The aim of this paper is to provide a dynamic interpretation of Kant’s logical hylomorphism. Firstly, various types of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate Kant’s constitutivity thesis about logic. Finally, I focus on the design of logical norms as specific kinds of artefacts.

We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on (...) which the purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs. (shrink)

This book presents a philosophical conception of logic -- "logical expressivism"-- according to which the role of logic is to make explicit reason relations, which are often neither monotonic nor transitive. It reveals new perspectives on inferential roles, sequent calculi, representation, truthmakers, and many extant logical theories.

A lean hylomorphism stands as a metaphysical holy grail. An embarrassing feature of traditional hylomorphic ontologies is prime matter. Prime matter is both so basic that it cannot be examined (in principle) and its engagement with the other hylomorphic elements is far from clear. One particular problem posed by prime matter is how it is to be understood both as a principle of individuation for material substances and as pure potency. I present Thomas Aquinas’s way of squeezing some intelligibility (...) out of prime matter by modeling it on the idea of logical genus. Such a modeling provides insight into understanding prime matter as substratum, as maximally indeterminate, and as ontologically vague. One of the unusual but exciting things that fall out from this analysis of prime matter is the Entirety Thesis: “For any substance x, if x has prime matter then the prime matter of x is the same* as x,” where ‘same*’ is understood as “indeterminately identical.”. (shrink)

This article offers a novel solution to the problem of material constitution: by including non-concrete objects among the parts of material objects, we can avoid having a statue and its constituent piece of clay composed of all the same proper parts. Non-concrete objects—objects that aren’t concrete, but possibly are—have been used in defense of the claim that everything necessarily exists. But the account offered shows that non-concreta are independently useful in other domains as well. The resulting view falls under a (...) ‘nonmaterial partist’ class of views that includes, in particular, Laurie Paul’s and Kathrin Koslicki’s constitution views; ones where material objects have properties or structures as parts respectively. The article gives reasons for preferring the non-concretist solution over these other non-material partist views and defends it against objections. (shrink)

This essay by Nishida Kitarō from 1927, translated into English here for the first time, is from the initial period of what has come to be called “Nishida philosophy” (Nishida tetsugaku), when Nishida was first developing his conception of “place” (basho). Nishida here inquires into the relationship between logic and consciousness in terms of place and implacement in order to overcome the shortcomings of previous philosophical attempts—from the ancient Greeks to the moderns—to dualistically conceive the relationship between being and knowing (...) in terms of subject-object or form-matter. During the course of articulating his novel approach to consciousness and cognition, Nishida discusses what he takes to be the weaknesses of Greek hylomorphism, Kantian (and neo-Kantian) dualism, and Husserlian phenomenology. Dissatisfied with the attribution of mere passivity to placiality, and turning away from consciousness objectified as a subject of statement, Nishida imparts to consciousness qua place a certain logical independence as an active yet un-objectifiable “predicate.” This investigation of consciousness as the unobjectifiable place for objectification leads Nishida to the notion of what precedes consciousness itself, a “place of nothing” (mu no basho) that envelops the dichotomized structures of subject-predicate, being-nothing, subject-object, universal-particular, et cetera. (shrink)

Hylomorphists hold that substances are, in some sense, composites of matter and form. The form of a substance is typically taken to play a fundamental role in determining the unity or identity of the whole. Staunch hylomorphists think that this role is of a kind that precludes the ontological reduction of form to the physical and thus take their position to be inconsistent with physicalism. Forms, according to staunch hylomorphism, play a fundamental role in grounding their bearers’ proper parts (...) and that, it seems, rules out the physical grounding of form itself. I shall develop a physicalist version of hylomorphism that treats form as geometric structure and which, I shall argue, entails many of the central theses endorsed by staunch hylomorphists. Based on Shoemaker’s notion of conditional powers, I shall argue that the geometric structures of complex wholes are the conditions on at least some of the conditional powers of their bearers’ proper parts, transforming those powers into powers simpliciter. Thus, forms play a fundamental role in the dynamical evolution of the physical world, but without bestowing causal powers themselves and hence without violating the causal closure of the physical domain. If a substance’s proper parts are taken to be individuated by their powers simpliciter, then they derive their identities from their places in the substantial whole, which thus determines the identities of its proper parts without changing their intrinsic natures. (shrink)

