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  1. 1 point
    Boydstun

    Peikoff's Dissertation

    I concur with the distinction Merlin draws between physical and formal necessity in the preceding post. That’s a good example from mathematics, and I should note additionally that (i) it is a fact—ascertained in the way one does for mathematics—that there are some continuous functions that are nowhere differentiable, and it remains a fact even if it is the case that there simply is nothing physical to which some such function applies and that (ii) we find great success in technology and in extending comprehension of the physical by applying many functions, each one both continuous and differentiable, to electricity, to fluids, and to solids, yet understanding perfectly well that such things are discontinuous at small enough scales. SL, I should not want to equate the physical with the metaphysical. When Rand claims that only living things can have values or when philosophers from time immemorial say nothing comes from nothing, those claims are consonant with modern physical science, but the claims are made in what I’d call a metaphysical perspective, not a scientific one. In his 1967 essay “The Analytic-Synthetic Dichotomy” Peikoff has a section on the traditional distinction within metaphysics between necessary and contingent facts (and how this feeds into the A-S distinction). The meaning of metaphysical necessary/contingent has changed over the centuries, but there is family-descendant resemblance under the continuing distinction. Peikoff did not think such a distinction is correct to make within metaphysics. However, he there drew a distinction between the metaphysical and the manmade (in tune with Rand’s later elaboration). Human free will is the root fact for this distinction. Unfortunately, Peikoff and Rand thought that the rule of Identity in metaphysics entailed complete determinism throughout metaphysics as contrasted with the realm of free will. Furthermore, Rand thought that such metaphysics rightly constrains (a bit) what physical science might find, but that the reverse flow does not soundly occur. That is, she thought metaphysical fundamentals could not be changed in light of advances in science. So for example, the development of chaos theory in the classical regime of physics (starting in the 1970’s as I recall) and the distinction within physics between a classical system in its regular regime as opposed to being in its chaotic regime could not suggest any reformation of general metaphysics. Really, the total determinism that Rand-Peikoff attached to metaphysics under identity was an inheritance from modern physics (Laplace et al.) and is not properly part of right metaphysics, rather should be left open for physics to settle. In his book OPAR, Peikoff does acknowledge that when it comes to value theory, biology supplies the characterized phenomena, pertinent for philosophical fundamentals concerning value. In his dissertation, Merlin, Peikoff included Blanshard’s books The Nature of Thoughtand Reason and Analysis. He does not cite the former in his text or notes. He cites and makes specific explicit use of the latter from its pages 252–54 and 271–75. The former stretch lays out the traditional view that necessity (the one, as it happens, to be most often sainted by philosophers traditionally) arises only at the level of universals and essences; discerned at the level of conception, not perception. The latter stretch concerns conventionalist theories of logic. Merlin, I’ve inclined to the view of logic put forth by Rand (1957) and Branden (c. 1968) and Peikoff (1967, 1991) in their orientation towards logic as tool for successful thinking. (I reject Rand’s definition of logic in its differentia. I expect she was misled by a remark in Aristotle’s Metaphysics, which seems oblivious to his great achievement, theory of the syllogism, in Prior Analytics.) It has seemed plain that on the Objectivist orientation towards logic, material implication should not be incorporated. A lot of other thinkers have thought material implication off the mark for deficiency in the relevance factor, as had Blanshard. They developed Relevance Logic (also called Relevant Logic) as replacement for classical modern logic, and I think that the way to go and a way consonant with Objectivism also. I have books telling the history, concerns, and purposes that brought on material implication, but I’ll have to open them. I’ll let you know on your blog what I find.
  2. 1 point
    dream_weaver

    Peikoff's Dissertation

    The weed-vine example strikes home to anyone who has tried it. In the example, a flowering vine, in the garden, pole beans, cucumber, to a lesser extent squash and pumpkin. Pulling the weed-vine meant being able to distinguish without being able to see, or where finding a viewing angle was just downright awkward. I took the physical-logical necessity as a neat example of ontologically based logic.
  3. 1 point
    merjet

    Peikoff's Dissertation

    Thank you for that, Stephen, especially for the distinction between logical necessity and physical necessity. Also, I liked your comments about John Locke. I have began a series on my blog about inference and necessity. Here is the first: Blanshard on Implication and Necessity #1. More to come.
  4. 1 point
    Boydstun

