http://zillion.homelinux.com/twiki/bin/view/Courses The Courses web of TWiki. TWiki is a Web-Based Collaboration Platform for the Enterprise. en-us Copyright 2009 by contributing authors Shaughan Lavine [shaughanREMOVE@q.com] The contributing authors of TWiki TWiki http://zillion.homelinux.com/twiki/bin/view/Courses http://zillion.homelinux.com/twiki/pub/TWiki/TWikiLogos/T-logo-140x40-t.gif http://zillion.homelinux.com/twiki/bin/view/Courses/SampleQuestionPhilosophyofMathematics Question. "The statement that if %$\mathfrak{a}$% is a numerical symbol, then %$\mathfrak{a} 1 1 \mathfrak{a}$% is universally true, is from our finitary perspective ... (last changed by TWikiGuest) 2009-11-23T01:19:11Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/PublishContribHistory Last Published Publisher ShaughanLavine Date 07 May 2007 17:13 {PublishContrib}{Dir} c:/home/philosophy/faculty/slavine/public html/ {PublishContrib}{URL} http ... (last changed by TWikiAdminGroup) 2009-11-22T09:04:53Z unknown http://zillion.homelinux.com/twiki/bin/view/Courses/SMNToolTip Let %$w 1$% be the G del number for %$\psi$%. Then %$h(\bullet ) s {1}{}^{1}(w {1},\bullet)$%. (last changed by TWikiGuest) 2009-11-21T17:08:09Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/ReceivedView The Received View Today's topic is what Suppe calls "the Received View." It is a paradigm of the views of the logical positivists. I doubt anyone ever held the received ... (last changed by TWikiGuest) 2009-11-21T17:04:31Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/CurryFormalism Curry's Philosophy: Formalism This article is out of sequence: he assumes you know what Hilbert's Program is and what (Brouwer's) intuitionism is. We'll read those ... (last changed by TWikiGuest) 2009-11-20T06:40:27Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/ChurchTuringThesis Church's Thesis Church's thesis is that the recursive functions, recursively decidable, enumerable sets are the (intuitively) computable functions, decidable sets ... (last changed by TWikiGuest) 2009-11-20T06:36:03Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/CurrysFormalism The problem As we have seen, mathematical theories don't determine their domain, and the logicist attempt to say what the objects of mathematics are seems to fail ... (last changed by TWikiGuest) 2009-11-19T00:06:50Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/JustificationsofRules Derivations LostmyZ 05 Dec 2004 Here is an attempt at proving some rules on page 64 3.3 (c) %$\Gamma,\neg\phi,\neg\psi$% %$\Gamma,\psi,\phi$% Solution 1. ... (last changed by TWikiGuest) 2009-11-18T18:44:23Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/CarnapPredicativity Predicativity Picking an object from several already existing objects is a very different process than building an object to specifications. The key point is this ... (last changed by TWikiGuest) 2009-11-17T02:51:29Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/EverythingHomework 1. Belnap http://www.jstor.org.ezproxy2.library.arizona.edu/stable/pdfplus/3326862.pdf discusses Prior's connective tonk, which obeys the following rules of inference ... (last changed by TWikiGuest) 2009-11-17T02:50:50Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/FictionalistExplanationofApplicabilityandPlatonistReplytoOckham Fictionalist Explanation of Applicability One standard platonist claim is that platonists can explain why mathematics is applicable in roughly these terms: mathematics ... (last changed by TWikiGuest) 2009-11-16T19:28:44Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/DefiningExponentiationfromPlusandTimes Defining Exponentiation from Plus and Times If we wanted to represent a sequence of numbers that are all less than 10 as a number using only and %$\times$%, we could ... (last changed by TWikiGuest) 2009-11-16T19:23:55Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/DummettonFregesContextualDefinitions Dummett on Frege's Contextual Definitions Frege rejects his own proposed theory of contextual definitions as inadequate because of the Julius Caesar problem, but the ... (last changed by TWikiGuest) 2009-11-16T19:23:54Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/HilbertOnTheInfinite Hilbert's On the Infinite He starts with some motivation: A. 1. Because of Quantum Mechanics, there is no reason to believe that there is anything physical ... (last changed by TWikiGuest) 2009-11-16T19:14:44Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/FreeChoiceSequences Free Choice Sequences There are many constructivists of a variety of flavors, all of whom agree on using intuitionistic logic. The chief place at which they differ ... (last changed by TWikiGuest) 2009-11-16T19:14:15Z guest http://zillion.homelinux.com/twiki/bin/view/Courses/FregeonArithmetic Frege on Arithmetic Frege is generally presented in philosophy of mathematics classes as the first logicist. He was. But the importance of his work in philosophy ... (last changed by TWikiGuest) 2009-11-16T19:14:04Z guest