First English translation of revolutionary paper that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds must be of the same kind; this has been called the parity thesis. I show that this thesis faces problems, and propose a hybrid account which rejects it: possible worlds are taken as concrete Lewisian worlds, and impossibilities are represented as (...) set-theoretic constructions out of them. This hybrid account (1) distinguishes many intuitively distinct impossible propositions; (2) identifies impossible propositions with extensional constructions; (3) avoids resorting to primitive modality, at least so far as Lewisian modal realism does. (shrink)

Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, or indeed objects at all. (...) Instead, I argue that realists should follow Prior (1971) and others in treating higher-order quantification (e.g. quantification into predicate or sentence position) as a genuine form of quantification in its own right, and so in particular, not to be analysed in terms of first-order quantification over abstract objects. I argue that from this ‘higher-orderist’ perspective, there is a relatively straightforward answer to the question of how possible worlds-as-propositions succeed in representing possibilities. (shrink)

A singular thought about an object o is one that is directly about o in a characteristic way—grasp of that thought requires having some special epistemic relation to the object o, and the thought is ontologically dependent on o. One account of the nature of singular thought exploits a Russellian Structured Account of Propositions, according to which contents are represented by means of structured n-tuples of objects, properties, and functions. A proposition is singular, according to this framework, if and (...) only if it contains an object as a constituent. One advantage of the framework of Russellian Structured propositions is that it promises to provide a metaphysical basis for the notion of a singular thought about an object, grounding it in terms of constituency. In this paper, we argue that the attempt to ground the peculiar features of singular thoughts in terms of metaphysical constituency fails, and draw some consequences of our discussion for other debates. (shrink)

This article rebuts Ramsey's earlier theory, in 'Universals of Law and of Fact', of how laws of nature differ from other true generalisations. It argues that our laws are rules we use in judging 'if I meet an F I shall regard it as a G'. This temporal asymmetry is derived from that of cause and effect and used to distinguish what's past as what we can know about without knowing our present intentions.

The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that (...) an object-theoretic analysis of the Kaplan paradox reveals that there is no genuine paradox at all, as the central premise of the paradox is simply a logical falsehood and hence can be rejected on the strongest possible grounds—not only in object theory but for the very framework of propositional modal logic in which Kaplan frames his argument. The authors close by fending off a possible objection that object theory avoids the Russell paradox only by refusing to incorporate set theory and, hence, that the object-theoretic solution is only a consequence of the theory’s weakness. (shrink)

In the first section of this paper I consider the practice of volume-measurement in baking, and I distinguish between two measurement schemes that can be extracted from this practice. In the second section I argue that the ascription of propositional content to utterances bears intuitive affinity to one of these schemes, that extant accounts of propositions are in the mold of the other scheme, and that therefore an alternative conception of propositions is called for.

(2013). What are Propositions? Canadian Journal of Philosophy: Vol. 43, Essays on the Nature of Propositions, pp. 702-719.

Most direct reference theorists about indexicals and proper names have adopted the thesis that singular propositions about physical objects are composed of physical objects and properties.1 There have been a number of recent proponents of such a view, including Scott Soames, Nathan Salmon, John Perry, Howard Wettstein, and David Kaplan.2 Since Kaplan is the individual who is best known for holding such a view, let's call a proposition that is composed of objects and properties a K-proposition. In this paper, (...) I will attempt to show that a direct reference view about the content of proper names and indexicals leads very naturally to the position that all singular propositions about physical objects are K-propositions.3 Then, I will attempt to show that this view of propositions is false. I will spend the bulk of the paper on this latter task. My goal in the paper, then, is to show that adopting the direct reference thesis comes at a cost problems the view has with problems such as opacity and the significance of some identity statements; it comes at even more of a cost). (shrink)

Several philosophers advance substantive theories of propositions, to deal with several issues they raise in connection with a concern with a long pedigree in philosophy, the problem of the unity of propositions. The qualification ‘substantive’ is meant to contrast with ‘minimal’ or ‘deflationary’ – roughly, views that reject that propositions have a hidden nature, worth investigating. Substantive views appear to create spurious problems by characterizing propositions in ways that make them unfit to perform their theoretical jobs. (...) I will present in this light some critical points against Hanks’ (2015, 2019) act-theoretic view, and Recanati’s (2019) recent elaboration of Hanks’ notion of cancellation. Both Hanks and Recanati, I’ll argue, rely on problematic conceptions of fiction and pretense. (shrink)

Over the past few years, _CL_ diagrams have gained popularity in diagrammatic reasoning, drawing inspiration from Lange’s _C_ubus _L_ogicus. The intuitive understanding of _CL_ diagrams is based on simple structures that are straightforward both to draw and to comprehend. This structure supports embedding of information and inferencing. Furthermore, these diagrams are more than just heuristic tools; _CL_ diagrams can actually be extended to full blown formal systems. The present paper shows that a formal system for _CL_ diagrams can have an (...) expressivity similar to standard Boolean algebra of propositions or propositional logic without losing their intuitive properties. It is also possible to combine this interpretation of _CL_ with elements from the class calculus. The syntax and semantics are presented separately, and the system’s soundness and completeness are proven using a variant of bitstring semantics. (shrink)

Many philosophers believe in things, propositions, which are the things that we believe, assert etc., and which are the contents of sentences. The act-type theory of propositions is an attempt to say what propositions are, to explain how we stand in relations to them, and to explain why they are true or false. The core idea of the act-type theory is that propositions are types of acts of predication. The theory is developed in various ways to (...) offer explanations of the important properties of propositions. I present the core idea of the theory, and some developments of it. I discuss the relationship between the theory and the content–force distinction. I also present an important type of objection that has been raised to the explanations offered by the act-type theory. (shrink)

