The Conceptual Roots of Mathematics by Lucas J. R

Author:Lucas, J. R. [J.R. LUCAS]
Language: eng
Format: epub
Publisher: Taylor & Francis Ltd
Published: 2011-11-14T16:00:00+00:00

First-order Peano Arithmetic is not decidable

First-order Peano Arithmetic is not complete

First-order Logic is not decidable

First-order Peano Arithmetic has non-standard models (see §6.3)

Second-order Peano Arithmetic is not recursively axioma-tizable

Second-order Logic is not recursively axiomatizable

First-order Peano Arithmetic cannot be proved consistent by the methods of First-order Peano Arithmetic alone

Truth outruns provability

Verificationist arguments against the Principle of Bivalence are invalid

However much proofs are formalised, there are further proofs not fully formalised, but evidently cogent

Hilbert’s Programme cannot be carried through to a successful conclusion

Reason is creative

Synthetic a priori truths are possible

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