We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut property. In the process we show that the (global) subformula property implies the (local) analytic cut property, thereby demonstrating their equivalence. Applying a version of Maehara technique modified in several ways, we prove that bi-intuitionistic logic enjoys the classical Craig interpolation property and Maximova variable separation property; its Halldén completeness follows.

It has been maintained by Smullyan that the importance of cut-free proofs does not stem from cut elimination per se but rather from the fact that they satisfy the subformula property. In accordance with such a viewpoint in this paper we introduce analytic cut trees, a system from which cuts cannot be eliminated but satisfying the subformula property. Like tableaux analytic cut trees are a refutation system but unlike tableaux they have a single inference rule and several branch (...) closure rules. The main advantage of analytic cut trees over tableaux is efficiency: while analytic cut trees can simulate tableaux with an increase in complexity by at most a constant factor, tableaux cannot polynomially simulate analytic cut trees. Indeed analytic cut trees are intrinsically more efficient than any cut-free system. (shrink)

This work studies the structure of proofs containing non-analytic cuts in the cut-based system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KE-tableau decision method. We study the structure of such proofs, proving the existence of a normal form for them in the form of a comb-tree proof. We then concentrate on the problem of efficiently computing non-analytic cuts. (...) For that, we study the generalisation of techniques present in many modern theorem provers, namely the techniques of conflict-driven formula learning. (shrink)

In derivations of a sequent system, $\mathcal{L}\mathcal{J}$, and a natural deduction system, $\mathcal{N}\mathcal{J}$, the trails of formulae and the subformula property based on these trails will be defined. The derivations of $\mathcal{N}\mathcal{J}$ and $\mathcal{L}\mathcal{J}$ will be connected by the map $g$, and it will be proved the following: an $\mathcal{N}\mathcal{J}$-derivation is normal $\Longleftrightarrow $ it has the subformula property based on trails $\Longleftrightarrow $ its $g$-image in $\mathcal{L}\mathcal{J}$ is without maximum cuts $\Longrightarrow $ that $g$-image has the subformula property based (...) on trails. In $\mathcal{L}\mathcal{J}$-derivations, another type of cuts, sub-cuts, will be introduced, and it will be proved the following: all cuts of an $\mathcal{L}\mathcal{J}$-derivation are sub-cuts $\Longleftrightarrow $ it has the subformula property based on trails. (shrink)

This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that (...) a particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoic axioms, the T1 rule and the instances of Cut with just two antecedent formulae in the first premiss. OPEN ACCESS. (shrink)

This issue of the journal includes papers across both analytical and empirical schools within bioethics.In his feature article, ‘The kindest cut? Surgical castration, sex offenders and coercive offers’, John McMillan asks whether surgical castration can be ethically provided as medical treatment for sex offenders . While surgical castration has previously been available in a number of European countries, in recent years it has only been available in the Czech Republic and in Germany. The European Committee for the Prevention of Torture (...) has attacked the Czech and German governments for engaging in degrading treatments. McMillan focuses on the nature of the relationship between psychiatrist and the detainee. Is the option of surgical castration a non-coercive ‘offer’, or is the option of non-castration a coercive threat? For McMillan, the nature of the intent is important, but he argues that the Czech and German approaches to surgical castration are not necessarily coercive, and can be a component of ethically praiseworthy self-transformation.Responding to McMillan, Alan Wertheimer and Franklin Miller focus on the question of coercion . They argue that the offer of castration is only coercive if psychiatrists or the state threaten to violate sex-offenders’ rights, or forego an obligation to the prisoner if he declines castration. On their view, such offers are not coercive, though they note that this does not settle the key ethical questions.Jesper Ryberg and Thomas Petersen, by contrast, argue both that offers can be coercive and that coercive offers could be morally legitimate - where there is a significant societal benefit . They suggest …. (shrink)

We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G 0(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G 0are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the (...) so-called analytical cut-rule.In addition we show that G 0is not compact (and therefore not canonical), and we proof with the tableau-method that G 0is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G 0is decidable and also characterised by the class of all frames for G 0. (shrink)

Most analytic philosophers are atheists, but is there a deep connection between analytic philosophy and atheism? The paper argues a) that the founding fathers of analytic philosophy were mostly teenage atheists before they became philosophers; b) that analytic philosophy was invented partly because it was realized that the God-substitute provided by the previously fashionable philosophy - Absolute Idealism – could not cut the spiritual mustard; c) that analytic philosophy developed an unhealthy obsession with meaninglessness which (...) led to a new kind of atheism that dismissed talk of God as factually meaningless (neither true nor false) rather than meaningful but false; but d) that this new-fangled atheism (unlike the old-fashioned atheism of the founders) is false, since it relies on theories of meaning – verificationism and falsificationism – which are themselves false. The primary focus is on Bertrand Russell, though other analytic philosophers such as Ayer, Neurath and Flew are also extensively discussed. (shrink)

We give complete sequent-like tableau systems for the modal logics KB, KDB, K5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation lemma for the mentioned logics.

