The aim of this paper is to introduce and explain displaycalculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal displaycalculi are considered and their properties detailed.
The aim of this paper is to outline a methodological framework for brand equity planning with structuralist rhetorical semiotics. By drawing on the connectionistconceptual model of the brand generative trajectory of signification it will be displayed in a stepwise fashion how a set of nuclear semes and classemes or anintended semic structure that underlies manifest discursive structures may be projected by its internal stakeholders with view to attaining differential brand associations. The suggested methodological framework focuses on the strength and uniqueness (...) of brand associations as integral aspects of a brand’s equity structure and comprises a set of calculi that aim at addressing from a brand textuality point of view how associations may be systematically linked to their key sources with an emphasis on the ad filmic text. The propounded methodology is exemplified by recourse to a corpus of ad filmic texts from the major brand players in the UK cereals market. The argumentative thrust is intent on demonstrating that structuralist rhetorical semiotics is not only useful for analysing/interpreting brand texts, but, moreover, for constructing and for managing them over time. This demonstration is deployed by adopting a synchronic/diachronic and intra--filmic/inter--filmic approach to the formation of brand associations that make up a projected brand equity structure, in the context of embedded product category dynamics. (shrink)
A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in (...) the number of truth values, and it is shown that this bound is tight. (shrink)
It has become standard to conceive of metalinguistic disagreement as motivated by a form of negotiation, aimed at reaching consensus because of the practical consequences of using a word with one content rather than another. This paper presents an alternative motive for expressing and pursuing metalinguistic disagreement. In using words with given criteria, we betray our location amongst social categories or groups. Because of this, metalinguistic disagreement can be used as a stage upon which to perform a social identity. The (...) ways in which metalinguistic disagreements motivated in this way diverge in character from metalinguistic negotiations are described, as are several consequences of the existence of metalinguistic disagreements motivated in this way. (shrink)
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable (...) proof-theoretic properties from its associated labelled calculus. (shrink)
We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.
This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In (...) the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)
We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the (...) original proof. We then present a linear natural deduction calculus that makes use of formal illocutionary expressions in such a way that unique readability for derivations is guaranteed – thus showing that formalizing illocutionary expressions can eliminate the need for commentary. (shrink)
We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.
We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC (...) frames. (shrink)
In this essay I give a complete join semi-lattice of possible display-equivalence schemes for Display Logic, using the standard connectives, and leaving fixed only the schemes governing the star. In addition to proving the completeness of this list, I offer a discussion of the basic properties of these schemes.
The actual and potential uses of holograms in museum displays, and the philosophy of knowledge and progress that they represent. Magazine journalists, museum curators, and historians sometimes face similar challenges in making topics or technologies relevant to wider audiences. To varying degrees, they must justify the significance of their subjects of study by identifying a newsworthy slant, a pedagogical role, or an analytical purpose. This chasse au trésor may skew historical story telling itself. In science and technology studies, the problem (...) potentially is worst for those subjects that do not retain an enduring capacity for spectacle or do not readily conform to templates of progress or economic importance. The case of holography is an excellent illustration of these points. An unusually wide-ranging subject, holography has attracted competing interpretations of intellectual novelty, technological application, and cultural significance. This paper examines the history of museum collections and exhibits of holography from the explosion of interest in the technique in 1964 to the end of the twentieth century. I argue that holography presents a particular challenge to museum collections and to popular representations of the history of science and technology. (shrink)
Post-Fregean theorists use 'quotation' to denote indifferently both colloquially called quotations (repetitions of prior utterances) and what I call 'displays': 'Rot' means red. Colloquially, quotation is a strictly historical property, not semantic or syntactic. Displays are semantically and syntactically distinctive sentential elements. Most displays are not quotations. Pure echo quotations (Cosmological arguments involve "an unnecessary shuffle") aren't displays. Frege-inspired formal languages stipulate that enquotation forms a singular term referring to the enquoted expression (type). Formalist enquotations differ semantically and syntactically from (...) natural language displays. Call them autonomes, and mark them with stars: *Rot* means red. In formal languages, an unenstarred expression has only one meaning, and an autonome has only one meaning viz., a name (or indexical) designating the unenstarred expression (type). Stars have semantic content and can’t disambiguate. Display punctuation only disambiguates; it says only: This material is displayed. Displays have a semantic function; their marks don't. Displays are not terms or lexical items. Displays are objects incorporable into utterances. Such incorporation enables them to be linguistically appropriated much as we appropriate speech-external objects by extrasentential supplementation (e.g., gesturing) to identify the extension of a term by ostending the object -- but now without any extrasentential supplement. Displays are always adjunctive to an (implicit or explicit) ostensionable term, a term whose extension is identifiable by ostending an object. The display-ostensionable term-extension relations are various. A display may (1) be the term's referent, or (2) represent the term's extension by (a) replicating or (b) instantiating or (c) expressing the term's referent, or (e) instantiating the property the term predicates. (shrink)
