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Let %$w 1$% be the G del number for %$\psi$%. Then %$h(\bullet ) s {1}{}^{1}(w {1},\bullet)$%.
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 Published Publisher ShaughanLavine Date 07 May 2007 17:13 {PublishContrib}{Dir} c:/home/philosophy/faculty/slavine/public html/ {PublishContrib}{URL} http ...
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 ...
Church's Thesis Church's thesis is that the recursive functions, recursively decidable, enumerable sets are the (intuitively) computable functions, decidable sets ...
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 ...
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. ...
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 ...
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 ...
Fictionalist Explanation of Applicability One standard platonist claim is that platonists can explain why mathematics is applicable in roughly these terms: mathematics ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
Abstract Language Some morals. There is no clear generally accepted distinction between abstract and concrete objects. There are various relevant criteria, like ...
Russell's theory of what numbers are is just like Frege's, except that it is completely different. His reasons for adopting his view of numbers are also just like ...
Symbolic Logic A You can view this site just like any web site. If you want to be able to edit it, you must register. Once you have a WikiName and password, all you ...
Intuitionistic Logic Last time, we discussed Dummett's motivation for insisting that each logical operator must be independently defined (molecularism required for ...
First vs. Second Order Logic There is a lot confusion, terminological and other, about the distinction between first and second order logic. Everyone agrees that ...
Poincar On the Nature of Mathematical Reasoning 1894 Poincar did not know about what we now think of as logic. When he is referring to logic as syllogisms, this is ...
Corcoran, "The Conceptual Structure of Classical Logic" Most everything we've read, and almost every philosopher, in discussing logic, in one way or another mixes ...
Some Theorems Concerning First Order Logic with Equality I shall always assume on this page that the languages with which we are concerned are finite or countably ...
Logicism Logicism is "the" view that mathematics is reducible to logic. Logicism foundered on the paradoxes. In order to avoid the paradoxes, Russell introduced the ...
Special Topics in Philosophy: Is There Any Such Thing as Everything? Shaughan Lavine ...
Pilate asked, "What is truth?" Colbert asked "What is truthiness?" A truth bearer is truthy if it has the ring of truth, sounds like it must be true, is widely and ...
Benacerraf WNCNB Today's article is the beginning of the contemporary philosophy of mathematics, at least along with Benacerraf's other article we'll read. It is referred ...
Cantor's Theory Was Never Intended to be a General Theory of Collections In particular, it was not the "naive set theory" that virtually everyone, following Russell ...
According to Corcoran, logic studies the correctness of arguments. We use the term "argument" in (at least) two ways, and there are two different, though related, ...
Plenitudinous Platonism Plenitudinous platonism, which Balaguer takes to be the most defensible form of platonism, is the view that all logically possible mathematical ...
Euler could show, by the same method, that %\ \infty 1 2 3 \dotsm ,\ % %\ 1 1 2 4 \dotsm ,\ % and %\ \frac{1}{2} 1 1 1 1 \dotsm .\ % He used all of these in ...
Russell Principles of Mathematics Why do we need to say what the numbers are, instead of merely giving axioms for them? The axioms only characterize the numbers "up ...
Benacerraf What Numbers Could Not Be The present article is one of the most influential on contemporary philosophy of mathematics. The "traditional" philosophies of ...
Weir's Theory, the mathematical background Logicians use theories in two ways: they reason about them and they reason within them. When you reason about a theory ...
The bulk of the Plantinga article discusses basic characterizations of modalities, possible worlds, and the like that I mostly discussed when we talked about Kripke ...
Today, we're switching from metametaphysics to "straight" metaphysics, or at least so it should seem. Instead of talking about how to tell what exists, we are talking ...
Definitional Extensions and Interpretations Definitional Extensions Let %$T$% be a theory in a in a language (set of constant, predicate, and function symbols) % ...
Quine is writing in response to Carnap, but Quine's article does more stage setting, and so we'll read him first. The positions of Carnap and Quine on ontology are ...
Section 3.1 1. Let %$A^{ } {S}$% be the set of sentences consisting of S1, S2, and all sentences of the form %\ \phi (0) \rightarrow \forall v 1(\phi (v 1) \rightarrow ...
Searching for Free Quarks By the late 1960s there were a huge number of "elementary" particles, over a 100. Gell Man and Zweig showed that all of the baryons and mesons ...
ShaughanLavine - 16 Jan 2009 - 01:21 - 1.3 " class="twikiLink">ShaughanLavine
r14 - 10 Nov 2009 - 02:55
Symbolic Logic A Shaughan Lavine Fall 2009 Philosophy 4/501A311 Sciences Building ...
Cantor's notion of cardinality is the notion of cardinality The argument is that if we can take one set and morph it into another, they have the same size, and if ...
Ok, I can't sleep. I need help. Here's my trouble: From the excerpt we have of Science Without Numbers , I don't see why mathematics has to be conservative. On page ...
Skolem's Paradox There are science fiction movies in which entire planets populated by alien civilizations appear. How do the movie makers manage to create an entire ...
HelenHabermannNeoFregeanism BenjaminZamzowNeoFregeanism DavidGlickNeoFregeanism TheresaLopezNeoFreganism AnnieSNeoFreganism Ian's Shorty: 1. How does Wright attempt ...
The syntax and semantics of first order predicate logic with equality. Two ordinary senses of "argument" An argument is a connected series of statements intended ...
ShaughanLavine - 16 Jan 2009 - 01:21 - 1.3 " class="twikiLink">ShaughanLavine
r14 - 08 Nov 2009 - 20:59
Symbolic Logic A %STOPPUBLISH% Due Dates %STARTPUBLISH% Final examination: Thursday, 17 December, 11 A.M. 1 P.M., 311 Sciences ...
Putatively Referring Expressions: Definite descriptions and proper names A singular term is a linguistic item that purports to refer to a single object (and that ...
Section 3.3 2. Theorem 33C . For any quantifier free sentence %$\tau$% true in %$\mathfrak{N}$%, %$A E \vdash \tau$%. We will need to prove this by induction. But ...
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