Re: Mathematics: art or science?

"T.H. Ray" <thray123@xxxxxxx> writes:

As I said, and which is not controversial, any
consistent result
from any self consistent system of axioms is true.

Really? So it is true that, say, Peano arithmetic is
inconsistent?

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man
schweigen"
- Ludwig Wittgenstein, Tractatus
s Logico-Philosophicus

"T.H. Ray" <thray123@xxxxxxx> writes:

As I said, and which is not controversial, any
consistent result
from any self consistent system of axioms is true.

Really? So it is true that, say, Peano arithmetic is
inconsistent?

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man
schweigen"
- Ludwig Wittgenstein, Tractatus
s Logico-Philosophicus

Why would you say that? The axioms of Peano (I
prefer to say Dedekind-Peano) are certainly self-
consistent.

If I venture to try and interpret what you mean--that
(as Godel proved) no system of axioms is strong enough
to prove its own consistency--such does not obviate
anything that I said.

Tom
.

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