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non classical logical systems

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Chapter 6 - Logical nihilism
from Part I - The Main Positions
- By Curtis Franks
Edited by Penelope Rush, University of Tasmania
Book:

The Metaphysics of Logic

Published online:

05 October 2014

Print publication:

16 October 2014, pp 109-127
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Summary

Our logical practices, it seems, already exhibit "truth by convention". A visible part of contemporary research in logic is the exploration of non classical logical systems. It's sad that almost no one notices that Quine's refutation of the conventionality of logic is a dilemma. The famous Lewis Carroll infinite regress assails only one horn of this dilemma, the horn that presupposes that the infinitely many needed conventions are all explicit. One of the oldest ways of begging the question against proponents of alternative logics (as well as a popular way of begging the question against logical conventionalism) is to implicitly adopt a lofty metalanguage stance, and then use the very words that are under contention against the opponent. That doing this is so intuitive evidently contributes to the continued popularity of the fallacy.