B261–65, A228–30 B281–82, A234–35 B286–87, A255-56 B311, A401–2; see also Kitcher 2011, 138–41, 144–50, 193–97. [14] Longuenesse 2008, 15–16; see also Kitcher 2011, 152–57, 170–73; Allison 2008, 107–12, 204–5. REFERENCES Allison, H. E. 2008. Custom and Reason in Hume – A Kantian Reading of the First Book of the Treatise. New York: Oxford University Press. Heidegger, M. 1953 [1927]. Being and Time. 7th ed. J. Stambaugh and D. J. Schmidt, translators, 2010. Albany: State University of New York Press. Kant, I. 1781, 1787. Critique of Pure Reason. W. S. Pluhar, translator. 1996. Indianapolis: Hackett Publishing. ——. 1798. Anthropology from a Pragmatic Point of View. In Immanuel Kant – Anthropology, History, and Education. G. Zöller and R. B. Louden, editors, 2007. G. Zöller, translator. Cambridge: Cambridge University Press. Kitcher, P. 2011. Kant’s Thinker. New York. Oxford University Press. Longuenesse, B. 2008. Kant’s “I Think” versus Descartes’ “I Am a Thing that Thinks.” In Kant and the Early Moderns. D. Garber and B. Longuenesse, editors. Princeton: Princeton University Press. Mensch, J. 2013. Kant’s Organicism – Epigenesis and the Development of Critical Philosophy. Chicago: The University of Chicago Press. Schulze, G. E. 1792. Aenesidemus. In Between Kant and Hegel – Texts in the Development of Post-Kantian Idealism. G. di Giovanni and H. S. Harris, translators, 2000. 2nd ed. Indianapolis: Hackett.
  3. (Click on photo to read verse.)
  4. I'd suggest, Human, after you finish Atlas Shrugged, you read either Objectivism in One Lesson by Andrew Bernstein or Objectivism: The Philosophy of Ayn Rand by Leonard Peikoff. Both of those use citations to the other writings of Rand and her associates, and you can then follow up with those references as your further interest may go this way or that.
  5. Rand thought the human animal to have no automatic, instinctual knowledge of what was good or evil for him. She held that man had a nature of rationality, and that this rationality is held as a value in the individual man only by choice (1957, 1013). Part of his rational nature would be the deliverances of the senses automatically giving information in general and pleasure/pain valence in particular. Those primitive elements for rationality, in Rand’s understanding, are not susceptible to human choice however much humans may try to rub out their validity and replace them with feelings (1037). She maintained, as mentioned earlier, that humans have a life-or-death need of self-esteem (also at 1057), that in truth this self-esteem is (and is at some level generally known to be) “reliance on one’s power to think,” that self-esteem is rightly attached to being morally right, and that a false morality—one valorizing not thinking, not thinking for oneself—can render one’s self-esteem incoherent, a mess (1030–31). Calling the name John Galt in that novel can be calling one’s own “betrayed self-esteem” (1060). In the 1961 essay “The Objectivist Ethics,” Rand wrote: “By what means does [man] first become aware of the issue of ‘good or evil’ in its simplest form? By means of the physical sensations of pleasure or pain. Just as sensations are the first step of the development of a human consciousness in the realm of cognition, so they are its first step in the realm of evaluation. “The capacity to experience pleasure or pain is innate in a man’s body; it is part of his nature, part of the kind of the kind of entity he is.” She described animals below man having automatic ways of living action enlisting only sensation or sensation together with the automatic integration of sensations into percepts, giving perceptual consciousness of entities in the world, though no freedom over the animal’s governing consciousness or over its range. She regarded man as having that much automatic correct, reality-given inputs to cognition and to evaluation. So his higher-order, volitional cognitive and evaluative powers do not take off from a blank or get no feedback from those lower-level processes. There are two levels to one’s “moral ideal, the image of Man.” There is what Rand would put into it for all men (not brain-damaged and so forth), and this is what she puts into the moral ideals of ethical theory. That is, that much she writes (explicitly) into basic values and virtues of her ethical theory. She personifies them in her fictional character John Galt. That much of John Galt is to be an ideal for everyone. But his love of particular areas of physics or of a particular woman are parts of him that are the realization of the general