Discussing the concept of duty in Groundwork 1, Kant refers to a ‘second proposition’ and a ‘third proposition’, the latter being a ‘Folgerung aus beiden vorigen’. However, Kant does not identify what the ‘first proposition’ is. In this paper, I will argue that the first proposition is this: An action from duty is an action from respect for the moral law. I defend this claim against a critique put forward by Allison according to which (...) ‘respect’ is a concept that is not, and could not be, introduced in paragraphs 9–13 of Groundwork 1. Further, I will argue that the first proposition as I understand it can also be reconstructed as the conclusion (‘Folgerung’) of a deductive argument proper; however, I will also discuss the option that ‘Folgerung’ could be understood as a corollary rather than a conclusion. Finally, Allison's own interpretation will be criticized. (shrink)

Theories of structured meanings are designed to generate fine-grained meanings, but they are also liable to overgenerate structures, thus drawing structural distinctions without a semantic difference. I recommend the proliferation of very fine-grained structures, so that we are able to draw any semantic distinctions we think we might need. But, in order to contain overgeneration, I argue we should insert some degree of individuation between logical equivalence and structural identity based on structural isomorphism. The idea amounts to forming an equivalence (...) class of different structures according to one or more formal criteria and designating a privileged element as a representative of all the elements, i.e., a first among equals. The proposed method helps us to a cluster of notions of co-hyperintensionality. As a test case, I consider a recent objection levelled against the act theory of structured propositions. I also respond to an objection against my methodology. (shrink)

A central dispute in discussions of self-locating attitudes is whether attitude relations like believing and knowing are relations between an agent and properties (things that vary in truth value across individuals) or between an agent and propositions (things that do not so vary). Proponents of the proposition view have argued that the property view is unable to give an adequate account of relations like communication and agreement. We agree with this critique of the property view, and in this essay (...) we show that the problems facing the property view are much more serious than has been appreciated. We then develop and explore two versions of the proposition view. In each case, we show how facts about the self-ascription of properties may be determined by facts about propositional attitudes in conjunction with certain other facts. (shrink)

We discuss first order theories in which individual concepts are admitted as mathematical objects along with the things that reify them. This allows very straightforward formalizations of knowledge, belief, wanting, and necessity in ordinary first order logic without modal operators. Applications are given in philosophy and in artificial intelligence. We do not treat general concepts, and we do not present any full axiomatizations but rather show how various facts can be expressed.

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.

Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes’ On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg’s modern edition (1881, 1913) to the first propositions in Eutocius’ commentary on EP 1, J. L. Berggren ([1976]. ‘Spurious Theorems in Archimedes’ Equilibrium of Planes: Book I’, Archive for History of (...) Exact Sciences 16.2 (1976), 87–103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1–5 to Props. 1–6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius’ remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes’ mechanics to the method of EP 1. (shrink)

This paper is part of a general programme of developing and investigating particular first- order modal theories. In the paper, a modal theory of propositions is constructed under the assumption that there are genuinely singular propositions, ie. ones that contain individuals as constituents. Various results on decidability, axiomatizability and definability are established.

We define the notion of a combinatorics of a first order structure, and a relation of covering between first order structures and propositional proof systems. Namely, a first order structure M combinatorially satisfies an L-sentence Φ iff Φ holds in all L-structures definable in M. The combinatorics Comb(M) of M is the set of all sentences combinatorially satisfied in M. Structure M covers a propositional proof system P iff M combinatorially satisfies all Φ for which the associated (...) sequence of propositional formulas 〈Φ〉 n , encoding that Φ holds in L-structures of size n, have polynomial size P-proofs. That is, Comb(M) contains all Φ feasibly verifiable in P. Finding M that covers P but does not combinatorially satisfy Φ thus gives a super polynomial lower bound for the size of P-proofs of 〈Φ〉 n . We show that any proof system admits a class of structures covering it; these structures are expansions of models of bounded arithmetic. We also give, using structures covering proof systems R * (log) and PC, new lower bounds for these systems that are not apparently amenable to other known methods. We define new type of propositional proof systems based on a combinatorics of (a class of) structures. (shrink)

