a n + b n = c n , where integer n ≥ 3, has no non-trivial solutions. This and, if all goes well, the next seven posts in this blog constitute an unprecedentedly ambitious project for me. I'll be attempting a very granular reading of the book I discussed in a more abstract fashion earlier, THE MURDER OF PROFESSOR SCHLICK: THE RISE AND FALL OF THE VIENNA CIRCLE. Let us start with the "rise" of that subtitle. In 1922 Schlick was offered and accepted the chair for natural philosophy at the University of Vienna. Edmonds calls this simple hiring "a turning point in the history of twentieth-century philosophy." The core of the study-and-discussion group that he seems to have formed almost immediately after that appointment consisted of Schlick himself, Neurath, and Hahn. Otto Neurath and Schlick had background and personality differences as far apart as the poles, as Edmonds tells it. Schlick was a gentile, Neurath a Jew. Schlick was soft-spoken...
Posts
I happened onto a logic blog recently and, before my eyes burnt out with the beauty of the abstractions involved, I learned a new term. ZFC Set Theory. The first two letters, "ZF," abbreviate names, Zemelo and Frankel. Both big names in the history of logic -- I need say no more of them now. The C stands for "choice" as in the "axiom of choice." Now, that sounds important. What choice can there be in logic? Well, the axiom of choice involves mutually disjoint nonempty sets. Take for example two such sets: the set of all teacups and the set of all named bodies of water on the planet. The axiom of choice means that for any set of such sets, it is possible to create a transversal set, containing exactly one element from each. Simple enough in this case: I can simple designate one set as consistent of teacup A plus Lake Erie. Another set consists of teacup B plus the Atlantic Ocean. And so forth. Why is this important? Well, Bertrand Russell in 1904 ...
David Hume is renowned for two pieces of cutlery, the guillotine and the fork. Hume's guillotine is the sharp cut he makes between "is" statements and "ought" statements, to make the point that the former never ground the latter. His "fork" is the division between what later came to be called "analytic" and "synthetic" statements, with the ominous observation that any books containing statements that cannot be assigned to one or the other prong should be burnt. Actually, I should acknowledge that there is some dispute as to how well or poorly the dichotomy Hume outlines really maps onto the analytic/synthetic dichotomy. Some writers maintain that Hume meant something quite different and has been hijacked. Personally, I've never seen the alleged difference however hard they've worked to point it out to me. The guillotine makes for a more dramatic graphic than a mere fork, hence the bit of clip art above. I'm c...
As is well known (at least in certain nerdy circles), the immaterialist philosopher George Berkeley sharply criticized Isaac Newton, and the branch of mathematics Newton had founded, in 1734. Berkeley's book of that year, THE ANALYST, said that calculus depends upon presuming that an "infinitesimal" is something at a certain point in one's reason, then assuming it is nothing at another point. That is internally incoherent. Berkeley thus earned himself a place within the usual story about calculus. The story goes -- Newton proposed certain rough-and-ready ideas, not yet fully developed. He developed them just far enough, and just deep enough, to figure out orbital mathematics. But he left holes in his reasoning. Berkeley saw the holes and called Newton out on this. Subsequent theorists re-worked the foundations to render this branch of mathematics safe from Berkeleyan assaults. That, as I say, is the usual story. In 1987, a fellow named David Sherry wrote an ar...
A recent essay by th e philosopher Galen Strawson has looked at the mind-body problem from a distinctive angle. The title of the essay seems more straightforward than it is. "Consciousness isn't a mystery. It's Matter." One first gets the impression that Strawson is taking a straightforward materialist/eliminativist view: consciousness simply is matter in one of its operations. But that is to presume that the "it" in the second sentence is an unambiguous reference to the word "consciousness" in the first sentence. Another reading suggests itself, though. The "it" could refer to the word "mystery." The second sentence would then mean, "It's matter that is the real mystery." Both meanings fall within the scope of Strawson's intention. It is what Strawson calls a Very Large Mistake to think that we know enough about matter, through the science of physics, to know that consciousness can't be a materi...
Critique of Pure Reason. "In the applications of the pure conceptions of the understanding to possible experience, the use of their synthesis is either mathematical or dynamical ; for it is directed partly merely to the intuition, and partly to the existence of a phenomenon in general. But the conditions a priori of the intuitions are, in respect to a possible experience, absolutely necessarily; those of the existence of the objects of a possible empirical intuition are only in themselves contingent. Hence the principles of mathematical use are ... absolutely necessary; that is, they strike apodictically; whilst those of dynamic use will also carry with them the character of a necessity a priori, but only under the condition of the empirical thinking in an experience...." I'm not sure I grasp this fully. The premise behind it is the old distinction between contingent and necessary truths. It is a contingent truth that Smith owns a Hewlett-Packard laptop. It is a...