It is commonly supposed that metaphysical modal claims are to be evaluated with respect to a single domain of possible worlds: a claim is metaphysically necessary just in case it is true in every possible world, and metaphysically possible just in case it is true in some possible world. We argue that the standard understanding is incorrect; rather, whether a given claim is metaphysically necessary or possible is relative to which world is indicatively actual. We motivate our view by attention (...) to discussions in Salmon 1989 and Fine 2005, in which various data are taken to support rejecting the transitivity of accessibility and modal monism ; we argue that relativized metaphysical modality can accommodate these data compatible with both standard modal logic and modal monism. Noting an analogy with two-dimensional semantics, we argue that metaphysical modality has a complex structure, reflecting what is counterfactually possible, relative to each indicatively actual world. In arguing for the need for relativization, we are broadly on the same side as Crossley and Humberstone and Davies and Humberstone ; our contribution here is, first, to offer distinctively metaphysical reasons for relativization, and second, to show that relativization can be incorporated in ways minimally departing from standard modal logic. (shrink)

Our topic is the theory of topics. My goal is to clarify and evaluate three competing traditions: what I call the way-based approach, the atom-based approach, and the subject-predicate approach. I develop criteria for adequacy using robust linguistic intuitions that feature prominently in the literature. Then I evaluate the extent to which various existing theories satisfy these constraints. I conclude that recent theories due to Parry, Perry, Lewis, and Yablo do not meet the constraints in total. I then introduce the (...) issue-based theory—a novel and natural entry in the atom-based tradition that meets our constraints. In a coda, I categorize a recent theory from Fine as atom-based, and contrast it to the issue-based theory, concluding that they are evenly matched, relative to our main criteria of adequacy. I offer tentative reasons to nevertheless favour the issue-based theory. (shrink)

I discuss Smokrović’s work on the normativity of logic (Smokrović 2017, Smokrović 2018). I agree that the classical formal logic is not an adequate model for real-life reasoning. But I present some doubts about his notion of deductive logic and his proposal to model such reasoning in non-monotonic logic. No branch of formal logic by itself is likely to capture real-life inferential links (reasoned-inference). I use the logic of relevance as my case study and extend the pessimistic morals to modern (...) systems of non-classical logic. Finally, I propose a more lax conception of normativty: there is a connection between logical assessment in the broad sense (as sanctioned by the notion of cogency) and the evaluation and criticism of reasoning. (shrink)

In an attempt to improve upon Alexander Pruss’s work (The principle of sufficient reason: A reassessment, pp. 240–248, 2006), I (Weaver, Synthese 184(3):299–317, 2012) have argued that if all purely contingent events could be caused and something like a Lewisian analysis of causation is true (per, Lewis’s, Causation as influence, reprinted in: Collins, Hall and paul. Causation and counterfactuals, 2004), then all purely contingent events have causes. I dubbed the derivation of the universality of causation the “Lewisian argument”. The Lewisian (...) argument assumed not a few controversial metaphysical theses, particularly essentialism, an incommunicable-property view of essences (per Plantinga’s, Actualism and possible worlds, reprinted in: Davidson (ed.) Essays in the metaphysics of modality, 2003), and the idea that counterfactual dependence is necessary for causation. There are, of course, substantial objections to such theses. While I think a fight against objections to the Lewisian argument can be won, I develop, in what follows, a much more intuitive argument for the universality of causation which takes as its inspiration a result from Frederic B. Fitch’s work (J Symb Logic 28(2):135–142, 1963) [with credit to who we now know was Alonzo church’s, Referee Reports on Fitch’s Definition of value, in: (Salerno (ed.), New essays on the knowability paradox, 2009)] that if all truths are such that they are knowable, then (counter-intuitively) all truths are known. The resulting Church–Fitch proof for the universality of causation is preferable to the Lewisian argument since it rests upon far weaker formal and metaphysical assumptions than those of the Lewisian argument. (shrink)

This paper assesses the prospects of a pragmatist theory of content. I begin by criticising the theory presented in D.H. Mellor’s essay ‘Successful Semantics’. I then identify problems and lacunae in the pragmatist theory of meaning sketched in Chapter 13 of Dummett’s The Logical Basis of Metaphysics. The prospects are brighter, I contend, for a tempered pragmatism, in which the theory of content is permitted to draw upon irreducible notions of truth and falsity. I sketch the shape of such a (...) theory and illustrate the role of its pragmatist elements by showing how they point towards a promising account of the truth conditions of indicative conditionals. A feature of the account is that it validates Modus Ponens whilst invalidating Modus Tollens. (shrink)

