For more than fifty years, taxonomists have proposed numerous alternative definitions of species while they searched for a unique, comprehensive, and persuasive definition. This monograph shows that these efforts have been unnecessary, and indeed have provably been a pursuit of a will o’ the wisp because they have failed to recognize the theoretical impossibility of what they seek to accomplish. A clear and rigorous understanding of the logic underlying species definition leads both to a recognition of the (...) inescapable ambiguity that affects the definition of species, and to a framework-relative approach to species definition that is logically compelling, i.e., cannot not be accepted without inconsistency. An appendix reflects upon the conclusions reached, applying them in an intellectually whimsical taxonomic thought experiment that conjectures the possibility of an emerging new human species. (shrink)

Traditionally, species have been treated as classes. In fact they may be considered individuals. The logical term “individual” has been confused with a biological synonym for “organism.” If species are individuals, then: 1) their names are proper, 2) there cannot be instances of them, 3) they do not have defining properties, 4) their constituent organisms are parts, not members. “ Species " may be defined as the most extensive units in the natural economy such that reproductive competition (...) occurs among their parts. Species are to evolutionary theory as firms are to economic theory: this analogy resolves many issues, such as the problems of “reality” and the ontological status of nomenclatorial types. (shrink)

We argue that the logical outcome of the cladistics revolution in biological systematics, and the move towards rankless phylogenetic classification of nested monophyletic groups as formalized in the PhyloCode, is to eliminate the species rank along with all the others and simply name clades. We propose that the lowest level of formally named clade be the SNaRC, the Smallest Named and Registered Clade. The SNaRC is an epistemic level in the classification, not an ontic one. Naming stops at that (...) level because there is no currently acceptable evidence for clades within it, not because no smaller clades exist. Later, included clades may be named. They would then become the SNaRCs, while the original SNaRC would keep its original name. We argue that all theoretical tasks of biology, in evolution and ecology, as well as practical tasks such as conservation assessment, are better approached using this rankless phylogenetic approach. (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)

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)

The so-called ‘‘species problem’’ has plagued evolution- ary biology since before Darwin’s publication of the aptly titled Origin of Species. Many biologists think the problem is just a matter of semantics; others complain that it will not be solved until we have more empirical data. Yet, we don’t seem to be able to escape discussing it and teaching seminars about it. In this paper, I briefly examine the main themes of the biological and philosophical liter- atures (...) on the species problem, focusing on identifying common threads as well as relevant differences. I then argue two fundamental points. First, the species problem is not primarily an empirical one, but it is rather fraught with philosophical questions that require—but cannot be settled by—empirical evidence. Second, the (dis-)solution lies in explicitly adopting Wittgenstein’s idea of ‘‘family resemblance’’ or cluster concepts, and to consider spe- cies as an example of such concepts. This solution has several attractive features, including bringing together apparently diverging themes of discussion among bio- logists and philosophers. The current proposal is con- ceptually independent (though not incompatible) with the pluralist approach to the species problem advocated by Mishler, Donoghue, Kitcher and Dupre ́, which implies that distinct aspects of the species question need to be emphasized depending on the goals of the researcher. From the biological literature, the concept of species that most closely matches the philosophical discussion pre- sented here is Templeton’s cohesion idea. (shrink)

In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and (...) relations, but if, for example, PM’s disjunction (∨) is a relation, what is it a relation between? There is no obvious answer to this given Russell’s other philosophical commitments at this time, although hints are left in some of the pre-PM manuscripts. In this paper, I explore this tension in Russell's philosophy and relate it to developments both before and after Problems. (shrink)

Book review of Richard A. Richards' The Species Problem: A Philosophical Analysis.

