We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, (...) Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for (...) possible paths. We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees. (shrink)

This paper introduces a framework for direct surface composition by online update. The surface string is interpreted as is, with each morpheme in turn updating the input state of information and attention. A formal representation language, Logic of Centering, is defined and some crosslinguistic constraints on lexical meanings and compositional operations are formulated.

In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial (...) orders (\nsbcdt\ for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. (shrink)

ABSTRACT We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical views that (...) its predecessors rule out by fiat. (shrink)

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze (...) his argument on why this version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted. (shrink)

We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state formulae in the full `strategically flat' fragment of ATL* is PSPACE-complete, whereas the satisfiability problems in the flat fragments of ATL and ATL$^{+}$ (...) are $\Sigma^P_3$-complete. We note that the nesting hierarchies for fragments of ATL* collapse in terms of expressiveness above nesting depth 1, hence our results cover all such fragments with lower complexities. (shrink)

ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and (...) class='Hi'>modal theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy. (shrink)

This book advertises itself as an exploration of the world-time parallel, that is, the parallel between the modal dimension, on the one hand, and the temporal dimension, on the other. It is that, and much more. As the authors point out, there is reasonable agreement that we can model times, through temporal logic, in ways that are analogous to those by which we model modality through the logic of possible worlds. But this formal parallel has almost universally (...) been taken to be a merely formal parallel: thus it is held that no metaphysical conclusions ought to be drawn from it. Thus, it is generally thought that one is free to accept an argument for actualism, say, but to reject a parallel argument for presentism. Rini and Cresswell compellingly argue that this is a mistake: the temporal and the modal are more than merely formally analogous. (shrink)

The master argument posits a metaphysical thesis: Diodorus does away with Aristotle’s dunamis understood as a power simultaneously oriented toward being and non-being and proclaims that possibilities that fail to actualize are simply nothing. My contention is that this claim is not a mere application of Diodorus’ contribution to modal logic. Rather, Diodorus creates an ontologico-temporal concept of possibility and impossibility. Diodorus envisions the future as the past that the future will become. Since what will have been can (...) never be the accomplishment of a possibility that did not obtain, and since the future is destined to become past, any futural possibility that doesn’t actualize is neither futural nor even possible. (shrink)

We discuss abstraction principles in the context of modal and temporal logic. It is argued that abstractionism conflicts with both serious presentism and serious actualism.

We study the modal logic M L r of the countable random frame, which is contained in and `approximates' the modal logic of almost sure frame validity, i.e. the logic of those modal principles which are valid with asymptotic probability 1 in a randomly chosen finite frame. We give a sound and complete axiomatization of M L r and show that it is not finitely axiomatizable. Then we describe the finite frames of that logic and show that (...) it has the finite frame property and its satisfiability problem is in EXPTIME. All these results easily extend to temporal and other multi-modal logics. Finally, we show that there are modal formulas which are almost surely valid in the finite, yet fail in the countable random frame, and hence do not follow from the extension axioms. Therefore the analog of Fagin's transfer theorem for almost sure validity in first-order logic fails for modal logic. (shrink)

This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal (...) logic. Those assumptions arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (shrink)

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and (...) time could be replaced with an appropriate justification logic. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal (...) frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

Jason Stanley has argued recently that Epistemic Contextualism (EC) and Subject‐Sensitive Invariantism (SSI) are explanatorily on a par with regard to certain data arising from modal and temporal embeddings of ‘knowledge’‐ascriptions. This paper argues against Stanley that EC has a clear advantage over SSI in the discussed field and introduces a new type of linguistic datum strongly suggesting the falsity of SSI.