To be a proposition is to possess propositional properties and to stand in inferential relations. This is the organic intuition, [OI], concerning propositional recognition. [OI] is not a circular characterization as long as those properties and relations that signal the presence of propositions are independently identified. My take on propositions does not depart from the standard approach widely accepted among philosophers of language. Propositions are truth-bearers, the arguments of truth-functions (‘not’, ‘or’, ‘and’, ‘if’), the arguments of propositional-attitude verbs (‘know’, (...) ‘believe’, ‘doubt’, ‘assume’, ‘reject’) and the kind of entity capable of standing in inferential relations (which are basically implication and incompatibility). The aim of this paper is to argue for [OI]. In doing so, I will show that even what is probably the most repeated argument against non-descriptivism, the so-called Frege-Geach Argument (FGA), presupposes something like [OI], a presupposition that Geach shares with his critics. Despite the huge success of FGA, a thorough analysis of the actual scope of this argument has yet to be given. I will provide such an analysis in section 3 below. In this paper, I argue that [OI] is a meta-theoretical principle which is neutral with respect to specific metaphysical debates about the nature of propositions, as well as specific proposals about the semantics of declarative sentences. (shrink)

We consider the problem about the length of proofs of the sentences $\operatorname{Con}_S(\underline{n})$ saying that there is no proof of contradiction in S whose length is ≤ n. We show the relation of this problem to some problems about propositional proof systems.

Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the (...) logic of so-called fusions of frames with equivalence relations. This generalizes a result due to Antonelli and Thomason, who construct such an embedding for the logic of such fusions. (shrink)

Paraconsistent extensions of 3-valued Gödel logic are studied as tools for knowledge representation and nonmonotonic reasoning. Particularly, Osorio and his collaborators showed that some of these logics can be used to express interesting nonmonotonic semantics. CG’3 is one of these 3-valued logics. In this paper, we introduce Fidel semantics for a certain calculus of CG’3 by means of Fidel structures, named CG’3-structures. These structures are constructed from enriched Boolean algebras with a special family of sets. Moreover, we also show that (...) the most basic CG’3-structures coincide with da Costa–Alves’ bi-valuation semantics; this connection is displayed through a Representation Theorem for CG’3-structures. By contrast, we show that for other paraconsistent logics that allow us to present semantics through Fidel structures, this connection is not held. Finally, Fidel semantics for the first-order version of the logic of CG’3 are presented by means of adapting algebraic tools. (shrink)

We prove the following surprising property of Heyting's intuitionistic propositional calculus, IpC. Consider the collection of formulas, φ, built up from propositional variables (p,q,r,...) and falsity $(\perp)$ using conjunction $(\wedge)$ , disjunction (∨) and implication (→). Write $\vdash\phi$ to indicate that such a formula is intuitionistically valid. We show that for each variable p and formula φ there exists a formula Apφ (effectively computable from φ), containing only variables not equal to p which occur in φ, and such that for (...) all formulas ψ not involving $p, \vdash \psi \rightarrow A_p\phi$ if and only if $\vdash \psi \rightarrow \phi$ . Consequently quantification over propositional variables can be modelled in IpC, and there is an interpretation of the second order propositional calculus, IpC2, in IpC which restricts to the identity on first order propositions. An immediate corollary is the strengthening of the usual interpolation theorem for IpC to the statement that there are least and greatest interpolant formulas for any given pair of formulas. The result also has a number of interesting consequences for the algebraic counterpart of IpC, the theory of Heyting algebras. In particular we show that a model of IpC2 can be constructed whose algebra of truth-values is equal to any given Heyting algebra. (shrink)

Structured propositions are often invoked to explain why intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. As the semantics is standardly developed—for example, in Salmon, Soames :47–87, 1987) and King :516–535, 1995), the semantic value of a complex expression is an ordered complex consisting of the semantic values of its components. Such views, however, trivialize semantic composition since they do not allow for independent constraints on the meaning of complexes. Trivializing semantic composition risks “trivializing semantics” Semantics versus (...) pragmatics, Oxford University Press, Oxford, 2005). Yet, proponents of structured propositions suggest a route to reimpose substantive compositionality. While the mapping from a sentence to the structured proposition it expresses is trivially compositional, there is a non-trivial mapping from the structured proposition to its truth-value. This non-trivial level of semantic composition allows the meanings assigned to complex expressions to impose substantive constraints on the meanings of the simple ones. I first articulate the basic desiderata: an account of structured propositions capable of explaining attitude attributions and of delivering a non-trivially compositional semantics. I then show that the two-stage semantics proposed by standard proponents of structured propositions does not satisfy these joint goals. (shrink)

