Deploying distinctions between ignorance of \ and ignorance that \ , and between knowledge of \ and knowledge that \ , I address a question that has hitherto received little attention, namely: what is it to have knowledge of propositions? I then provide a taxonomy of ontological conceptions of the nature of propositions, and explore several of their interesting epistemological implications.

Transient Truths: An Essay in the Metaphysics of Propositions provides the first book-length exposition and defense of semantic temporalism, the view that propositions are contents or semantic values that can change their truth-values across time.

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)

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.

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.

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 recent years a number of authors sympathetic to Referentialistaccounts of proper names have argued that utterances containingempty names express `gappy,' or incomplete, propositions. In this paper I want to take issue with this suggestion.In particular, I argue versions of this approach developedby David Braun, Nathan Salmon, Ken Taylor, and by Fred Adams,Gary Fuller, and Robert Stecker.

The work of Bertrand Russell had a decisive influence on the emergence of analytic philosophy, and on its subsequent development. The prize-winning Russell scholar Peter Hylton presents here some of his most celebrated essays from the last two decades, all of which strive to recapture and articulate Russell's monumental vision. Relating his work to that of other philosophers, particularly Frege and Wittgenstein, and featuring a previously unpublished essay and a helpful new introduction, the volume will be essential for anyone engaged (...) with the history of twentieth-century ideas. (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)

Nondescriptivist views in many areas of philosophy have long been associated with the commitment that in contrast to other domains of discourse, there are no propositions in their particular domain. For example, the ‘no truth conditions’ theory of conditionals1 is understood as the view that conditionals don’t express propositions, noncognitivist expressivism in metaethics is understood as advocating the view that there are not really moral propositions,2 and expressivism about epistemic modals is thought of as the view that (...) there is no such thing as the proposition that Jack might be at home, over and above the proposition that Jack is at home.3 Of course, it is nearly always acknowledged that advocates of a nondescriptivist theory need not deny that there are conditional, moral, or modal propositions ‘at the end of the day’ – for if they also endorse a deflationary reading of talk about propositions, as famously advocated by Simon Blackburn, then they can employ such deflationary talk just as much as the rest of us. They just don’t appeal to propositions to do any of the work in their theories. Rather, they ‘earn the right’ to talk about propositions.4 It is the aim of this paper to upset this way of thinking about the proper attitude of nondescriptivists toward propositions, and to advocate a more constructive and in some ways more radical alternative on behalf of the nondescriptivist. I will begin by introducing and developing a set of problems that are faced by any nondescriptivist theory which tries to do without propositions. All of these problems are easily solved by any view which postulates propositions across the board, but none of them are solved by merely deflationary talk about propositions – their most promising solutions require propositions to do real theoretical work, and therefore the problems themselves remind us of and illustrate some of the important reasons why it is worth positing propositions in the first place.. (shrink)

Are there ‘self-referential’ propositions? That is, propositions that say of themselves that they have a certain property, such as that of being false. There can seem reason to doubt that there are. At the same time, there are a number of reasons why it matters. For suppose that there are indeed no such propositions. One might then hope that while paradoxes such as the Liar show that many plausible principles about sentences must be given up, no such (...) fate will befall principles about propositions. But the existence of self-referential propositions would dash such hopes. Further, the existence of such propositions would also seem to challenge the widespread claim that Liar sentences fail to express propositions. The aim of this paper is thus to settle the question–at least given an assumption. In particular, I argue that if propositions are structured, then self-referential propositions exist. (shrink)

This paper discusses two distinct strategies that have been adopted to provide fine-grained propositions; that is, propositions individuated more finely than sets of possible worlds. One strategy takes propositions to have internal structure, while the other looks beyond possible worlds, and takes propositions to be sets of circumstances, where possible worlds do not exhaust the circumstances. The usual arguments for these positions turn on fineness-of-grain issues: just how finely should propositions be individuated? Here, I compare (...) the two strategies with an eye to the fineness-of-grain question, arguing that when a wide enough range of data is considered, we can see that a circumstance-based approach, properly spelled out, outperforms a structure-based approach in answering the question. (Part of this argument involves spelling out what I take to be a reasonable circumstance-based approach.) An argument to the contrary, due to Soames, is also considered. (shrink)

This is a paper in which I argue that problems of transworld identity and the truth in-truth at distinction are motivated by unhelpful pictures we have in mind while doing metaphysics.

