Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional (...) phenomena, such as the aforementioned validity of attitude-report inferences. It then shows that the notion of a predication act-type, which remains importantly Russellian in spirit, is sufficient to explain the range of propositional phenomena in question, in particular the validity of attitude-report inferences. The paper concludes with a discussion of whether predication act-types are really just propositions by another name. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this (...) paper is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

Bertrand Russell was neither the first nor the last philosopher to engage in serious theorizing about propositions. But his work between 1903, when he published The Principles of Mathematics, and 1919, when his final lectures on logical atomism were published, remains among the most important on the subject. And its importance is not merely historical. Russell’s rapidly evolving treatment of propositions during this period was driven by his engagement with – and discovery of – puzzles that either continue (...) to shape contemporary theorizing about propositions, or ought to do so. Russell’s creative responses to these puzzles also laid the foundation for many later accounts (most obviously, contemporary ‘Russellian’ accounts of propositions). In this entry we provide an opinionated overview of Russell’s influential treatment of propositions, with a focus on the evolution of his views from 1903 to 1919. A growing secondary literature is dedicated to Russell’s changing views during this period, and their often complex or opaque motivations. We do not intervene overmuch in this ongoing scholarly discussion. Instead, our aim is to trace some of the central motivations for Russell’s evolving views, and highlight the extent to which these motivations remain relevant to contemporary theorizing about propositions. (shrink)

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. (...) We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.

Proposition and sentence are two separate entities indicating their specific purposes, definitions and problems. A proposition is a logical entity. A proposition asserts that something is or not the case, any proposition may be affirmed or denied, all proportions are either true (1’s) or false (0’s). All proportions are sentences but all sentences are not propositions. Propositions are factual contains three terms: subject, predicate and copula and are always in indicative or declarative mood. While sentence is a grammatical (...) entity, a unit of language that expresses a complete thought; a sentence may express a proposition, but is distinct from the proposition it may be used to express: categories, declarative sentences, exclamatory, imperative and interrogative sentences. Not all sentences are propositions, propositions express sentence. Sentence is a proposition only in condition when it bears truth values i.e. true or false. We use English sentences governed by imprecise rule to state the precise rules of proposition. In logic we use sentence as logical entity having propositional function but grammatical sentences are different from logical sentences while the former are having only two divisions namely subject and predicate and may express wishes, orders, surprise or facts and also have multiple subjects and predicates and the latter must be in a propositional form which states quantity of the subject and the quality of the proposition and multiple subjects and multiple predicate make the proposition multiple. (shrink)

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...) be computed from the calculus. (shrink)

In this paper, we discuss three probabilistic arguments for the existence of multiple universes. First, we provide an analysis of total evidence and use that analysis to defend Roger White's "this universe" objection to a standard fine-tuning argument for multiple universes. Second, we explain why Rodney Holder's recent cosmological argument for multiple universes is unconvincing. Third, we develop a "Cartesian argument" for multiple universes. While this argument is not open to the objections previously noted, we show (...) that, given certain highly plausible assumptions about evidence and epistemic probability, the proposition which it treats as evidence cannot coherently be regarded as evidence for anything. This raises the question of whether to reject the assumptions or accept that such a proposition cannot be evidence. (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)

Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the (...) problem by canvassing what we may call the arbitrary reference strategy. The main claims of such strategy are 2. First, we do not know which objects are the referents of proposition and numerical terms since their reference is fixed arbitrarily. Second, our ignorance of which object is picked out as the referent does not entail that no object is referred to by the relevant expression. Different articulations of the strategy are assessed, and a new one is defended. (shrink)