We provide a non-Gentzen, though fully syntactical, cut-elimination algorithm for classical propositional logic. The designed procedure is implemented on $$\textsf{GS4}$$ GS 4, the one-sided version of Kleene’s sequent system $$\textsf{G4}$$ G 4. The algorithm here proposed proves to be more ‘dexterous’ than other, more traditional, Gentzen-style techniques as the size of proofs decreases at each step of reduction. As a corollary result, we show that analyticity always guarantees minimality of the size of $$\textsf{GS4}$$ GS 4 -proofs.

Whether some condition is equivalent to a conjunction of some conditions has been a major issue in analytic philosophy. Examples include: knowledge, acting freely, causation, and justice. Philosophers have striven to offer analyses of these, and other concepts, by showing them equivalent to such a conjunction. Timothy Williamson offers a number of arguments for the idea that knowledge is ‘prime’, hence not equivalent to or composed by some such conjunction. I focus on one of his arguments: the requirement that (...) such conjuncts must be freely recombinable. Although there has been a great deal of discussion of Williamson's arguments, the flaw I describe has gone unnoticed. Williamson's argument is expressed in terms of conditions, and cases of the condition. Does the condition include specific information, or is the specific information only part of the case? His argument equivocates between more and less general specifications of the conditions. Once this distinction is clarified, his argument can be seen to be vitiated by this conflation. Neither option yields a sound argument for Williamson's desired conclusion. (shrink)

Let ⊢ be the ordinary deduction relation of classical first-order logic. We provide an "analytic" subrelation ⊢a of ⊢ which for propositional logic is defined by the usual "containment" criterion Γ ⊢a φ iff Γ⊢φ and Atom ⊆ Atom, whereas for predicate logic, ⊢a is defined by the extended criterion Γ⊢aφ iff Γ⊢aφ and Atom ⊆' Atom, where Atom ⊆' Atom means that every atomic formula occurring in φ "essentially occurs" also in Γ. If Γ, φ are quantifier-free, then (...) the notions "occurs" and "essentially occurs" for atoms between Γ and φ coincide. If ⊢ is formalized by Gentzen's calculus of sequents, then we show that ⊢a is axiomatizable by a proper fragment of analytic inference rules. This is mainly due to cut elimination. By "analytic inference rule " we understand here a rule r such that, if the sequent over the line is analytic, then so is the sequent under the line. We also discuss the notion of semantic relevance as contrasted to the previous syntactic one. We show that when introducing semantic sequents as axioms, i.e. when extending the pure logical axioms and rules by mathematical ones, the property of syntactic relevance is lost, since cut elimination no longer holds. We conclude that no purely syntactic notion of analytic deduction can ever replace successfully the complex semantico-syntactic deduction we already possess. (shrink)

I argue that there are analytic claims that, if true, can be known a priori, but which also can turn out to be false: they are expressive of merely default instructions from the language faculty to the conceptual system, which may be overridden by pragmatic or scientific considerations, in which case, of course, they would not be known at all, a priori or otherwise. More surprisingly, I also argue that they might not be, strictly speaking, conceptual: concepts may be (...) importantly different from the meaning instructions for the words we use to express them. I will press all this in the context of a general Quinean “naturalism,” where the epistemology that interests me is “a chapter of natural science,” but where the science won't be Quine's behaviorism, but a Chomskyan theory of the “I-semantics” of “I-language.” But, relying on a distinction I draw between an explanatory and a working epistemology, I will be pressing it largely as an explanatory claim, not one that will have serious consequences for on-going philosophical practice, neither with regard to the world, nor, more surprisingly, even with regard to armchair “conceptual analysis.” As Putnam observed, there may be analytic truths, but they don't cut much philosophical ice. (shrink)