The longstanding species problem in biology has a history that suggests a solution, and that history is not the received history found in many texts written by biologists or philosophers. The notion of species as the division into subordinate groups of any generic predicate was the staple of logic from Aristotle through the middle ages until quite recently. However, the biological species concept during the same period was at first subtly and then overtly different. Unlike (...) the logic sense, which relied on definitions of the essence of both genus and species, biological species from the time of Epicurus were consistently considered to involve a reproductive element: in short, living species relied not on essential definitions, but on the generative cause, which might not be definable. I term this the generative conception of species: species were the generation by reproduction of form. This undercuts the claim that species before Darwin were essentialist, and divorces the notion of a type from that of essence. In fact, as late as the end of the nineteenth century, logicians explicitly treated biological “species” as a homonym only of logical essentialist species, and permitted considerable deviation from the type or form. At every point, species in logic were thought to be a subset, in effect, of some more general notion. I sketch a history of both philosophical and biological traditions of the species concept, before turning to the current conceptions. These are reconsidered in the light of this history, and in particular Mayr’s changing views are shown to be somewhat Whiggish, historiographically. Of the many touted biological species concepts, only one of which (Mayr’s) is called _the_ Biological Species Concept, none appears to capture all the relevant facts, intuitions, and operational requirements of biology. Cladistic conceptions, however, have much in common with the older philosophical literature, in that the natural group of cladism is the clade, or monophyletic group. After considering the Individuality Thesis, and the metaphysics of species, we see that species are the most particular terminal taxa in a clade, and that they are “defined” in terms of the particular synapomorphies, or evolved characters, that are causally responsible for keeping the lineages that organisms form distinct from one another. In this way, we can remain within the generative conception of species that has been in play for over two millennia, and yet avoid the pitfalls of prior attempts to find a universal conception of species. (shrink)

Can Wittgenstein's famous family resemblance concept be applied to resolve the problem of defining species in biology?

The tripartite account of propositional, fallibilist knowledge that p as justified true belief can become adequate only if it can solve the Gettier Problem. However, the latter can be solved only if the problem of a successful coordination of the resources (at least truth and justification) necessary and sufficient to deliver propositional, fallibilist knowledge that p can be solved. In this paper, the coordination problem is proved to be insolvable by showing that it is equivalent to the (...) ''''coordinated attack'''' problem, which is demonstrably insolvable in epistemic logic. It follows that the tripartite account is not merely inadequate as it stands, as proved by Gettier-type counterexamples, but demonstrably irreparable in principle, so that efforts to improve it can never succeed. (shrink)

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch (...) a decomposition result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

The species problem is often described as the abundance of conflicting definitions of _species_, such as the biological species concept and phylogenetic species concepts. But biologists understand the notion of species in a non-definitional as well as a definitional way. In this article I argue that when they understand _species_ without a definition in their mind, their understanding is often mediated by the notion of _good species_, or prototypical species, as the idea of ``prototype'' (...) is explicated in cognitive psychology. This distinction helps us make sense of several puzzling phenomena regarding biologists' dealing with species, such as the fact that in everyday research biologists often behave as if the species problem is solved, while they should be fully aware that it is not. I also briefly discuss implications of this finding, including that some extant attempts to answer what the nature of species is have an inadequate assumption about how the notion of species is represented in biologists' minds. (shrink)

The precondition of any feminist politics – a usable category of ‘woman’ – has proved to be difficult to construct, even proposed to be impossible, given the ‘problem of exclusion’. This is the inevitable exclusion of at least some women, as their lives or experiences do not fit into the necessary and sufficient condition(s) that denotes group membership. In this paper, I propose that the problem of exclusion arises not because of inappropriate category membership criteria, but because of (...) the presumption that categories can only be organised by identity relations or shared properties among their members. This criterion of sameness as well as the characterisation of this exclusion as essentialism attests to a metaphysics that is not conducive to resistance and liberatory projects. Following a strain of hybrid thinking in feminist and post-colonial theory, I outline an alternative pluralist logic that confronts oppressive binaries that impede theory work in gender, sexuality, and race theory, and limit political action and resistance. The problem of exclusion is neither irresolvable nor is it essentialism. Instead it is a denial of subjectivity due to pseudodualistic self/Other dichotomies that can be resisted by adopting a new categorial logic. While this paper focuses on the specific problem of formulating a category of ‘woman’, it has implications for other areas of gender, critical race, and postcolonial theory. Rather than working toward an inclusive category founded on sameness, theorists need to develop independent and positive categories grounded in difference. Our current categorial logic does not permit such a project, and therefore a new metaphysics must be adopted. (shrink)