ethical ideal, but can vary from person to person still holding the same general ideal “image of Man.” Sorry so much of this is old hat, but I needed to recount it to reach the point that whether one is crafting a general frame in the “moral ideal, the image of Man” or whether one is persuaded that Rand’s general specification is right and one is only figuring out what to do with one’s own particular likes, aversions, and abilities in bringing about the ideal in one’s own case, one doesn’t need to ignore one’s feelings nor accept them without critically examining them as they are used as inputs for one’s craft of “values of character that make [one’s] life worth sustaining.” Before I read Rand’s 1943 and 1957, I was a devout altruist. The way in which she changed me was by subjecting different systems to rational criticism and by appeal to other values (feelings, a key manifestation of them) that we both already shared. And those two factors could also persuade one to some new virtues of character, significantly modifying the old ones. “The image of Man” is image of fundamental nature of man but also a norm in Rand’s presentation (for man must be Man by choice). It’s somewhat like “image of God” in man taking after God by possessing reason, although God can’t be a full normative model for man because of radical differences of nature between the two. ~~~~~~~~~~~~~~~~ ET, an elderly woman dear to me would say to me, Why is God still keeping me here? I can’t do anything or be of any use to anyone anymore. I think I told her of how good it was for her younger loved ones to be able to enjoy her company. She was still able to talk, as she and I were doing on the phone, and we could stir up each other’s recollections of people and experiences we had shared decades ago. I am 70. I’m still doing my same creating most important to me. I still have an important work or two in progress. Even if their completion would complete my reach (really, no grasp could match my reach), I think I could still find continued, closing life meaningful. With enough health and memory, I hope to just keep looking back to my accomplishments, including loves attained, here where is the place and future of any value and meaning.
  6. Rand said that life is an end in itself, and I incline to think having a meaningful life includes in its center knowing and being true to human life as an end in itself. I incline to think also that having a meaningful human life has in its structure what Rand said about Pride as virtue in human life: “As man must produce the physical values he needs to sustain his life, so he must acquire the values of character that make his life worth sustaining . . . to live requires a sense of self-value, but man, who has no automatic values, has no automatic sense of self-esteem and must earn it by shaping his soul in the image of his moral ideal, in the image of Man, the rational being he is born able to create, but must create by choice.” (1957, 1021) What should be in that “image of Man” I kind of think are elements I’ve noticed people derive meaning from. Indeed, continuous rationality, but more particularly productions such as earning a living or bringing one’s creative tugs to a reality or productions such as good relationships or accomplishing care of one’s loved ones or indeed of humans more generally or accomplishing making children. We seem rigged up to find meaning in accomplishment in those various channels. I mean that all under the wing of rationality. People find semblance of meaning in irrational, destructive projects, of course, but those are not rightly housed in the “image of Man.”
  7. Thank you, GM, for the stab at it. I appreciate this thread's info, as I mentioned earlier. I'll try to add to this thread in weeks ahead. It is pertinent for getting arms around the relation of Hilbert ideas to Godel and to Carnap---for my book in progress and for my treatment at this site of Peikoff's dissertation and S/A essay for Rand's phi (1960's)---concerning analyticity and the nature of knowledge of pure mathematics.
  8. Merlin, we should stick to A for your example, not go back up to his a. We do not succeed in showing that for all A, where A is any given number, that (A + 1) = (1 + A) by showing that it works for any A we try. That is not enough, and we have methods for going absolutely all the way. How might we show it works for all given A? Hopefully, GrandMinnow can explain what further Hilbert means here, and hopefully respond to my questions to him in the final paragraph of my previous post.