Post-Fregean theorists use 'quotation' to denote indifferently both colloquially called quotations (repetitions of prior utterances) and what I call 'displays': 'Rot' means red. Colloquially, quotation is a strictly historical property, not semantic or syntactic. Displays are semantically and syntactically distinctive sentential elements. Most displays are not quotations. Pure echo quotations (Cosmological arguments involve "an unnecessary shuffle") aren't displays. Frege-inspired formal languages stipulate that enquotation forms a singular term referring to the enquoted expression (type). Formalist enquotations differ semantically and syntactically from (...) natural language displays. Call them autonomes, and mark them with stars: *Rot* means red. In formal languages, an unenstarred expression has only one meaning, and an autonome has only one meaning viz., a name (or indexical) designating the unenstarred expression (type). Stars have semantic content and can’t disambiguate. Display punctuation only disambiguates; it says only: This material is displayed. Displays have a semantic function; their marks don't.nDisplays are not terms or lexical items. Displays are objects incorporable into utterances. Such incorporation enables them to be linguistically appropriated much as we appropriate speech-external objects by extrasentential supplementation (e.g., gesturing) to identify the extension of a term by ostending the object -- but now without any extrasentential supplement. Displays are always adjunctive to an (implicit or explicit) ostensionable term, a term whose extension is identifiable by ostending an object. The display-ostensionable term extension relations are various. A display may (1) be the term's referent, or (2) represent the term's extension by (a) replicating or (b) instantiating or (c) expressing the term's referent, or (e) instantiating the property the term predicates. (shrink)
By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty name (...) in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued. (shrink)
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated (...) labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)
The experiments reported herein probe the visual cortical mechanisms that control near–far percepts in response to two-dimensional stimuli. Figural contrast is found to be a principal factor for the emergence of percepts of near versus far in pictorial stimuli, especially when stimulus duration is brief. Pictorial factors such as interposition (Experiment 1) and partial occlusion Experiments 2 and 3) may cooperate, as generally predicted by cue combination models, or compete with contrast factors in the manner predicted by the FACADE model. (...) In particular, if the geometrical con guration of an image favors activation of cortical bipole grouping cells, as at the top of a T-junction, then this advantage can cooperate with the contrast of the con guration to facilitate a near–far percept at a lower contrast than at an X-junction. Varying the exposure duration of the stimuli shows that the more balanced bipole competition in the X-junction case takes longer exposure times to resolve than the bipole competition in the T-junction case (Experiment 3). (shrink)
The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...) be computed from the calculus. (shrink)
We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting (...) to embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)
In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...) relations will in general require developing four tableaux, while proving that they are in the ⊧ relation may require six. (shrink)
Humans typically display hindsight bias. They are more confident that the evidence available beforehand made some outcome probable when they know the outcome occurred than when they don't. There is broad consensus that hindsight bias is irrational, but this consensus is wrong. Hindsight bias is generally rationally permissible and sometimes rationally required. The fact that a given outcome occurred provides both evidence about what the total evidence available ex ante was, and also evidence about what that evidence supports. Even (...) if you in fact evaluate the ex ante evidence correctly, you should not be certain of this. Then, learning the outcome provides evidence that if you erred, you are more likely to have erred low rather than high in estimating the degree to which the ex ante evidence supported the hypothesis that that outcome would occur. (shrink)
Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)
This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent (...) class='Hi'>calculi for S*fde, dS*fde, crossS*fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar, Hallden, Deutsch and Daniels, we provide a general recipe to define containment logics, we explore the single-premise/single-conclusion fragment of S*fde, dS*fde, crossS*fdeand the connections between crossS*fde and the logic Eq of equality by Epstein. Also, we present S*fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley, and we briefly examine three further systems that are closely related to our main logics. Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues. (shrink)
This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, further reflections (...) on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)
This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of (...) Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)
A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.
