In this paper we propose to present from a new perspective some loci comunes of traditional logic. More exactly, we intend to show that some hypothetico-disjunctive inferences (i.e. the complex constructive dilemma, the complex destructive dilemma, the simple constructive dilemma, the simple destructive dilemma) and two hypothetico-categorical inferences (namely modus ponendo-ponens and modus tollendo-tollens) particularize two more abstract inferential structures: the constructive n-lemma and the destructive nlemma.

The categoricity problem for a system of logic reveals an asymmetry between the model-theoretic and the proof-theoretic resources of that logic. In particular, it reveals prima facie that the proof-theoretic instruments are insufficient for matching the envisaged model-theory, when the latter is already available. Among the proposed solutions for solving this problem, some make use of new proof-theoretic instruments, some others introduce new model-theoretic constrains on the proof-systems, while others try to use instruments from both sides. On the proof-theoretical side, (...) two main approaches for solving the categoricity problem for propositional classical logic consist in the enforcement of the formal systems of this logic by introducing rules of inference of a new kind. A multiple-conclusions logic allows rules of inference with more than one conclusion, while a bilateralist system contains rules of inference formulated in terms of assertion and rejection. Both these approaches reveal interesting formal features of logical reasoning. This paper analyses some of the advantages and limitations of these two approaches as solutions for a full formalization of logic, i.e., for a categorical formalization. (shrink)

This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...) This categorical harmony is stated in terms of adjoints and says that any concept definable by iterated adjoints from general categorical operations is harmonious. Moreover, it has been shown that identity in a categorical setting is determined by an adjoint in the relevant way. Furthermore, path induction as a rule comes from this definition. Thus we arrive at an account of how path induction, as a rule of inference governing identity, can be justified on mathematically motivated grounds. (shrink)

Discussions about the nature of essence and about the inference problem for non-Humean theories of nomic modality have largely proceeded independently of each other. In this article I argue that the right conclusions to draw about the inference problem actually depend significantly on how best to understand the nature of essence. In particular, I argue that this conclusion holds for the version of the inference problem developed and defended by Alexander Bird. I argue that Bird’s own argument that this problem (...) is fatal for David Armstrong’s influential theory of the laws of nature but not for dispositional essentialism is seriously flawed. In place of this argument, I develop an argument that whether Bird’s inference problem raises serious difficulties for Armstrong’s theory depends on the answers to substantial questions about how best to understand essence. The key consequence is that considerations about the nature of essence have significant, underappreciated implications for Armstrong’s theory. (shrink)

The type-level abstraction is a formal way to represent molecular structures in biological practice. Graphical representations of molecular structures of biological objects are also used to identify functional processes of things. This paper will reveal that category theory is a formal mathematical language not only to visualize molecular structures of biological objects as type-level abstraction formally but also to understand how to infer biological functions from the molecular structures of biological objects. Category theory is a toolkit to understand biological knowledge (...) at the type-level formally, not individual token-level, as well as typical heuristic strategies in molecular biology. (shrink)

The paper addresses the phenomenology of inference. It proposes that the conscious character of conscious inferences is partly constituted by a sense of meaning; specifically, a sense of what Grice called ‘natural meaning’. In consciously drawing the (outright, categorical) conclusion that Q from a presumed fact that P, one senses the presumed fact that P as meaning that Q, where ‘meaning that’ expresses natural meaning. This sense of natural meaning is phenomenologically analogous, I suggest, to our sense of (...) what is said in fluently comprehending everyday utterances in our first language. The proposal that conscious inference involves a sense of natural meaning is compared with views according to which conscious inference involves taking the premises (i) to be good reasons for the conclusion (as defended by Thomson and Grice), (ii) to support it (as argued by Audi and, recently, Boghossian), or (iii) to imply it (as lately contended by Broome). I argue our proposal can explain certain phenomena handled by alternatives (i) and (ii), but that some further phenomena is handled by our account but not these alternatives. In relation to alternative (iii), I argue that, in so far as implicational and natural-meaning relations come apart, the latter are a better fit for what we sense or take to be so in conscious inference. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the (...) categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the (...) categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