The categoricity problem for a system of logic reveals an asymmetry between the model-theoretic and the proof-theoretic resources of that logic. In particular, it reveals prima facie that the proof-theoretic instruments are insufficient for matching the envisaged model-theory, when the latter is already available. Among the proposed solutions for solving this problem, some make use of new proof-theoretic instruments, some others introduce new model-theoretic constrains on the proof-systems, while others try to use instruments from both sides. On the proof-theoretical side, (...) two main approaches for solving the categoricity problem for propositional classical logic consist in the enforcement of the formal systems of this logic by introducing rules of inference of a new kind. A multiple-conclusions logic allows rules of inference with more than one conclusion, while a bilateralist system contains rules of inference formulated in terms of assertion and rejection. Both these approaches reveal interesting formal features of logical reasoning. This paper analyses some of the advantages and limitations of these two approaches as solutions for a full formalization of logic, i.e., for a categorical formalization. (shrink)

Linguistic meaning underdetermines what is said. This has consequences for philosophical accounts of meaning, communication, and propositional attitude reports. I argue that the consequence we should endorse is that utterances typically express many propositions, that these are what speakers mean, and that the correct semantics for attitude reports will handle this fact while being relational and propositional.

Since the earliest commentaries on Heidegger's Being & Time, its theory of judgment and of propositions has been widely misrepresented as relativistic, psychologistic, anthropologistic, pragmatic, etc. Even Edmund Husserl allowed himself to be persuaded to this point of view, to the great detriment of his phenomenological movement. And most of Heidegger's interpreters, whether friendly or hostile, have adopted this point of view, which normally includes the notion that there can be no fundamental difference between circumspective and apophantic forms of (...) explication. This misreading ignores important aspects of the theory of propositional explication in Being & Time, ignores the fact that forms of interpretation would not be genera or species of interpretation, and is a clear instance of genetic fallacy. Yet it pervades the literature on Heidegger still. (shrink)

In this paper, I defend the heterogeneity problem for sensitivity accounts of knowledge against an objection that has been recently proposed by Wallbridge in Philosophia. I argue in, 479–496, 2015) that sensitivity accounts of knowledge face a heterogeneity problem when it comes to higher-level knowledge about the truth of one’s own beliefs. Beliefs in weaker higher-level propositions are insensitive, but beliefs in stronger higher-level propositions are sensitive. The resulting picture that we can know the stronger propositions without (...) being in a position to know the weaker propositions is too heterogeneous to be plausible. Wallbridge objects that there is no heterogeneity problem because beliefs in the weaker higher-level propositions are also sensitive. I argue against Wallbridge that the heterogeneity problem is not solved but only displaced. Only some beliefs in the weaker higher-level propositions are sensitive. I conclude that the heterogeneity problem is one of a family of instability problems that sensitivity accounts of knowledge face and that Wallbridge’s account raises a further problem of this kind. (shrink)

We pose two arguments for the view that sentences containing definite descriptions semantically express multiple propositions: a general proposition as Russell suggested, and a singular proposition featuring the individual who uniquely satisfies the description at the world-time of utterance. One argument mirrors David Kaplan's arguments that indexicals express singular propositions through a context-sensitive character. The second argument mirrors Kent Bach's and Stephen Neale's arguments for pluralist views about terms putatively triggering conventional implicatures, appositive, and nonrestrictive relative clauses. (...) After presenting these arguments, we show that rival explanations (appeals to implicature, referential use, presupposition, etc.) do not offer equally compelling explanations of the data, and defend the methodology employed in the arguments against some criticisms. (shrink)

Natural language contains simple lexical items for some but not all Boolean operators. English, for example, contains conjunction and, disjunction or, negated disjunction nor, but no word to express negated conjunction *nand nor any other Boolean connective. Natural language grammar can be described by a logic that expresses what the lexicon can express by its primitives, and the rest compositionally. Such logic for propositional connectives is described here as a bilateral extension of update semantics. The basic intuition is that a (...) context can be updated by assertion or by rejection, and by one or multiple propositions at once. These distinctions suffice to characterize the logic of the lexicon. (shrink)

