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A proof-theoretic view of necessity

Synthese 148 (3):659 - 673 (2006)

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  1. Offline and Online Data: on upgrading functional information to knowledge.Giuseppe Primiero - 2013 - Philosophical Studies 164 (2):371-392.
    This paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth (...)
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  • Direct Proofs of Lindenbaum Conditionals.René Gazzari - 2014 - Logica Universalis 8 (3-4):321-343.
    We discuss the problem raised by Miller to re-prove the well-known equivalences of some Lindenbaum theorems for deductive systems without an application of the Axiom of Choice. We present five special constructions of deductive systems, each of them providing some partial solutions to the mathematical problem. We conclude with a short discussion of the underlying philosophical problem of deciding, whether a given proof satisfies our demand that the Axiom of Choice is not applied.
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