We initially characterize what we’ll call existence problems as problems where there is evidence that a putative entity exists and this evidence is not easily dismissed; however, the evidence is not adequate to justify the claim that the entity exists, and in particular the entity hasn’t been detected. The putative entity is elusive. We then offer a strategy for determining whether an existence problem is philosophical or scientific. According to this strategy (1) existence problems are characterized in terms of causal (...) roles, and (2) these problems are categorized as scientific or philosophical on the basis of the epistemic context of putative realizers. We argue that the first step of the strategy is necessary to avoid begging the question with regard to categorization of existence problems, and the second step categorizes existence problems on the basis of a distinction between two ways in which an entity can be elusive. This distinction between kinds of elusiveness takes as background a standard account of inference to the best explanation. Applying this strategy, we argue that the existence of a multiverse is a scientific problem. (shrink)

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on a (...) case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial (...) philosophic problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. -/- KEY WORDS: hypothesis, theorem, argumentation, proof, deduction, premise-conclusion argument, valid, inference, implication, epistemic, ontic, cogent, fallacious, paradox, formal, validation. (shrink)

It is well known in contemporary Madhyamaka studies that the seventh century Indian philosopher Candrakīrti rejects the foundationalist Abhidharma epistemology. The question that is still open to debate is: Does Candrakīrti offer any alternative Madhyamaka epistemology? One possible way of addressing this question is to find out what Candrakīrti says about the nature of buddha’s epistemic processes. We know that Candrakīrti has made some puzzling remarks on that score. On the one hand, he claims buddha is the pramāṇabhūta-puruṣa (person of (...) epistemic and moral authority), sarvākārajñatājñānaṃ (omniscient, wise), pratyakṣalakṣaṇam (exclusively perceptual in characteristic) [Candrakīrti (MABh VI.214)], and claims that there are clearly four pramāṇas—epistemic warrants—direct perception (pratyakṣa), inference (anumāna), testimony (āgama) and analogy (upamāna) [Candrakīrti (Pp I.3), cf. MacDonald 2015, pp. 287–288]. On the other hand, somewhat paradoxically, Candrakīrti claims that buddhahood is an embodiment of a complete cessation of “mind and mental processes” [Candrakīrti (MABh XI.1, 155a; MAB XI.17d)] Now how are we to make sense of these two seemingly contradictory statements? Do these statements reflect any deeper conflicts within Candrakīrti’s system or is there a coherent way to interpret these statements? The Tibetan Prāsaṅgika interpreters of Candrakīrti’s Madhyamaka largely agree that there is no internal contradiction in Candrakīrti’s system, and agree there is a way to make coherent sense of these statements. Nevertheless, the Tibetans exegetes bring to the table two radically conflicting proposals to approach Candrakīrti’s Mādhyamaka; both claiming to successfully address the apparent tension arising from Candrakīrti’s statements. One proposal is made by Tsongkhapa Losang Dakpa (Tsong kha pa bLo bzang grags pa, 1357–1419), who maintains the tension can be plausibly resolved by demonstrating that Candrakīrti’s unique non-foundationalist epistemological program renders him an epistemological coherentist. In contrast Taktsang Lotsawa Sherap Rinchen (sTag tshang Lo tsā ba Shes rab rin chen, 1405–1477) argues that according to Candrakīrti buddha is a global agnostic, on the ground of the nonexistence of mind and mental processes for those who have attained fully awakening. Taktsang instead proposes the no-mind thesis as a more plausible way to resolve the tension in Candrakīrti’s philosophy, categorically refusing to attribute to buddha any cognitive processes and epistemic warrants. This paper is an analysis of Taktsang’s no-mind thesis—the claim that buddhas utterly lack any knowledge of the world because they do not have epistemic processes and warrants to perceive the world—in what follows a rational reconstruction of his arguments is developed in order to evaluate his thesis. We shall then assess the implications of accepting Taktsang’s no-mind thesis. (shrink)