Hylomorphism is the Aristotelian theory according to which objects are composites of form and matter. Form is what unifies the various parts of an object – the matter – into a cohesive whole. Some contemporary hylomorphists argue their theory applies beyond the realm of concreta, and that it explains the unity of various abstract entities. Not everyone agrees. Recent criticism alleges that hylomorphism fails to explain the unity of certain abstract entities, namely, complex properties – properties with other (...) properties as proper parts. Here, I both respond to this criticism and show that and how hylomorphism extends to the domain of complex properties. By discussing hylomorphism’s applicability to the hitherto unchartered domain of complex properties, I hope to defend its credentials as a general mereological theory. (shrink)

The hard problem of consciousness has held center stage in the philosophy of mind for the past two decades. It claims that the phenomenal character of conscious experiences—what it’s like to be in them—cannot be explained by appeal to the operation of physiological subsystems. The hard problem arises, however, only given the assumption that hylomorphism is false. Hylomorphism claims that structure is a basic ontological and explanatory principle. A human is not a random collection of physical materials, but (...) an individual composed of physical materials with a structure that accounts for what it is and what it can do—the powers it has. What is true of humans is true of their activities as well. The latter are not random physiological changes, but structured ones: we engage in them by coordinating the ways our parts manifest their powers. Structured activities include perceptual experiences. Consequently, everything about a perceptual experience, including its phenomenal character, can be explained by describing the perceiver’s perceptual subsystems, the powers of those subsystems, and the coordination that unifies their activities into the activity of the perceiver as a whole. Conscious experiences thus fit unproblematically into the natural world—just as unproblematically as the phenomenon of life. Even exponents of the hard problem of consciousness agree that there is no hard problem of life. Consequently, if hylomorphism is true, there can be no hard problem of consciousness. To insist that there is such a problem, then, is implicitly to reject hylomorphism. The concept of consciousness that motivates the hard problem is as much a theoretical construct, therefore, as the concept of life that motivates an obstinate vitalist. (shrink)

Hylomorphism provides an attractive framework for addressing issues in philosophical anthropology. After describing a hylomorphic theory that dovetails with current work in philosophy of mind and in scientific disciplines such as biology and neuroscience, I discuss how this theory meshes with Christian eschatology, the doctrine of resurrection in particular.

Mereonominalism, holonominalism, and part-whole realism represent competing views on the metaphysics of parts and wholes. Mereonominalism claims that what parts exist is a function of the concepts we use in describing composite wholes. Holonominalism claims that what composite wholes exist is a function of the concepts we use in describing things that can qualify as parts. Part-whole realism claims that parts and wholes exist independent of our concepts. I argue that all three views face problems, but that the problem facing (...) part-whole realism can be solved by adopting a version of hylomorphism that takes its cue from Aristotle’s account of form. (shrink)

William Whewell’s 19th century philosophy of science is sometimes glossed over as a footnote to Kant. There is however a key feature of Whewell’s account worth noting. This is his appeal to Aristotle’s form/matter hylomorphism as a metaphor to explain how mind and world merge in successful scientific inquiry. Whewell’s hylomorphism suggests a middle way between rationalism and empiricism reminiscent of experience pragmatists like Steven Levine’s view that mind and world are entwined in experience. I argue however that (...) Levine does not adequately explain exactly how mind and world entwine. He could nonetheless do so if he appealed to Whewell’s hylomorphic metaphor. We may prefer a reductive metaphysical explanation, but I suggest that pragmatists only have recourse to metaphor in this case. Both reductive and metaphorical explanations can enjoy great explanatory power if they exhibit a suitable measure of what I will call sematic distance. Semantic distance measures how close or how far apart explanandum and explanans are from each other in meaning. Metaphorical explanation - as evident in Whewell’s hylomorphism and as detailed via the notion of semantic distance - presents a valuable new explanatory tool to those who hold that mind and world are entwined sans recourse to metaphysics. (shrink)