In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider this inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard doctrine of ampliation, (...) Paul takes A to be equivalent to 'Everything that is or will be true will be false'. But he proceeds to argue that it is possible that B's premise ('A will signify only that everything true will be false') could be true and its conclusion false, so B is not only valid but also invalid. Thus A and B are the basis of an insoluble. In his Logica Parva, a self-confessedly elementary text aimed at students and not necessarily representing his own view, and in the Quadratura, Paul follows the solution found in the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses Swyneshed's solution, which stood out against this ''multiple-meanings'' approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say. On this account, insolubles imply their own falsity, and that is why, in so falsifying themselves, they are false. We consider how both types of solution apply to B and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected. (shrink)

This paper traces a lost genealogical connection between Charles S. Peirce’s later theory of signs and contemporary work in the philosophy of language by John Perry. As is shown, despite some differences, both accounts offer what might be termed a multi-level account of meaning. Moreover, it is claimed that by adopting a ‘Peircian turn’ in his theory, Perry might overcome alleged shortcomings in his account of cognitive significance.

Eliminativists sometimes invoke evolutionary debunking arguments against ordinary object beliefs, either to help them establish object skepticism or to soften the appeal of commonsense ontology. I argue that object debunkers face a self-defeat problem: their conclusion undermines the scientific support for one of their premises, because evolutionary biology depends on our object beliefs. Using work on reductionism and multiple realizability from the philosophy of science, I argue that it will not suffice for an eliminativist debunker to simply appeal to (...) some object-free surrogate theory of evolution that results from converting any scientific proposition about some object K into a proposition about simples arranged K-wise. In the process, I examine some hazards peculiar to eliminative reductions of scientific theories, and propose a trilemma for eliminativists who attempt to recoup generality for ontologically sparse reducing theories by appealing to pluralities of simples arranged K-wise. The paper is intended to define and develop the object debunker’s self-defeat problem for further study, and to clarify some of the ways sparse and abundant ontologies interact with scientific theory. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of (...) Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for (...) the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof. (shrink)

Russell’s initial project in philosophy (1898) was to make mathematics rigorous reducing it to logic. Before August 1900, however, Russell’s logic was nothing but mereology. First, his acquaintance with Peano’s ideas in August 1900 led him to discard the part-whole logic and accept a kind of intensional predicate logic instead. Among other things, the predicate logic helped Russell embrace a technique of treating the paradox of infinite numbers with the help of a singular concept, which he called ‘denoting phrase’. Unfortunately, (...) a new paradox emerged soon: that of classes. The main contention of this paper is that Russell’s new conception only transferred the paradox of infinity from the realm of infinite numbers to that of class-inclusion. Russell’s long-elaborated solution to his paradox developed between 1905 and 1908 was nothing but to set aside of some of the ideas he adopted with his turn of August 1900: (i) With the Theory of Descriptions, he reintroduced the complexes we are acquainted with in logic. In this way, he partly restored the pre-August 1900 mereology of complexes and simples. (ii) The elimination of classes, with the help of the ‘substitutional theory’, and of propositions, by means of the Multiple Relation Theory of Judgment, completed this process. (shrink)

Anyone familiar with Russell’s work on the multiple-relation theory of judgment will at some point have puzzled over the map of the five-term understanding complex at the end of Chapter 1, Part II of his Theory of Knowledge (1913). Russell presents the map with the intention of clarifying what goes on when a subject S understands the “proposition” that A and B are similar. But the map raises more questions than it answers. In this paper I present and develop (...) some of the central issues that arise from Russell’s map, and I offer an interpretation of it that reflects his evolving views in the manuscript. I argue that multiple lines in the map are not meant to represent many relations, but rather one comprehensive multiple relation of understanding. And I argue that such a relation relates in a complex way due to the distinctive nature of its relata. (shrink)