This paper isolates a hard, long-standing species problem: developing a comprehensive and exacting theory about the constitutive conditions of the species category, one that is accurate for most of the living world, and which vindicates the widespread view that the species category is of more theoretical import than categories such as genus, sub-species, paradivision, and stirp. The paper then uncovers flaws in several views that imply we have either already solved that hard species (...) class='Hi'>problem or dissolved it altogether – so-called We Are Done views. In doing so the paper offers new criticisms of the general lineage species concept (GLSC), evolutionary species concept (EvSC), biological species concept (BSC), other similar concepts, Ereshefsky’s eliminative pluralism about the species category, and both Mishler’s pessimism and Wilkins’ phenomenalism about that category. Opposed to We Are Done views, the paper argues for a Revving Up view, on which we are nearly ready to begin the hard species problem in earnest. To help work towards these conclusions, the paper begins with an outline of a new kind of view of species (Barker 2019a), which proposes they are feedback systems of a mathematically specifiable and empirically testable sort. (shrink)

In this article I present some characteristics of logics and semantics of an uncertain world. I confront two-valued and fuzzy logic. I use Kafka’s novel Process as an example, which is designed as an uncertain context with words which are rigid designators without rigid meaning. That produces an uncertain world of logical and semantical relations. In presentation of problems I introduce basic concepts of Frege’s, Wittgenstein’s, Tarsky’s, Searle’s, Quine’s and Davidson’s philosophy of language. I differ the logical and semantical (...) identification of identity. I differ reference and inference, or representation and identification as two components which are fundamental for the identification of identity. I found this difference on the role of logical unification and granulation of predicates in the structure of thought and semantical unification and granulation of attributes in the structure of statements and their relation to ontology of context. Through the confrontation of the logical and semantical unification and granulation I find that the limits of logic are not also the limits of language. The semantical unification goes over the highest genre and below the lowest species. That enables the extra-logical, non-scientifical, con-fessional, pro-phetical, artistic, and ordinary use of language. (shrink)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the (...) standard meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

This book was completed by the early 1960s and published in 1984 but it has not lost its topicality, for it contains an important re-assessment of the relations of two main streams of contemporary philosophy - the Analytical and the Dialectic. Adherents and critics of these traditions tend to assurnethat they are diametrically opposed, that their roots, concerns and approaches contradict each other, and that no reconciliation is possible. In contradistinction Russell derives both traditions from the common root of the (...) dissatisfaction with the arguments against speculative philosophy. These according to the author leave a lacuna - certain elementsof our Weltanschaaung have been removed, but they cannot be removed without replacement lest we have an incomplete world view, so incomplete in fact that it cannot be viable. According to Russell part of this vacuum is taken up by the analytical tradition but this tradition is not capable of taking up the remainder of it. That portion of the vacant space is however taken up by the dialectical tradi tion, which in turn cannot itself handle the whole of the problem. Thus the two reactions to the demise of speculative philosophy appear to be complementary in at least this sense. But the author goes further, for according to hirn the analytical arguments themselves clearly point to the emergence of dialectical problems, and the dialectical problems themselves need some such background to arise. (shrink)

The main goal of this paper is to investigate what explanatory resources Robert Brandom’s distinction between acknowledged and consequential commitments affords in relation to the problem of logical omniscience. With this distinction the importance of the doxastic perspective under consideration for the relationship between logic and norms of reasoning is emphasized, and it becomes possible to handle a number of problematic cases discussed in the literature without thereby incurring a commitment to revisionism about logic. One such case (...) in particular is the preface paradox, which will receive an extensive treatment. As we shall see, the problem of logical omniscience not only arises within theories based on deductive logic; but also within the recent paradigm shift in psychology of reasoning. So dealing with this problem is important not only for philosophical purposes but also from a psychological perspective. (shrink)