In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We (...) then show that for most of the systems under consideration the labelling mechanism can be avoided by choosing an appropriate way of structuring theories. One peculiar feature of our proof systems is the use of restart rules which allow to re-ask the original goal of a deduction. In case of K, K4, S4 and G, we can eliminate such a rule, without loosing completeness. In all the other cases, by dropping such a rule, we get an intuitionistic variant of each system. The present results are part of a larger project of a goal directed proof theory for non-classical logics; the purpose of this project is to show that most implicational logics stem from slight variations of a unique deduction method, and from different ways of structuring theories. Moreover, the proof systems we present follow the logic programming style of deduction and seem promising for proof search [Gabbay and Reyle 84, Miller et al. 91]. (shrink)

The goal of this article is to take a step toward the resolution of the problem of finding an analytic sequent calculus for the logic of proofs. For this, we focus on the system Ilp, the intuitionistic version of the logic of proofs. First we present the sequent calculus Gilp that is sound and complete with respect to the system Ilp; we prove that Gilp is cut-free and contraction-free, but it still does not enjoy the subformula property. Then, we (...) enrich the language of the logic of proofs and we formulate in this language a second Gentzen calculus Gilp∗. We show that Gilp∗ is a conservative extension of Gilp, and that Gilp∗ satisfies the subformula property. (shrink)

We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.

This paper is concerned. with the contrast between simulation- and deduction-based approaches to reasoning about physical objects. We show that linear logic can give a unified account of both simulation and deduction concerning physical objects; it also allows us to draw a principled distinction between simulation and deduction, since simulations correspond to cut-free proofs, whereas deductions correspond to proofs in general.

Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.

The paper introduces Hilbert– and Gentzen-style calculi which correspond to systems ${\mathsf{C}_{n}}$ from Gupta and Belnap [3]. Systems ${\mathsf{C}_{n}}$ were shown to be sound and complete with respect to the semantics of finite revision. Here, it is shown that Gentzen-style systems ${\mathsf{GC}_{n}}$ admit a syntactic proof of cut elimination. As a consequence, it follows that they are consistent.

In the first part of this paper I contend that Michael Dummett’s works contain a distinction between analytic and synthetic (logical) deductions. Dummett does not use Kant’s terminology. Nevertheless, based on general considerations about theories of meaning, Dummett shows how one can distinguish between deductions whose validity is recognised by merely grasping the concepts and deductions whose validity can be recognised only by “going beyond the concepts”, as Kant wrote. The latter are synthetic deductions, through which we can increase (...) our knowledge. A special merit of Dummett’s distinction is its theoretical flexibility and generality. He does not propose a single clear-cut distinction between analytic and synthetic deductions; rather in his works we find an indication of how to draw a distinction once a theory of meaning is adopted. In the second part of the paper I consider possible developments within an inferentialist theory of meaning and draw some conclusions concerning the fallibility of deductions. (shrink)

In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n<ω, for da Costa's hierarchy of propositional paraconsistent logics Cn, 1≤n<ω. In our tableaux formulation, we introduce da Costa's “ball” operator “o”, the generalized operators “k” and “(k)”, for 1≤k, and the negations “~k”, for k≥1, as primitive operators, differently to what has been done in the literature, where these operators are usually defined operators. We prove a version of Cut Rule for the TNDC n, 1≤n<ω, (...) and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤n<ω. The systems TNDC n constitute completely automated theorem proving systems for the systems of da Costa's hierarchy Cn, 1≤n<ω. (shrink)

In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n (...) and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤nshrink)

We prove that the boundedness theorem of generalized recursion theory can be derived from the ω-completeness theorem for number theory. This yields a proof of the boundedness theorem which does not refer to the analytical hierarchy theorem.

In this paper we present a finitary sequent calculus for the S5 multi-modal system with common knowledge. The sequent calculus is based on indexed hypersequents which are standard hypersequents refined with indices that serve to show the multi-agent feature of the system S5. The calculus has a non-analytic right introduction rule. We prove that the calculus is contraction- and weakening-free, that (almost all) its logical rules are invertible, and finally that it enjoys a syntactic cut-elimination procedure. Moreover, the use (...) of the non-analytic rule can be restricted so that the calculus can be considered as suitable for proof search. (shrink)

I reply here to an article by philosopher Paul Boghossian in which my article "Cutting-Edge Equivocation: Conceptual Moves and Rhetorical Strategies in Contemporary Anti-Epistemology" (Smith, *SAQ* 2002) provides him with an occasion for a supposed exposure and refutation of the alleged illogic of the "unpalatable relativism" of what Boghossian, at some distance from his topic, (mis)understands as the "constructivism" of contemporary sociology of science.

