Abstract

In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.

Highlights

  • Graham Priest is known for defending three unorthodox theses in logic and metaphysics, which he refers to as “three heresies” (Priest, 2013): 1. Dialetheism, the thesis that some contradictory sentences are true, 2

  • If we assume that there is a unique actual world, @, and that it belongs to the unique actual structure, dialetheism can be presented as what may be called single model dialetheism: Single model dialetheism is a metaphysical view: some contradictions are true at the unique actual world, @, in the unique actual model

  • A distinction has been drawn between various versions of dialetheism as a metaphysical view

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Summary

Introduction

Graham Priest is known for defending three unorthodox theses in logic and metaphysics, which he refers to as “three heresies” (Priest, 2013): 1. Dialetheism, the thesis that some contradictory sentences are true, 2. The three heresies form a closely interrelated part of Priest’s thinking, the focus of the present paper is only on the first heresy, dialetheism.. The three heresies form a closely interrelated part of Priest’s thinking, the focus of the present paper is only on the first heresy, dialetheism.2 It will be scrutinized, an alternative to it will be presented, and the attention will be directed to a certain orthodoxy in philosophical logic, namely the view that logic is a normative. Priest appears to be a die-hard heretic, he endorses the quite orthodox view that logic is a normative discipline. Whilst dialetheism is a metaphysical view, dimathematism is an informational thesis. 5, I will address the orthodox thesis, subscribed to by Priest, that logic is a normative discipline. I will argue that dimathematism helps dissociate logic from normativity

What is Graham Priest’s Dialetheism?
Single Model Dialetheism and Multiple Models Dialetheism
Dialetheism and Strong Dialetheism
Dimathematism and Strong Dimathematism We may now introduce dimathematism
Turning Off on a Slippery Slope
Logic’s Non‐normativity
Normativity Understood as the Generation of Norms
Normativity Understood as the Study of the Meaning of Normative Notions
Summary
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