I shall explain the notions of propositions and states of affairs as they are understood in the current ontological debate and I shall briefly relate them to similar notions in Aristotle and some Medieval authors. In contrast with the point of view of some philosophers who identify propositions and states of affairs, I shall argue that they need to be sharply distinguished. I shall then move on to a problem for propositions and, above all, states of affairs, (...) known as Bradley’s regress, and hint at discussions of this or analogous puzzles in the philosophical tradition before Bradley. Finally, I shall present my own approach to this issue, Fact Infinitism, focusing on why it would have been hardly acceptable before ontology came to have the Cantorian conception of the infinite at its disposal. (shrink)

In 'On the nature of truth and falsehood' Russell offers both a multiple relation theory of judgment and a correspondence theory of truth. It has been a prevailing understanding of the Tractatus that Wittgenstein rejects Russell’s multiple relation idea but endorses the correspondence theory. Ramsey took the opposite view. In his 'Facts and Propositions', Ramsey endorses Russell’s multiple relation idea, rejects the correspondence theory, and then asserts that these moves are both due to Wittgenstein. This chapter will argue that (...) Ramsey’s ascriptions are both correct. The extent of the agreement between Ramsey and Wittgenstein will be argued, moreover, to count definitively against standard understandings of Ramsey as a redundancy theorist of truth. Wittgenstein is no correspondence theorist and Ramsey is no redundancy theorist; rather, both philosophers offer identity theories of truth. (shrink)

Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.

Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some (...) of the uses to which modern descendente of Russell's paradox of propositions have been put in recent literature. (shrink)

A typical approach to semantics for relevance (and other) logics: specify a class of algebraic structures and take amodelto be one of these structures, α, together with some function or relation which associates with every formulaAa subset ofα. (This is the approach of, among others, Urquhart, Routley and Meyer and Fine.) In some cases there are restrictions on the class of subsets of α with which a formula can be associated: for example, in the semantics of Routley and Meyer [1973], (...) a formula can only be associated with subsets which are closed upwards. It is natural to take apropositionof α to be such a subset of α, and, further, to take the propositional quantifiers to range over these propositions. (Routley and Meyer [1973] explicitly consider this interpretation.) Given such an algebraic semantics, we call (following Routley and Meyer [1973], who follow Henkin [1950]) the above-described interpretation of the quantifiers theprimaryinterpretation associated with the semantics. (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)

I formulate an account, in terms of essence and ground, that explains why atomic Russellian propositions have the truth conditions they do. The key ideas are that (i) atomic propositions are just 0-adic relations, (ii) truth is just the 1-adic version of the instantiation (or, as I will say, holding) relation (Menzel 1993: 86, note 27), and (iii) atomic propositions have the truth conditions they do for basically the same reasons that partially plugged relations, like being an (...) x and a y such that Philip gave x to y, have the holding conditions they do. The account is meant to be mainly of intrinsic interest, but I hope that it goes some distance toward answering an objection to classical theories of propositions put forward by King (2014), who writes that ‘since the classical conception of propositions as things that have truth conditions by their very natures and independently of minds and languages is incapable of explaining how or why propositions have truth conditions, it is unacceptable’ (2014: 47). Propositions do have their truth conditions ‘by their very natures’ and ‘independently of minds and languages’. But a fact about a given entity can hold by the very nature of that entity without being a fundamental fact. I argue that this is plausibly the case for atomic Russellian propositions and the facts about their truth conditions. A fact about the truth conditions of such a proposition holds by the very nature of the given proposition but is metaphysically grounded in facts about that proposition’s parts and their essences. If my account is correct, then the supposedly intractable problem of explaining why the given propositions have the truth conditions they do reduces to the problem of explaining why relations have the holding essences they do, which few seem to have found worrisome . (shrink)

In this paper, I argue that Scott Soames’ theory of naturalized cognitive propositions faces a serious objection: there are true propositions for which NCP cannot account. More carefully, NCP cannot account for certain truths of mathematics unless it is possible for there to be an infinite intellect. For those who reject the possibility of an infinite intellect, this constitutes a reductio of NCP.

The aim of this paper is to analyse categorical propositions and their oppositional relations in Avicenna’s frame. For Avicenna’s expression and conception of categorical propositions is different from those of the authors who preceded him, due to the various conditions he adds to these categorical propositions. These additions make the oppositional relations richer and give rise to many more figures than a simple square. Our analysis exhibits some of these figures by relating all kinds of quantified (...) class='Hi'>propositions in various ways. We thus find many squares of oppositions, several octagons, two hexagons and many complex figures which are different from each other and have specific and original structures, due to the propositions they contain. The hexagons are of Blanché’s kind, but one of them is asymmetric. Some octagons are of Buridan’s kind, but one of them is very unusual and seems to be a reversal of Buridan’s octagon. These octagons can also be replaced by cubes, which are three dimensional figures having the same number of vertices. (shrink)

Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there may be coherent accounts of epistemically (...) possible worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)