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations (...) are closely related in a canonical way. The two direct translations turn out to be complete. The paper fulfills the program of Church [1932], [1933] and Curry [1930] to base logic on a consistent system of λ-terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent). (shrink)

One can add the machinery of relation symbols and terms to a propositional modal logic without adding quantifiers. Ordinarily this is no extension beyond the propositional. But if terms are allowed to be non-rigid, a scoping mechanism (usually written using lambda abstraction) must also be introduced to avoid ambiguity. Since quantifiers are not present, this is not really a first-order logic, but it is not exactly propositional either. For propositional logics such as K, T and D, adding such machinery (...) produces a decidable logic, but adding it to S5 produces an undecidable one. Further, if an equality symbol is in the language, and interpreted by the equality relation, logics from K4 to S5 yield undecidable versions. (Thus transitivity is the villain here.) The proof of undecidability consists in showing that classical first-order logic can be embedded. (shrink)

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center'' – we describe two serious flaws in the (...) Principia's argument for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given'' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.''. (shrink)

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both (...) translations are closely related in a canonical way. In a preceding paper, Barendregt, Bunder and Dekkers, 1993, we proved completeness of the two direct translations. In the present paper we prove completeness of the two indirect translations by showing that the corresponding illative systems are conservative over the two systems for the direct translations. In another version, DBB (1997), we shall give a more direct completeness proof. These papers fulfill the program of Church and Curry to base logic on a consistent system of $\lambda$ -terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent). (shrink)

Propositional justification pertains to propositions: it is the sort of justification that a proposition enjoys for an agent when the agent is epistemically justified to believe it. By contrast, doxastic justification is justification of beliefs, i.e., of doxastic states actually instantiated by an agent. The ‘orthodox’ view of the relationship between propositional and doxastic justification is that the latter should be explained in terms of the former, so that an agent’s belief is (doxastically) justified just in case (i) it (...) is a belief in a proposition that is (propositionally) justified for the agent and (ii) it is held on the basis of that which (propositionally) justifies its content. This view has been challenged by John Turri in his paper ‘On the Relationship between Propositional and Doxastic Justification’ (Philosophy and Phenomenological Research, 80, 2010, pp. 312–326). There he offers two putative counterexamples to the orthodoxy and goes on to argue that the order of explanation should be reversed: it is propositional justification that should be explained in terms of doxastic justification, and not vice versa. Though I share Turri’s feeling that there is something amiss with the way a number of contemporary epistemologists talk of propositional and doxastic justification, I do not believe he has managed to put his finger on the real trouble. So the first point I make is that his counterexamples fall short of refuting the orthodox view, which I argue should be maintained. Then I try to diagnose the real source of the trouble. It lies, I suggest, in the way a number of recent epistemologists talk of propositional justification, a way which commits them to the questionable view that the basis upon which facts concerning propositional justification supervene does not include facts concerning the doxastic states of agents, but only facts concerning the evidence to which agents have access. So I observe that there are different degrees of idealisation involved in judgments of ‘propositional justification’, propose to distinguish what an agent is propositionally justified to believe given his overall doxastic state from what an agent is propositionally justified to believe irrespective of his overall doxastic state, and argue that, whenever it is the former relation that is at stake, an agent can be propositionally justified to believe a proposition p at time t only if it is reasonably easy for him to form a doxastically justified belief in p at t. It is most likely an awareness of this fact - or of some fact in the vicinity - that encourages the belief that propositional justification should be explained in terms of doxastic justification. But I suggest that this fact, far from being evidence that the notion of doxastic justification is in any sense more fundamental than that of propositional justification, can be accounted for by paying attention to the relationship that links the relevant sort of (epistemic) justification to (epistemic) responsibility. So I conclude that there is an important sense in which facts concerning epistemic justification supervene not merely on facts concerning the evidential states of agents, but on facts concerning their overall doxastic states. (shrink)

Contrary to the target article's claims, social cognition research shows considerable learning (about other people) that is relatively automatic. Some of this learning is propositional (spontaneous trait inferences) and some is associative (spontaneous trait transference). Other dichotomies are also important. However conceived, human conditioning is not synonymous with human learning.