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

Claims about what justice “requires” and the “requirements” of justice are pervasive in political philosophy. However, there is a highly significant ambiguity in such claims that appears to have gone unnoticed. Such claims may pick out either one of two categorically distinct and noncoextensive kinds of requirement that we call 1) requirements-as-necessary-conditions for justice and 2) requirements-as-demands of justice. This is an especially compelling instance of an ambiguity that John Broome has famously observed in the context of claims about other (...) requirements (notably the requirements of rationality and morality). But it appears to have been overlooked by political philosophers in the case of claims about the requirements of justice. The ambiguity is highly significant inasmuch as failing to notice it is liable to distort our normative thinking about politics and make us vulnerable to certain kinds of normatively consequential errors: both mistakenly drawing inferences about what justice demands of us from claims that certain states or societies are not just; and mistakenly drawing inferences about what states or societies are or would be just from claims that justice does not demand of states or societies that they do certain things. Paying greater attention to the distinction between these two different kinds of requirements and the ways in which they come apart is helpful, not merely in avoiding these distortions and errors, but also in resolving, or at least clarifying, a number of other notoriously murky meta-normative debates, especially various important debates about realism and idealism in political philosophy. (shrink)

The paper sets out from Göodel's question about primitive concepts, in connection with Gödel's proposal of the employment of phenomenological method. The author assumes that the answer that can be found in Kant is relevant as a starting point. In a modification of the approach by K. Reich, a reconstruction of Kant's "deduction'' of logical forms of judgment is presented, which serve Kant as the basis for his "metaphysical deduction of categories'' including substantiality and causality. It is proposed that different (...) aspects of Kant's "original unity of self-consciousness'' as applied and attached to concrete representations step by step yield different forms of concepts, judgments, and inferences. Categorical, hypothetical and disjunctive judgments are shown to be gradually strengthening the conditions of bringing our representations under the "objective unity of consciousness", and in this way gradually implementing logical laws. The corresponding concepts of substantiality, causality, and mutual influence appear to be grounded in the primitive forms of our thinking. (shrink)

Some philosophers think that there is a gap between is and ought which necessarily makes normative enquiry a different kind of thing than empirical science. This position gains support from our ability to explicate our inferential practices in a way that makes it impermissible to move from descriptive premises to a normative conclusion. But we can also explicate them in a way that allows such moves. So there is no categorical answer as to whether there is or is not (...) a gap. The question of an is-ought gap is a practical and strategic matter rather than a logical one, and it may properly be answered in different ways for different questions or at different times. (shrink)

Ludwig Wittgenstein’s Tractatus logico-philosophicus and Edmund Husserl’s Experience and Judgement (Erfahrung und Urteil) are based on remarkably different conceptual frameworks and methodologies. After analyzing their respective accounts on the foundations of (formal) logic, I map out their common aims and different conclusions. I hold that Husserl and Wittgenstein both use the epistemic necessity of the existence of logical relations among things as an argument against philosophical scepticism, but their different epistemological convictions lead them to decisively diverging accounts of the nature (...) of those relations. Wittgenstein assumes a syntactic correspondence theory of truth, which identifies general logical form as a necessary condition for accurate representation, apparent in the existence of local truth-functions between propositions. As logical form is the (transcendental) necessary condition of every meaningful proposition, he infers that it is itself not representable and without ontological status. Husserl, by contrast, does not draw from a correspondence theory, but from a processual theory of certainty and truth, which offers genetic instead of categorical distinctions between perception and the logical relations apparent in conceptual knowledge. His theory of formal logic ultimately offers a coherent ontology for logical objects, which avoids logical mysticism. (shrink)