Many concerned citizens, including judges, bureaucrats, politicians, activists, journalists, and academics, have been claiming that Indian democracy has been imperilled under the premiership of Narendra Modi, which began in 2014. To examine this claim, the Article sets up an analytic framework for accountability mechanisms liberal democratic constitutions put in place to provide a check on the political executive. The assumption is that only if this framework is dismantled in a systemic manner can we claim that democracy itself is in (...) peril. This framework helps distinguish between actions that one may disagree with ideologically but are nonetheless permitted by an elected government, from actions that strike at the heart of liberal democratic constitutionalism. Liberal democratic constitutions typically adopt three ways of making accountability demands on the political executive: vertically, by demanding electoral accountability to the people; horizontally, by subjecting it to accountability demands of other state institutions like the judiciary and fourth branch institutions; and diagonally, by requiring discursive accountability by the media, the academy, and civil society. This framework assures democracy over time – i.e. it guarantees democratic governance not only to the people today, but to all future peoples of India. Each elected government has the mandate to implement its policies over a wide range of matters. However, seeking to entrench the ruling party’s stranglehold on power in ways that are inimical to the continued operation of democracy cannot be one of them. The Article finds that the first Modi government in power between 2014 and 2019 did indeed seek to undermine each of these three strands of executive accountability. Unlike the assault on democratic norms during India Gandhi’s Emergency in the 1970s, there is little evidence of a direct or full-frontal attack during this period. The Bharatiya Janata Party government’s mode of operation was subtle, indirect, and incremental, but also systemic. Hence, the Article characterizes the phenomenon as “killing a constitution by a thousand cuts.” The incremental assaults on democratic governance were typically justified by a combination of a managerial rhetoric of efficiency and good governance (made plausible by the undeniable imperfection of our institutions) and a divisive rhetoric of hyper-nationalism (which brands political opponents of the party as traitors of the state). Since its resounding victory in the 2019 general elections, the Modi government appears to have moved into consolidation mode. No longer constrained by the demands of coalition partners, early signs suggest that it may abandon the incrementalist approach for a more direct assault on democratic constitutionalism. (shrink)

This article develops a model first proposed in my book Jurisprudence and communication [67]. It takes as its starting point the generally conception that legal rules are valid norms, involving a normative content and expressing themselves in reality through observable conduct. This dualistic character of law is central. Law is both fiction and factual, ideal and real. But the viewpoint that a legal rule is a manifestation of validity in reality, through empirical acts, raises the question how rules as (valid) (...) fictions can be known and understood in their linguistic form. How is meaning attributed to the legal words and how do these words relate to the world of fact? Taking an institutional-pragmatic approach as a starting point, an analytical model is created that can be used as an instrument for the relationship between legal rules as thought objects existing only in the mind, and legal rules as observable conduct. This model seeks to revise the classical models of legal communication that basically focus on the unilateral flow of legal information between ‘senders and receivers’ and their claim of linear causality between rules and conduct. The model here constructed in the theoretical part is then applied to several case studies, in order to analyze the construction of meaning in actual use. Two fundamental rights—the older codified in 1798 and the more recent codified in 1983—in the Dutch Constitution have been analyzed using the model as an instrument. Further, the remarkable shifts in article 96 of the Constitution, the declaration of war, and its consequences, resulting in a new category of war—the armed conflict—have been analyzed, as well as the phenomenon of ‘peacekeeping missions’ involving actual warfare. The new war terminology has created vagueness with respect to the clear-cut division between war and peace, which has been reflected in several cases before Court, including the Eric O. case. The present analysis of the case studies indicates that the model was not in all cases completely tailored to the facts: for example, in the case study on article 96 a broad spectrum of observable legal and non-legal actors dominated the facts in such a way that the model did not fully cover it. The observations on my book by the three respondents in this special issue have contributed to the adaptation and extension of the model. In the Postscript my responses suggest some ways in which their ideas can be implemented. (shrink)