Members of the field of philosophy have, just as other people, political convictions or, as psychologists call them, ideologies. How are different ideologies distributed and perceived in the field? Using the familiar distinction between the political left and right, we surveyed an international sample of 794 subjects in philosophy. We found that survey participants clearly leaned left (75%), while right-leaning individuals (14%) and moderates (11%) were underrepresented. Moreover, and strikingly, across the political spectrum, from very left-leaning individuals and moderates to (...) very right-leaning individuals, participants reported experiencing ideological hostility in the field, occasionally even from those from their own side of the political spectrum. Finally, while about half of the subjects believed that discrimination against left- or right-leaning individuals in the field is not justified, a significant minority displayed an explicit willingness to discriminate against colleagues with the opposite ideology. Our findings are both surprising and important, because a commitment to tolerance and equality is widespread in philosophy, and there is reason to think that ideological similarity, hostility, and discrimination undermine reliable belief formation in many areas of the discipline. (shrink)
The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first (...) order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)
A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.
Many of our most important goals require months or even years of effort to achieve, and some never get achieved at all. As social psychologists have lately emphasized, success in pursuing such goals requires the capacity for perseverance, or "grit." Philosophers have had little to say about grit, however, insofar as it differs from more familiar notions of willpower or continence. This leaves us ill-equipped to assess the social and moral implications of promoting grit. We propose that grit has an (...) important epistemic component, in that failures of perseverance are often caused by a significant loss of confidence that one will succeed if one continues to try. Correspondingly, successful exercises of grit often involve a kind of epistemic resilience in the face of failure, injury, rejection, and other setbacks that constitute genuine evidence that success is not forthcoming. Given this, we discuss whether and to what extent displays of grit can be epistemically as well as practically rational. We conclude that they can be (although many are not), and that the rationality of grit will depend partly on features of the context the agent normally finds herself in. In particular, grit-friendly norms of deliberation might be irrational to use in contexts of severe material scarcity or oppression. (shrink)
In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated in (...) terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)
Theories of emotional justification investigate the conditions under which emotions are epistemically justified or unjustified. I make three contributions to this research program. First, I show that we can generalize some familiar epistemological concepts and distinctions to emotional experiences. Second, I use these concepts and distinctions to display the limits of the ‘simple view’ of emotional justification. On this approach, the justification of emotions stems only from the contents of the mental states they are based on, also known as (...) their cognitive bases. The simple view faces the ‘gap problem’: If cognitive bases and emotions (re)present their objects and properties in different ways, then cognitive bases are not sufficient to justify emotions. Third, I offer a novel solution to the gap problem based on emotional dispositions. This solution (1) draws a line between the justification of basic and non-basic emotions, (2) preserves a broadly cognitivist view of emotions, (3) avoids a form of value skepticism that threatens inferentialist views of emotional justification, and (4) sheds new light on the structure of our epistemic access to evaluative properties. (shrink)
This paper deals with, prepositional calculi with strong negation (N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them.