Anti-exceptionalism about logic takes logic to be, as the name suggests, unexceptional. Rather, in naturalist fashion, the anti-exceptionalist takes logic to be continuous with science, and considers logical theories to be adoptable and revisable accordingly. On the other hand, the Adoption Problem aims to show that there is something special about logic that sets it apart from scientific theories, such that it cannot be adopted in the way the anti-exceptionalist proposes. In this paper I assess (...) the damage the Adoption Problem causes for anti-exceptionalism, and show that it is also problematic for exceptionalist positions too. My diagnosis of why the Adoption Problem affects both positions is that the self-governance of basic logical rules of inference prevents them from being adoptable, regardless of whether logic is exceptional or not. (shrink)

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological (...) models of knowledge and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

This article aims to introduce a new solution to the Logical Problem of the Trinity. This solution is provided by utilising a number of theses within the field of contemporary metaphysics in order to establish a conceptual basis for a novel account and model of the doctrine of the Trinity termed Monarchical Aspectivalism, which will provide the means for proposing an alternative reading of the Athanasian Creed that is free from any consistency problems.

Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models (...) of knowledge and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB- logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. Keywords. Stalnaker’s logic KB of knowledge and belief; Topological epistemology; Epistemic Invisibility; Doxastic invisibility; Gettier cases; . (shrink)

The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. -/- Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. I (...) argue that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. -/- I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.”. (shrink)

My aim in this paper is to explore how we might understand the relation of Deleuze’s early works to ethics, and to develop the connections between this way of understanding Deleuze and the work of Søren Kierkegaard. I will claim that we can view both figures as arguing that the sense or meaning we take from the world, and the metaphysical structure we ascribe to it, is secondary to an ethical stance we take in the face of a world of (...) becoming. As such, the central preoccupation of both Kierkegaard and Deleuze is how we make sense of an existence which is necessarily temporal. As we shall see, recognizing the importance of temporality involves a move away from the traditional resolution of the problem of sense that operates by making temporality an accidental aspect of a world. In the first half of this paper, I want to explore this claim in relation to Deleuze’s reading of Plato, tying his claim that Plato is essentially developing an ethical rather than metaphysical doctrine with the claim that “the task of modern philosophy has been defined: to overturn [renversement] Platonism” (DR 59). My emphasis in this section is how Deleuze, rather than “overturning” Platonism by simply rejecting the priority it gives to Forms or essences over appearances, the renversement of Deleuze’s reading inverts the relation to show how the search for essence is in fact grounded in an ethical decision, or “selection,” in the world of appearances/simulacra itself. As such, both Plato and Deleuze can be seen as presenting different trajectories for making sense of a world of becoming, either by grounding it in a transcendent, atemporal realm, or by seeing it as an intensive field of processes. In the second half, I will argue that Kierkegaard’s philosophy rests on a claim, similar to the one we find in Deleuze’s work, that we need to develop a logic of sense in response to a world of becoming. I will conclude that Deleuze’s reading of Kierkegaard is limited by a focus on the theological aspects of his thought, and that Kierkegaard provides a sophisticated and complementary taxonomy of the ways in which we try to make sense of our existence in a world of becoming by developing diverse ethical postures. (shrink)

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)

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After (...) having shown that IL can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also (...) presented important programmatic remarks on the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

Work in philosophy of mind often engages in descriptive phenomenology, i.e., in attempts to characterize the phenomenal character of our experience. Nagel’s famous discussion of what it’s like to be a bat demonstrates the difficulty of this enterprise (1974). But while Nagel located the difficulty in our absence of an objective vocabulary for describing experience, I argue that the problem runs deeper than that: we also lack an adequate subjective vocabulary for describing phenomenology. We struggle to describe our own (...) phenomenal states in terms we ourselves find adequately expressive. This paper aims to flesh out why our phenomenological vocabulary is so impoverished – what I call the impoverishment problem. As I suggest, this problem has both practical and philosophical import. After fleshing out the problem in more detail, I draw some suggestive morals from the discussion in an effort to point the way forward towards a solution. (shrink)