Natural languages exhibit a great variety of grammatical paradigms. For instance, in English verbs are grammatically marked for tense, whereas in the tenseless Eskimo-Aleut language Kalaallisut they are marked for illocutionary mood. Although time is a universal dimension of the human experience and speaking is part of that experience, some languages encode reference to time without any grammatical tense morphology, or reference to speech acts without any illocutionary mood morphology. Nevertheless, different grammatical systems are semantically parallel in certain respects. Specifically, (...) I propose that English tenses form a temporal centering system, which monitors and updates topic times, whereas Kalaallisut moods form a modal centering system, which monitors and updates modal discourse referents. To formalize these centering parallels I define a dynamic logic that represents not only changing information but also changing focus of attention in discourse (Update with Centering, formalizing Grosz et al 1995). Different languages can be translated into this typed logic by directly compositional universal rules of Combinatory Categorial Grammar (CCG) The resulting centering theory of tense and illocutionary mood draws semantic parallels across different grammatical systems. The centering generalizations span the extremes of the typological spectrum, so they are likely to be universal. In addition, the theory accounts for the translation equivalence of tense and illocutionary mood in a given utterance context. Following Stalnaker (1978) I assume that the very act of speaking up has a ‘commonplace effect’ on the context. It focuses attention on the speech act and thereby introduces default modal and temporal topics. These universal defaults complement language-specific grammars, e.g. English tenses and Kalaallisut moods. In a given utterance context the universal discourse-initial defaults plus language-specific grammatical marking may add up to the same truth conditions.. (shrink)

Rumfitt has given two arguments that in unilateralist verificationist theories of meaning, truth collapses into correct assertibility. In the present paper I give similar arguments that show that in unilateral falsificationist theories of meaning, falsehood collapses into correct deniability. According to bilateralism, meanings are determined by assertion and denial conditions, so the question arises whether it succumbs to similar arguments. I show that this is not the case. The final section considers the question whether a principle central to Rumfitt's first (...) argument, ‘It is assertible that if and only if it is assertible that it is assertible that ’, is one that bilateralists can reject, and concludes that they cannot. It follows that the logic of assertibility and deniability, according to a result by Williamson, is the little known modal logic K4 studied by Sobociński. The paper ends with a plaidoyer for bilateralists to adopt this logic. (shrink)

ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly (...) incorporates the semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

ABSTRACT: A detailed presentation of Stoic logic, part one, including their theories of propositions (or assertibles, Greek: axiomata), demonstratives, temporal truth, simple propositions, non-simple propositions(conjunction, disjunction, conditional), quantified propositions, logical truths, modal logic, and general theory of arguments (including definition, validity, soundness, classification of invalid arguments).

In this article, I am interested in four versions of what is often referred to as "the Humphrey objection". This objection was initially raised by Kripke against Lewis's modal counterpart theory, so this is where I will start the discussion. As we will see, there is a perfectly good answer to the objection. I will then examine other places where a similar objection can be raised: it can arise in the case of temporal counterpart theory (in fact, it (...) can arise in the case of all kinds of counterpart theories, independently on modal realism), and a very similar worry can also arise against modal realism itself or against an ersatzist theory of possible worlds itself. For similar reasons, in similar situations, a similar objection will arise. What is interesting is that it is not the case that a similar response can be given in all of these similar cases. So, in the end, we will see what dissimilarities there are and how and why they are relevant. In particular, we will see the differences there are between alethic modalities and temporal modalities. In the case of alethic modalities (metaphysical necessity and possibility), the objection can be answered by appealing to the notion of representation, while this does not work very well in the case of temporal modalities. (shrink)

ABSTRACT A complete axiomatic system CTLrp is introduced for a temporal logic for finitely branching ω+ -trees in a language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTLrp. In particular, that yields a complete axiomatization for the translations of all valid CTL*-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive (...) medium for reasoning about branching time. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of propositional logic; 4. (...) Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

What makes a valid argument valid? Generally speaking, in a valid argument, if the premisses are true, then the conclusion must necessarily also be true. But on its own, this doesn’t tell us all that much. What is truth? And what is necessity? In what follows, I consider answers to these questions proposed by the fourteenth century logician John Buridan († ca. 1358). My central claim is that Buridan’s logic is downstream from his metaphysics. Accordingly, I treat his metaphysical discussions (...) as the key to his logic. As has been often noted, Buridan’s metaphysics are radically anti-realist about universals, though I think the depth and scope of his anti-realism has at times been papered over. Buridan constructs his logic on an amazingly spartan ontology, and this accomplishment is overdue for reconsideration. To the foregoing questions: truth is a feature of propositions, and of propositions only—not of proposition-like states of affairs, or anything like that. It is a function of the reference or supposition (suppositio) of their terms, which depends on predication in a propositional context. And necessary truth is grounded in causation: a predication is necessary if it cannot be falsified by any power, natural or supernatural, without ii annihilating what its terms stand for. “Socrates is a human”, for instance, can only be falsified by annihilating Socrates, and so it is a necessary truth. -/- These considerations provide an ample theoretical basis for a thorough examination of Buridan’s modal logic. This is what the thesis culminates with. In the final chapter, I set forth some novel and surprising findings, chief of which is this: Buridan’s modal syntax and semantics are nothing like Kripke’s—and indeed are incompatible with them. This has significant implications not only for modal logic and metaphysics, but for how we think about medieval logic and philosophy more generally. -/- Throughout the thesis, I advocate a methodology of emphasising the differences, rather than the similarities, between past and present thought. Buridan is wildly unlike what we’re used to, and we should let him speak for himself. (shrink)