  9. I appreciate the information in this thread. There are a couple of terms “ideal number” and “ideal proposition” in the text below that can be googled or are provided in the SEP article Merlin and GM have mentioned. Otherwise I think the following from Hilbert’s paper “The Foundations of Mathematics” (1927) is pretty self-contained: “If we now begin to construct mathematics, we shall first set our sights upon elementary number theory; we recognize that we can obtain and prove its truths through contentual intuitive considerations. The formulas that we encounter when we take this approach are used only to impart information. Letters stand for numerals, and an equation informs us of the fact that two signs stand for the same thing. “The situation is different in algebra; in algebra we consider the expressionsformed with letters to be independent objects in themselves, and the propositions of number theory, which are included in algebra, are formalized by means of them. Where we had numerals, we now have formulas, which themselves are concrete objects that in their turn are considered by our perceptual intuition, and the derivation of one formula from another in accordance with certain rules takes the place of the number-theoretic proof based on content. “Thus algebra already goes considerably beyond contentual number theory. Even the formula (1 + a) = (a+ 1), for example, in which a is a genuine number-theoretic variable, in algebra no longer merely imparts information about something contentual but is a certain formal object, a provable formula, which in itself means nothing and whose proof cannot be based on content but requires appeal to the induction axiom. . . . “We have an urgent reason for . . . extending the formal point of view of algebra to all of mathematics. For it is the means of relieving us of a fundamental difficulty that already makes itself felt in elementary number theory. Again I take as an example the equation (a + 1) = (1 + a); if we wanted to regard it as imparting the information that (A + 1) = (1 + A), where A stands for any given number, then this communication could not be negated, since the proposition that there exists a number A for which (A + 1) not= (1 + A) holds has no finitary meaning; one cannot, after all, try out all numbers. Thus, if we adopted the finitist attitude, we could not make use of the alternative according to which an equation like the one above, in which an unspecified numeral occurs either is satisfied for every numeral or can be refuted by a counterexample. For, as an application of the ‘principle of excluded middle’, this alternative depends essentially on the assumption that it is possible to negate the assertion that the equation in question always holds. “But we cannot relinquish the use either of the principle of excluded middle or of any other law of Aristotelian logic expressed in our axioms, since the construction of analysis is impossible without them. “Now the fundamental difficulty that we face here can be avoided by the use of ideal propositions. For, if to the real propositions we adjoin the ideal ones, we obtain a system of propositions in which all the simple rules of Aristotelian logic hold and all the usual methods of mathematical inference are valid. Just as, for example, the negative numbers are indispensable in elementary number theory and just as modern number theory and algebra become possible only through the Kummer-Dedekind ideals, so scientific mathematics becomes possible only through the introduction of ideal propositions. “To be sure, one condition, a single but indispensible one, is always attached to the use of the method of ideal elements, and that is the proof of consistency; for, extension by the addition of the ideal elements is legitimate only if no contradiction is thereby brought about in the old, narrower domain, that is, if the relations that result for the old objects whenever the ideal objects are eliminated are valid in the old domain. “In the present situation, however, this problem of consistency is perfectly amenable to treatment. . . . “ The translators are Stefan Bauer-Mengelberg and Dagfinn Follesdal, as reprinted in From Frege to Godel (1967). GM, I think I see some of Hilbert’s motivation for a view of algebraic symbols as free of content here, although one puzzle I have about Hilbert’s remarks here is: An algebraic equation such as y = (Mx+ B) can be, via coordinate geometry, plotted into a particular line when merely the M and B are given definite values, leaving the algebraic variables as algebraic variables. I mean why isn’t analytic geometry yielding facts about synthetic geometry enough to give some meaning to algebraic symbols? Wouldn’t it be sensible to say that algebraic variables mean just any and all magnitude relations (spatial or otherwise) that might be captured in such analytic relations as we have in this case? Do you think Hilbert would object to that sort of picture of algebraic symbols?
  10. No, even when I'm signed in, no heart icon shows for him/her. It shows for everyone else (except for myself, which is sensible). I am signed in under Safari---I'm unable to make posts here if signed in under Chrome.
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