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The Definition of Points
The Definition of Points ~v~~ In the swansong of modern math lines are composed of points. But then we must ask how points are defined? However I seem to recollect intersections of lines determine points. But if so then we are l... 5 May 2007 21:52
On Ultrafinitism
Is the following a reasonable point of view, do people think? I'm still kind of wondering where Yessenin-Volpin, Edward Nelson, and other ultrafinitists are coming from. They purport to find, or rather take the public stance of finding, that the concept of "all the naturals" is confusing and vague, whereas it ... 10 Nov 2006 03:51
Modal Logic
Hi all, Is there anybody interested in "Modal Logic" ? I need a debater! Thanks ... 8 Oct 2006 15:32
Why Has None of Computer Science been Formalized?
Do we all agree that Computer Science definitely should be formalized? While the definitions of common terms (e.g. recursively enumerable) are formal, the manipulations of these concepts (e.g. the derivation of proofs) is not. Can anybody show a single example of a formal derivation of a result from any branch o... 6 Nov 2006 09:53
Simple yet Profound Metatheorem
Prove ( P = |- Q ) => |- ( P = Q ) (P and Q have the same sets of free variables.) This simple theorem (I created 12/1/05) provides the link between Theory of Computation and Proof Theory (Incompleteness in Logic) that theoreticians such as myself have been looking for since the 1930's. (Each Theory of Computa... 23 Jan 2006 15:18
Obections to Cantor's Theory (Wikipedia article)
I'm in the process of writing an article about objections to Cantor's Theory, which I plan to contribute to the Wikipedia. I would be interested in having some intelligent feedback. Here' the article so far. *** While the pure mathematicians almost unanimously accept Cantor's Theory (with the exception of a... 2 Aug 2005 17:22
Hey all, We have recently moved on to the wonderful world of "derivations." :P I have found that there is more than one way to derive a sentence in SL from the premis. How would you guys go about showing that the following derviation claims hold in SD? Obviously we need to construct a derivation. How can I type ... 21 Jun 2005 12:09
Dear Dave Rusin, thank you for revealing your personal point of view. Being in the weakest possible position, I will nonetheless not swallow that set theory has a sound basis. The reason for me to deal with Cantor's original papers was not interest in history, religion, or philosophy. I am an experienced enginee... 28 Apr 2005 06:07
arithmetic in ZF
In a recent post, Bhup pointed out (correctly) that we can interpret PA into ZF. But then the post went on to say: 6. Hence, if ZF is consistent, then every Arithmetical proposition is syntactically (i.e., independently of the semantic connotations of the above definitions of "truth" and "satisfiability") de... 11 May 2005 11:19
What is wrong with this argument?
What is wrong with saying that God works in Mysterious ways? ... 11 May 2005 03:31
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