At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true (...) that, looking backwards, it was the case that there would be a sea battle? This tension forms, in large part, what might be called the problem of future contingents. A dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition--including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et. al (2001) and MacFarlane (2003, 2014)--have argued that the apparent tension between the intuitions is in fact merely apparent. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions. (shrink)

A solid foundation of modal logic requires a clear conception of the notion of modality. Modern modal logic treats modality as a propositional operator. I shall present an alternative according to which modality applies primarily to illocutionary force, that is, to the force, or mood, of a speech act. By a first step of internalization, modality applied at this level is pushed to the level of speech-act content. By a second step of internalization, we reach a propositional operator (...) validating the modal logic S4. After a brief discussion of problematic modality and possibility, the article concludes with an extension of the account that identifies modality with illocutionary force. Throughout, close attention is paid to the intended interpretation of the formalism. All of the rules stipulated will be justified on the basis of this interpretation. (shrink)

The article deals with some current pioneering formal reconstructions and interpretations of the problem well known in antiquity as The Master Argument. This problem is concerning with enrichment of formal logical systems with modal and temporal notions. The opening topic is devoted to reconstruction of Arthur Prior. while the other here included approach to the problem arc mostly reactions. revisions or additions to this one.

This paper considers two problems—one in philosophy of religion and another in philosophy of physics—and shows that the two problems have one solution. Some Christian philosophers have endorsed the views that (i) there was a first finitely long period of time, (ii) God is in time, and yet (iii) God did not have a beginning. If there was a first finitely long period of time and God is in time then there was a first finitely long period of time in (...) God’s life. But if God’s life includes a first finitely long period of time, then, on one initially intuitive conception of beginning to exist, God began to exist. Thus, at first glance, (i)–(iii) are not mutually compatible. Meanwhile, on a variety of proposals for quantum gravity theories or interpretations of quantum theory, space-time is not fundamental to physical reality and instead can (somehow) be explained in terms of yet more fundamental physical substructures. As I show, there is a strong intuition that if space-time is not fundamental to physical reality, then, even if there were a first finitely long period in the life of physical reality, physical reality would be beginningless. Thus, both theistic philosophers and philosophers of physics have developed theories on which some beginningless entities have a first finitely long temporal period in their lives and so both groups should be interested in developing criteria that distinguish such entities from entities with a beginning. In this paper, I offer one necessary (but not sufficient) condition, namely, that entities that begin to exist are absent from the closest possible worlds without time. The view that I defend has one significant upshot: no sound argument can use the mere fact (if it is a fact) that past time is finite to reach the conclusion that the totality of physical reality had a beginning. (shrink)

We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

In this essay, I consider some logical treatises and commentaries from the first decades of the 12th century (many of which are still unedited) which contain a discussion on modalities and modal logic. After presenting a short catalogue of these sources and a description of their common features, I shall focus on some definitions of the modal term “necessarium” which are provided in them. As we will see, Abelard and logicians of his time advanced three different characterizations of (...) this term: necessity was either defined in terms of unavoidability (ineuitabilitas), or in terms of immutability and omnitemporality (impermutabilitas, sempiternitas), or again in terms of absolute necessity as opposed to conditioned one (necessitas absoluta vs. determinata). I argue that the temporal understanding of necessity in terms of omnitemporality, inherited from ancient sources and extensively used by Abelard and others in the first years of the twelfth-century, started to disappear in texts datable from around the 1120, perhaps due to several difficulties that were related to this definition when applied in logical contexts. I also discuss how the notion of necessitas determinata was used by Abelard’s contemporaries to qualify the modal status of present and past events, which were generally believed to be necessary only in a “weak” and harmless sense that did not prevent them from being contingent. -/- . (shrink)