It is often observed in metaethics that moral language displays a certain duality in as much as it seems to concern both objective facts in the world and subjective attitudes that move to action. In this paper, I defend The Dual Aspect Account which is intended to capture this duality: A person’s utterance of a sentence according to which φing has a moral characteristic, such as “φing is wrong,” conveys two things: The sentence expresses, in virtue of its conventional meaning, (...) the belief that φing has a moral property, and the utterance of the sentence carries a generalized conversational implicature to the effect that the person in question has an action-guiding attitude in relation to φing. This account has significant advantages over competing views: (i) As it is purely cognitivist, it does not have the difficulties of expressivism and various ecumenical positions. (ii) Yet, in spite of this, it can explain the close, “meaning-like,” connection between moral language and attitudes. (iii) In contrast to other pragmatic accounts, it is compatible with any relevant cognitivist view. (iv) It does not rest on a contentious pragmatic notion, such as conventional implicature. (v) It does not imply that utterances of complex moral sentences, such as conditionals, convey attitudes. In addition, the generalized implicature in question is fully calculable and cancellable. (shrink)
In this paper I will introduce a practical explication for the notion of expertise. At first, I motivate this attempt by taking a look on recent debates which display great disagreement about whether and how to define expertise in the first place. After that I will introduce the methodology of practical explications in the spirit of Edward Craig’s Knowledge and the state of nature along with some conditions of adequacy taken from ordinary and scientific language. This eventually culminates in (...) the respective explication of expertise according to which this term essentially refers to a certain kind of service-relation. This is why expertise should be considered as a predominantly social kind. This article will end up with a discussion of advantages and prima facie plausible objections against my account of expertise. (shrink)
Many philosophers display relaxed scepticism about the Doctrine of Doing and Allowing and the Doctrine of Double Effect, suspecting, without great alarm, that one or both of these Doctrines is indefensible. This relaxed scepticism is misplaced. Anyone who aims to endorse a theory of right action with Nonconsequentialist implications should accept both the DDA and the DDE. First, even to state a Nonconsequentialist theory requires drawing a distinction between respecting and promoting values. This cannot be done without accepting some (...) deontological distinction. Second, if someone is going to accept any deontological distinction she should accept either the DDE or the DDA or some replacement. Finally, anyone who accepts either the DDE or the DDA should accept both doctrines or a replacement of each. Unless both Doctrines can be defended or given a defensible replacement, any Nonconsequentialist is in trouble. (shrink)
It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)
This text addresses a problem that is not sufficiently dealt with in most of the recent literature on emotion and feeling. The problem is a general underestimation of the extent to which affective intentionality is essentially bodily. Affective intentionality is the sui generis type of world-directedness that most affective states – most clearly the emotions – display. Many theorists of emotion overlook the extent to which intentional feelings are essentially bodily feelings. The important but quite often overlooked fact is (...) that the bodily feelings in question are not the regularly treated, non-intentional bodily sensations (known from Jamesian accounts of emotion), but rather crucial carriers of world-directed intentionality. Consequently, most theories of human emotions and feelings recently advocated are deficient in terms of phenomenological adequacy. This text tries to make up for this deficit and develops a catalogue of five central features of intentional bodily feelings. In addition, Jesse Prinz’s embodied appraisal theory is criticized as an exemplary case of the misconstrual of the bodily nature of affective experience in naturalistic philosophy of mind. (shrink)
Many philosophers maintain that causation is to be explicated in terms of a kind of dependence between cause and effect. These “dependence” theories are opposed by “production” accounts which hold that there is some more fundamental causal “oomph”. A wide range of experimental research on everyday causal judgments seems to indicate that ordinary people operate primarily with a dependence-based notion of causation. For example, people tend to say that absences and double preventers are causes. We argue that the impression that (...) commonsense causal discourse is largely dependence-based is the result of focusing on a very narrow class of causal verbs. Almost all of the vignette-based experimental work on causal judgment has been prosecuted using the word “cause”. But much ordinary causal discourse involves special causal verbs, such as “burn” and “crack”. We find that these verbs display a quite different pattern from the verb “cause”. For instance, for absences and double preventers (Studies 1-3), we find that while people are inclined to say that X caused Y to burn, turn, crack or start, they are less inclined to think that X burned, turned, cracked or started Y. In Study 4, we find that for chains involving a distal and proximal event, people are inclined to say that the distal event is not a special cause of the outcome, though it is a “cause” of the outcome. Together, we find a surprising double dissociation between “cause” and a stock of special causal verbs. We conclude by suggesting that much commonsense causal judgment, which heavily trades in special causal verbs, might be better captured by production-based accounts of causation. (shrink)
Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.