In a 1978 lecture in Tokyo, Foucault drew a comparison between his own philosophical methodology and that of ‘Anglo-Saxon analytic philosophy’, claiming the label ‘analytic philosophy of politics’ for his own approach. This may seem like a somewhat surprising comparison given the gulf between contemporary analytic and continental philosophy, but I argue that it is a very productive one which indeed might help us reconsider this gulf. I proceed through a comparison between Foucault and the speech act (...) theory of J. L. Austin, one of the analytic philosophers Foucault had in mind in his Tokyo lecture. By focusing on the methodological commonalities between Foucault and Austin, this article identifies the core of a philosophical methodology that cuts across the analytic/continental divide in philosophy in general while constituting a powerful alternative to the methods applied by analytic political philosophers specifically. This approach, which I term ‘analytic critique’, is one that starts from a critical analysis of what happens in ordinary lived experience and theorizes ‘bottom-up’ in an avowedly politically engaged way – thereby challenging the conceptual and political aloofness of contemporary political philosophy in the liberal-Rawlsian tradition. Foucault’s appropriation of the label ‘analytic philosophy’, it is argued, ought to function as a call to more imaginative methodological-theoretical engagement across the traditional division between continental and analytic approaches. (shrink)

A renegade positivist himself, Quine eschewed apriority, necessity, and analyticity, while (for a time) adopting a holistic version of verificationism. Despite similarities in their opposition to Quine, the differences between Lewis and Kripke were large ‐ especially in the semantics and metaphysics of modality. They also had different philosophical styles. Lewis's (1970b) was one of the cutting‐edge texts of its time ‐ along with work by Richard Montague, David Kaplan, and Robert Stalnaker. Together, they laid out a powerful framework for (...) the use of intensional logic in semantic theories of natural language. Lewis was, of course, the author of many more influential articles in the philosophy of language. A final one that must be mentioned is Lewis (1975a). In it, he argues that sentence adverbs such as ′always′, ′usually′, ′often′, sometimes′, and ′never′ are unselective quantifiers that bind all free variables in their scope. (shrink)

Few will dispute the fact that Sri Sankara, the most exciting philosopher of Advaita Vedanta has no clear-cut answers to the problem of reality. The shifting focus and emphasis on the various philosophical issues cited in the original exegetics of Sri Sankara by the modern thinkers certainly need a consensus on arriving at the meaningful and purposeful understanding of the true nature of reality. The concept of Adhyasa in its three variants has to be asserted from the non-contradictory ground of (...) reality. In this context, there is a need to differentiate between 'mere appearance' and the 'actual appearance' or the unmanifest reality. The present work attempts to establish the valid tones of a sound philosophy of Advaita Vedanta at its best. (shrink)

The present special issue of Disputatio brings together some of the best work recently done in Brazil and Portugal in the tradition of analytic philosophy (broadly conceived). Over the past ten years or so we have witnessed an impressive growth of analytic philosophy in both countries, either in terms of quantity or in terms of quality of the produced philosophy. We hope that this volume capture, at least partly, the dynamics and strength of such development. The range of (...) philosophical problems and topics covered by the contributed essays is vast, cutting across several philosophical disciplines. Indeed, one can find therein issues in philosophical logic, meta-philosophy, ethics, aesthetics, philosophy of science, philosophy of language, philosophy of mathematics and metaphysics. Such variety of subject-matter is also a trait of recent Luso-Brazilian analytic philosophy. (shrink)

The paper advances a realist analytical model for case studies of national soft power policies. First, it argues that for the purposes of realist analysis, a soft power policy must be considered as a rational strategy pursued under the conditions of competition. Furthermore, it emphasises the importance of taking into account the specificities of the recipient state as well as the fact that a soft power strategy is targeted at both its elite and its public. In addition, the article substantiates (...) the necessity to draw a clear-cut distinction between soft power sources and instruments and shows possible shortcomings that research can have should this distinction fail to be made. Finally, the paper discusses the impact of a competitor’s presence on a soft power strategy and specifies the terms under which disregarding this impact may engender a wrong conclusion. (shrink)

