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3 results

Relevance Logic

Relevance Logic
  • Shay Allen Logan
  • Published online:
    28 March 2024
    Print publication:
    18 April 2024
  • Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of the cutting edge on variable sharing results and a guide to further topics in the field.
God and the Problem of Logic

God and the Problem of Logic
  • Andrew Dennis Bassford
  • Published online:
    15 May 2023
    Print publication:
    08 June 2023
  • Classical theists hold that God is omnipotent. But now suppose a critical atheologian were to ask: Can God create a stone so heavy that even he cannot lift it? This is the dilemma of the stone paradox. God either can or cannot create such a stone. Suppose that God can create it. Then there's something he cannot do – namely, lift the stone. Suppose that God cannot create the stone. Then, again, there's something he cannot do – namely, create it. Either way, God cannot be omnipotent. Among the variety of known theological paradoxes, the paradox of the stone is especially troubling because of its logical purity. It purports to show that one cannot believe in both God and the laws of logic. In the face of the stone paradox, how should the contemporary analytic theist respond? Ought they to revise their belief in theology or their belief in logic? Ought they to lose their religion or lose their mind?
Paraconsistency in Mathematics

Paraconsistency in Mathematics
  • Zach Weber
  • Published online:
    25 July 2022
    Print publication:
    11 August 2022
  • Paraconsistent logic makes it possible to study inconsistent theories in a coherent way. From its modern start in the mid-20th century, paraconsistency was intended for use in mathematics, providing a rigorous framework for describing abstract objects and structures where some contradictions are allowed, without collapse into incoherence. Over the past decades, this initiative has evolved into an area of non-classical mathematics known as inconsistent or paraconsistent mathematics. This Element provides a selective introductory survey of this research program, distinguishing between `moderate' and `radical' approaches. The emphasis is on philosophical issues and future challenges.