This chapter connects the phenomenon of double bookkeeping to two critical debates in the philosophy of delusion: one from the analytic tradition and one from the phenomenological tradition. First, I will show how the failure of action guidance on the part of some delusions suggests an argument to the standard view that delusions are beliefs (doxasticism about delusion) and how its proponents have countered it by ascribing behavioral inertia to avolition, emotional disturbances, or a failure of the surrounding environment in (...) supporting the agent’s motivation to act. Second, I will show how the mismatch between the experience of double bookkeeping and that of having the usual propositional attitudes of folk psychology suggests another, more recalcitrant argument not only against doxasticism but against the very attempt to fit delusion into folk psychology. Third, I will show how phenomenologically inspired theories of delusion, such as the multiple realities hypothesis, bypass the debates above and focus on describing and understanding the disturbances in the structure of experience undergone by patients. I conclude that the philosophical discussions ensuing from an appreciation of double bookkeeping show some of the limitations of the analytic philosophical approach to delusion. (shrink)

The argument presented in this paper is not a direct attack or defence of the Chinese Room Argument (CRA), but relates to the premise at its heart, that syntax is not sufficient for semantics, via the closely associated propositions that semantics is not intrinsic to syntax and that syntax is not intrinsic to physics. However, in contrast to the CRA’s critique of the link between syntax and semantics, this paper will explore the associated link between syntax and physics. The (...) main argument presented here is not significantly original – it is a simple reflection upon that originally given by Hilary Putnam (Putnam 1988) and criticised by David Chalmers and others: instead of seeking to justify Putnam’s claim that, “every open system implements every Finite State Automaton (FSA)”, and hence that psychological states of the brain cannot be functional states of a computer, I will seek to establish the weaker result that, over a finite time window every open system implements the trace of a particular FSA Q, as it executes program (p) on input (x). That this result leads to panpsychism is clear as, equating Q (p, x) to a specific Strong AI program that is claimed to instantiate phenomenal states as it executes, and following Putnam’s procedure, identical computational (and ex hypothesi phenomenal) states (ubiquitous little ‘pixies’) can be found in every open physical system. (shrink)

This paper defends an interpretation of Gottlob Frege’s views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in multiple, distinct ways. These multiple decompositions will often have distinct logical forms. I also argue against Michael Dummett and others that Frege was committed to the sense of a predicate being a function from the sense (...) of a name (or names) to a complete thought. I defend my Frege interpretation against a puzzle often discussed in the Frege literature; namely, that the Multiple Decompositions Thesis is incompatible with Frege’s stated view that a thought is built up out of its component senses as parts. I provide textual evidence and argument that Frege thought of the part/whole relation in such a way that a whole can be analyzed into (or built up out of) parts in multiple, distinct ways, thus dissolving the puzzle. I conclude with discussion of every sort of example of multiple decompositions that can be found in Frege's work. (shrink)

On Kratzer’s canonical account, modal expressions (like “might” and “must”) are represented semantically as quantifiers over possibilities. Such expressions are themselves neutral; they make a single contribution to determining the propositions expressed across a wide range of uses. What modulates the modality of the proposition expressed—as bouletic, epistemic, deontic, etc.—is context.2 This ain’t the canon for nothing. Its power lies in its ability to figure in a simple and highly unified explanation of a fairly wide range of language use. (...) Recently, though, the canon’s neat story has come under attack. The challenge cases involve the epistemic use of a modal sentence for which no single resolution of the contextual parameter appears capable of accommodating all our intuitions.3 According to these revisionaries, such cases show that the canonical story needs to be amended in some way that makes multiple bodies of information relevant to the assessment of such statements. Here I show that how the right canonical, flexibly contextualist account of modals can accommodate the full range of challenge cases. The key will be to extend Kratzer’s formal semantic account with an account of how context selects values for a modal’s.. (shrink)

In this paper, I defend teleological theories of belief against the exclusivity objection. I argue that despite the exclusive influence of truth in doxastic deliberation, multiple epistemic aims interact when we consider what to believe. This is apparent when we focus on the processes involved in specific instances (or concrete cases) of doxastic deliberation, such that the propositions under consideration are specified. First, I out- line a general schema for weighing aims. Second, I discuss recent attempts to defend (...) the teleological position in relation to this schema. And third, I develop and defend my proposal that multiple epistemic aims interact in doxastic deliberation—a possibility which, as of yet, has received no serious attention in the literature. (shrink)

