```Date: Aug 21, 2013 12:01 AM
Author: William Elliot
Subject: Re: Foundations of mathematics... the order of bootstrapping the<br> foundations

On Tue, 20 Aug 2013, Lax Clarke wrote:> > > Please correct me if I'm wrong please:> > > This is the order of bootstrapping the foundations of mathematics:> > Boot strapping has nothing to do with mathematics.> > It's part of computer science.> Ok.  I just want to know the order of learning I guess.  Or say a really smart and "rigor-loving" alien landed in our backyard, in what order would we explain thing to him in (assuming the alien learns English first).> > > 1) Naive logic (like the ones the Greeks played with).> > > 2) Use 1) to talk about Naive Set theory (like Halmos' book).> > > 3) Use 2) above to define Mathematical Logic / First-Order Logic> > > 4) Use 3) above to define axiomatic set theory.> > A metalanguage is used to describe a formal language.> 1, 2 would be metalanguages? These would be used to build up formal > languages 3,4?The metalanguage is usually a simple native language with	simple logic which usually includes simple induction.The metalanguage is used to describe a formal language and it's logic,	such as rules of inference.It could be used to describe a FOL.  If axioms are added then it would be describing a theory.The theory could be one of the set theories ML, ZF, ZFC or NBG.	Abbreviations are part of the metalanguage and within a simple book, say ML, abbreviations can quickly represent hundredsor thousands, perhaps millions, of primitive symbols.
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