Relativized Metaphysical Modality (RMM: Murray and Wilson, 'Relativized metaphysical modality', Oxford Studies in Metaphysics, 2012; Murray, Perspectives on Modal Metaphysics, 2017) exploits 'two-dimensionalist' resources to metaphysical, rather than epistemological, ends: the second dimension offers perspective-dependence without contingency, diverting attacks on 'Classical' analyses of modals (in effect, analyses validating S5 and the Barcan Formulae). Here, we extend the RMM program in two directions. First, we harvest resources for RMM from Lewis's 1980 'Context--Index' (CI) framework: (a) the ban in CI on binding (...) into context-arguments (akin to Kaplan's 'monstrosity' ban) projects a bright line between perspective-dependence and contingency; and (b) CI-postulated connections among meaning, content, truth, argument-structure, context, and modality collectively generate a 'Generalized Humphrey Problem' for any non-Classical analysis (examples covered include appeals to accessibility, contingent domains, and counterpart relations). Second, we sharpen the tools of RMM-based metaphysical analysis, and extend their domain of coverage across familiar anomalies for Classical modals: we revisit earlier RMM-based bulwarks for S5 (against 'Chisholm's Paradox' for moderate flexibility of essence, and nomological necessitarianism); and we now similarly shore up the Barcan Formulae (against the apparent contingency of existence and nonexistence). (shrink)

According to an intuitive picture of relevant entailment, an entailment is relevant if all the formulas it contains contribute to its validity. In this paper, we provide a ground-theoretic analysis of this notion of contribution, and as a result of relevant entailment. We build a system of bilateral logical grounding within which we can derive classical entailment and analyze the contribution of premises and conclusions, in terms of a certain type of connection between their respective logical grounds. The resulting framework (...) is shown to have a strong unifying and explanatory power by bringing together the notions of grounding and relevance and explaining the commonalities and differences between alternative contribution-based accounts of relevance. (shrink)

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into (...) the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne. (shrink)

It is widely accepted by formal and informal logicians alike that a formal logic which, by the lights of English, gets the connectives wrong, nevertheless conspires to get entailment right—right that is, modulo English. There is a vexing problem occasioned by this semantic alienation of formal logic. It is next to impossible for formal logic to meet the expectations of realism. What, then, of informal logic?

In this paper we first develop a logic independent account of relevant implication. We propose a stipulative denition of what it means for a multiset of premises to relevantly L-imply a multiset of conclusions, where L is a Tarskian consequence relation: the premises relevantly imply the conclusions iff there is an abstraction of the pair such that the abstracted premises L-imply the abstracted conclusions and none of the abstracted premises or the abstracted conclusions can be omitted while still maintaining valid (...) L-consequence. Subsequently we apply this denition to the classical logic consequence relation to obtain NTR-consequence, i.e. the relevant CL-consequence relation in our sense, and develop a sequent calculus that is sound and complete with regard to relevant CL-consequence. We present a sound and complete sequent calculus for NTR. In a next step we add rules for an object language relevant implication to the sequent calculus. The object language implication reflects exactly the NTR-consequence relation. One can see the resulting logic NTR-> as a relevant logic in the traditional sense of the word. By means of a translation to the relevant logic R, we show that the presented logic NTR is very close to relevance logics in the Anderson-Belnap-Dunn-Routley-Meyer tradition. However, unlike usual relevant logics, NTR is decidable for the full language, Disjunctive Syllogism and Adjunction are valid, and neither Modus Ponens nor the Cut rule are admissible. (shrink)

An argument is presented for the truth of the conditional, ‘If New York is not in the United States, it's in California’. Several possible objections to this argument are then examined and evaluated. Further argument establishes that if the argument for the truth of ‘If New York is not in the United States, it's in California’ is sound, it follows that an indicative conditional is true if and only if it has either a false antecedent or a true consequent.