In the presentation I will analyse Kant’s conception of modalities and consider its relevance to his critical metaphysics. With his Tables of Judgements and of Categories Kant makes an important division between two kinds of modality, of which the former is only logical and the latter transcendental, i.e., objective. Only judgements that are necessary in both ways are properly metaphysical. This distinction is important for Kant’s distinction between Transcendental Analytic and Transcendental Dialectic, i.e., between acceptable and unacceptable metaphysics. I submit (...) that not only is Kant’s theory of modality useful for properly understanding his arguments in the Dialectic, but that only by distinguishing between the two types of modality can one can make sense of his theory that the ideas of reason are simultaneously inevitable and erroneous. This modal analysis thus offers a new and important point of view to Kant’s metaphysics and its critique. (shrink)

We develop an approach to temporal logic that replaces the traditional objective, agent- and event-independent notion of time with a constructive, event-dependent notion of time. We show how to make this event-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render event-dependent time functorial and to construct memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We then develop a condensed formalism that represents (...) memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular constructive functor. (shrink)

This article tries to present a possible way of proliferating bivalent, trivalent, etc. calculation. Beyond the controversies as to the effects that involve the presence versus the absence of the temporal factor, no significant attempts of adapting a bivalent logic to other pairs of values have been mentioned. Should the transformation of the alethiologic modalities into logic values be possible, five more bivalent calculations may be added to the classic bivalent calculation. All these new calculations are compatible with the (...) traditional one, to the extent that they submit to the conditions of non-contradictoriness and exhaustibility, and the connectors receive, even if partially, the corresponding value interpretations. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, (...) undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Logic has sometimes been seen as an alternative to metaphysics and to speculation. In this paper it is argued that a different story should be told when it comes to temporal logic and tense-logic in particular. A. N. Prior’s first formulation of tense logic was mainly established in order to qualify the discussion of certain metaphysical and conceptual problems. Although temporal logic has now been developed in various abstract and rather technical ways, it may still serve as a (...) great help for anyone who wants to clarify the discussion of important existential questions like the nature of time, determinism, future contingency or freedom of choice. (shrink)

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' (...) temporal logic of linear discrete time with gaps follows. (shrink)

Kant's speculative theistic proof rests on a distinction between “logical” and “real” modality that he developed very early in the pre-critical period. The only way to explain facts about real possibility, according to Kant, is to appeal to the properties of a unique, necessary, and “most real” being. Here I reconstruct the proof in its historical context, focusing on the role played by the theory of modality both in motivating the argument (in the pre-critical period) and, ultimately, in undoing it (...) as a source of knowledge of God's existence (in the critical period). Along the way I examine Kant's version of the now-popular “actualist” thesis that facts about what is possible must be explained by facts about what is actual. I conclude by discussing why the critical Kant claims both that there are rational grounds for accepting the conclusion of his theistic proof, and that such acceptance can not count as knowledge. This is important, I argue, because the same considerations ultimately motivate his prohibition on knowledge of things-in-themselves generally. -/- . (shrink)

Kit Fine famously objected against the idea that essence can be successfully analyzed in terms of de re necessity. In response, I want to explore a novel, interesting, but controversial modal account of essence in terms of intrinsicality and grounding. In the first section, I will single out two theoretical requirements that any essentialist theory should meet—the essentialist desideratum and the essentialist challenge—in order to clarify Fine’s objections. In the second section, I will assess Denby’s improved modal account, (...) which appeals to the notion of intrinsicality, and argue that it is untenable. In the third section, I will explain how, when combined with a modal-existential criterion, a hyperintensional account of intrinsicality—in the same vein as Bader (J Philos 110(10): 525–563, 2013) and Rosen (in: Hale and Hoffman (eds) Modality: Metaphysics, logic, and epistemology, Oxford, OUP, 2010)—can help successfully address Fine’s counterexamples. In the fourth section, I will evaluate how this novel analysis of essence stands with respect to sortal, origin, and natural kinds essentialism and discuss potential objections and difficulties. (shrink)