This article aims to provide a new solution to the Logical Problem of the Incarnation by proposing a novel metaphysical reconstrual of the method of reduplicative predication. This reconstrual will be grounded upon the metaphysical thesis of ‘Ontological Pluralism, proposed by Kris McDaniel and Jason Turner, and the notion of an ‘aspect’ proposed by Donald L. M. Baxter. Utilising this thesis and notion will enable the method of reduplicative predication to be further clarified, and the central objection that is (...) often raised against this approach can be successfully answered. (shrink)

In this paper, I argue that even if the Hard Problem of Content, as identified by Hutto and Myin, is important, it was already solved in natu- ralized semantics, and satisfactory solutions to the problem do not rely merely on the notion of information as covariance. I point out that Hutto and Myin have double standards for linguistic and mental representation, which leads to a peculiar inconsistency. Were they to apply the same standards to basic and linguistic minds, (...) they would either have to embrace representationalism or turn to semantic nihilism, which is, as I argue, an unstable and unattractive position. Hence, I conclude, their book does not offer an alternative to representation- alism. At the same time, it reminds us that representational talk in cognitive science cannot be taken for granted and that information is different from men- tal representation. Although this claim is not new, Hutto and Myin defend it forcefully and elegantly. (shrink)

The logicality of language is the hypothesis that the language system has access to a ‘natural’ logic that can identify and filter out as unacceptable expressions that have trivial meanings—that is, that are true/false in all possible worlds or situations in which they are defined. This hypothesis helps explain otherwise puzzling patterns concerning the distribution of various functional terms and phrases. Despite its promise, logicality vastly over-generates unacceptability assignments. Most solutions to this problem rest on specific stipulations about (...) the properties of logical form—roughly, the level of linguistic representation which feeds into the interpretation procedures—and have substantial implications for traditional philosophical disputes about the nature of language. Specifically, contextualism and semantic minimalism, construed as competing hypotheses about the nature and degree of context-sensitivity at the level of logical form, suggest different approaches to the over-generation problem. In this paper, I explore the implications of pairing logicality with various forms of contextualism and semantic minimalism. I argue that to adequately solve the over-generation problem, logicality should be implemented in a constrained contextualist framework. (shrink)

In this paper, the ethical and spiritual aspects of the trolley problem are discussed in connection with the dropping of atomic bombs on Hiroshima and Nagasaki. First, I show that the dropping of atomic bombs was a typical example of the events that contained the logic of the trolley problems in their decision-making processes and justifications. Second, I discuss five aspects of “the problem of the trolley problem;” that is to say, “Rarity,” “Inevitability,” “Safety Zone,” “Possibility (...) of Becoming a Victim,” and “Lack of Perspective of the Dead Victims Who Were Deprived of Freedom of Choice,” in detail. Third, I argue that those who talk about the trolley problem are automatically placed in the sphere of the expectation of response on the spiritual level. I hope that my contribution will shed light on the trolley problem from a very different angle, which has not been made by our fellow philosophers. (shrink)

Prior to Kripke's seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano-Tarski notion of logical truth. According to this interpretation, `it is necessary that A' is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality and some views (...) in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman's 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

In this paper I present a formalization of the theory of ideal concepts applied to the concept of God. It is done within a version of the Simplest Quantified Modal Logic (SQML) and attempts to solve three meta-problems related to the concept of God: the unicity of extension problem, the homogeneity/heterogeneity problem and the problem of conceptual unity.