Although contemporary metaphysics has recently undergone a neo-Aristotelian revival wherein dispositions, or capacities are now commonplace in empirically grounded ontologies, being routinely utilised in theories of causality and modality, a central Aristotelian concept has yet to be given serious attention – the doctrine of hylomorphism. The reason for this is clear: while the Aristotelian ontological distinction between actuality and potentiality has proven to be a fruitful conceptual framework with which to model the operation of the natural world, the distinction (...) between form and matter has yet to similarly earn its keep. In this chapter, I offer a first step toward showing that the hylomorphic framework is up to that task. To do so, I return to the birthplace of that doctrine - the biological realm. Utilising recent advances in developmental biology, I argue that the hylomorphic framework is an empirically adequate and conceptually rich explanatory schema with which to model the nature of organisms. (shrink)

This paper investigates Péter Pázmány’s theory of mixtures from his exegesis of Meteorologica IV, in the context of sixteenth-century scholarship on Aristotle’s Meteorologica. It aims to contribute to a discussion of Anneliese Maier’s thesis concerning the incompatibility between hylomorphism and the theory of elements in the Aristotelian tradition. It presents two problems: the placement of Meteorologica IV in the Jesuit cursus on physics and the conceptualization of putrefaction as a type of substantial mutation. Through an analysis of these issues, (...) it shows how sixteenth-century exegesis imposes the hylomorphic thesis onto the subject matter of meteorology and how the hylomorphic theory of substantial change can be adapted in order to accommodate the theory of elements. The case being made is that Meteorologica is a privileged place where hylomorphism and the theory of elements meet and that the late Aristotelian theory of mixtures sought to accommodate both theories of material substance. (shrink)

Aquinas’s Fifth Way is usually taken to be an adumbration of Paley-like design arguments. Paley-like design arguments have fallen on hard times over the past few centuries, and most contemporary defenders of design arguments in support of theism favor some version of the fine-tuning argument. But fine-tuning designarguments, like Paley’s design argument, are consistent with atomism. And all such arguments are vulnerable to the objection that, given a long enough stretch of time and a sufficient number of universes, there would (...) be no need to posit a designer. In this paper we argue that a deep understanding of Aquinas’s Fifth Way depends upon understanding his hylomorphic account of the nature of composite substance, an account that is inconsistent with atomism. We argue that if one grants hylomorphism, Aquinas’s Fifth Way is difficult to resist. And we defend Aquinas’s hylomorphism against several common objections. (shrink)

Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only (...) those epistemic scenarios which are not obviously impossible. Whether something is obvious is not always a determinate matter and so the resulting picture is of an epistemic space with fuzzy boundaries. (shrink)

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in a (...) dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. (shrink)

Hylomorphism is a metaphysical theory that accounts for the unity of the material parts of composite objects by appeal to a structure or ‘form’ characterizing those parts. I argue that hylomorphism is not merely a plausible or appealing solution to problems of material composition, but a position entailed by any coherent metaphysics of ordinary material objects. In fact, not only does hylomorphism have Aristotelian defenders, but it has had independent lives in both East and West. -/- I (...) review three contemporary hylomorphic theories appeal to ‘structure’ to explain the unity of material objects. Each, however, accepts a controversial principle: that substances can have other substances as proper parts. Such a principle is implausible and severely threatens the coherence of the theory. -/- I begin by showing that Thomas Aquinas’ account of form, which does not accept that substances can have other substances as parts, gives us a more coherent version of hylomorphism. Then I argue Zhu Xi, a Song dynasty Confucian thinker, developed a non-Aristotelian hylomorphism. Unlike Aristotelians, Zhu Xi’s metaphysics was formed in opposition to Buddhist versions of skepticism and gives us reasons to think that anyone who holds a view of objects stronger than Buddhists is committed to forms. In conclusion, I show directly, by appeal to some of those same considerations from Zhu Xi, why it is that all those who believe there are unified material objects will appeal to something like a substantial form. The traditional hylomorphic picture of material composition, then, remains a plausible framework for contemporary metaphysicians – and for good reason. (shrink)

Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of (...) reality. For naturalists of all stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back. (shrink)

