... contentual elementary number theory, which relies only on a “purely intuitive basis of concrete signs.” Whereas the operating with abstract concepts was considered “inadequate and uncertain,” there is a realm of extra-logical discrete ...
... contentual number theory to formalized arithmetic and its attendant metatheory . We shall now deal with the relationships between the language of intuitive number theory ( henceforth referred to as Ls ) , the language of formalized ...
... contentual considerations take place , i.e. , proper thought is practiced . In this way , the contentual considerations , which of course we can never wholly do without or eliminate , are removed elsewhere , as it were , to a higher ...
... contentual correctness proof” as “P is contentual.” The same abbreviation is used also for formal correctness proofs.) Furthermore, one could ask another question: If the 1936 proof is both contentual and formal, how do its contentual ...
... contentual reasoning to traditional mathematics. Hilbert did not deny the importance of contentual judgement and proof to traditional mathematics. He insisted only that non-contentual methods also figured importantly in making ...
... contentual nature of genuine proof the focal point of his disagreements with Hilbert and those others (e.g., Heine and Thomae) he saw as advocating non-contentualist views of proof. [A]n inference does not consist of signs. We can only ...
... contentual investigation. But for this purpose the usual contentual ideas of the mathematical theory must be replaced by formulae and rules, and imitated by formalisms. In other words, we need to have a strict formalization of the ...
... contentual practice and that it promoted simplicity or efficiency in the production of real knowledge ( 1900 : 439-40 , 1905 : 135-6 , 1926 : 372 , 379 ) . Dedekind also spoke of the ' freedom ' of the axiomatic method . However , he ...
... contentual models and ' part ' paradigms , accepted for a time by specific groups within a particular science . Acceptance of contentual models of less than universal character does occur in psychology and other social sciences . The ...
... contentual reasoning. Ideal reasoning does not, therefore, displace contentual reasoning. Rather, it supplements it by adding signs that produce an overall body of reasoning that is psychologically more natural and epistemically more ...