[FOM] First-order arithmetical truth

Stephen Pollard spollard at truman.edu
Fri Oct 13 08:52:37 EDT 2006

Francis Davey wrote:

> I personally don't know how to see if mathematical statements are  
> "true". I might believe that the godel sentence is true in the  
> "intended model", but no-one has ever been able to explain exactly  
> what they mean by the intended model, so I am far from sure about  
> that.

The first-order number theoretic truths are exactly the first-order  
sentences in the language of arithmetic that follow from the axioms  
of Peano Arithmetic supplemented by the following version of the  
least number principle: "Among any numbers there is always a  
least." (This principle is not firstorderizable; but that doesn't  
make it unintelligible.)

Stephen Pollard
Professor of Philosophy
Division of Social Science
Truman State University
spollard at truman.edu

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