Katz offers such a grammatical account, in which makes it possible for the first time to explain the illocutionary potential of sentences within grammar.

I argue that there is an inherent tension in the notion of a proposition that gives us reason to doubt that there can be any single entity that plays all the roles and possesses all the features normally attributed to propositions. The tension is that some of the roles and features of propositions require them to be essentially representational, while others require them to be non-representational. I first present what I call the standard view of propositions: a series (...) of theses outlining the roles they are normally thought to play and the features they are normally thought to possess. I then highlight a number of tensions inherent in the standard view. I illustrate how this very tension creates problems for some realist theories of propositions. I discuss the distinction between the truth of a proposition and its existence, and argue that paying heed to this distinction allows us to identify, and clear up, a particular confusion that leads us to posit propositions in the first place. Finally, I consider where a rejection of propositions leaves us, ontologically and theoretically. (shrink)

This paper explores a neglected category of propositions in Arabic logic, propositions with negative predicates (sālibat al-maḥmūl), by addressing two pivotal questions concerning this propositional form: first, whether it is possible to defend it as distinct from metathetic and simple negative propositions and second, whether affirmative instances of these propositions have existential import. The paper argues for the existence of two distinct and conflicting theories of existential import frequently implicit in the views of Arabic logicians: one centered on the (...) copula and the other on the predicate. (shrink)

This essay explores questions first posed by Ernst Tugendhat: Can Edmund Husserl’s conception of truth help philosophers connect the concept of propositional truth with a more comprehensive and life-oriented idea of truth? Can it do so without short-circuiting either side? If so, to what extent? I focus on the conception of truth in Husserl’s path breaking Logical Investigations, originally published in 1900-01. First, I review critical interpretations of Husserl by three influential post-Heideggerian philosophers: Emmanuel Levinas, Theodor Adorno, and (...) Jacques Derrida. Next, I examine selected passages in the Logical Investigations. Finally, I initiate a critical retrieval of early Husserl’s conception of truth, one that not only evaluates his contribution in light of influential assessments by Levinas, Adorno, and Derrida but also proposes revisions to it. (shrink)

In Proposition 10, Book 2 of the Principia, Newton applied his geometrical calculus and power series expansion to calculate motion in a resistive medium under the action of gravity. In the first edition of the Principia, however, he made an error in his treatment which lead to a faulty solution that was noticed by Johann Bernoulli and communicated to him while the second edition was already at the printer. This episode has been discussed in the past, and the (...) source of Newton’s initial error, which Bernoulli was unable to find, has been clarified by Lagrange and is reviewed here. But there are also problems in Newton’s corrected version in the second edition of the Principia that have been ignored in the past, which are discussed in detail here. (shrink)

A study of the reception of Aristotle's Prior Analytics in the first half of the twelfth century. It is shown that Peter Abaelard was perhaps acquainted with as much as the first seven chapters of Book I of the Prior Analytics but with no more. The appearance at the beginning of the twelfth century of a short list of dialectical loci which has puzzled earlier commentators is explained by noting that this list formalises the classification of extensional relations (...) between general terms and that this classification had already be put forward by Boethius in his de Syllogismo Categorico and Introductio ad Syllogismos Categoricas . It is pointed out the kind of text referred to as an ` Introductio ' at the beginning of the twelfth-century follows very closely the structure of Boethius own Introductio and adds to it material drawn from his accounts of loci and the conditional propositions. It is argued that the reception of the Prior Analytics has to be understood against the background of this well developed tradition of treating together syllogisms, loci , and conditional propostions. Referring to a challenge to the formal validity of Darapti in the Ars Meliduna the paper concludes by illustrating that the theory of the syllogism presented in Prior Analytics was still controversial in the middle of the twelfth-century. (shrink)

