Morgan Steele
University of Southampton
I argue that truth-valueless propositions cannot be asserted to exist without serious, detrimental, consequence. Regardless of which propositions are deemed to be truth-valueless, and for what reason, I claim that a dilemma arises. This dilemma originally stems from Dummett and is concerning propositions of the form “P” and “it is true that P”. In particular, it is concerning the truth-value of “it is true that P”, when “P” has no truth-value. This paper begins with two starting constraints which disallow “it is true that P” to be true when “P” is truth-valueless, as well as preventing either “P” or “it is true that P” from being false, when the other is true. Given these constraints, when “P” is truth-valueless, there are two mutually exclusive, and exhaustive, options. Either, maintain the material equivalence of “P” and “it is true that P”, meaning they are both truth-valueless. Or, reject this material equivalence and therefore claim that when “P” is truth-valueless, “it is true that P” is false. In this paper, I consider both potential options.
First, I systematically move through three attempts to maintain the material equivalence of “P” and “it is true that P”. Each account will achieve all that the previous account achieves, and overcome the hurdle that the previous account fell at, but ultimately reach an issue of its own. The first of such accounts will be one that Dummett raises in the same paper in which he presents his dilemma. This account will solve his dilemma, and indeed the variation of his dilemma that I am presenting, but it will reach an issue regarding propositions of the form “it is neither true nor false that P”. The second account is one considered by Field as a way in which some may attempt to overcome the Liar Paradox. This account will solve the dilemma, and have an acceptable outcome with propositions of the form “it is neither true nor false that P”, but it is not an option for those who wish to assert the existence of truth-valueless propositions. The third account will do all that its predecessors can do, whilst being a viable option for those who wish to assert the existence of truth-valueless propositions, but at the cost of claiming that all talk of truth is truth-valueless. Since none of these three options will be appealing, the fist horn of the dilemma as a whole, is not a good option for those who wish to posit the existence of truth-valueless propositions.
The paper then turns to the second horn of the dilemma. In order for this horn to be taken, there must be some part of “it is true that P” which permits it to have a different truth-value from “P”. There are seemingly only two options that can explain this. Firstly, it may be claimed that “is true” substantively contributes to the semantics of the proposition that it is a part of. Secondly, it may be claimed that the “that”-clause changes the reference of the proposition, thereby providing a prima facie explanation for their differing truth-values. Before considering these two options, I shall first present a motivation for maintaining the material equivalence of “P” and “it is true that P” through appeal to particular inferences it justifies and absurdities it prevents. I then consider the claim that “is true” makes a substantive contribution to the semantics of the proposition that it is a part of. In order to provide this account, I will need to explain the concept of truthmaking as it is key to understanding how “P” and “it is true that P” can have differing truth-values. Having done this, I will find that this account reaches a dilemma of its own with regard to the truthmakers of the proposition “it is true that P”. This dilemma was inspired by one presented by Asay, but has a crucial difference since the accounts I am considering are unable to claim that there is an entailment connection between the truthmakers in “P” and “it is true that P”. This inability is present since claiming that there is such an entailment connection would cause the accounts to maintain material equivalence, and consequently, lead them directly back into the issue that Dummett’s originally considered account falls into. Given this inability, regardless of which horn is taken, by attempting to add an additional truthmaker, the possibility of “it is true that P” being false when “P” is true, is permitted. This goes against the constraints set out in the beginning of the paper, as well as common sense. The other option to reject this material equivalence is to claim that the “that”-clause in “it is true that P” does not actually denote “P”, thereby providing a prima facie explanation for their differing truth-values. This account is one raised by Recanati, which claims that “that”-clauses are actually restricted existential quantifiers. I will first explain what Recanati means by this, and apply his account to propositions such as “it is true that P”. Having done this, I will demonstrate why this account actually fails to reject the material equivalence, despite its face-value ability to do so. This means that Recanati’s account also falls into exactly the same problem as the account that Dummett originally considers. Since neither “is true” nor the “that”-clause seem capable of explaining how “it is true that P” can be false when “P” is truth-valueless, this horn of the dilemma is also unappealing for those who wish to assert the existence of truth-valueless propositions.
With this dilemma presenting two very unappealing horns to those who wish to assert the existence of truth-valueless propositions, there is motivation for defending the claim that no such truth-valueless propositions exist.
Chair: Danila Ivanov
Time: September 7th, 10:40-11:10
Location: SR 1.007
SOPhiA 2026 