Concomitant with the rise of rationalizing accountability in higher education has been an increase in theoretical reflection about the forms accountability has taken and the ones it should take. The literature is now peppered by a wide array of distinctions (e.g. internal/external, inward/ outward, vertical/horizontal, upward/downward, professional/public, political/economic, soft/ hard, positive/negative), to the point that when people speak of ‘accountability’ they risk speaking past one another, having some of these distinctions in mind and not others. Furthermore, often these distinctions are (...) vague and cross-cut each other in ways that are as yet unclear. The field could benefit from having a comprehensive framework in which to place these distinctions and to view their relations. My aim in this article is to provide an analytical tool by which to classify important debate about what accountability in higher education has been and ought to be. Beyond organizing such debate, this schema will serve the purposes of revealing ambiguities in terms, conflations of ideas, assumptions that warrant questioning, and gaps in present research agendas. (shrink)

Analytical philosophy abounds in tours de force [[sic]], but these are usually directed against other genres of philosophy, particularly the brand which passes under the various titles of "speculative," "systematic," or "substantive" philosophy. What distinguishes Fain's tour de force is that he turns the cutting edge of analytical philosophy on itself and, in so doing, seeks to revalidate speculative philosophy on analytical grounds. The main attack is against the stereotypes of a dichotomy between history and the philosophy of history, of (...) analytical philosophy presented as the true basis of philosophy of history, and of speculative philosophy of history as some kind of pseudo-discipline which is neither philosophy nor history. At the same time, the author rejects the standard division of philosophy of history into analytical and speculative approaches. His positive arguments center around the crucial role of narration in history. It is not the historical facts which give intelligibility to history, but the story-line or plot which combines them into a coherent narrative. Narration is counterposed to the analytical philosopher's emphasis on descriptive explanation of the facts. Fain argues that narration not only does not preclude consideration of history as a science, but that science itself often requires narration for purposes of intelligibility. He downgrades the importance of the debate which has raged for the last three decades over the nature of historical explanation. Absorption with the pros and cons of the covering law model of historical explanation has tended to preempt the whole field of philosophy of history and to obscure other more basic issues such as the relationship of history to science. On the other hand, Fain could not resist the temptation to append an epilogue on Hempel's covering law model, thus denying in practice what he proclaimed in principle. The examples of speculative philosophy are drawn mainly from the works of Hegel, Marx, and Collingwood. They are expounded and criticized within the context of Fain's definition of philosophy of history as "the formulation and the critique of criteria of intelligibility of historical concepts." Although he finds shortcomings in the story-lines of all three from the standpoint of intelligibility, the author concludes with a call for historians and philosophers to debate the story-line that a history of mankind should adopt. The bibliography is informative and selective.--H. B. (shrink)

A proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuit-size is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: (1) (...) Feasible interpolation theorems for the following proof systems: (a) resolution (b) a subsystem of LK corresponding to the bounded arithmetic theory S 2 2 (α) (c) linear equational calculus (d) cutting planes. (2) New proofs of the exponential lower bounds (for new formulas) (a) for resolution ([15]) (b) for the cutting planes proof system with coefficients written in unary ([4]). (3) An alternative proof of the independence result of [43] concerning the provability of circuit-size lower bounds in the bounded arithmetic theory S 2 2 (α). In the other direction we show that a depth 2 subsystem of LK does not admit feasible monotone interpolation theorem (the so called Lyndon theorem), and that a feasible monotone interpolation theorem for the depth 1 subsystem of LK would yield new exponential lower bounds for resolution proofs of the weak pigeonhole principle. (shrink)

We study an extension of first-degree entailment (FDE) by Dunn and Belnap with a non-contingency operator |$\blacktriangle \phi $| which is construed as ‘|$\phi $| has the same value in all accessible states’ or ‘all sources give the same information on the truth value of |$\phi $|’. We equip this logic dubbed |$\textbf {K}^\blacktriangle _{\textbf {FDE}}$| with frame semantics and show how the bi-valued models can be interpreted as interconnected networks of Belnapian databases with the |$\blacktriangle $| operator modelling search (...) for inconsistencies in the provided information. We construct an analytic cut system for the logic and show its soundness and completeness. We prove that |$\blacktriangle $| is not definable via the necessity modality |$\Box $| of |$\textbf {K}_{\textbf{FDE}}$|⁠. Furthermore, we prove that in contrast to the classical non-contingency logic, reflexive, |$\textbf {S4}$| and |$\textbf {S5}$| (among others) frames are definable. (shrink)

The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity representation is rather (...) independent of the underlying proof method, provided that some form of (analytic) cut is admissible. We will also discuss some generalisations of the system and compare it with other formalizations of linearity. (shrink)