The paper argues against a commitment to metaphysical necessity, semantic modalities are enough. The best approaches to elucidate the semantic modalities are (still) versions of lingustic ersatzism and fictionalism, even if only developed in parts. Within these necessary properties and the difference between natural and semantic laws can be accounted for. The proper background theory for this is an updated version of Logical Empiricism, which is congenial to recent trends in Structural Realism. The anti-metaphysical attitude of Logical Empiricism deserves revitalization. (...) Another target besides metaphysical necessity are substantial forms of iterated modalities, as used, for instance, in the philosophy of religion. (shrink)

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to (...) undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods (...) for modeling the dynamics of conceptual engineering for intensions and hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal and hyperintensional expressivist approaches here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

When embedding data are used to argue against semantic theory A and in favor of semantic theory B, it is important to ask whether A could make sense of those data. It is possible to ask that question on a case-by-case basis. But suppose we could show that A can make sense of all the embedding data which B can possibly make sense of. This would, on the one hand, undermine arguments in favor of B over A on the basis (...) of embedding data. And, provided that the converse does not hold—that is, that A can make sense of strictly more embedding data than B can—it would also show that there is a precise sense in which B is more constrained than A, yielding a pro tanto simplicity-based consideration in favor of B. In this paper I develop tools which allow us to make comparisons of this kind, which I call comparisons of potential expressive power. I motivate the development of these tools by way of exploration of the recent debate about epistemic modals. Prominent theories which have been developed in response to embedding data turn out to be strictly less expressive than the standard relational theory, a fact which necessitates a reorientation in how to think about the choice between these theories. (shrink)

Sorensen (1992) has provided two modal-logical schemas to reconstruct the logical structure of two types of destructive thought experiments: the Necessity Refuter and the Possibility Refuter. The schemas consist of five propositions which Sorensen claims but does not prove to be inconsistent.We show that the five propositions, as presented by Sorensen, are not inconsistent, but by adding a premise (and a logical truth), we prove that the resulting sextet of premises is inconsistent. Häggqvist (2009) has provided a different (...) class='Hi'>modal-logical schema (Counterfactual Refuter), which is equivalent to four premises, again claimed to be inconsistent. We show that this schema also is not inconsistent, for similar reasons. Again, we add another premise to achieve inconsistency. The conclusion is that all three modal-logical reconstructions of the arguments that accompany thought experiments, two by Sorensen and one by Häggqvist, have now been made rigorously correct. This may inaugurate new avenues to respond to destructive thought experiments. (shrink)

Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...) framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...) so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

