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University of the Philippines Diliman | College of Social Sciences and Philosophy
  • Author: Smyel Noelin S. De Guzman
  • Year: 2021
  • Type: Peer-Reviewed Journal Article

Citation:

De Guzman, S.N.S. “Tarski and Modality”. Suri 9:2 (2021): 1-22

Abstract:

Subscription to meta-language for self-referencing statements has been put forth by Tarski as solution to the Liar Paradox, suggestively indicative of the existence of higher order system through logic and language capable of substantiating truth. The paper aims to argue that the same methodology can be used to attribute truth values to propositions otherwise subsumed by many-valued logic. In many-valued logic, answers yield probabilities and multivalues versus definite truth values found in classical logic, yet this proves to be paradoxical as probabilities as a whole can be deemed to be either true or false. Wave function collapse yield stochastic states of affairs based on plugged eigenvalues, eliminating true from false states of affairs. Due to its aleatory nature, establishing truth values comes after decoherence, ensuing to probabilistic arguments such as the infamous Schrodinger’s cat-in-a-box experiment’s results, which is evaluated in terms of probability. Classical truth values “true” and “false” can thus be retained provided that the principles of non-contradiction and excluded middle are relaxed. To argue that a state of affair (post-decoherence state) is true is to coordinate spacetime dimension along with indicative markers of possible world actualized via modalities; to state however that something is true in all possible world does not necessitate subscribing to quantum logic. Truth thus transcends multivalued truth as meta- language trumps object language, as modalities encompass quantum logic.

Key Words:

many-valued logic, quantum mechanics, Tarski, probabilities, meta-language, truth

Link:

https://suri.pap73.org/issue14/deguzman_suri_october2021.pdf