It is often presumed by those who use propositions in their theories that propositions are representational; that is, that propositions represent the world as being some way. This paper makes two claims against this presumption. First, it argues that it does not follow from the fact that propositions play the theoretical roles usually attributed to them that they are representational. This conclusion is reached by rebutting three arguments that can be made in support of the claim that propositions are (...) representational. This paper then advances the further claim that propositions are not representational. It considers several ways to overcome the difficulties traditionally associated with this claim, particularly how to account for falsity. (shrink)

Propositions are a useful tool in philosophical theorizing, even though they are not beyond reasonable nominalistic doubts. Stephen Schiffer’s pleonasticism about propositions is a paradigm example of a realistic account that tries to alleviate such doubts by grounding truths about propositions in ontologically innocent facts. Schiffer maintains two characteristic theses about propositions: first, that they are so-called pleonastic entities whose existence is subject to what he calls something-from-nothing transformations ; and, second, that they are the referents of ‘that’-clauses that (...) function as singular terms in propositional attitude ascriptions. The paper turns the first thesis against the second: if propositions are pleonastic entities, it is argued, we should not take them to be referred to in propositional attitude ascriptions. Rather, propositional attitude ascriptions should be available as bases for propositional something-from-nothing transformations. (shrink)

Propositional attitudes, states like believing, desiring, intending, etc., have played a central role in the articulation of many of our major theories, both in philosophy and the social sciences. Until relatively recently, psychology was a prominent entry on the list of social sciences in which propositional attitudes occupied center stage. In this century, though, behaviorists began to make a self-conscious effort to expunge "mentalistic" notions from their theorizing. Behaviorism has failed. Psychology therefore is again experiencing "formative years," and two themes (...) have caught the interest of philosophers. The first is that psychological theories evidently must exploit a vast array of relations obtaining among internal states. The second is that the use of mentalistic idioms seems to be explicit again in much of current theorizing. These two observations have led philosophers to wonder about the probable as well as the proper role of propositional attitudes in future psychological theories. Some philosophers wonder, in particular, about the role of the contents of propositional attitudes in the forthcoming theories. Their strategy is in part to discern what sorts of theory psychologists now will want to construct, and then discern what role propositional attitude contents might play in theories of those sorts. I consider here two sorts of theory, what I call minimal functional theories and what is known as propositional attitude psychology. ;I outline these two kinds of theory, and show how each defines a role for contents. Contents are ultimately eliminable in minimal functional theories. Although they play an apparently ineliminable role in propositional attitude psychology, they do so at an apparent cost. Propositional attitude psychology does not seem to accommodate a certain methodological principle, a principle of individualism in psychology, which is endorsed even by some of the philosophers most enamored of the approach. Such philosophers have two options: they can attempt to show that the conflict between the approach and the principle is not genuine, or they can reject the principle. I argue that the conflict is real, and recommend a qualified rejections of the principle. (shrink)

The paper presents a family of propositional epistemic logics such that languages of these logics are extended by quantification over modal operators or over agents of knowledge and extended by predicate symbols that take modal operators as arguments. Denote this family by \}\). There exist epistemic logics whose languages have the above mentioned properties :311–350, 1995; Lomuscio and Colombetti in Proceedings of ATAL 1996. Lecture Notes in Computer Science, vol 1193, pp 71–85, 1996). But these logics are obtained from (...) class='Hi'>first-order modal logics, while a logic of \}\) can be regarded as a propositional multi-modal logic whose language includes quantifiers over modal operators and predicate symbols that take modal operators as arguments. Among the logics of \}\) there are logics with a syntactical distinction between two readings of epistemic sentences: de dicto and de re. We show the decidability of logics of \}\) with the help of the loosely guarded fragment of first-order logic. Namely, we generalize LGF to a higher-order decidable loosely guarded fragment. The latter fragment allows us to construct various decidable propositional epistemic logics with quantification over modal operators. The family of this logics coincides with \}\). There are decidable propositional logics such that these logics implicitly contain quantification over agents of knowledge, but languages of these logics are usual propositional epistemic languages without quantifiers and predicate symbols :345–378, 1993). Some logics of \}\) can be regarded as counterparts of logics defined in Grove and Halpern :345–378, 1993). We prove that the satisfiability problem for these logics of \}\) is Pspace-complete using their counterparts in Grove and Halpern :345–378, 1993). (shrink)