Dâwûd al-Qarisî (Dâvûd al-Karsî) was a versatile and prolific 18th century Ottoman scholar who studied in İstanbul and Egypt and then taught for long years in various centers of learning like Egypt, Cyprus, Karaman, and İstanbul. He held high esteem for Mehmed Efendi of Birgi (Imâm Birgivî/Birgili, d.1573), out of respect for whom, towards the end of his life, Karsî, like Birgivî, occupied himself with teaching in the town of Birgi, where he died in 1756 and was buried next to (...) Birgivî. Better known for his following works on Arabic language and rhetoric and on the prophetic traditions (hadith): Sharḥu uṣûli’l-ḥadîth li’l-Birgivî; Sharḥu’l-Ḳaṣîdati’n-nûniyya (two commentaries, in Arabic and Turkish); Şarḥu’l-Emsileti’l-mukhtalifa fi’ṣ-ṣarf (two commentaries, in Arabic and Turkish); Sharḥu’l-Binâʾ; Sharḥu’l-ʿAvâmil; and Sharḥu İzhâri’l-asrâr, Karsî has actually composed textbooks in quite different fields. Hence the hundreds of manuscript copies of his works in world libraries. Many of his works were also recurrently printed in the Ottoman period. One of the neglected aspects of Karsî is his identity as a logician. Although he authored ambitious and potent works in the field of logic, this aspect of him has not been subject to modern studies. Even his bibliography has not been established so far (with scattered manuscript copies of his works and incomplete catalogue entries). This article primarily and in a long research based on manuscript copies and bibliographic sources, identifies twelve works on logic that Karsî has authored. We have clarified the works that are frequently mistaken for each other, and, especially, have definitively established his authorship of a voluminous commentary on al-Kâtibî’s al-Shamsiyya, of which commentary a second manuscript copy has been identified and described together with the other copy. Next is handled his most famous work of logic, the Sharhu Îsâghûcî, which constitutes an important and assertive ring in the tradition of commentaries on Îsâghûcî. We describe in detail the nine manuscript copies of this work that have been identified in various libraries. The critical text of Karsî’s Sharhu Îsâghûcî, whose composition was finished on 5 March 1745, has been prepared based on the following four manuscripts: (1) MS Kayseri Raşid Efendi Kütüphanesi, No. 857, ff.1v-3v, dated 1746, that is, only one year after the composition of the work; (2) MS Bursa İnebey Yazma Eser Kütüphanesi, Genel, No.794B, ff.96v-114v, dated 1755; (3) MS Millet Kütüphanesi, Ali Emiri Efendi Arapça, No. 1752, ff.48v-58r, dated 1760; (4) MS Beyazıt Yazma Eser Kütüphanesi, Beyazıt, No. 3129, ff.41v-55v, dated 8 March 1772. While preparing the critical text, we have applied the Center for Islamic Studies (İslam Araştırmaları Merkezi, İSAM)’s method of optional text choice. The critical text is preceded by a content analysis. Karsî is well aware of the preceding tradition of commentary on Îsâghûcî, and has composed his own commentary as a ‘simile’ or alternative to the commentary by Mollâ Fanârî which was famous and current in his own day. Karsî’s statement “the commentary in one day and one night” is a reference to Mollâ Fanârî who had stated that he started writing his commentary in the morning and finished it by the evening. Karsî, who spent long years in the Egyptian scholarly and cultural basin, adopted the religious-sciences-centered ‘instrumentalist’ understanding of logic that was dominant in the Egypt-Maghrib region. Therefore, no matter how famous they were, he criticized those theoretical, long, and detailed works of logic which mingled with philosophy; and defended and favored authoring functional and cogent logic texts that were beneficial, in terms of religious sciences, to the seekers of knowledge and the scholars. Therefore, in a manner not frequently encountered in other texts of its kind, he refers to the writings and views of Muhammad b. Yûsuf al-Sanûsî (d.1490), the great representative of this logical school in the Egyptian-Maghrib region. Where there is divergence between the views of the ‘earlier scholars’ (mutaqaddimûn) like Ibn Sînâ and his followers and the ‘later scholars’ (muta’akhkhirûn), i.e., post-Fakhr al-dîn al-Râzî logicians, Karsî is careful to distance himself from partisanship, preferring sometimes the views of the earliers, other times those of the laters. For instance, on the eight conditions proposed for the realization of contradiction, he finds truth to be with al-Fârâbî, who proposed “unity in the predicative attribution” as the single condition for the realization of contradiction. Similarly, on the subject matter of Logic, he tried to reconcile the mutaqaddimûn’s notion of ‘second intelligibles’ with the muta’akhkhirûn’s notion of ‘apprehensional and declarational knowledge,’ suggesting that not much difference exists between the two, on the grounds that both notions are limited to the aspect of ‘known things that lead to the knowledge of unknown things.’ Karsî asserts that established and commonly used metaphors have, according to the verifying scholars, signification by correspondence (dalâlat al-mutâbaqah), adding also that it should not be ignored that such metaphors may change from society to society and from time to time. Karsî also endorses the earlier scholars’ position concerning the impossibility of quiddity (mâhiyya) being composed of two co-extensive parts, and emphasizes that credit should not be given to later scholars’ position who see it possible. According to the verifying scholars (muhaqqîqûn), it is possible to make definition (hadd) by mentioning only difference (fasl), in which case it becomes an imperfect definition (hadd nâqis). He is of the opinion that the definition of the proposition (qadiyya) in al-Taftâzânî’s Tahdhîb is clearer and more complete: “a proposition is an expression that bears the possibility of being true or false”. He states that in the division of proposition according to quantity what is taken into consideration is the subject (mawdû‘) in categorical propositions, and the temporal aspect of the antecedent (muqaddam) in hypothetical propositions. As for the unquantified, indefinite proposition (qadiyya muhmalah), Karsî assumes that if it is not about the problems of the sciences, then it is virtually/potentially a particular proposition (qadiyya juz’iyyah); but if it is about the problems of the sciences, then it is virtually/potentially a universal proposition (qadiyya kulliyyah). This being the general rule about the ambiguous (muhmal) propositions, he nevertheless contends that, because its subject (mawdû‘) is negated, it is preferable to consider a negative ambiguous (sâliba muhmalah) proposition like “human (insân) is not standing” to be a virtually/potentially universal negative (sâliba kulliyyâh) proposition. He states that a disjunctive hypothetical proposition (shartiyya al-munfasila) that is composed of more than two parts/units is only seemingly so, and that in reality it cannot be composed of more than two units. Syllogism (qiyâs), according to Karsî, is the ultimate purpose (al-maqsad al-aqsâ) and the most valuable subject-matter of the science of Logic. For him, the entire range of topics that are handled before this one are only prolegomena to it. This approach of Karsî clearly reveals how much the ‘demonstration (burhân)-centered’ approach of the founding figures of the Muslim tradition of logic like al-Fârâbî and Ibn Sînâ has changed. al-Abharî, in his Îsâghûjî makes no mention of ‘conversion by contradiction’ (‘aks al-naqîd). Therefore, Karsî, too, in his commentary, does not touch upon the issue. However, in his Îsâghûjî al-jadîd Karsî does handle the conversion by contradiction and its rules. Following the method of Îsâghûjî, in his commentary Karsî shortly touches on the four figures (shakl) of conjuctive syllogism (qiyâs iqtirânî) and their conditions, after which he passes to the first figure (shakl), which is considered ‘the balance of the sciences’ (mi‘yâr al-‘ulûm), explaining the four moods (darb) of it. In his Îsâghûjî al-jadîd, however, Karsî handles all the four figures (shakl) with all their related moods (darb), where he speaks of fife moods (darb) of the fourth figure (shakl). The topic of ‘modal propositions’ (al-muwajjahât) and of ‘modal syllogism’ (al-mukhtalitât), both of which do not take place in the Îsâghûjî, are not mentioned by Karsî as well, either in his commentary on Îsâghûjî or in his Îsâghûjî al-jadîd. Karsî proposes that the certainties (yaqîniyyât), of which demonstration (burhân) is made, have seven, not six, divisions. After mentioning (1) axioms/first principles (awwaliyyât), (2) observata/sensuals (mushâhadât), (3) experta/empiricals (mujarrabât), (4) acumenalia (hadthiyyât), (5) testata (mutawâtirât), and (6) instictives (fitriyyât), that is, all the ‘propositions accompanied by their demonstrations,’ Karsî states that these six divisions, which do not need research and reflection (nazar), are called badîhiyyât (self-evidents), and constitute the foundations (usûl) of certainties (yaqîniyyât). As the seventh division he mentions (7) the nazariyyât (theoreticals), which are known via the badîhiyyât, end up in them, and therefore convey certainty (yaqîn). For Karsî, the nazariyyât/theoreticals, which constitute the seventh division of yaqîniyyât/certainties, are too numerous, and constitute the branches (far‘) of yaqîniyyât. Every time the concept of ‘Mughâlata’ (sophistry) comes forth in the traditional sections on the five arts usually appended to logic works, Karsî often gives examples from what he sees as extreme sûfî sayings, lamenting that these expressions are so widespread and held in esteem. He sometimes criticizes these expressions. However, it is observed that he does not reject tasawwuf in toto, but excludes from his criticism the mystical views and approaches of the truth-abiding (ahl al-haqq), shârî‘â-observant (mutasharri‘) leading sufis who have reached to the highest level of karâmah. (shrink)

Is the flavor of mint reducible to the minty smell, the taste, and the menthol-like coolness on the roof of one’s mouth, or does it include something over and above these—something not properly associated with any one of the contributing senses? More generally, are there features of perceptual experiences—so-called novel features—that are not associated with any of our senses taken singly? This question has received a lot of attention of late. Yet surprisingly little attention has been paid to the question (...) of what it means to say that a feature is associated with a sensory modality in the first place. Indeed, there is only one fully developed proposal in the literature, due to Casey O’Callaghan. I argue that this proposal is too permissive to inform the debate over novel features. I go on to argue that all attempts to formulate a better proposal along these lines fail. The corollary of my arguments is that the question of the existence of novel features is poorly formed. Furthermore, the problem generalizes, with the result that we should not rely on our pre-theoretical notions of the senses as the basis of theorizing about the features of perceptual experiences. (shrink)