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What is a Proof?

Axiomathes 25 (1):79-91 (2015)

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  1. The Role of Gestures in Logic.Andrea Reichenberger, Jens Lemanski & Reetu Bhattacharjee - forthcoming - Multimodal Communication.
    Gestures are usually regarded as a casual element of communication processes between logicians. By contrast, we aim to show that gestures have played a significant role in logic. We argue that the development of communication techniques and their standardization have led to the rise of formal notation systems commonly used in logic today. In order to substantiate this claim, the historical development of the use of gestures in (early) modern logic is investigated. This investigation uncovers exemplary communication and proof techniques (...)
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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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