Bertrand Russell presented three systems of propositional logic, one first in Principles of Mathematics, University Press, Cambridge, 1903 then in “The Theory of Implication”, Routledge, New York, London, pp. 14–61, 1906) and culminating with Principia Mathematica, Cambridge University Press, Cambridge, 1910. They are each based on different primitive connectives and axioms. This paper follows “Peirce’s Law” through those systems with the aim of understanding some of the notorious peculiarities of the 1910 system and so revealing some of the early (...) history of classical propositional logic. “Peirce’s Law” is a valid formula of elementary propositional logic: [ ⊃ p] ⊃ p This sentence is not even a theorem in the 1910 system although it is one of the axioms in 1903 and is proved as a theorem in 1906. Although it is not proved in 1910, the two lemmas from the proof in 1906 occur as theorems, and Peirce’s Law could have been derived from them in a two step proof. The history of Peirce’s Law in Russell’s systems helps to reconstruct some of the history of axiomatic systems of classical propositional logic. (shrink)

Reprinted in Philosophy of Religion: An Anthology, Wadsworth 2015, 6th edition, eds Michael Rea and Louis Pojman. What is propositional faith? At a first approximation, we might answer that it is the psychological attitude picked out by standard uses of the English locution “S has faith that p,” where p takes declarative sentences as instances, as in “He has faith that they’ll win”. Although correct, this answer is not nearly as informative as we might like. Many people say that (...) there is a more informative answer. They say that, at the very least, propositional faith requires propositional belief. More precisely, they say that faith that p requires belief that p or that it must be partly constituted by belief that p. This view is common enough; call it the Common View. I have two main aims in this paper: (i) to exhibit the falsity of the Common View and the paucity of reasons for it, and (ii) to sketch a more accurate and comprehensive account of what propositional faith is. (shrink)

Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically (...) attempts to reduce propositions to extensional entities-either extensional functions or sets. The second group concerns problems of fine grained content-both traditional 'Cicero'/'Tully' puzzles and recent variations on them which confront scientific essentialism. After characterizing the problems, I outline a non-reductionist approach-the algebraic approach-which avoids the problems associated with reductionism. I then go on to show how the theory can incorporate non-Platonic (as well as Platonic) modes of presentation. When these are implemented nondescriptively, they yield the sort of fine-grained distinctions which have been eluding us. The paper closes by applying the theory to a cluster of remaining puzzles, including a pair of new puzzles facing scientific essentialism. (shrink)

This paper explores a neglected category of propositions in Arabic logic, propositions with negative predicates (sālibat al-maḥmūl), by addressing two pivotal questions concerning this propositional form: first, whether it is possible to defend it as distinct from metathetic and simple negative propositions and second, whether affirmative instances of these propositions have existential import. The paper argues for the existence of two distinct and conflicting theories of existential import frequently implicit in the views of Arabic logicians: one centered on the (...) copula and the other on the predicate. (shrink)

This chapter argues that some have wanted to reserve the term 'propositional attitude' for states which are 'in principle accessible' to consciousness, or that are 'inferentially integrated' with other propositional attitudes. Some of the contention and research surrounding propositional attitudes and sentences ascribing them results from their importance to epistemology, philosophy of mind, and action theory. Perhaps the primary reason is the view that propositional attitudes are relations to propositions. On many views, propositions both are closely related to meanings and (...) are what is in the first instance true or false. The chapter talks about two most significant alternatives to relational accounts of attitude ascription: Relationism and Descriptivism. It concludes by reviews of Lewis's example and topic of belief de se, which involves a distinctive way of ascribing a property. All believers can self‐ascribe properties, and all properties are open to self‐ascription. (shrink)

There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception (...) of propositions, concerning their role in natural language semantics and apparent quantification over propositions within natural language. It will emerge that even if these arguments are sound, there need be no deep question about Quinean propositions’ true nature, contrary to much recent work on the metaphysics of propositions. (shrink)