Some investigators of the rubber hand illusion (RHI) have suggested that when standard RHI induction procedures are employed, if the rubber hand is experienced by participants as owned, their corresponding biological hands are experienced as disowned. Others have demurred: drawing upon a variety of experimental data and conceptual considerations, they infer that experience of the RHI might include the experience of a supernumerary limb, but that experienced disownership of biological hands does not occur. Indeed, some investigators even categorically deny that (...) any experimental paradigm has been employed or any evidence can be adduced to support the claim that disownership experiences occur during the RHI. It goes without saying that RHI experiences can be elusive, and that there is some evidence to support claims that supernumerary limb experiences can sometimes occur. Here, however, we test the claim that the conscious experience of disownership can occur during the RHI. In order to test this claim, we developed two new online proxies—onset time for the illusion and illusion duration—and combined these with established questionnaires that concern the conscious contents of the RHI, in particular ownership/disownership experiences. Both online proxy data and post hoc questionnaire data converge in supporting the claim that disownership experiences do occur, at least when the left hand is the object of investigation. Our findings that onset time and illusion duration are reliable measures suggest that investigations of the RHI stand to benefit by devoting more attention to data collected while the RHI is being experienced, in particular data concerning temporal dynamics. (shrink)

Recent work in epistemology defends the unorthodox theses that belief is (1) an evidentially weak, and (2) question-sensitive attitude, and (3) that forming beliefs is sometimes a matter of guessing. What motivates these theses are examples of rationally permissible belief-ascriptions that exhibit these traits. The main aim of this paper is to outline a semantic account of categorical and conditional belief-ascriptions that captures the motivating data. We then survey some consequences of the proposed semantics, particularly with respect to the (...) question of whether closure under rules of inference is rationally required for weak, question-sensitive belief. (shrink)

This paper provides both a solution and a problem for the account of compositionality in Christopher Peacocke’s modest inferentialism. The immediate issue facing Peacocke’s account is that it looks as if compositionality can only be understood at the level of semantics, which is difficult to reconcile with inferentialism. Here, following up a brief suggestion by Peacocke, I provide a formal framework wherein compositionality occurs the level of the determining relation between inference and semantics. This, in turn provides a “test” for (...) compositionality, which, problematically, Peacocke’s natural deduction framework for classical logic can not meet. To finish, I briefly outline an alternative, bilateralist, framework for modest inferentialism, for which compositionality holds. (shrink)

proposition. Universal proposition is defined as the proposition in which the relation between the subject term and the predicate term is without any condition, in which the predicate is either affirmed or denied of the subject unconditionally. In nyaya logic the term vyapti is a universal proposition or invariable relation between the middle term (linga/hetu) and the major term (sadya) . According to the category of relation propositions are divided into categorical and the conditional. Although proposition is a logical (...) entity which is an assertion, either affirm or deny the subject. Truth and falsity are the values of proposition. Universal proposition is of two kinds: universal affirmative proposition and universal negative proposition while universality is the quantity of the subject and affirmation or negation is the quality of the proposition. Anumana (inference) is the knowledge of the objects which follows some other knowledge. In nyaya logic Inference is a combined deductive-inductive reasoning consisting of at least three categorical propositions and in it there are at least three propositions consisting of three terms, viz. the paksa or minor term about which we infer something, the sadhya or major term which inferred object, and the linga(probans) or sadana or middle which is invariably related to the major, and is present in the minor. Indian inference resembles to the categorical syllogism of western logic. In nyaya logic inference consisting of three propositions the first proposition is the conclusion of the syllogism , the second is the minor premise and last the major premise which is totally opposite of western logic. Syllogism of nyaya logic contains five propositions, called its Avayavas or members. These are pratijna, hetu, udarana, upanaya, and nigamana. Middle term have five characteristics in order to make five Figures of syllogism as Figure is the form of the syllogism. These five characteristics, or at least four of them , must be found in the middle term of a valid inference. If not, there will be fallacies(error in reasoning). Nyayikas give us three classifications of inference. According to first inference is of two kinds, namely, svartha and parartha. According to another inference is of three kinds, purvavat, sesavat and samanyatodrsta. According to third classification inference is distinguished into kevalanvayi, kevala-vyatireki and anvaya-vyatireki. (shrink)