Trevor Teitel (2017) has recently argued that combining the assumption that modality reduces to essence with the assumption that possibly some objects contingently exist leads to problems if one wishes to uphold that the logic of metaphysical modality is S5. In this paper I will argue that there is a way for the essentialist to evade the problem described by Teitel. The proposed solution crucially involves the assumption that some propositions possibly fail to exist. I will show how this (...) assumption affords a motivated contingentist response to Teitel’s argument. (shrink)

In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, but (...) if, for example, PM’s disjunction (∨) is a relation, what is it a relation between? There is no obvious answer to this given Russell’s other philosophical commitments at this time, although hints are left in some of the pre-PM manuscripts. In this paper, I explore this tension in Russell's philosophy and relate it to developments both before and after Problems. (shrink)

The paper gives a detailed reconstruction and discussion of Peirce’s doctrine of propositions, so-called Dicisigns, developed in the years around 1900. The special features different from the logical mainstream are highlighted: the functional definition not dependent upon conscious stances nor human language, the semiotic characterization extending propositions and quasi-propositions to cover prelinguistic and prehuman occurrences of signs, the relations of Dicisigns to the conception of facts, of diagrammatical reasoning, of icons and indices, of meanings, of objects, of (...) syntax in Peirce’s logic-as-semiotics. (shrink)

Some propositions are structurally unknowable for certain agents. Let me call them ‘Moorean propositions’. The structural unknowability of Moorean propositions is normally taken to pave the way towards proving a familiar paradox from epistemic logic—the so-called ‘Knowability Paradox’, or ‘Fitch’s Paradox’—which purports to show that if all truths are knowable, then all truths are in fact known. The present paper explores how to translate Moorean statements into a probabilistic language. A successful translation should enable us to derive (...) a version of Fitch’s Paradox in a probabilistic setting. I offer a suitable schematic form for probabilistic Moorean propositions, as well as a concomitant proof of a probabilistic Knowability Paradox. Moreover, I argue that traditional candidates to play the role of probabilistic Moorean propositions will not do. In particular, we can show that violations of the so-called ‘Reflection Principle’ in probability need not yield structurally unknowable propositions. Among other things, this should lead us to question whether violating the Reflection Principle actually amounts to a clear case of epistemic irrationality, as it is often assumed. This result challenges the importance of the principle as a tool to assess both synchronic and diachronic rationality—a topic which is largely independent of Fitch’s Paradox—from a somewhat unexpected source. (shrink)

In order to fulfil their essential roles as the bearers of truth and the relata of logical relations, propositions must be public and shareable. That requirement has favoured Platonist and other nonmental views of them, despite the well-known problems of Platonism in general. Views that propositions are mental entities have correspondingly fallen out of favour, as they have difficulty in explaining how propositions could have shareable, objective properties. We revive a mentalist view of propositions, inspired by (...) Artificial Intelligence work on perceptual algorithms, which shows how perception causes persistent mental entities with shareable properties that allow them to fulfil the traditional roles of (one core kind of) propositions. The clustering algorithms implemented in perception produce outputs which are (implicit) atomic propositions in different minds. Coordination of them across minds proceeds by game-theoretic processes of communication. The account does not rely on any unexplained notions such as mental content, representation, or correspondence (although those notions are applicable in philosophical analysis of the result). (shrink)

This paper defends a key aspect of the Peircean conception of truth—the idea that truth is in some sense epistemically-constrained. It does so by exploring parallels between Peirce’s epistemology of inquiry and that of Wittgenstein in On Certainty. The central argument defends a Peircean claim about truth by appeal to a view shared by Peirce and Wittgenstein about the structure of reasons. This view relies on the idea that certain claims have a special epistemic status, or function as what are (...) popularly called ‘hinge propositions’. (shrink)

Semantic Minimalists make a proprietary claim to explaining the possibility of utterances sharing content across contexts. Further, they claim that an inability to explain shared content dooms varieties of Contextualism. In what follows, I argue that there are a series of barriers to explaining shared content for the Minimalist, only some of which the Contextualist also faces, including: (i) how the type-identity of utterances is established, (ii) what counts as repetition of type-identical utterances, (iii) how it can be determined whether (...) semantically minimal content has been repeated, and (iv) what the nature of such content is. (shrink)

Propositions, the abstract, truth-bearing contents of sentences and beliefs, continue to be the focus of healthy debates in philosophy of language and metaphysics. This article is a critical survey of work on propositions since the mid-90s, with an emphasis on newer work from the past decade. Topics to be covered include a substitution puzzle about propositional designators, two recent arguments against propositions, and two new theories about the nature of propositions.

Unfortunately, there is a mistake in line 10 of Section 1.2. The correct reference should read: As Kripke pointed out, we can produce one simply by baptizing the string ‘Jack is short’: Jack.

The principal claims supported include: (i) that 'believe' and 'know' take the same grammatical object 'that p'; (ii) that each may take grammatical objects that the other cannot take; (iii) that merely grammatical considerations cannot determine whether 'that p' designates a proposition or a fact; (iv) that, on an epistemically relevant interpretation, 'that p' may be construed either as designating a proposition or a fact or both; (v) that propositions and facts are correlative and heuristic entities. The issues are (...) developed in the context of exploring chiefly the views of Zeno Vendler, Alan White, and Peter Geach. Complications bearing on the distinction between thought and speech are considered. (shrink)

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. 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. (shrink)