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where (...) agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

Analytic theologians have proposed numerous “solutions” to the Logical Problem of the Trinity (LPT), mostly versions of Social Trinitarianism (ST) and Relative Identity Trinitarianism (RI). Both types of solution are controversial, but many hold out hope that further “Trinitarian theorizing” may yield some as yet unimagined, and somehow importantly different, solution to the LPT. I first give a precise definition of the LPT and of what would count as a solution to it. I then show how, though there are (...) infinitely many possible solutions, all solutions can be grouped together into a finite, exhaustive taxonomy, based precisely on those features which make them either controversial, heretical, or inconsistent. The taxonomy reveals why ST and RI have been the major proposed solutions, and also proves that there can be no importantly different, new solutions to the LPT. (shrink)

James Sterba uses the Pauline Principle to argue that the occurrence of significant, horrendous evils is logically incompatible with the existence of a good God. The Pauline Principle states that (as a rule) one must never do evil so that good may come from it, and according to Sterba, this principle implies that God may not permit significant evils even if that permission would be necessary to secure other, greater goods. By contrast, I argue that the occurrence of significant evils (...) is logically compatible with the existence of a good God because victims of significant evils may themselves reasonably consent to their suffering. In particular, I argue that they may be able to accept their suffering if it turns out that there was no way for God to secure relevant greater goods (or prevent other, greater evils) except by way of allowing their suffering, and God also provides them with other compensating, heavenly comforts. After using this consent-based argument to address Sterba’s logical problem from evil, I briefly consider how this argument may also help address a related evidential problem from evil, which suggests that while it is possible that victims of significant evils would consent to their suffering, it is unlikely that they would do so. While I do not provide a definitive solution to this evidential problem of evil, I highlight one important example of a trade-off that God may need to make that would—along with the provision of compensating, heavenly comforts—potentially persuade victims of significant evils to consent to their suffering. Specifically, I argue that there may be a necessary trade-off that God needs to make between permitting significant evils (on the one hand) and protecting a certain, morally significant form of free will (on the other hand). (shrink)

In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. (...) This raises two puzzles. First, as I show in section 2, Quine's mature thoroughly naturalized view has it that logic is simply obvious, and this is explains why we do not typically consider revising it. While Quine presents this naturalized view as a way to make good on his earlier metaphor of centrality in a web of belief, I argue that the resources of Quine's naturalized epistemology cannot adequately explain why we are reluctant to revise logic. And, Quine seems to recognize this point himself. In light of this, I explain in section 3 how Quine can allow that our overall scientific theory has systematic structure in a way that is consistent with his naturalistic strictures. Second, the asymmetrical internal structure of the web of belief seems to be inconsistent with its being a holistic web at all. I defuse this problem in section 4 by showing how Quine distinguishes between structural and confirmational considerations. I close by using this distinction to show how Quine's view can evade Michael Friedman’s criticisms, and allow for important methodological distinctions between areas of the web of belief. (shrink)

Understanding Hegel's account of particularity has proven to be anything but straightforward. Two main accounts of particularity have been advanced: the particular as an example or instance and the particular as a subjective perspective on a universal concept. The problem with these accounts is that they reduce particularity either to singularity or to universality. As Derrida's analyses make apparent, the ‘structure of exemplarity’ in Hegel is quite intricate. Hegel uses ‘example’ in three senses: it means (1) ‘instance’, ‘illustration’, or (...) (2) ‘model’, ‘exemplary individual’, ‘paradigm’, or (3) a by-play (a meaning derived from Hegel's neologismbeiherspielen, in whichBeispielis understood quasi-etymologically as a ‘by-play’ of accidental moments). ABeispielin the first sense can be replaced by another instance in a free play (by-play). This play of accidental moments, however, is not entirely free; it generates a series (of replacements) that ultimately leads to an example in the second sense, to an exemplary individual. I argue that particularity can be taken as exemplarity of this kind, oscillating between a singular example and a universal paradigm. Within this by-play, the universal concept, its law, is supposed to be mediated and determined. However, out of the differences between the examples the by-play induces another law, the law of non-mediation, which may, in Derrida's view, actually negate the dialectical movement towards universality. I argue, utilizing Malabou's concept of plasticity, that this disruption may be recovered. This implies that each individual example within a series is a particular determination of the universal. Hence, we can take literally Hegel's claim that the movement of the concept is play. (shrink)