In this paper, we argue that the usual approach to modelling knowledge and belief with the necessity modality |$\Box $| does not produce intuitive outcomes in the framework of the Belnap–Dunn logic (⁠|$\textsf{BD}$|⁠, alias |$\textbf{FDE}$|—first-degree entailment). We then motivate and introduce a nonstandard modality |$\blacksquare $| that formalizes knowledge and belief in |$\textsf{BD}$| and use |$\blacksquare $| to define |$\bullet $| and |$\blacktriangledown $| that formalize the unknown truth and ignorance as not knowing whether, respectively. Moreover, we introduce another modality (...) |$\textbf{I}$| that stands for factive ignorance and show its connection with |$\blacksquare $|⁠. We equip these modalities with Kripke-frame-based semantics and construct a sound and complete analytic cut system for |$\textsf{BD}^{\blacksquare }$| and |$\textsf{BD}^{\textbf{I}}$|—the expansions of |$\textsf{BD}$| with |$\blacksquare $| and |$\textbf{I}$|⁠. In addition, we show that |$\Box $| as it is customarily defined in |$\textsf{BD}$| cannot define any of the introduced modalities, nor, conversely, neither |$\blacksquare $| nor |$\textbf{I}$| can define |$\Box $|⁠. We also demonstrate that |$\blacksquare $| and |$\textbf{I}$| are not interdefinable and establish the definability of several important classes of frames using |$\blacksquare $|⁠. (shrink)

We present tableau proof systems for the annotated version of propositional justification logics, that is, justification logics which are formulated using annotated application operators. We show that the tableau systems are sound and complete with respect to Mkrtychev models, and some tableau systems are analytic and provide a decision procedure for the annotated justification logics. We further show Craig’s interpolation property and Beth’s definability theorem for some annotated justification logics.

In his essay “Analytic Philosophy and Metaphysics,” Frederick Stoutland argues that an unspoken metaphysical spirit underlies much of twentieth-century analytic philosophy, in spite of the fact that the word “metaphysics” has had a pejorative ring. The metaphysical habit of mind results in an activity which at best is an unproductive diversion, at worst a dialectical illusion, making claims which only appear to be truth-evaluable. I agree with Stoutland’s diagnosis, which is inspired by Wittgenstein, Georg Henrik von Wright, and (...) Cora Diamond, but argue that there is a bifurcation in the metaphysical temptation which Stoutland overlooks. One form is the assumption that questions of meaning can be raised outside the context of meaningful use of an expression, the other is the urge to impose a scientific form of inquiry onto philosophy, the aims of which are quite different from those of science. The former temptation is the deeper one, running through the history of philosophy, while the attempt to model philosophical inquiry onto scientific explanation is the contemporary form taken by this temptation. As an example of the metaphysical spirit Stoutland criticizes Marion David’s defense of the correspondence theory of truth. I argue that David’s progress could have been cut off at an earlier stage, by pointing out that the examples of truth claims David uses as his starting points are themselves bewildering and far removed from anything that would intelligibly be said in the course of a normal conversation. (shrink)

This book collects 13 papers that explore Wittgenstein's philosophy throughout the different stages of his career. The author writes from the viewpoint of critical rationalism. The tone of his analysis is friendly and appreciative yet critical. Of these papers, seven are on the background to the philosophy of Wittgenstein. Five papers examine different aspects of it: one on the philosophy of young Wittgenstein, one on his transitional period, and the final three on the philosophy of mature Wittgenstein, chiefly his Philosophical (...) Investigations. The last of these papers, which serves as the concluding chapter, concerns the analytical school of philosophy that grew chiefly under its influence. Wittgenstein’s posthumous Philosophical Investigations ignores formal languages while retaining the view of metaphysics as meaningless -- declaring that all languages are metaphysics-free. It was very popular in the middle of the twentieth century. Now it is passé. Wittgenstein had hoped to dissolve all philosophical disputes, yet he generated a new kind of dispute. His claim to have improved the philosophy of life is awkward just because he prevented philosophical discussion from the ability to achieve that: he cut the branch on which he was sitting. This, according to the author, is the most serious critique of Wittgenstein. (shrink)