Over the course of the past ten-plus years, Peter Hanks and Scott Soames have developed detailed versions of Act-Based views of propositions which operate with the notions of reference to objects, indicating properties, predication, and judgment (or entertaining). In this paper I discuss certain foundational aspects of the Act-Based approach having to do with the relations between these notions. In particular, I argue for the following three points. First, that the approach needs both an atomistically understood thin notion of (...) reference, a bare act of thinking of o, as well as a more involved notion, something like making o a target of predication. Second, that the acts of thinking of o and indication of the property of being F are in no sense parts of the acts of predication of being F of o and judgment that o is F. Rather, the former are simply necessary preconditions for the performance of the latter. The acts of predication or judgment are emphatically not structured sequences of separate acts but unities in and of themselves. Finally, that we should understand the Act-Based theorists’ claim that to predicate is to judge as the claim that judgment can be reductively analyzed in terms of predication. Furthermore, while predication is metaphysically a multiple relation between a predicator, a target, and the property predicated, judgment is a monadic property, just one that has propositional content. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...) the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated in (...) terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)

The debate between Uniqueness and Permissivism concerns whether a body of evidence sometimes allows multiple doxastic attitudes towards a proposition. An important motivation for Uniqueness is the so-called ‘arbitrariness argument,’ which says that Permissivism leads to some unacceptable arbitrariness with regard to one's beliefs. An influential response to the argument says that the arbitrariness in beliefs can be avoided by invoking epistemic standards. In this paper, I argue that such a response to the arbitrariness argument is unsuccessful. Then I (...) defend a new response: contrary to common conception, the arbitrariness resulted by Permissivism is acceptable. The basic idea is that the arbitrariness resulted by Permissivism is analogous to the arbitrariness in permissive actions and the latter arbitrariness is intuitively acceptable. I answer three possible objections against this analogy, which are all motivated by the thought that beliefs aim at the truth. In addressing the last objection, I draw inspiration from the recent debate on transformative experience. (shrink)

The ``doctrinal paradox'' or ``discursive dilemma'' shows that propositionwise majority voting over the judgments held by multiple individuals on some interconnected propositions can lead to inconsistent collective judgments on these propositions. List and Pettit (2002) have proved that this paradox illustrates a more general impossibility theorem showing that there exists no aggregation procedure that generally produces consistent collective judgments and satisfies certain minimal conditions. Although the paradox and the theorem concern the aggregation of judgments rather than preferences, (...) they invite comparison with two established results on the aggregation of preferences: the Condorcet paradox and Arrow's impossibility theorem. We may ask whether the new impossibility theorem is a special case of Arrow's theorem, or whether there are interesting disanalogies between the two results. In this paper, we compare the two theorems, and show that they are not straightforward corollaries of each other. We further suggest that, while the framework of preference aggregation can be mapped into the framework of judgment aggregation, there exists no obvious reverse mapping. Finally, we address one particular minimal condition that is used in both theorems – an independence condition – and suggest that this condition points towards a unifying property underlying both impossibility results. (shrink)