Two primary roles for propositions are to be i) the objects of the attitudes (especially belief) and ii) the primary bearers of truth and falsity. Interpreters of John Locke are in very broad agreement that propositions, as he presents them, serve this second role. However, whether Locke’s propositions can be said to serve the first role is a more difficult question, as Locke was frequently regarded as having overlooked the force/content distinction, meaning that many interpreters regard him as taking (...) the propositions not to be the objects of the attitudes, but instead, to be identical to the attitudes themselves. In this paper, I present the basics of Locke’s accounts of propositions, truth, and judgment. I then explain the interpretive divide between those scholars who interpret Locke as offering a more philosophically appealing proto-Fregean account of propositions (one which does recognize the force/content distinction), and those who defend the philosophically less satisfying account which identifies propositions with judgments on textual grounds. Finally, I defend the conflation account against one of it’s largest philosophical challenges, by showing how that view can address the Frege-Geach problem. (shrink)

This paper examines the potential for abstracting propositions – an as yet untested way of defending the realist thesis that propositions as abstract entities exist. I motivate why we should want to abstract propositions and make clear, by basing an account on the neo-Fregean programme in arithmetic, what ontological and epistemological advantages a realist can gain from this. I then raise a series of problems for the abstraction that ultimately have serious repercussions for realism about propositions in general. I (...) class='Hi'>first identify problems about the number of entities able to be abstracted using these techniques. I then focus on how issues of language relativity result in problems akin to the Caesar problem in arithmetic by exposing circularity and modal concern over the status of the criterion of identity for propositions. (shrink)

This paper is roughly in two parts. The first deals with whether know-how is constituted by propositional knowledge, as discussed primarily by Gilbert Ryle (1949) The concept of mind. London: Hutchinson, Jason Stanley and Timothy Williamson (2001). Knowing how. Journal of Philosophy, 98, pp. 411–444 as well as Stephen Hetherington (2006). How to know that knowledge-that is knowledge-how. In S. Hetherington (Ed.) Epistemology futures. Oxford: Oxford University Press. The conclusion of this first part is that know-how sometimes does (...) and sometimes does not consist in propositional knowledge. The second part defends an analysis of know-how inspired by Katherine Hawley’ (2003). Success and knowledge-how. American Philosophical Quarterly, 40, pp. 19–31, insightful proposal that know-how requires counterfactual success. I conclude by showing how this analysis helps to explain why know-how sometimes does and sometimes does not consist of propositional knowledge. (shrink)

Formalizing categorical propositions of traditional logic in the language of quantifiers and propositional functions is no straightforward matter, especially when modalities get involved. Starting...

We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and SOPML.

An important issue for visual argumentation is its relationship to propositions, since it has been argued that, in order to be arguments, images should be propositional. The first part of the paper will approach this debate from a theoretical perspective. After quickly surveying the field on the issue, I will address the relationship between images and propositions. Three specific questions will be examined: can propositions accurately account for the way images express arguments?; are verbal propositions necessary to reconstruct arguments (...) that images alone cannot convey, due to their lacking linguistic tools?; are images essentially non-propositional because they don’t have truth-value? The second part of the paper will include a detailed analysis of two posters. From these analyses, I will ultimately conclude that some images can display a visual argument without necessarily being propositional. (shrink)

First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with a relevant logic that (...) has all classical theorems as theorems. (shrink)

To understand what non-propositional content is and whether there are any such contents, we first need to know what propositional content is. That issue will be the focus of the first section of this essay. In the second section, with an understanding of propositional content in hand, we will consider representations that fail to have propositional content. In contrast to recent literature, it will be argued that metaphysical considerations concerning what's represented, rather than linguistic considerations, are a more (...) promising way of establishing non-propositional contents. To keep the discussion containable, focus will be on representational mental states, though many of the considerations can be extended to other forms of representation. (shrink)

Gaskin's book The Unity of the Proposition is very rich in material. I will focus only on its central thesis: Gaskin holds that Bradley's regress (more precisely, one particular version of it) is not only innocent, but in fact philosophically significant because it plays a crucial role in solving what Gaskin calls the problem of the unity of the proposition . In what follows, I first explain what that problem is meant to be ( section 1 ), (...) then I present and criticise Gaskin's proposal about how Bradley's regress bears on the problem ( section 2 ), and finally I sketch an alternative approach to the problem ( section 3 ). (shrink)