Lewis proposed to test the validity of a modal thesis by checking whether its possible-world translation is a theorem of counterpart theory. However, that criterion fails to validate many standard modal laws, thus raising doubts about the logical adequacy of the Lewisian framework. The present paper considers systems of counterpart theory of increasing strength and shows how each can be motivated by exhibiting a suitable intended model. In particular, perfect counterpart theory validates all the desired modal laws and therefore provides (...) a way out of the logical objection. Finally, a weakening of perfect counterpart theory is put forward as a response to some metaphysical objections. (shrink)

The paper begins with an account of the emergence of analytic philosophy of language in the twentieth century in the context of the development of logic and the linguistic turn. Subsequently, it describes two examples of analytic philosophy of language in its heyday when the discipline was conceived as first philosophy. Finally, it provides, by way of conclusion, a succinct outline of the current state of philosophy of language, marked by modesty and fragmentation. It is claimed that even if one (...) retains optimism about the prospects of philosophy of language in the first century of the new millennium, it would be unreasonable to disagree with the opinion that the present-day philosophy of language is a highly specialized and diversified discipline and no longer so central for philosophical enterprise as it used to be. (shrink)

A‐theorists of time postulate a deep distinction between the present, past and future. Settling on an appropriate logic for such a view is no easy matter. This Philosophy Compass article describes one of the most vexing formal problems facing A‐theorists. It is commonly thought that A‐theories can only be formally expressed in a tense logic: a logic with operators like P and F . And it seems natural to think that we live in a world where objects come to exist (...) and cease to exist as time passes. Indeed, this is typically a key component of the most prominent kind of A‐theory, presentism. But the temporary existence assumption cannot be upheld in any tense logic with a standard quantification theory. I will explain the problem and outline the philosophical and logical considerations that generate it. I will then consider two possible solutions to the problem – one that targets our logic of quantification and one that targets our assumptions about change. I survey the costs of each solution. (shrink)

A-theorists think there is a fundamental difference between the present and other times. This concern shows up in what kinds of properties they take to be instantiated, what objects they think exist and how they formalize their views. Nearly every contemporary A-theorist assumes that her metaphysics requires a tense logic – a logic with operators like and. In this paper, I show that there is at least one viable A-theory that does not require a logic with tense operators. And I (...) will argue that three common indispensability arguments for tense operators are unsound. (shrink)

In this paper we elaborate a conception of entailment based on what we call the Ackermann principle, which explicates valid entailment through a logical connection between sentences depending on their informational content. We reconstruct Dunn’s informational semantics for entailment on the basis of Restall’s approach, with assertion and denial as two independent speech acts, by introducing the notion of a ‘position description’. We show how the machinery of position descriptions can effectively be used to define the positive and the negative (...) information carried by sentences of a given language and to present a formalized version of the Ackermann principle as an inclusion relationship between the informational contents of the conclusions and the premises of a valid entailment. Being so interpreted, the entailment relation exhibits certain properties, including the property of transitivity. Whereas properties such as Anderson and Belnap’s variable sharing property or Parry’s proscriptive principle are normally presented as imposing a relevance requirement on valid entailment, the suggested formalization of the Ackermann principle supports all of Gentzen’s structural rules, including weakening, a rule that is normally given up in sequent-style proof systems for relevance logics. In this way we propose an Ackermann-inspired explication of the nature of entailment as a relation between the informational contents of sentences. (shrink)

This essay assesses the account of truth presented in Wiggins's 2002 paper ‘An indefinibilist cum normative view of truth and the marks of truth'. I agree with Wiggins that we should seek, not to define truth, but to elucidate it by unfolding its connections with other basic notions. However, I give reasons for preferring an elucidation based on Ramsey's account of truth to Wiggins's Tarski-inspired approach. I also cast doubt on Wiggins's thesis that convergence is a mark of truth, arguing (...) instead that a claim which is up for assessment as true or false must be one to which different speakers/hearers can attach, and know that they are attaching, the same sense. I use this principle to rule out an account of indicative conditionals, and bring some considerations to bear on the question of whether those conditionals have truth values. An appendix revisits a debate about the determinateness of distinctness. (shrink)