Epistemic luck is a generic notion used to describe any of a number of ways in which it can be accidental, coincidental, or fortuitous that a person has a true belief. For example, one can form a true belief as a result of a lucky guess, as when one believes through guesswork that “C” is the right answer to a multiple-choice question and one’s belief just happens to be correct. One can form a true belief via wishful thinking; for (...) example, an optimist’s belief that it will not rain may luckily turn out to be correct, despite forecasts for heavy rain all day. One can reason from false premises to a belief that coincidentally happens to be true. One can accidentally arrive at a true belief through invalid or fallacious reasoning. And one can fortuitously arrive at a true belief from testimony that was intended to mislead but unwittingly reported the truth. In all of these cases, it is just a matter of luck that the person has a true belief. -/- Until the twenty-first century, there was nearly universal agreement among epistemologists that epistemic luck is incompatible with knowledge. Call this view “the incompatibility thesis.” In light of the incompatibility thesis, epistemic luck presents epistemologists with three distinct but related challenges. The first is that of providing an accurate analysis of knowledge (in terms of individually necessary and jointly sufficient conditions for “S knows that p,” where ‘S’ represents the knower and ‘p’ represents the proposition known). An adequate analysis of knowledge must succeed in specifying conditions that rule out all instances of knowledge-destroying epistemic luck. The second challenge is to resolve the skeptical paradox that the ubiquity of epistemic luck generates: As will become clear in section 2c, epistemic luck is an all-pervasive phenomenon. Coupling this fact with the incompatibility thesis entails that we have no propositional knowledge. The non-skeptical epistemologist must somehow reconcile the strong intuition that epistemic luck is not compatible with knowledge with the equally evident observation that it must be. The third challenge concerns the special skeptical threat that epistemic luck seems to pose for more reflective forms of knowledge, such as knowing that one knows. Each of these challenges will be explored in the present article. (shrink)

In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, (...) whether a certain outcome is associated with a non-measurable region or a measurable one. (shrink)

ABSTRACT: In its strongest unqualified form, the principle of wholistic reference is that in any given discourse, each proposition refers to the whole universe of that discourse, regardless of how limited the referents of its non-logical or content terms. According to this principle every proposition of number theory, even an equation such as "5 + 7 = 12", refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. This principle, its history, (...) and its relevance to some of Oswaldo Chateaubriand's work are discussed in my 2004 paper "The Principle of Wholistic Reference" in Essays on Chateaubriand's "Logical Forms". In Chateaubriand's réplica (reply), which is printed with my paper, he raised several important additional issues including the three I focus on in this tréplica (reply to his reply): truth-values, universes of discourse, and formal ontology. This paper is self-contained: it is not necessary to have read the above-mentioned works. The principle of wholistic reference (PWR) was first put forth by George Boole in 1847 when he espoused a monistic fixed-universe viewpoint similar to the one Frege and Russell espoused throughout their careers. Later, Boole elaborated PWR in 1854 from the pluralistic multiple-universes perspective. (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a (...) slightly weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) Also see https://www.academia.edu/s/a6bf02aaab This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical point (...) of view. In normal English these two sentences are idiomatically taken to express the true proposition that ‘the number 3 is the number 2+1’. Another idiomatic convention that interferes with clarity about equality and identity occurs in discussion of numbers: it is usual to write ‘3 equals 2+1’ when “3 is 2+1” is meant. When ‘3 equals 2+1’ is written there is a suggestion that 3 is not exactly the same number as 2+1 but that they merely have the same value. This becomes clear when we say that two of the sides of a triangle are equal if the two angles they subtend are equal or have the same measure. -/- Acknowledgements: Robert Barnes, Mark Brown, Jack Foran, Ivor Grattan-Guinness, Forest Hansen, David Hitchcock, Spaulding Hoffman, Calvin Jongsma, Justin Legault, Joaquin Miller, Tania Miller, and Wyman Park. -/- ► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] The two halves of one line are equal but not identical [one and the same]. Otherwise the line would have only one half! Every line equals infinitely many other lines, but no line is [identical to] any other line—taking ‘identical’ strictly here and below. Knowing that two lines equaling a third are equal is useful; the condition “two lines equaling a third” often holds. In fact any two sides of an equilateral triangle is equal to the remaining side! But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition “two things identical to a third” never holds, nor does the consequent condition “two things being identical”. If two things were identical to a third, they would be the third and thus not be two things but only one. The plural predicate ‘are equal’ as in ‘All diameters of a given circle are equal’ is useful and natural. ‘Are identical’ as in ‘All centers of a given circle are identical’ is awkward or worse; it suggests that a circle has multiple centers. Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty—a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing. There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one’s length is identical to the other’s. Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins: -/- Among the logical concepts […], the concept of IDENTITY or EQUALITY […] has the greatest importance. -/- Not until page 62 is there an equality-identity distinction. His only “notion of equality”, if such it is, is geometrical congruence—having the same size and shape—an equivalence relation not admitting any unit. Does anyone but Tarski ever say ‘this triangle is equal to that’ to mean that the first is congruent to that? What would motivate him to say such a thing? This lecture treats the history and philosophy of equality-identity distinctions. [1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995. [This is expanded from the printed abstract.] . (shrink)

