Logic

~~~~~~~~~~~~~~ VALPROIC ACID ~~~~~~~~~~~~~~
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SILENT PHARTS OF SCIENCE
Pentcho Valev wrote: A couple of weeks ago I posted on PHILOS-L, a philosophy list with 4,853 subscribers, the following quotation: http://listserv.liv.ac.uk/cgi-bin/wa?A2=ind0911&L=philos-l&T=0&O=D&P=50126 Peter Hayes "The Ideology of Relativity: The Case of the Clock Paradox" : Social Epistemology,... 25 Dec 2009 20:10

~~~~~~~~~~~~~~ CABBAGE SOUP ~~~~~~~~~~~~~~
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What are Sets?
Hi all, One of the facts of set theory is that the primitive relation "e" is totally vague relation, there is no way of understanding this relation at all, even at informal level! Which is actually a great drawback, since in set theory we are building hierarchy of objects using this relation, a relation that n... 20 Jan 2010 21:56

concept of Consistency as a variable, not a constant for math and physics #263: Correcting Math
My foray into the legal system and reflecting on laws that are contradictory to one another, unless, of course as in the Legal System you have an overriding principle of that of "precedence". So I think I may have stumbled upon something of huge importance to mathematics and to physics. We commonly understand m... 23 Dec 2009 21:51

Russel Prawitz Operator, the interesting Case
Dear All Lets define an operator M as follows: M(A) := forall p ((A -> p) -> p) In minimal logic we can show |- M A -> A and |- exists p(p <-> A). Maybe in a weaker logic, we can not show the above both, but instead only some similar to: exists p(p <-> A) <-> (M(A) <-> A) But are we on the rig... 27 Dec 2009 06:33

MADNESS IN EINSTEINIANA
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/big_bang/index.html John Norton: "Here's a light wave and an observer. If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer. That would mean that moving observer would ... 7 Feb 2010 06:30

is this theory consistent?
On p. 218 of "Naturalism in Mathematics" Penelope Maddy writes "Consider the theory ZFC+V=L+there is a transitive model of 'ZFC+0# exists' " Is there an upper bound for the consistency strength of this? If there is a measurable cardinal then there must be a transitive model of ZFC +0# exists in L[U] where L[... 15 Dec 2009 02:28

Does inductive reasoning lead to knowledge?
What is the justification for either: 1. generalising about the properties of a class of objects based on some number of observations of particular instances of that class (for example, the inference that "all swans we have seen are white, and therefore all swans are white," before the discovery of black swans) ... 26 Jan 2010 14:22

The ambivalence of identity
(This is hard, so bear with it.) Firstly: We associate material objects with their observed properties; in this case they are spatio-temporal properties. Secondly: However, if we do the same for piano's and cars then we would be claiming that piano's make music and cars reach destinations. This is animism, ... 21 Dec 2009 10:11