Epistemic Logic is our basic universal science, the method of our cognitive confrontation in reality to prove the truth of our basic cognitions and theories. Hence, by proving their true representation of reality we can self-control ourselves in it, and thus refuting the Berkeleyian solipsism and Kantian a priorism. The conception of epistemic logic is that only by proving our true representation of reality we achieve our knowledge of it, and thus we can prove our cognitions to be either true (...) or rather false, and otherwise they are doubtful. Therefore, truth cannot be separated from being proved and we cannot hold anymore the principle of excluded middle, as it is with formal semantics of metaphysical realism. In distinction, the intuitionistic logic is based on subjective intellectual feeling of correctness in constructing proofs, and thus it is epistemologically encapsulated in the metaphysical subject. However, epistemic logic is our basic science which enable us to prove the truth of our cognitions, including the epistemic logic itself. (shrink)

There is consensus among computer scientists, logicians, and philosophers that good reasoning with qualitative beliefs must have the structural property of cumulative transitivity or, for short, cut. This consensus is typically explicitly argued for partially on the basis of practical and mathematical considerations. But the consensus is also implicit in the approach philosophers take to almost every puzzle about reasoning that involves multiple steps: philosophers typically assume that if each step in reasoning is acceptable considered on its own, the whole (...) chain of reasoning must also acceptable. In this paper I focus on whether there are good philosophical reasons for thinking that the consensus that good reasoning must satisfy cut is true. My central claim is that we should not accept the consensus—good reasoning might not satisfy cut. In particular, I consider four arguments for the consensus and explain why they are unpersuasive. (§2-5). I then show that the issue of whether good reasoning is cut turns on a substantive yet until now unnoticed question in epistemology (§6). (shrink)

Since at least the 1960s, deontic logicians and ethicists have worried about whether there can be normative systems that allow conflicting obligations. Surprisingly, however, little direct attention has been paid to questions about how we may reason with conflicting obligations. In this paper, I present a problem for making sense of reasoning with conflicting obligations and argue that no deontic logic can solve this problem. I then develop an account of reasoning based on the popular idea in ethics that reasons (...) explain obligations and show that it solves this problem. (shrink)

Most philosophers seem to be under a misleading impression about the difference between ‘and’ and ‘but’. They hold that they are truth-functional equivalents but that ‘but’ adds a Gricean ‘conventional implicature’ to ‘and’. Frege thought that the implicature attached to ‘but’ was that the second clause is unlikely given the first; others have simply said they express a contrast between the two. Though the second formulation may seem more general, in practice writers seem to agree with Frege's idea. The present (...) note will argue against this conventional view. Indeed, ‘and’ and ‘but’ may both convey conflicting implicatures; and the traditional characterization of the implicature of ‘but’ is outright mistaken, or at least misleading. (shrink)

Accounts of logical independence which coincide when applied in the case of classical logic diverge elsewhere, raising the question of what a satisfactory all-purpose account of logical independence might look like. ‘All-purpose’ here means: working satisfactorily as applied across different logics, taken as consequence relations. Principal candidate characterizations of independence relative to a consequence relation are that there the consequence relation concerned is determined by only by classes of valuations providing for all possible truth-value combinations for the formulas whose independence (...) is at issue, and that the consequence relation ‘says’ nothing special about how those formulas are related that it does not say about arbitrary formulas. Each of these proposals returns counterintuitive verdicts in certain cases—the truth-value inspired approach classifying certain cases one would like to describe as involving failures of independence as being cases of independence, and the de Jongh approach counting some intuitively independent pairs of formulas as not being independent after all. In final section, a modification of the latter approach is tentatively sketched to correct for these misclassifications. The attention is on conceptual clarification throughout, rather than the provision of technical results. Proofs, as well as further elaborations, are lodged in the ‘longer notes’ in a final Appendix. (shrink)

Expressivists about epistemic modals deny that ‘Jane might be late’ canonically serves to express the speaker’s acceptance of a certain propositional content. Instead, they hold that it expresses a lack of acceptance. Prominent expressivists embrace pragmatic expressivism: the doxastic property expressed by a declarative is not helpfully identified with that sentence’s compositional semantic value. Against this, we defend semantic expressivism about epistemic modals: the semantic value of a declarative from this domain is the property of doxastic attitudes it canonically serves (...) to express. In support, we synthesize data from the critical literature on expressivism—largely reflecting interactions between modals and disjunctions—and present a semantic expressivism that readily predicts the data. This contrasts with salient competitors, including: pragmatic expressivism based on domain semantics or dynamic semantics; semantic expressivism à la Moss [2015]; and the bounded relational semantics of Mandelkern [2019]. (shrink)

What does it take for two logics to be mere notational variants? The present paper proposes a variety of different ways of cashing out notational variance, in particular isolating a constraint on any reasonable account of notational variance which makes plausible that the only kinds of translations which can witness notational variance are what are sometimes called definitional translations.

