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This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode (as opposed to displayed mode). Moreover, procedures are not mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality.

The dominant account of propositions holds that they are structured entities that have, as constituents, the semantic values of the constituents of the sentences that express them. Since such theories hold that propositions are structured, in some sense, like the sentences that express them, they must provide an answer to what I will call Soames' Question: \"What level, or levels, of sentence structure does semantic information incorporate?\" (Soames in Philos Mind Action Theory 3:575-596,1989). As it turns out, answering Soames' Question is no easy task. I argue in this paper that the two most promising ways of answering it, the Logical Form Account and the LF Account, are both unsatisfactory. This result casts doubt on the very idea that propositions are structured.

Renewed worries about the unity of the proposition have been taken as a crucial stumbling block for any traditional conception of propositions. These worries are often framed in terms of how entities independent of mind and language can have truth conditions: why is the proposition that Desdemona loves Cassio true if and only if she loves him? I argue that the best understanding of these worries shows that they should be solved by our theory of truth and not our theory of content. Specifically, I propose a version of the redundancy theory according to which 'it is true that Desdemona loves Cassio' expresses the same proposition as 'Desdemona loves Cassio'. Surprisingly, this variant of the redundancy theory treats 'is true' as an ordinary predicate of the language, thereby defusing many standard criticisms of the redundancy theory.

Jeffrey King, Scott Soames, and others have recently challenged the familiar identification of a Russellian proposition, such as the proposition that Brutus stabbed Caesar, with an ordered sequence constructed out of objects, properties, and relations. There is, as they point out, a surplus of candidate sequences available that are each equally serviceable. If so, any choice among these candidates will be arbitrary. In this paper, I show that, unless a controversial assumption is made regarding the nature of nonsymmetrical relations, none of the proffered candidate sequences are in fact adequate to the play the role. Moreover, as I argue, the most promising alternative theory of relations—one that avoids the problematic assumption and, in addition, fits most naturally into the sequentialist's framework—fails to meet a basic requirement: it cannot distinguish between the proposition that Brutus stabbed Caesar and the proposition that Caesar stabbed Brutus. The upshot is that the conspicuously structured entities that are widely assumed to be up to the task of \"playing the proposition role\" shed no light on the very structure they are invoked to represent.

In Hanks (Philos Stud 134:141-164, 2007; Mind 120:11-52; 2011; Philos Phenom Res 86:155-182, 2013, Propositional Content, Oxford University Press, Oxford, 2015) I defend a theory of propositions that locates the source of propositional unity in acts of predication that people perform in thought and speech. On my account, these acts of predication are judgmental or assertoric in character, and they commit the speaker to things being the way they are represented to be in the act of predication. This leads to a problem about negations, disjunctions, conditionals, and other kinds of embeddings. When you assert that a is F or b is G you do not assert that a is F, nor do you commit yourself to a's being F. According to my theory, however, in uttering the disjunction you predicate F of a. What is going on? I account for these cases using the concept of cancellation. In uttering the disjunction, the act of predicating F of a is cancelled, and when an act of predication is cancelled it does not count as an assertion and does not commit the speaker to anything. But what is it for an act of predication to be cancelled? One immediate concern is that cancelled predication won't provide a unified proposition to be the input to disjunction. In this paper I answer this and related objections by explaining and defending my concept of cancellation.

I show that the assumption of highly structured propositions can be leveraged to provide a unified semantics for various propositional logics of impure ground in a very expressive and flexible way. It is shown, in particular, that the induced models are capable of capturing an infinitude of grounding facts that follow from unrestricted logics of ground, but, due to certain artificial restrictions, are left unaccounted for by the existing semantics in the literature. It is also shown that our models, unlike the ones in the literature, are easily extendable to capture certain distinct views about iterated as well as identity grounding.

An argument going back to Russell shows that the view that propositions are structured is inconsistent in standard type theories. Here, it is shown that such type theories may nevertheless provide entities which can serve as proxies for structured propositions. As an illustration, such proxies are applied to the case of grounding, as standard views of grounding require a degree of propositional structure which suffices for a version of Russell’s argument. While this application solves some of the problems grounding faces, it introduces problematic limitations: it becomes impossible to quantify unrestrictedly over the relata of ground. The proposed proxies may thus not save grounding, but they shed light on what exactly Russell’s argument does and does not show.

Peter Hanks and Scott Soames both defend pragmatic solutions to the problem of the unity of the proposition. According to them, what ties together Tim and baldness in the singular proposition expressed by 'Tim is bald' is an act of the speaker (or thinker) : the act of predicating baldness of Tim. But Soames construes that act as force neutral and noncommittal while, for Hanks, it is inherently assertive and committal. Hanks answers the Frege-Geach challenge by arguing that, in complex sentences, the force inherent in the content of an embedded sentence is cancelled. Indrek Reiland has recently objected to Hanks's proposal that it faces a dilemma: either force cancellation dissolves the unity of the proposition secured by the cancelled act of assertion (and Hanks's proposal does not work), or Hanks's proposal reduces to Soames's. In this paper, I respond to Reiland by offering an analysis of force cancellation which gets rid of the alleged dilemma. The proposal is based on a set of distinctions from speech act theory : between two senses of 'force', two types of act, and two types of context. The role of simulation in force cancellation is emphasized, and connections drawn to broader issues such as the evolution of complex language.

Alonzo Church proposed a powerful and elegant theory of sequences of functions and their arguments as surrogates for Russellian singular propositions and singular concepts. Church’s proposed theory accords with his Alternative (0), the strictest of his three competing criteria for strict synonymy. The currently popular objection to strict criteria like (0) on the basis of the Russell–Myhill antinomy is here rebutted. Russell–Myhill is not a problem specifically for Alternative (0); it is a refutation of unrestrained concept comprehension. Unrestricted comprehension is also inconsistent with facts about sets of properties. Criteria more lax than (0) are philosophically inadequate. In particular, the rival conception of propositions as classes of possible worlds is subject to a fatal philosophical collapse. It follows on that conception, given that each of us is fallible, that everyone believes everything. It is shown, however, that Church’s proposed theory is vulnerable under (0) to a version of Russell’s notorious Gray’s Elegy objection. Some amendments to Church’s proposal are proffered, including an amendment, first proposed in the author’s Frege’s Puzzle  ( 1986 ), that addresses Russell’s objection. Church’s response (personal correspondence) is considered.

The paper reviews the central components of the cognitive theory of propositions and explains both its empirical advantages for theories of language and mind and its foundational metaphysical and epistemological advantages over other theories. It then answers a leading objection to the theory, before closing by raising the issue of how questions, which are the contents of interrogative sentences, and directives, which are the contents of imperative sentences, are related to propositions.