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math and logic

grupo sandra 2013

ver concepciones de lgica enhttp://plato.stanford.edu/entries/logic-ontology/

quizs haga falta al menos una nota al pie sobre ontologa.

http://rationallyspeaking.blogspot.com.ar/2012/12/the-complicated-relationship-

between.html

Quine, Introduction to Mathematical Logic

Quine, Truth by convention en Putnan & Benacerraf 1984

Church, Mathematics and logic en Nagel, Suppes, Tarski 1962 (p. 181-186)

Curry 1963, intro

Kline, Mathematics: the loss of certainty. 229ff

Henkin, 1962. Are Logic and Mathematics Identical?: An old thesis of Russell's is reexamined in

the light of subsequent developments in mathematical logic.Science.1962 Nov

16;138(3542):788-94.

Rodrguez, las prcticas matemticas en contexto. en martinez et al, 2012

Friedman 2008: Wissenschaftslogik: The role of logic in the philosophy of science

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-2. logicism?-1. hilbert-----> turing/church/gdel?

0. mathematicalpractice?

1. Logic to mathematics ----> (foundationalism? only?)

2. Logic to mathematical logic. /cf. Henkin 1952/ (is this the transition from philosophy to

mathematics? what does that mean?) frege? calculus? (cf. crossley et al 1972, cap 1). russell??

If 1., what logic? what def. of logic? there is no such thing as alogic, nor is there amathematics.

Russells on mathematics being merely tautological...

hasta qu punto hay que debilitar el concepto de lgica para que la matemtica entre en ellla?

3. es la completud un aspecto relevante (cf. Kneale 1956, 258-9)3.1 y el de decibilidad? (cf. -1?)

4. lgica como ciencia de relaciones entre objetos? qu objetos?

5. model theory! (cf. 2.)

6. Reduction?(like in, say, physics?) (like chemistry can be in principle reduced to quantum

theory, etc).

7. practice again.

8. reverse mathematics.

http://plato.stanford.edu/entries/logic-ontology/http://plato.stanford.edu/entries/logic-ontology/http://plato.stanford.edu/entries/logic-ontology/http://rationallyspeaking.blogspot.com.ar/2012/12/the-complicated-relationship-between.htmlhttp://rationallyspeaking.blogspot.com.ar/2012/12/the-complicated-relationship-between.htmlhttp://rationallyspeaking.blogspot.com.ar/2012/12/the-complicated-relationship-between.htmlhttp://www.ncbi.nlm.nih.gov/pubmed/17820990http://www.ncbi.nlm.nih.gov/pubmed/17820990http://www.ncbi.nlm.nih.gov/pubmed/17820990http://www.ncbi.nlm.nih.gov/pubmed/17820990http://rationallyspeaking.blogspot.com.ar/2012/12/the-complicated-relationship-between.htmlhttp://rationallyspeaking.blogspot.com.ar/2012/12/the-complicated-relationship-between.htmlhttp://plato.stanford.edu/entries/logic-ontology/

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x. the very notion of proof. (cf. 2?)

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Lgica revisitada: de la filosofa a la matemtica y de regreso.

Logic revisitada: from philosophy to mathematics and back.

Es lgicala matemticao es matemtica la lgica?

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Mathematics: a formal system resulting from some possible axiomatization that historically

happened as a curve fitting procedure, one of which 3000000 axioms have been proofed so far,

but on which operations, that is, proofs, are carried out informally. (therefore an axiomatic

system instead of formal????)

Is it, as Gdel 1964 remark, that formal system = turing machine?

\end{comments}

There is no mathematical substitute for philosophy.

S. Kripke, 1976.

The fake philosophical terminology of mathematical logic has misled philosophers into believing

that mathematical logic deals with the truth in the philosophical sense. But this is a mistake.

Mathematical logic deals not with the truth, but with the game of truth.

1. Filosofa de la lgica, filosofa de la matemtica.

1.1 vsmetalgica y metamatemtica. (kleene? chaitin?) (?)

TOC AND ROADMAP

2. Lgica como filosofa, lgica como matemtica.

Intentar ver la transicin.

3. Logicismo.

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3.5 neo logicismo

4. Computabilidad.

Problema de la decisin, quote von neumann

Leibniz

5. Reduccionismos.

quote suppes 1962

After all, even if you knew everything about water molecules and you had a computer

good enough to follow how every molecule in a glass of water moved in space, all you

would have would be a mountain of computer tape. How in that mountain of computer

tape would you ever recognize the properties that interest you about the water,

properties like vorticity, turbulence, entropy, and temperature? (S. Weinberg, 1987)

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