Definition of axiomatize in English:


(also axiomatise)


  • Express (a theory) as a set of axioms.

    ‘the attempts that are made to axiomatize linguistics’
    • ‘Hilbert believed that all of mathematics could be precisely axiomatized.’
    • ‘Economic theories have been axiomatized, and articles and books of economics are full of theorems.’
    • ‘The Godel Incompleteness Theorem applies only to formal logic systems axiomatized in a certain way.’
    • ‘Rather it prompted him to make the first attempt to axiomatise set theory and he began this task in 1905.’
    • ‘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.’
    • ‘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.’
    • ‘Gentzen's was the most outstanding contribution to Hilbert's programme of axiomatising mathematics.’
    • ‘Within politics, the eventual Truth is axiomatised according to the strategic perpetuation of hegemonic rule.’
    • ‘Many other mathematicians attempted to axiomatise set theory.’
    • ‘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.’
    • ‘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.’
    • ‘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.’
    • ‘Italian mathematician Giuseppe Peano axiomatized the mathematical theory of natural numbers.’
    • ‘Moreover, the geometries axiomatized in the book have consistent and decidable extensions, namely, Euclidean or hyperbolic geometry over real-closed fields.’
    • ‘System PC is only one of many possible ways of axiomatizing propositional logic.’
    • ‘Poincaré was absolutely correct, however, in his criticism of those like Russell who wished to axiomatise mathematics.’