Set Theory and Logic

   

Denial of Suzko's Problem

Authors: Colin James III

We examine a sentential logic description, as based on set theory, in support of Suzko's theorem that only two truth values are required as a universal logic. Under syntactic notions, we evaluate three definitions (monotonicity, transivity, permeability) out of six definitions (trivial are substitution-invariance, reflexivity, combined consequence relation). Monotonicity and transivity are not tautologous. Right-to-left permeability is not tautologous. What follows is that a Malinowski extension of mixed-consequence by relaxation of the two values for three logical values is spurious, especially due to the fact that Suzko's theorem is a conjecture based on the assumption of set theory. What also follows is that compositionality as based on Suzko-Scott reductions are not bivalent and exact, but rather a vector space and probabilistic. Our results point further to the equations analyzed as being non tautologous fragments of the universal logic VL4.

Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

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Submission history

[v1] 2019-03-12 15:08:14

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