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Register a new userConsistent ultrafinitist logic
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Added by
Micha{\\l} Gajda
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Micha{l} J. Gajda
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Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes stemming from enumeration theorems. However, philosophers still disagree of whether such a finitist logic would be consistent. We present preliminary work on a proof system based on Curry-Howard isomorphism. We also try to present some well-known theorems that stop being true in such systems, whereas opposite statements become provable. This approach presents certain impossibility results as logical paradoxes stemming from a profligate use of transfinite reasoning.
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