In this article, I outline a logic of design of a system as a specific kind of conceptual logic of the design of the model of a system, that is, the blueprint that provides information about the system to be created. In section two, I introduce the method of levels of abstraction as a modelling tool borrowed from computer science. In section three, I use this method to clarify two main conceptual logics of information inherited from modernity: Kant’s transcendental logic (...) of conditions of possibility of a system, and Hegel’s dialectical logic of conditions of in/stability of a system. Both conceptual logics of information analyse structural properties of given systems. Strictly speaking, neither is a conceptual logic of information about the conditions of feasibility of a system, that is, neither is a logic of information as a logic of design. So, in section four, I outline this third conceptual logic of information and then interpret the conceptual logic of design as a logic of requirements, by introducing the relation of “sufficientisation”. In the conclusion, I argue that the logic of requirements is exactly what we need in order to make sense of, and buttress, a constructionist approach to knowledge. (shrink)

It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib without qualification.” And Stalnaker writes, “we can agree (...) with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense.” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it. (shrink)

There is an apparent conflict in Quine’s work between, on the one hand, his clear commitment to the rational revisability of logic and, on the other, his principle of charitable translation and ‘change of logic, change of subject’ argument. I argue that the apparent conflict is mostly resolved under close exegesis, but that the translation argument normatively rules out collaborative revision and allows only revision by individuals. However, I articulate a Neo-Quinean view that preserves the rational acceptability of collaborative revision. (...) On that view, everything is rationally revisable in some manner or other — it’s just that the logical principles that laypersons find (actually or potentially) obvious and tacitly use to govern their everyday inferences can’t be rationally revised quickly and all at once. Since, in Quine’s view, what most people find obvious resists change, rational changes to laymen’s logic must be gradual. (shrink)

Investiga-se a possibilidade de uma abordagem do fenômeno do pluralismo lógico a partir de uma perspectiva inspirada no pensamento de Quine. A matematização da lógica termina por levar à flexibilização da teoria lógica, logo surgindo, não apenas sistemas complementares e alternativos à lógica clássica, mas também a questão da admissibilidade de mais do que um sistema lógico. A tal posição se dá o nome “pluralismo lógico”. Quine foi um destacado defensor da lógica clássica a partir de uma perspectiva monista, ainda (...) que admitisse em princípio a possibilidade de sua revisão. Pode-se, contudo, investigar se as linhas gerais do pensamento quineano são compatíveis com uma perspectiva pluralista. Algumas possibilidades são levantadas tomando em consideração propostas como as teorias pluralistas de Carlo Dalla Pozza e Richard Epstein. Conclui-se que, embora Quine não concebesse a possibilidade de apoiar o pluralismo lógico, a sua filosofia ajuda a enquadrar e avaliar as maneiras de estudar o assunto. (shrink)

Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...) philosophical questions around logic. -/- Logic: the Basics is essential reading for first-year undergraduate philosophy students on standard introductory logic courses. (shrink)

En este ensayo respondo negativamente a la pregunta del título al sostener que el enunciado “La suma de los ángulos internos de un triángulo es igual a 180°” es contingentemente verdadero. Para ello, intento refutar la tesis de Ramsey de que las verdades geométricas necesariamente son verdades necesarias, así como la tesis de Kripke de que no puede haber proposiciones matemáticas contingentemente verdaderas. Además, recurriendo a la concepción fregeana sobre lo a priori y lo a posteriori, sostengo que hay verdades (...) geométricas que pueden ser a priori sin tener que serlo. -/- . (shrink)

The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...) In sections 5 and 6 I discuss some problems arising with regard to Prawitz’s views. (shrink)

This paper focuses on two interrelated issues about the prospects for research projects in experimental philosophical logic. The first issue is about the role that logic plays in such projects; the second involves the role that experimental results from the cognitive sciences play in them. I argue that some notion of logic plays a crucial role in these research projects, and, in turn, the results of these projects might inform substantive debates in the philosophy of logic.

I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism.