Peano

For instance, in a certain group the cognitive significance carried by the name ˜Peano™ might be the same as that of the description ˜the discoverer of the Peano axioms™ (the assumption is that the members of the group believe no more and no less than this about Peano), yet as it turns out Dedekind, not Peano, discovered the (misnamed) axioms.

Names Cumming, Sam 2009

The First Incompleteness Theorem provides a counterexample to completeness by exhibiting an arithmetic statement which is neither provable nor refutable in Peano arithmetic, though true in the standard model.

Backing Into an Evidentiary Standard for ID 2007

Even after Frege, logicians such as Peano kept formalizing the language of mathematical arguments, but without any explicit list of rules of proof.

Chores 2009

There were efforts — by Peano and so on — to come up with definitive axiomatization of mathematics.

Wolfram Blog : Stephen Wolfram on the Quest for Computable Knowledge 2009

Any theory which includes Peano arithmetic will be incomplete, hence if a final Theory of Everything includes Peano arithmetic, then the final theory will also be incomplete.

Theories of Everything and Godel's theorem Gordon McCabe 2009

A final Theory of Everything might have no need of Peano arithmetic, and might well be complete and decidable.

Theories of Everything and Godel's theorem Gordon McCabe 2009

The use of Peano arithmetic is fairly pervasive in mathematical physics, hence, at first sight, this appears to be highly damaging to the prospects for a final Theory of Everything in physics.

Theories of Everything and Godel's theorem Gordon McCabe 2009

The use of Peano arithmetic is fairly pervasive in mathematical physics, hence, at first sight, this appears to be highly damaging to the prospects for a final Theory of Everything in physics.

Archive 2009-06-01 Gordon McCabe 2009

It transpires that the theory of arithmetic (technically, Peano arithmetic) is both incomplete and undecidable.

Theories of Everything and Godel's theorem Gordon McCabe 2009

Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable.

Theories of Everything and Godel's theorem Gordon McCabe 2009