Traditional inflationary approaches that specify the nature of truth are attractive in certain ways; yet, while many of these theories successfully explain why propositions in certain domains of discourse are true, they fail to adequately specify the nature of truth because they run up against counterexamples when attempting to generalize across all domains. One popular consequence is skepticism about the efficaciousness of inflationary approaches altogether. Yet, by recognizing that the failure to explain the truth of disparate propositions often (...) stems from inflationary approaches' allegiance to alethic monism, pluralist approaches are able to avoid this explanatory inadequacy and the resulting skepticism, though at the cost of inviting other conceptual difficulties. A novel approach, alethic functionalism, attempts to circumvent the problems faced by pluralist approaches while preserving their main insights. Unfortunately, it too generates additional problems---namely, with its suspect appropriation of the multiple realizability paradigm and its platitude-based strategy---that need to be dissolved before it can constitute an adequate inflationary approach to the nature of truth. (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a (...) slightly weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself.Em sua forma mais forte e geral, o princípio da referência universalista afirma que toda proposição refere-se ao universo completo do discurso propriamente dito, independentemente de quão limitados sejam os referentes de seus termos não-lógicos ou com conteúdo. Embora Boole mudasse de um modelo monístico de universo-fixo nos seus trabalhos iniciais de 1847 e 1848 para um modelo pluralista de universo-múltiplo no seu tratado maduro de 1854, ele nunca hesitou em sua aceitação franca do princípio da referência universalista, possivelmente em uma forma ligeiramente mais fraca. De fato, ele considerou este princípio como um acompanhamento essencial para a sua teoria de formação de conceitos e de proposições. Visões semelhantes são encontradas em lógicos posteriores, e algumas das mais recentes formulações da lógica clássica de primeira ordem parecem estar de acordo com uma forma deste, se é que elas não implicam, de fato, o próprio princípio. (shrink)

Cognitive Penetration holds that cognitive states and processes, specifically propositional attitudes (e.g., beliefs), sometimes directly impact features of perceptual experiences (e.g., the coloring of an object). In contrast, more traditional views hold that propositional attitudes do not directly impact perceptual experiences, but rather are only involved in interpreting or judging these experiences. Understandably, Cognitive Penetration is controversial and has been criticized on both theoretical and empirical grounds. I focus on defending it from the latter kind of objection and in doing (...) so, highlight important features of Cognitive Penetration mechanisms and effects. I first sketch promising criteria for Cognitive Penetration and then address widespread Replication and Demonstration worries about purported instances of it. Next, I present one of the most compelling Cognitive Penetration studies and address specific objections against it and others. I demonstrate that each of these objections misunderstands important features of either Cognitive Penetration mechanisms or the specific studies to which they are applied. Ultimately, I conclude that multiple key studies are not undermined by these objections and con- tinue to provide support for Cognitive Penetration. Correcting these misunderstandings bolsters empirical support for Cognitive Penetration and contributes to a better understand- ing of the mechanisms involved in perceptual processing. (shrink)

