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actual analysis answer anti-realism arithmetical statements aspects asserting Assume axiom of choice axioms believe Boolean algebra canonical proofs certainty classical eclecticism classical logic classical mathematics commensurate Common Sense view concepts considered context continuum hypothesis Dag Prawitz Defence Definition determined essay evidence existence explain expression know external world factual assumptions Fermat primes finite Fomalhaut series formulated fundamental G. E. M. Anscombe given Goldbach's conjecture hand Hence human ignorabimus implies inaccessible cardinal intuitionistic justification kind language-game Lemma linguistic expressions linguistic interplay linguistic rules logic mathematical realism mathematical statements metaphysical mistake Moore and Wittgenstein natural number notion ordinary sense philosophers physical objects possible premisses principle probability measure probability system problem proposition proved question realistic view reason regarded remarks sceptical doubts situations Stockholm Studies strongly coherent Theorem theoretical provability theory of meaning things true truth conditions truth or falsity understand understood utterance verificationist world-view