This paper takes into account the loops within the anti-suicide arguments - we can clearly understand that their theories were emerging either from their personal beliefs or irrelevant inferences. As discussed later, they overlooked the fact that human beings have ultimate freedom over their death and that is one thing that serves their ego. We see a mere categorical problem on behalf of Camus and his Sisyphus; that how he failed to realise the difference of circumstance and choices. (...) How Kant’s Categorical Imperative is like Plato’s Ideal World that can never exist and how Rousseau failed to recognise individuals as humans. The paper also examine the pro-suicide arguments of Arthur Schopenhauer, Phillip Mainlander, Max Stirner and David Hume. The paper concludes that although suicide is logical, however, there is a need to further categorise the types of suicides in order to create a better compass on this topic of self annihilation. (shrink)

In the article we consider the relationship of traditional provisions of basic logical concepts and confront them with new and modern approaches to the same concepts. Logic is characterized in different ways when it is associated with syllogistics (referential – semantical model of logic) or with symbolic logic (inferential – syntactical model of logic). This is not only a difference in the logical calculation of (1) concepts, (2) statements, and (3) predicates, but this difference also appears in the treatment of (...) the calculative abilities of logical forms, the ontological-referential status of conceptual content and the inferential-categorical status of logical forms. The basic markers or basic ideas that separate ontologically oriented logic from categorically oriented logic are the (1) concept of truth, the (2) concept of meaning, the (3) concept of identity, and the (4) concept of predication. Here, this differences are explicitly demonstrated by the introduction of differential terminology. From this differential methodology follows a new set of characterizations of logic. (shrink)

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules (...) for the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s (2013) local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e. non-compact. Consequently, I reconsider the use of the ω-rule and I show that the addition of the ω-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement. (shrink)

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity (...) theorem for second-order —these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic. (shrink)

After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...) involving the distinction between characterizing a system and axiomatizing the truths of a system. (shrink)

Deprivation views of the badness of death are almost universally accepted among those who hold that death can be bad for the person who dies. In their most common form, deprivation views hold that death is bad because (and to the extent that) it deprives people of goods they would have gained had they not died at the time they did. Contrast this with categorical desire views, which hold that death is bad because (and to the extent that) it (...) thwarts people’s categorical desires. Categorical desires are desires that are not conditional upon one being alive; yet provide reason for the agent to continue living to ensure that those very desires are satisfied. I argue that categorical desire views are subject to two serious problems that deprivation views are not. First, categorical desire views entail that it is not bad for someone to not be resuscitated after dying a bad death. Second, categorical desire views cannot account for cases in which it is good to prevent people from coming into existence or cases in which it is good to prevent them from continuing to exist. After considering, and rejecting, various replies on behalf of categorical desire proponents, I conclude that we have good reason to reject categorical desire views in favor of deprivation views. (shrink)

Why do we draw the boundaries between “blue” and “green”, where we do? One proposed answer to this question is that we categorize color the way we do because we perceive color categorically. Starting in the 1950’s, the phenomenon of “categorical perception” (CP) encouraged such a response. CP refers to the fact that adjacent color patches are more easily discriminated when they straddle a category boundary than when they belong to the same category. In this paper, I make three (...) related claims. (1) Although what seems to guide discrimination performances seems to indeed be categorical information, the evidence in favor of the fact that categorical perception infl uences the way we perceive color is not convincing. (2) That CP offers a useful account of categorization is not obvious.While aiming at accounting for categorization, CP itself requires an account of categories. This being said, CP remains an interesting phenomenon. Why and how is our discrimination behavior linked to our categories? It is suggested that linguistic labels determine CP through a naming strategy to which participants resort while discriminating colors. This paper’s fi nal point is (3) that the naming strategy account is not enough. Beyond category labels, what seems to guide discrimination performance is category structure. (shrink)

We argue that, if taken seriously, Kripke's view that a language for science can dispense with a negation operator is to be rejected. Part of the argument is a proof that positive logic, i.e., classical propositional logic without negation, is not categorical.

