# Bivalence and Determinacy

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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**Bivalence and Determinacy.** / Rumfitt, Ian.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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*The Oxford Handbook of Truth.*Oxford University Press, Oxford.

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*The Oxford Handbook of Truth*Oxford University Press.

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## RIS

TY - CHAP

T1 - Bivalence and Determinacy

AU - Rumfitt, Ian

PY - 2018/6

Y1 - 2018/6

N2 - The principle that every statement is bivalent (i.e. either true or false) has been a bone of philosophical contention for centuries, for an apparently powerful argument for it (due to Aristotle) sits alongside apparently convincing counterexamples to it. I analyse Aristotle’s argument (§§1-2), showing that it relies crucially on the logical laws of Excluded Middle and Proof by Cases. Even given these logical laws, however, the argument only shows that every determinate statement is true or false, where a determinate statement ‘says one thing’, i.e. has univocal truth-conditions. In the light of this analysis, I examine three sorts of problem case for bivalence. Future contingents, I contend, are bivalent (§3). Certain statements of higher set theory, by contrast, are not. Pace the intutionists, though, this is not because Excluded Middle does not apply to such statements, but because they are not determinate (§§4-6). Vague statements too are not bivalent, in this case because the law of Proof by Cases does not apply (§§7-8). I show how this opens the way to a solution to the ancient Paradox of the Heap or Sorites (§9) that draws on quantum logic.

AB - The principle that every statement is bivalent (i.e. either true or false) has been a bone of philosophical contention for centuries, for an apparently powerful argument for it (due to Aristotle) sits alongside apparently convincing counterexamples to it. I analyse Aristotle’s argument (§§1-2), showing that it relies crucially on the logical laws of Excluded Middle and Proof by Cases. Even given these logical laws, however, the argument only shows that every determinate statement is true or false, where a determinate statement ‘says one thing’, i.e. has univocal truth-conditions. In the light of this analysis, I examine three sorts of problem case for bivalence. Future contingents, I contend, are bivalent (§3). Certain statements of higher set theory, by contrast, are not. Pace the intutionists, though, this is not because Excluded Middle does not apply to such statements, but because they are not determinate (§§4-6). Vague statements too are not bivalent, in this case because the law of Proof by Cases does not apply (§§7-8). I show how this opens the way to a solution to the ancient Paradox of the Heap or Sorites (§9) that draws on quantum logic.

KW - Bivalence

KW - future contingents

KW - Continuum Hypothesis

KW - Georg Kreisel

KW - Sorites Paradox

KW - Paradox of the Heap

KW - quantum logic

KW - vagueness

M3 - Chapter

SN - 978-0199557929

BT - The Oxford Handbook of Truth

A2 - Glanzberg, Michael

PB - Oxford University Press

CY - Oxford

ER -