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Express (a theory) as a set of axioms:‘the attempts that are made to axiomatize linguistics’
- ‘Italian mathematician Giuseppe Peano axiomatized the mathematical theory of natural numbers.’
- ‘Now Frege axiomatized arithmetic with an intuitive collection of axioms, and proofs of number theory results which he had only sketched earlier he now gave formally.’
- ‘Many other mathematicians attempted to axiomatise set theory.’
- ‘Economic theories have been axiomatized, and articles and books of economics are full of theorems.’
- ‘Moreover, the geometries axiomatized in the book have consistent and decidable extensions, namely, Euclidean or hyperbolic geometry over real-closed fields.’
- ‘Gentzen's was the most outstanding contribution to Hilbert's programme of axiomatising mathematics.’
- ‘Grammar formalisms - special-purpose systems for the description of linguistic systems and subsystems - can be thought of as logics designed to axiomatize the association of linguistic structures with strings of symbols.’
- ‘System PC is only one of many possible ways of axiomatizing propositional logic.’
- ‘Any one of the ordinary, everyday proofs mathematicians deal with in their work can be re-written in a formal way that fits into this framework the logicians have axiomatized.’
- ‘Hilbert believed that all of mathematics could be precisely axiomatized.’
- ‘Within politics, the eventual Truth is axiomatised according to the strategic perpetuation of hegemonic rule.’
- ‘Poincaré was absolutely correct, however, in his criticism of those like Russell who wished to axiomatise mathematics.’
- ‘The Godel Incompleteness Theorem applies only to formal logic systems axiomatized in a certain way.’
- ‘It would build on the early work in axiomatizing branches of mathematics, as well as the monumental efforts of logicists like Frege in developing rigorous logical systems.’
- ‘Rather it prompted him to make the first attempt to axiomatise set theory and he began this task in 1905.’
- ‘The construction of the reals from the integers proceeds in several stages: first axiomatize the positive integers, then construct negative from positive integers, then rationals from integers, and finally reals from rationals.’
- ‘The sciences - at any rate the theoretical sciences - are to be axiomatised.’
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