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument focuses on (...) cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

I argue that inference can tolerate forms of self-ignorance and that these cases of inference undermine canonical models of inference on which inferrers have to appreciate (or purport to appreciate) the support provided by the premises for the conclusion. I propose an alternative model of inference that belongs to a family of rational responses in which the subject cannot pinpoint exactly what she is responding to or why, where this kind of self-ignorance does nothing to undermine the intelligence of the (...) response. (shrink)

We argue that stereotypes associated with concepts like he-said–she-said, conspiracy theory, sexual harassment, and those expressed by paradigmatic slurs provide “normative inference tickets”: conceptual permissions to automatic, largely unreflective normative conclusions. These “mental shortcuts” are underwritten by associated stereotypes. Because stereotypes admit of exceptions, normative inference tickets are highly flexible and productive, but also liable to create serious epistemic and moral harms. Epistemically, many are unreliable, yielding false beliefs which resist counterexample; morally, many perpetuate bigotry and oppression. Still, some normative (...) inference tickets, like some activated by sexual harassment, constitute genuine moral and hermeneutical advances. For example, our framework helps explain Miranda Fricker’s notion of “hermeneutical lacunae”: what early victims of “sexual harassment” — as well as their harassers — lacked before the term was coined was a communal normative inference ticket — one that could take us, collectively, from “this is happening” to “this is wrong.”. (shrink)

Consider the following three claims. (i) There are no truths of the form ‘p and ~p’. (ii) No one holds a belief of the form ‘p and ~p’. (iii) No one holds any pairs of beliefs of the form {p, ~p}. Irad Kimhi has recently argued, in effect, that each of these claims holds and holds with metaphysical necessity. Furthermore, he maintains that they are ultimately not distinct claims at all, but the same claim formulated in different ways. I find (...) his argument suggestive, if not entirely transparent. I do think there is at least an important kernel of truth even in (iii), and that (i) ultimately explains what’s right about the other two. Consciousness of an impossibility makes belief in the obtaining of the corresponding state of affairs an impossibility. Interestingly, an appreciation of this fact brings into view a novel conception of inference, according to which it consists in the consciousness of necessity. This essay outlines and defends this position. A central element of the defense is that it reveals how reasoners satisfy what Paul Boghossian calls the Taking Condition and do so without engendering regress. (shrink)

The paper offers an account of inference. The account underwrites the idea that inference requires that the reasoner takes her premises to support her conclusion. I reject views according to which such ‘takings’ are intuitions or beliefs. I sketch an alternative view on which inferring consists in attaching what I call ‘inferential force’ to a structured collection of contents.

What is the connection between justification and the kind of consequence relations that are studied by logic? In this essay, I shall try to provide an answer, by proposing a general conception of the kind of inference that counts as justified or rational.

The paper sketches an argument against modal monism, more specifically against the reduction of physical possibility to metaphysical possibility. The argument is based on the non-categoricity of quantum logic.

The concept of “life” certainly is of some use to distinguish birds and beavers from water and stones. This pragmatic usefulness has led to its construal as a categorical predicate that can sift out living entities from non-living ones depending on their possessing specific properties—reproduction, metabolism, evolvability etc. In this paper, we argue against this binary construal of life. Using text-mining methods across over 30,000 scientific articles, we defend instead a degrees-of-life view and show how these methods can contribute (...) to experimental philosophy of science and concept explication. We apply topic-modeling algorithms to identify which specific properties are attributed to a target set of entities (bacteria, archaea, viruses, prions, plasmids, phages and the molecule of adenine). Eight major clusters of properties were identified together with their relative relevance for each target entity (two that relate to metabolism and catalysis, one to genetics, one to evolvability, one to structure, and—rather unexpectedly—three that concern interactions with the environment broadly construed). While aligning with intuitions—for instance about viruses being less alive than bacteria—these quantitative results also reveal differential degrees of performance that have so far remained elusive or overlooked. Taken together, these analyses provide a conceptual “lifeness space” that makes it possible to move away from a categorical construal of life by empirically assessing the relative lifeness of more-or-less alive entities. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of IBE, (...) the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