    Peikoff's Dissertation

    PNC Ground Shifts to the Side of the Subject– Conventionalism III To set myself the task “weed this patch of periwinkles” I may need to use language. The two popular weeds there at this season are dog violets and a native vine I don’t know the name of. Getting to the nub of that weed-vine among the thicket of periwinkle vines and pulling out the former without pulling out the latter is a challenge. Names and language do not seem to be enlisted in executing the task; they enable only my report of this work. The weed-vine and the periwinkle are of different leaf shape and color. Tug gently on the end of the weed-vine reaching for the sun. You won’t be able to see the weed-vine you’re tugging but a few inches before it disappears (leafless in this portion of it) among the thicket of periwinkle vines hugging the earth and putting down their roots continually along their way. But as you tug on the weed-vine, you’ll be able to find with your other hand that single vine being tugged. It is tightly tensed and in synchrony with any rhythm of tugs you apply with the other hand. Repeat from there, and eventually you arrive at the nub of the weed-vine and pull out that vine by the root. Pause at a step in which you have the single obscured weed-vine in each hand. Pull with the one hand, feel the pull in the other. That is a perceived connection between two distinct events. At this point, philosophers from Plato and Aristotle to Hume and Kant stick up their noses. Not Locke. That applied force can be conveyed along a vine is a physical necessity. That different things in general (as example, weed-vines and periwinkle vines) are not same things is another type of necessity, logical necessity, however neatly it coincides with physical necessity. Logical necessity holds unconditionally and in all contexts. What I’ve called physical necessity is traditionally taken to be necessity under some sort of limiting conditions, and this necessity has been called a contingent connection, reserving necessary connectionfor logical (and other formal) necessity. The real distinction, I think contrariwise, should be in what aspects of things we are accessing and the different ways these two aspects are accessed. Peikoff 1964 points out that Locke avoided the contingent/necessaryterminology. Locke instead applied probable/certainto the division. We have seen in my section Aristotle II that Locke maintained we have by sensory perception instances of the general fact that different things are not same things and that a thing is never both A and not A at the same time and in the same respect. Philosophers, including Peikoff in 1964, are correct to fault Locke’s blurring under probable/certaina clear understanding that ampliative inductive generalizations over perceived instances do not suffice to land the absolute necessity in general principles of logic or pure mathematics. Peikoff notes on page 218 the parallel criticism in Hume’s famous dictum that we do not find in sense perception any necessary connection between distinct events (distinct impressions,in Hume’s own parlance and perspective). Countering Hume’s quandary, Kant attempted a radical subject-sided formulation of necessities such as the necessity in a principle of causality, a reformulation in which Kant would have objective temporal order of distinct events get the necessity of that order from a necessity of causal structure demanded by human mind. (Cf. Peikoff 2012, 32–33.) Locke had fogged up by his softening of the distinction between (i) the physical necessities one can sense and manipulate with the weed-vine in one’s hands and (ii) formal and metaphysical necessities. Nevertheless, I maintain Locke right in taking (i) to be the driver of (ii) and not the other way around, as philosophers from Plato to Kant and beyond would have it. British empiricism has its good sense even if it was never good enough. Locke was not really of one mind in this. Peikoff lays out an opposite strand also inAn Essay Concerning Human Understanding: IV 3.31, 4.6, 4.8, 9.1, 11.13–14. “What is Locke doing in such passages as these? He is now contrastingeternal truths and existential truths. The former are to be discovered only by ‘the examining of our own ideas’, and ‘concern not existence’ . . .” (222). Peikoff points out that the likes of platonist Cudworth or Leibniz had also maintained such a division, but for them consideration of our own ideas accesses the eternal truths as immutable relations in the divine understanding. Eternal truths such as the laws of identity and noncontradiction, as well as the essences of existing things, are givens to the human mind, independently of our self-examinations accessing them. But for an empiricist such as Locke, rejecting that rationalism, and joining considerable nominalism (the conceptualist wing of nominalism) concerning universal ideas to the empiricism, the divide between matters of fact and the eternal, formal truths can make conventionalism concerning the ground of logic “almost inevitable” (223). The leading German spokesman for conventionalism in science, geometry, and logic in the early years of the twentieth century was Hugo Dingler: “The application of the law of contradiction rests on my free will. . . and this is just what is called a stipulation [Festsetzung]” (1919, 14-15; quoted in Carus 2007, 120n14). “There is no other way to guarantee the general validity of a law other than its stipulation by the will” (1919, 13; Carus 119). Peikoff would not likely have known much about this history in 1964, much beyond, that is, what Popper wrote against it in his 1934 The Logic of Scientific Discovery. I want to point it out because although Dingler rejected as unfounded Kant’s basis of the necessity in geometry as arising from synthetic a priori judgments and Kant’s picture of how certain laws are a priori conditions of the possibility of any experience (Wolters 1988). Dingler is nonetheless a redo of Kant, of the first Critique,with conscious choice (of alleged conventions) replacing Kant’s mandatory structure in any sensory intuition and in any conceptualization of things external to mind. Though crucial, fundamental organization of mind on Dingler’s view is voluntary, and although Kant would shake his head over such free play as that, it remains that the organization is an a priori condition for the possibility of any experience or knowledge. Carnap will resist such radical conventionalism in the 20’s and 30’s. I’ll return in the next installment to the course of Logical Empiricism and the role of (still overextended) conventionalism in their characterization of logic and in the characterization by Dewey and by C. I. Lewis. I expect to yet dig into the fate of conventionalism concerning logic to the present day. Jumping out of chronological order, just now I want to be sure to mention—to show that conventionalism in logic remains a current and a concern in philosophy today—the section 6.5 “Logical Conventionalism” in Theodore Sider’s Writing the Book of the World (2011 Oxford). ~~~~~~~~~~~~~~~ Carus, A. W. 2007. Carnap and Twentieth-Century Thought – Explication as Enlightenment.Cambridge. Dingler, H. 1919. The Foundations of Physics: Synthetic Principles of Mathematical Natural Philosophy.Union for Scientific Publishing, Berlin and Leipzig. (In German.) Peikoff, L. 2012. The DIM Hypothesis.New American Library. Wolters, G. 1988. Hugo Dingler. Science in Context2(2):359–67.
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