The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of (...) papers which are not easily available, even to the Polish reader: (1) J. Słupecki, Funkcja Łukasiewicza (Łukasiewicz’s function), Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, nr 3 (1959), 33-40; (2) U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131; (3) G. Bryll, Kilka uzupełnień teorii zdań odrzuconych (Some supplements to the theory of rejcted sentences), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Mnografie, Nr 22 (1969), 153-154. The paper also contains a good number of results which have not been published yet. Chapter I contains results presented in the papers (1)-(3). It provides an extension of Alfred Tarski’s theory of deductive systems presented by him in the papers [1930]: Fundamentale Begriffe der Methodologie der deduktiven Wssenschaften, I and Über einige fundamentale Begriffe der Metamathematik. The enriched theory is marked with T. The most essential new concept in T is the function Cn-1, whose definition was given by Słupecki in (1) on the basis of the so-called Tarski’s general theory of deductive systems. It has the form: y e Cn-1X iff Ex e X (x e Cn {y}), where Cn is Tarski’s consequence operation. In accordance with the definition: A sentence y is rejected on the basis of the sentences of the set X iff at least one of sentences of X is a consequence of y (is deducible from y). The intuitive meaning of the rejection function Cn-1: on the basis of false sentences we can reject false sentences only (while by means of the consequence operation Cn on the basis of true sentences we can deduce true sentences only). The function Cn-1 is a generalization of the notion of rejected sentences which was introduced into logic by Łukasiewicz. The essential property of the rejection function Cn-1 is that it satisfies the axioms of general Tarski’s consequence Cn, so it is a consequence operation, called the rejection consequence. In addition, it is an additive and normal operation. In Chapter I, there are given notions analogous to those of the theory of deductive systems, but they are written down by means of the symbol ‘Cn-1’ and not ‘Cn’. There are established the properties of introduced notions and differences and analogies taking place between them and properties of respective notions of the theory T. There are also given generalizations of the notions of ‘decidable system’ and ‘consistent system’ used by Łukasiewicz. The short Chapter II contains axioms of the system T’ which is equivalent to the system T. The only difference between sets of primitive notions of these systems consists in the appearance of the function Cn-1 in the system T’ instead of the function Cn. This chapter reproduces the results given in (2), but they are partially simplified. (shrink)

Some Presentists—according to whom everything is present—identify instants of time with propositions of a certain kind. However, the view that times are propositions seems to be at odds with Presentism: if there are times then there are past times, and therefore things that are past; but how could there be things that are past if everything is present? In this paper, we describe the Presentist view that times are propositions ; we set out the argument that Presentism (...) is incompatible with the view that times are propositions ; and then we describe three possible responses to that argument on behalf of Presentists who identify times with propositions. We argue that each of these responses comes with significant costs. Finally, we describe a fourth possible response—according to which times are irreducibly higher-order entities—which appears to avoid the costs of the other three. We also describe and respond to two objections to the higher-order strategy. (shrink)

This monograph is a defence of the Fregean take on logic. The author argues that Frege ́s projects, in logic and philosophy of language, are essentially connected and that the formalist shift produced by the work of Peano, Boole and Schroeder and continued by Hilbert and Tarski is completely alien to Frege's approach in the Begriffsschrift. A central thesis of the book is that judgeable contents, i.e. propositions, are the primary bearers of logical properties, which makes logic embedded in (...) our conceptual system. This approach allows coherent and correct definitions of logical constants, logical consequence, and truth and connects their use to the practices of rational agents in science and everyday life. (shrink)

In this paper, we argue that, contra Strevens (2013), understanding in the sciences is sometimes partially constituted by the possession of abilities; hence, it is not (in such cases) exhausted by the understander’s bearing a particular psychological or epistemic relationship to some set of structured propositions. Specifically, the case will be made that one does not really understand why a modeled phenomenon occurred unless one has the ability to actually work through (meaning run and grasp at each step) a (...) model simulation of the underlying dynamic. (shrink)

In this paper, I motivate a modal account of propositions on the basis of an iterative conception of propositions. As an application, I suggest that the account provides a satisfying solution to the Russell-Myhill paradox. The account is in the spirit of recently developed modal accounts of sets motivated on the basis of the iterative conception of sets.

A first-person proposition is a proposition that only a single subject can assert or believe. When I assert ‘I am on fire’ I assert a first-person proposition that only I have access to, in the sense that no one else can assert or believe this proposition. This is in contrast to third-person propositions, which can be asserted or believed by anyone.

Both Russell and Frege were inclined to think that there is nothing essentially linguistic about thought: any actual reliance of ours upon language is a mere psychological contingency. If so then it should be possible to formulate logic in such a way that logical relationships are not represented or expressed as principles pertaining to linguistic forms. Russell and Frege take pains to achieve this, but fail. I explain this by looking at some features of Grundgesetz and Principia . Their failure, (...) I suggest, is due to the nature of the case. (shrink)