Some arguments include imperative clauses. For example: ‘Buy me a drink; you can’t buy me that drink unless you go to the bar; so, go to the bar!’ How should we build a logic that predicts which of these arguments are good? Because imperatives aren’t truth apt and so don’t stand in relations of truth preservation, this technical question gives rise to a foundational one: What would be the subject matter of this logic? I argue that declaratives are used to (...) produce beliefs, imperatives are used to produce intentions, and beliefs and intentions are subject to rational requirements. An argument will strike us as valid when anyone whose mental state satisfies the premises is rationally required to satisfy the conclusion. For example, the above argument reflects the principle that it is irrational not to intend what one takes to be the necessary means to one’s intended ends. I argue that all intuitively good patterns of imperative inference can be explained using off-the-shelf formulations of our rational requirements. I then develop a formal-semantic theory embodying this view that predicts a range of data, including free-choice effects and Ross’s paradox. The resulting theory shows one way that our aspirations to rational agency can be discerned in the patterns of our speech, and is a case study in how the philosophy of language and the philosophy of action can be mutually illuminating. (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. (...) Thus, supervaluationists can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

Is imagination a source of knowledge? Timothy Williamson has recently argued that our imaginative capacities can yield knowledge of a variety of matters, spanning from everyday practical matters to logic and set theory. Furthermore, imagination for Williamson plays a similar epistemic role in cognitive processes that we would traditionally classify as either a priori or a posteriori, which he takes to indicate that the distinction itself is shallow and epistemologically fruitless. In this chapter, I aim to defend the a priori-a (...) posteriori distinction from Williamson’s challenge by questioning his account of imagination. I distinguish two notions of imagination at play in Williamson’s account – sensory vs. belief-like imagination – and show that both face empirical and normative issues. Sensory imagination seems neither necessary nor sufficient for knowledge. Whereas, belief-like imagination isn’t adequately disentangled from inference. Additionally, Williamson’s examples are ad hoc and don’t generalize. I conclude that Williamson’s case against the a priori-a posteriori distinction is unconvincing, and so is the thesis that imagination is an epistemic source. (shrink)

This paper presents a new problem for the inference rule commonly known as Inference to the Best Explanation (IBE). The problem is that uncertainty about parts of one’s evidence may undermine the inferrability of a hypothesis that would provide the best explanation of that evidence, especially in cases where there is an alternative hypothesis that would provide a better explanation of only the more certain pieces of evidence. A potential solution to the problem is sketched, in which IBE is generalized (...) to handle uncertain evidence by invoking a notion of evidential robustness. (shrink)

How reliable are causal inferences in complex empirical scenarios? For example, a physician prescribes a drug to a patient, and then the patient undergoes various changes to their symptoms. They then increase their confidence that it is the drug that causes such changes. Are such inferences reliable guides to the causal relation in question, particularly when the physician can gain a large volume of such clinical experience by treating many patients? The evidence-based medicine movement says no, while some (...) physicians and philosophers support such appeals to first-person experience. We develop a formal model and simulate causal inference based on clinical experience. We conclude that in very particular clinical scenarios such inference can be reliable, while in many other routine clinical scenarios such inferences are not reliable. (shrink)

Suppose that X and Y can’t possibly exist apart in reality; then—by definition—there’s no real distinction between them, only a conceptual distinction. There’s a conceptual distinction between a rectilinear figure’s triangularity and its trilaterality, for example, but no real distinction. In fundamental metaphysics there is no real distinction between an object’s categorical properties and its dispositional properties. So too there is no real distinction between an object and its properties. And in fundamental metaphysics, for X and Y to be (...) such that there is no real distinction between them is for them to be identical. (shrink)

"Correlation is not causation" is one of the mantras of the sciences—a cautionary warning especially to fields like epidemiology and pharmacology where the seduction of compelling correlations naturally leads to causal hypotheses. The standard view from the epistemology of causation is that to tell whether one correlated variable is causing the other, one needs to intervene on the system—the best sort of intervention being a trial that is both randomized and controlled. In this paper, we argue that some purely correlational (...) data contains information that allows us to draw causal inferences: statistical noise. Methods for extracting causal knowledge from noise provide us with an alternative to randomized controlled trials that allows us to reach causal conclusions from purely correlational data. (shrink)

