Necessity and triviality

Australasian Journal of Philosophy 88 (3):401-415 (2010)
Abstract
In this paper I argue that there are some sentences whose truth makes no demands on the world, being trivially true in that their truth-conditions are trivially met. I argue that this does not amount to their truth-conditions being met necessarily: we need a non-modal understanding of the notion of the demands the truth of a sentence makes, lest we be blinded to certain conceptual possibilities. I defend the claim that the truths of pure mathematics and set theory are trivially true, and hence accepting their truth brings no ontological commitment; I further defend the claim that the truths of applied mathematics and set theory do not demand the existence of numbers or sets. While the notion of a demand must not be reduced to anything modal, I nonetheless argue that sentences that are trivially true must also be necessary, lest we violate a very weak version of the principle that truth depends on the world. I further argue that all necessary truths are trivially true, lest we admit unexplained necessities. I end by showing one important consequence of this: I argue that if there are truthmakers for intrinsic predications, they must be states of affairs rather than tropes
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References found in this work BETA
Kit Fine (1994). Essence and Modality. Philosophical Perspectives 8:1-16.
Agustín Rayo (2007). Ontological Commitment. Philosophy Compass 2 (3):428–444.
Agustin Rayo (2008). On Specifying Truth-Conditions. Philosophical Review 117 (3):385 - 443.
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