The Multiverse Response to the problem of evil has it that God made our universe because God makes every universe meeting a certain standard. The main problem for that response is that there’s no explanation for why God didn’t just keeping making duplicates of perfect universes. This paper introduces the ‘Multiactualities Response’, which says that God actualises every possible world that meets a certain standard of value. It avoids the corresponding problem about duplication because different propositions must always be (...) true at distinct worlds. The Multiactualities Response nevertheless has its own problem, namely that it requires the possibility of multiple actual worlds. This paper argues that if we consider spacetimes with wormholes, we have good cause to think there can be multiple metaphysically privileged present moments; given a suitable analogy between time and modality, it follows that there can be multiple metaphysically privileged (i.e. actual) worlds. This paper includes an in–depth examination of the metaphysics of both the temporal and modal cases. (shrink)

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of (...) Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory. (shrink)

Expressions are synonymous if they have the same semantic content. Complex expressions are synonymously isomorphic in Alonzo Church’s sense if one is obtainable from the other by a sequence of alphabetic changes of bound variables or replacements of component expressions by syntactically simple synonyms. Synonymous isomorphism provides a very strict criterion for synonymy of sentences. Several eminent philosophers of language hold that synonymous isomorphism is not strict enough. These philosophers hold that ‘Greeks prefer Greeks’ and ‘Greeks prefer Hellenes’ express different (...) propositions even if they are synonymously isomorphic. They hold that the very recurrence (multiple occurrence) of ‘Greeks’ contributes to the proposition expressed something that indicates the very recurrence in question. Kit Fine argues that this thesis, which he labels semantic relationism calls for a radically new conception of semantics. I have argued that the relevant phenomenon is wholly pragmatic, entirely non-semantic. Here I supplement the case with a new argument. No cognition without recognition—or almost none. With this observation, standard Millianism has sufficient resources to confront Frege’s puzzle and related problems without injecting pragmatic phenomena where they do not belong. (shrink)

In this paper I argue that J. L. Schellenberg’s Divine Hiddenness Argument is committed to a problematic implication that is weakened by research in cognitive psychology on affective forecasting. Schellenberg’s notion of a nonresistant nonbeliever logically implies that for any such person, it is true that she would form the proper belief in God if provided with what he calls “probabilifying” evidence for God’s existence. In light of Schellenberg’s commitment to the importance of both affective and propositional belief components for (...) entering into the proper relationship with God, this implication of his argument becomes an affective prediction or forecast. However, research in cognitive psychology has shown that in multiple and varied circumstances humans often make inaccurate predictions of their future affective states or reactions. Thus, this research provides strong empirical reasons to doubt that the implication is warranted. (shrink)

Dilip Ninan has raised a puzzle for centered world accounts of de re attitude reports extended to accommodate what he calls “counterfactual attitudes.” As a solution, Ninan introduces multiple centers to the standard centered world framework, resulting in a more robust semantics for de re attitude reports. However, while the so-called multi-centered world proposal solves Ninan’s counterfactual puzzle, this additional machinery is not without problems. In Section 1, I present the centered world account of attitude reports, followed by the (...) extension to counterfactual attitudes which Ninan targets with his puzzle. In Section 2, I pose the counterfactual puzzle and present Ninan’s multi-centered world solution, emphasizing similarities and differences between multi-centered and centered world accounts of attitude reports. In Section 3, I argue the counterfactual attitude wishing falls under the purview of the multi-centered proposal, but that the proposal generates false predictions for wish reports concerning unsatisfiable content. I canvass responses, ultimately concluding Ninan’s proposal requires substantial revisions. (shrink)

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource (...) models extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatisation and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the l.. (shrink)

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O (...) comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type. (shrink)

The Foucault’s conception of power, so as those instructions that lead to think the body as a surface or exteriority, enable to suppose that body transcends the restrictive context with the one usually associated with. For that, it’s necessary to inquire into the Foucault’s form to think about the exteriority; principally the one that persists between visibility and enunciation. This subject will be analyzed starting from the multiples forms with which they appear in the foucaultian’s proposition, especially about the clinic (...) and the explanation of the passage from classic to modern culture. (shrink)