User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

Tarski's Axioms of Geometry
I'm going to have to figure out how to precisely and accurately express what are the disciplines preceding Tarski's geometry. I'll post my progress here for anyone who wants to follow.

GFP to Steven Givant:

If you have time, I'd like to ask you a question about your essay.

...

Is this to say that Aristotelian logic precedes Tarski's Geometry? That is, does Tarski's system depend on the law of excluded middle, the principle of non-contradiction, modus ponendo ponens, etc. etc. ? -GFP

Stevent Givant to GFP:

Tarski assumes the language and axioms of first -order logic (which is substantially stronger than propositional logic---what you might be referring to when you speak of Aristotelian logic). - Givant

Comments are welcome. Does PW have a page on the order of a logical statement? I couldn't find one. --GFauxPas 15:00, 25 January 2012 (EST)


 * First-order logic is stronger than propositional logic as it allows quantification ($\forall, \exists$). The proofs of Tarski-Vaught Test and Łoś's Theorem implicitly use an order on formulas. This however has not been properly defined on PW. So go ahead :). --Lord_Farin 15:19, 25 January 2012 (EST)