Each thing is fundamental. Not only is no thing any more or less real than any other, but no thing is prior to another in any robust ontological sense. Thus, no thing can explain the very existence of another, nor account for how another is what it is. I reach this surprising conclusion by undermining two important positions in contemporary metaphysics: hylomorphism and hierarchical views employing so-called building relations, such as grounding. The paper has three main parts. First, I (...) observe hylomorphism is alleged by its proponents to solve various philosophical problems. However, I demonstrate, in light of a compelling account of explanation, that these problems are actually demands to explain what cannot be but inexplicable. Second, I show how my argument against hylomorphism illuminates an account of the essence of a thing, thereby providing insight into what it is to exist. This indicates what a thing, in the most general sense, must be and a correlative account of the structure in reality. Third, I argue that this account of structure is incompatible not only with hylomorphism, but also with any hierarchical view of reality. Although hylomorphism and the latter views are quite different, representing distinct philosophical traditions, I maintain they share untenable accounts of structure and fundamentality and so should be rejected on the same grounds. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...) connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators. (shrink)

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...) logic. Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest. (shrink)

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the invariance (...) criterion is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force. (shrink)

In this paper, I offer a novel analysis of logical arguments from evil. I claim that logical arguments from evil have three parts: (1) characterisation (attribution of specified attributes to God); (2) datum (a claim about evil); and (3) link (connection between attributes and evil). I argue that, while familiar logical arguments from evil are known to be unsuccessful, it remains an open question whether there are successful logical arguments from evil.

The purpose of this paper is to explore the question of how truthmaker theorists ought to think about their subject in relation to logic. Regarding logic and truthmaking, I defend the view that considerations drawn from advances in modal logic have little bearing on the legitimacy of truthmaker theory. To do so, I respond to objections Timothy Williamson has lodged against truthmaker theory. As for the logic of truthmaking, I show how the project of understanding the logical features of (...) the truthmaking relation has led to an apparent impasse. I offer a new perspective on the logic of truthmaking that both explains the problem and offers a way out. (shrink)

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also by (...) their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals. (shrink)

The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of (...) S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)

Identity-Over-Time has been a favorite subject in the literature concerning Thomas Aquinas. Aquinas addresses this issue in many discussions, including especially the identity of material things and artifacts, the identity of the human soul after the corruption of body, the identity of the body of Christ in the three days from his death to his resurrection and the identity of the resurrected human body at the end of time. All these discussions have a point in common: they lead Aquinas to (...) raise the question of Identity-Over-Time with respect to things that fully exist in act, i.e., things that possess an identity of their own and change some of their parts or properties over time while continuing to be what they are. In this article, I investigate this topic from a different angle, considering the case of the trans-temporal identity of things that do not yet have an identity of their own or fully exist in act. The case at stake is that of the identity of the human embryo through the process of human generation. It is a puzzle that Aquinas seems to have some difficulties to solving, given his account of human embryogenesis as a process that alternates generations and corruptions of the subject. At the same time, though, Aquinas does not want to renounce the idea that the subject of generation must be numerically one and the same throughout all the process. In order to solve this puzzle, Aquinas seems to suggest distinguishing the identity of the subject from the identity of its matter and/or form. At given conditions, a thing can even change its matter and form while continuing to be the same thing in number. Specifically, the numerical identity of the subject of generation is justified by the identity entailed by the metaphysical notions of potency and act. (shrink)

Imagine a sculptor who molds a lump of clay to create a statue. Hylomorphism claims that the statue and the lump of clay are two different colocated objects that have different forms, even though they share the same matter. Recently, there has been some discussion on the requirements of consistency for hylomorphist theories. In this paper, we focus on an argument presented by Maegan Fairchild, according to which a minimal version of hylomorphism is inconsistent. We argue that the (...) argument is unsound or, at best, it just points to a well-known problem for hylmorphist theories. Additionally, we explore some general consequences of this fact. (shrink)

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, (...) logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

This paper aims at developing a logical theory of perspectival epistemic attitudes. After presenting a standard framework for modeling acceptance, where the epistemic space of an agent coincides with a unique epistemic cell, more complex systems are introduced, which are characterized by the existence of many connected epistemic cells, and different possible attitudes towards a proposition, both positive and negative, are discussed. In doing that, we also propose some interesting ways in which the systems can be interpreted on well (...) known epistemological standpoints. (shrink)