This cutting-edge collection of essays showcases the work of some of the most influential theorists of the past thirty years as they grapple with the question of how literature should be treated in contemporary theory. The contributors challenge trends that have recently dominated the field--especially those that emphasize social and political issues over close reading and other analytic methods traditionally associated with literary criticism. Written especially for this collection, these essays argue for the importance of aesthetics, poetics, and aesthetic (...) theory as they present new and stimulating perspectives on the directions which theory and criticism will take in the future. In addition to providing a selection of distinguished critics writing at their best, this collection is valuable because it represents a variety of fields and perspectives that are not usually found together in the same volume. Michael Clark's introduction provides a concise, cogent history of major developments and trends in literary theory from World War II to the present, making the entire volume essential reading for students and scholars of literature, literary theory, and philosophy. (shrink)

Within his overarching program aiming to defend an epistemic conception of analyticity, Boghossian (1996 and 1997) has offered a clear-cut explanation of how we can acquire a priori knowledge of logical truths and logical rules through implicit definition. The explanation is based on a special template or general form of argument. Ebert (2005) has argued that an enhanced version of this template is flawed because a segment of it is unable to transmit warrant from its premises to the conclusion. This (...) article aims to defend the template from this objection. We provide an accurate description of the type of non-transmissivity that Ebert attributes to the template and clarify why this is a novel type of non-transmissivity. Then, we argue that Jenkins (2008)’s response to Ebert fails because it focuses on doxastic rather than propositional warrant. Finally, we rebut Ebert’s objection on Boghossian’s behalf by showing that it rests on an unwarranted assumption and is internally incoherent. (shrink)

This book examines the complex and varied ways in which fictions relate to the real world, and offers a precise account of how imaginative works of literature can use fictional content to explore matters of universal human interest. While rejecting the traditional view that literature is important for the truths that it imparts, the authors also reject attempts to cut literature off altogether from real human concerns. Their detailed account of fictionality, mimesis, and cognitive value, founded on the methods of (...) analytical philosophy, restores to literature its distinctive status among cultural practices. The authors also explore metaphysical and skeptical views, prevalent in modern thought, according to which the world itself is a kind of fiction, and truth no more than a social construct. They identify different conceptions of fiction in science, logic, epistemology, and make-believe, and thereby challenge the idea that discourse per se is fictional and that different modes of discourse are at root indistinguishable. They offer rigorous analyses of the roles of narrative, imagination, metaphor, and "making" in human thought processes. Both in their methods and in their conclusions, Lamarque and Olsen aim to restore rigor and clarity to debates about the values of literature, and to provide new, philosophically sound foundations for a genuine change of direction in literary theorizing. (shrink)

Why did such highly abstract ideas as truth, knowledge, or justice become so important to us? What was the point of coming to think in these terms? This book presents a philosophical method designed to answer such questions: the method of pragmatic genealogy. Pragmatic genealogies are partly fictional, partly historical narratives exploring what might have driven us to develop certain ideas in order to discover what these do for us. The book uncovers an under-appreciated tradition of pragmatic genealogy which cuts (...) across the analytic-continental divide, running from the state-of-nature stories of David Hume and the early genealogies of Friedrich Nietzsche to recent work in analytic philosophy by Edward Craig, Bernard Williams, and Miranda Fricker. However, these genealogies combine fictionalizing and historicizing in ways that even philosophers sympathetic to the use of state-of-nature fictions or real history have found puzzling. To make sense of why both fictionalizing and historicizing are called for, the book offers a systematic account of pragmatic genealogies as dynamic models serving to reverse-engineer the points of ideas in relation not only to near-universal human needs, but also to socio-historically situated needs. This allows the method to offer us explanation without reduction and to help us understand what led our ideas to shed the traces of their practical origins. Far from being normatively inert, moreover, pragmatic genealogy can affect the space of reasons, guiding attempts to improve our conceptual repertoire by helping us determine whether and when our ideas are worth having. (shrink)

This volume offers an array of newly commissioned essays, addressing the topic of love in the Christian tradition. Drawn from a range of expert theologians and philosophers in contemporary analytic and non-analytic theology, these essays join current debates within the theology of love, and aim to propose new avenues for future research. Including the last essay written by Marilyn McCord Adams, Love, Divine and Human deals with a rich variety of issues related to divine and human love. The (...) broad scope of the book includes divine transcendence and its methodological bearing on the doctrine of divine love, the nature and scope of divine love, the interrelation between God's love and wrath, the plausibility of an impassable God of love, and the application of various conceptions of divine love to the problem of divine hiddenness, human ethics, and human free will, among other topics. This unified collection of cutting-edge papers will advance discussion for all those focused on the theology of love. (shrink)