In this chapter, we begin by sketching in the broadest possible strokes the ideas behind two formal systems that have been introduced with to goal of explicating the ways in which reasons interact to support the actions and conclusions they do. The first of these is the theory of defeasible reasoning developed in the seminal work of Pollock; the second is a more recent theory due to Horty, which adapts and develops the default logic introduced by Reiter to provide (...) an account of reasons. However, the implementations are complex enough, in both cases, to prevent anything more than this sketch. And we would not want to give the impression that we think that work on the logic of reasons must follow the path mapped out in either of these theories—indeed, we feel that the field is wide open. In the remainder of the chapter, therefore, will concentrate on a number of issues bearing on the logic of reasons that are either not treated in the work of Pollock and Horty, or whose treatment there is, we feel, either inadequate or incomplete. These are: first, the question of whether it is necessary to understand logical interactions among reasons themselves, rather than simply between reasons and the actions or conclusions they support, and if so, what principles might govern these interactions; second, priority relations among reasons and the notion of reason accrual; and third, some problems posed by undercutting defeat. (shrink)

This paper introduces the special issue on the Concept of God of the Journal of Applied Logics (College Publications). The issue contains the following articles: Logic and the Concept of God, by Stanisław Krajewski and Ricardo Silvestre; Mathematical Models in Theology. A Buber-inspired Model of God and its Application to “Shema Israel”, by Stanisław Krajewski; Gödel’s God-like Essence, by Talia Leven; A Logical Solution to the Paradox of the Stone, by Héctor Hernández Ortiz and Victor Cantero; No New Solutions (...) to the Logical Problem of the Trinity, by Beau Branson; What Means ‘Tri-’ in ‘Trinity’ ? An Eastern Patristic Approach to the ‘Quasi-Ordinals’, by Basil Lourié; The Éminence Grise of Christology: Porphyry’s Logical Teaching as a Cornerstone of Argumentation in Christological Debates of the Fifth and Sixth Centruies, by Anna Zhyrkova; The Problem of Universals in Late Patristic Theology, by Dirk Krasmüller; Intuitionist Reasoning in the Tri-unitrian Theology of Nicolas of Cues, by Antonino Drago. (shrink)

The truth table method, natural deduction, and the truth tree method, the three validity proving methods standardly taught in an introductory logic course, are too clumsy for the battlefield of real-life. The “short truth table” test is handy at times, but it stumbles at many other times. In this paper, we set up a general method that can beat all the methods mentioned above in a contest of speed. Furthermore, the procedure can be step-by-step paraphrased in a natural language, (...) so that, unlike the other methods, a real-life logical problem can be analyzed and explained in a real-life language too. (shrink)

This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...) consists in working out the claim that one can have Hempel's cake and eat it too - in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, a is an acceptable theory for evidence β if and only if a is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap's positive relevance account, thereby shedding new light on Carnap's analysis as well as solving another problem of confirmation theory. (shrink)

The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the (...) laws of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent. (shrink)

Recently, professors Christian List and Laura Valentini attempt to develop a new concept of freedom, criticizing the ones under the liberal and republican traditions. Their strategy is to find a concept of freedom satisfying the robust and nonmoralized conditions and to argue that the liberal and republican conceptions are not plausible. However, my view is that List and Valentini do not reasonably criticize the republican conception led by Philip Pettit. In other words, they do not see the real problem (...) of republican freedom so that the straw man fallacy would arise. The real issue for the republican freedom is the problem of political legitimacy, not the nonmoralized one. In this paper, I would like to examine the arguments from List and Valentini to explain why the real problem of republican freedom is the problem of political legitimacy. I would also explain that if we can take the issue seriously, then we know the relationship between the political freedom and the institution in a further step. (shrink)

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation (...) of the bounds of logic as formal ontology of abstract objects. (shrink)

In a recent paper Shieva Kleinschmidt has argued that if certain scenarios involving extended simple regions are possible (so-called ‘Place Cases’), then no logic of location with only one primitive locative notion (i.e., no ‘parsimonious logic of location’) will suffice to describe all of the locative possibilities. Since almost all existing logics of location are parsimonious (and apparently for good reason) the argument is a considerable obstacle to the development of a satisfactory logic of location. Kleinschmidt suggests (...) that the best way out of the difficulty is to deny the possibility of Place Cases by denying that extended simple regions are possible. I argue that much the same problem arises even in cases not involving extended simple regions or indeed exotic regions of any kind. Thus, simply denying the possibility of extended simple regions will not save parsimonious logics of location. (shrink)

The logic of academic writing is the argumentative strategy on which our papers, our sections, and our paragraphs are based. It is a strategy, as it is a plan that connects different steps and has a specific goal, namely convincing the audience of an original and important idea. And it is argumentative, for two reasons. First, we can defend our idea and we can convince our audience only through arguments, which only in very few disciplines are formal deductions. In (...) most cases, the arguments that we use are based on premises accepted by a community and the conclusions are drawn from principles that in the ancient dialectics were called “maxims,” principles shared by everyone. Second, a paper is a dialogue between the author and his or her readers. An idea can be considered as interesting and worth reading only when it addresses a topic that is perceived as important by the readers and tackles a problem that is open and needs to be solved. Our arguments are acceptable when they start from the premises of our community of readers, avoiding repeating what is obvious for them or taking for granted what is obscure or unknown to them. In this book, we present the argumentative approach to academic writing that we used in classroom. What characterizes it and makes it unique is the perspective that is adopted. We do not start from preexisting ideas that only need to be presented in a way that is suitable to an academic public. We intend to show that writing academically is a consequence of thinking academically, or rather “strategically.” We want to explain how the linguistic and presentational devices are the result of a much deeper plan underlying them, and how mastering the logic of a paper leads to understanding and even developing academic styles. The logic of academic writing is not aimed at teaching how to use language and write texts academically, but at enabling readers to create their own style based on their own argumentative strategies. (shrink)

We consider semantic and syntactic transformations of the concept of "the logical" in the ancient philosophy in the form of crypto-logos, para-logismos, dia-logos, and syl-logismos. We interpret Heraclitus' concept of Logos as a cryptologos through which intuitive insight (epístasthai gnóomen) reveals hidden or implicit harmony (harmoníe aphanés) in nature (phýsis) as a conceptual unity of ontic opposites (tà enantía). In Pramenides' paraconsistent concept of the identity of Being and thought, we point to para-logical hypotheses about the One that are carried (...) out through antithetical deductions of thought and which maintain the dynamics of the ontic determinations of being (ón) in the statics of the conceptual determinations of Being (tò eînai). As the beginning of the explicative granulation of ''the logical'' we consider Plato's concept of the dialectical skill (dialektikè tékhne) of dividing concepts of genus into species and sub-species that logically represent ontic opposites in problem-formulated questions. Finally Aristotle's concept of lógos as a statement-making sentence / proposition (lógos apophantikós) made explicit the Being (tò eînai), or the Being as Being (tò ón hê ón), in semantic and syntactic figures and modes of syllogistic inferences in which ontological (eînai), ontic (ón), conceptual (logikôos) and linguistic (légomenon) correspondence is shown. We conclude that with these changes in the concept of lógos, the path has been taken from the hidden or implicit Truth of the phenomena of nature and the world (pân) to explicit truthfulness of propositions as the unhiddeness (alétheia) of Being trough the semantical and syntactical visibility of the logical structures of being, thought and language in scientific knowledge based on demonstration (apoódeiksis). (shrink)