Inferences from the absence of evidence to something are common in ordinary speech, but when used in scientific argumentations are usually considered deficient or outright false. Yet, as demonstrated here with the help of various examples, archaeologists frequently use inferences and reasoning from absence, often allowing it a status on par with inferences from tangible evidence. This discrepancy has not been examined so far. The article analyses it drawing on philosophical discussions concerning the validity of inference from (...) absence, using probabilistic models that were originally developed to show that such inferences are weak and inconclusive. The analysis reveals that inference from absence can indeed be justified in many important situations of archaeological research, such as excavations carried out to explore the past existence and time-span of sedentary human habitation. The justification is closely related to the fact that archaeology explores the human past via its material remains. The same analysis points to instances where inference from absence can have comparable validity in other historical sciences, and to research questions in which archaeological inference from absence will be problematic or totally unwarranted. (shrink)

What is sexual orientation? The contemporary consensus among philosophers is that it is a disposition. Unsurprisingly, recent debates about the metaphysics of sexual orientation are almost entirely intramural. Behavioral dispositionalists argue that sexual orientation is a disposition to behave sexually. Desire dispositionalists argue that it is a disposition to desire sexually. We argue that sexual orientation is not best understood in terms of dispositions to behave or dispositions to desire before arguing that dispositions tout court fail to illuminate sexual orientation. (...) We then introduce and defend the idea that sexual orientation is best understood in terms of categorical phenomenal properties of sexual arousal. (shrink)

David Gauthier suggested that all genuine moral problems are Prisoners Dilemmas (PDs), and that the morally and rationally required solution to a PD is to co-operate. I say there are four other forms of moral problem, each a different way of agents failing to be in PDs because of the agents’ preferences. This occurs when agents have preferences that are malevolent, self-enslaving, stingy, or bullying. I then analyze preferences as reasons for action, claiming that this means they must not target (...) the impossible, they must be able to be acted on in the circumstances, their targets must be attainable, and having the preferences must make their targets more likely. For groups of agents to have a distribution of preferences, their preferences must jointly have those four features, this imposing a kind of universalizability requirement on possible preferences. I then claim that, if all agents began with preferences satisfying these requirements, their preferences would not be of the morally problematic sort (on pain, variously, of circularity or contradiction in the specification of their targets). Instead, they would be either morally innocent preferences, or ones which put the agents in PDs. And it would then be instrumentally rational for the agents to prefer mutual co-operation. Thus if all agents initially had rationally permissible preferences and made rational choices of actions and preferences thereafter, they would never acquire immoral preferences, and so never be rationally moved to immoral actions. Further, the states of affairs such agents would be moved to bring about would be compatible with what Rawls’ agents would chose behind a veil of ignorance. Morality therefore reduces to rationality; necessarily, the actions categorically required by morality are also categorically required by rationality. (shrink)

Dharmakīrti argues that there is no pramāṇa (valid means of cognition or source of knowledge) for a thesis that is a self-contradiction (svavacanavirodha). That is, self-contradictions such as ‘everything said is false’ and ‘my mother is barren’ cannot be known to be true or false. The contemporary scholar Tillemans challenges Dharmakīrti by arguing that we can know that self-contradictions are false by means of a formal logical inference. The aims of the paper are to answer Tillemans’ challenge from what we (...) take to be Dharmakīrti’s or Dharmakīrtian (someone who is like Dharmakīrti) perspective and to demonstrate the unique features of Dharmakīrti’s view of inference. By so doing, we show that the epistemology in relation to the formal conception of logic that underlies Tillemans’ challenge is problematic from Dharmakīrti’s or Dharmakīrtian perspective. The paper, thus, presents Dharmakīrti’s view of inference and logical reasoning as well as a Dharmakīrtian challenge to the formal conception of logic that is the dominant contemporary conception. (shrink)