Donald Davidson contributed to the discussion of logical form in two ways. On the one hand, he made several influential suggestions on how to give the logical forms of certain constructions of natural language. His account of adverbial modification and so called action-sentences is nowadays, in some form or other, widely employed in linguistics (Harman (forthcoming) calls it "the standard view"). Davidson's approaches to indirect discourse and quotation, while not as influential, also still attract attention today. On the (...) other hand, Davidson provided a general account of what logical form is. This paper is concerned with this general account. Its foremost aim is to give a faithful and detailed picture of what, according to Davidson, it means to give the logical form of a sentence. The structure of the paper is as follows. (1) I will first informally introduce a notion of logical form as the form that matters in certain kinds of entailments, and indicate why philosophers have taken an interest in such a notion. (2) The second section develops constraints that we should arguably abide by in giving an account of logical form. (3) I then turn to Davidson’s view of what is involved in giving such an account. To this end, I will try to reconstruct Davidson’s view of the connection between an assignment of logical forms, a truth theory and a meaning theory. (4) Finally, I will briefly discuss possible problems of Davidson’s account as developed in this paper. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

Overview of fundamental work in deontic logic.

Many philosophers take purportedly logical cases of ground ) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of (...) ground even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents (...) that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

This chapter intervenes in recent debates in Kant scholarship about the possibility of a general logical alien. Such an alien is a thinker whose laws of thinking violate ours. She is third-personal as she is radically unlike us. Proponents of the constitutive reading of Kant’s conception of general logic accordingly suggest that Kant rules out the possibility of such an alien as unthinkable. I add to this an often-overlooked element in Kant’s thinking: there is reason to think that he (...) grants—and in fact presupposes—the possibility of a transcendental logical alien. Such an alien is a knower whose laws of experience purport to violate ours. She is first-personal as she is radically like us. In other words, she is us, insofar as we are alienated from ourselves and our experience. I go on to draw an analogy between her, a dogmatist, and another transcendental alien, an evil agent. Just as a dogmatist is alienated from her (our) experiential laws, an evil agent is alienated from her (our) moral law. These forms of theoretical and practical self-conceit require self-knowledge in the form of a critique of speculative or practical reason. In bringing this point out, I aim to shift from the question of whether logical laws constitute our thinking to the question of whether grasping our experiential and moral laws as our laws constitutes our reason. (shrink)

This paper introduces a novel strategy for responding to skeptical arguments based on the epistemic possibility of error or lack of certainty. I show that a nonclassical logic motivated by recent work on epistemic modals can be used to render such skeptical arguments invalid. That is, one can grant that knowledge is incompatible with the possibility of error and grant that error is possible, all while avoiding the skeptic’s conclusion that we lack knowledge.

I address a type of circularity threat that arises for the view that we employ general basic logical principles in deductive reasoning. This type of threat has been used to argue that whatever knowing such principles is, it cannot be a fully cognitive or propositional state, otherwise deductive reasoning would not be possible. I look at two versions of the circularity threat and answer them in a way that both challenges the view that we need to apply general (...) class='Hi'>logical principles in deductive reasoning and defuses the threat to a cognitivist account of knowing basic logical principles. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages (...) containing the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

Logical positivism is often characterized as a set of naive doctrines on meaning, method, and metaphysics. In recent decades, however, historians have dismissed this view as a gross misinterpretation. This new scholarship raises a number of questions. When did the standard reading emerge? Why did it become so popular? And how could commentators have been so wrong? This essay reconstructs the history of a “caricature” and rejects the hypothesis that it was developed by ill-informed Anglophone scholars who failed to (...) appreciate the subtleties of European scientific philosophy. It argues that the received view has a more complicated history and was frequently promoted by the European positivists themselves. The essay shows that the view has roots in both American and European scientific philosophy and emerged as a result of the complex interplay between the two communities in the years before the intellectual migration. (shrink)

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: an intension, taking care of truth conditions; and a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the (...) logic of knowledge per se for arbitrary agents, and isolate three explanatory factors for them: the topic-sensitivity of content; the fragmentation of knowledge states; the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. (shrink)

Logical reasoning is not only a component of religious faith (cf., for instance, the "Golden rule"), but, in addition, the religious faith itself can be conceived as a logical pragmatic function applied to sentences and their meanings. Pragmatic role of religious faith is shown on the examples of the analogy of seed and spoken word (e.g., Mt 13:3-23) and on the degrees of faith described in the episode about Nicodemus (John 3). Pragmatics adds (different grades of) perseverance to (...) the correctness of reasoning and to the truth-preservation of the consequence relation. Correspondingly, religious faith is described by formally defined model and satisfaction relation, which are applied to and examined on the text of John 3. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence (...) according to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any (...) given time; an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)