The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth (...) value and the exclusion of the opposite truth value describe the same situation.). (shrink)
Ouraiminthischapteristodelineatetheformofsharedagencythatwe take to be manifested in collective memory. We argue for two theses. First, we argue that, given a relatively weak conception of episodicity, certain small-scale groups display a form of emergent (i.e., genuinely collective) episodic memory, while large-scale groups, in contrast, do not display emergent episodic memory. Second, we argue that this form of emergent memory presupposes (high-level and possibly low-level) metamemorial capacities, capacities that are, however, not themselves emergent group-level features but rather strictly individual-level features. The (...) form of shared agency that we delineate is thus revealed as being minimal in three senses. First, the relevant groups are themselves minimal in terms of their size. Second, the form of memory in question is minimally episodic. And finally, the cognitive capac- ities attributed to the relevant groups are minimal, in the sense that they need not themselves be capable of metacognition. (shrink)
In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once the (...) right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)
Can stable regularities be explained without appealing to governing laws or any other modal notion? In this paper, I consider what I will call a ‘Humean system’—a generic dynamical system without guiding laws—and assess whether it could display stable regularities. First, I present what can be interpreted as an account of the rise of stable regularities, following from Strevens [2003], which has been applied to explain the patterns of complex systems (such as those from meteorology and statistical mechanics). Second, (...) since this account presupposes that the underlying dynamics displays deterministic chaos, I assess whether it can be adapted to cases where the underlying dynamics is not chaotic but truly random—that is, cases where there is no dynamics guiding the time evolution of the system. If this is so, the resulting stable, apparently non-accidental regularities are the fruit of what can be called statistical necessity rather than of a primitive physical necessity. (shrink)
This chapter introduces a novel account of fake news and explains how it differs from other definitions on the market. The account locates the fakeness of an alleged news report in two main aspects related to its production, namely that its creators do not think to have sufficient evidence in favor of what they divulge and they fail to display the appropriate attitude towards the truth of the information they share. A key feature of our analysis is that it (...) does not require that fake news must be circulated with the intention to deceive one’s audience. In this way, our account overcomes a potential limitation of the current philosophical discussion about fake news, which appears to individuate the main problem with this phenomenon in the fact that fake news consumers are misled and misinformed. In contrast, the proposed analysis shows that an additional (and perhaps equally fundamental) problem uncovered by the spread of fake news is a widespread pathological relationship with information, one on which we consume information not to satisfy our interest in the truth but to strengthen our social identities and quench our hunger for social recognition. (shrink)
Interactive social cognition theory and approaches of developmental psychology widely agree that central aspects of emotional and social experience arise in the unfolding of processes of embodied social interaction. Bi-directional dynamical couplings of bodily displays such as facial expressions, gestures, and vocalizations have repeatedly been described in terms of coordination, synchrony, mimesis, or attunement. In this paper, I propose conceptualizing such dynamics rather as processes of affective resonance. Starting from the immediate phenomenal experience of being immersed in interaction, I develop (...) the philosophical notion of affective resonance to refer to a dynamic entanglement of moving and being-moved in relation. The concept of affective resonance makes visible that the interaction dynamic itself creates an affective experience rather than transmitting internal feeling states between pre-existent individuals. This leads to a philosophical framework in which relationality and ontogeny are primary over separate individuals, and in which the naturalistic distinction of a fundamental physical level versus an emerging level of social processes has to be given up. (shrink)
Nihilism, Nietzsche and the Doppelganger Problem Was Nietzsche a nihilist? Yes, because, like J. L. Mackie, he was an error-theorist about morality, including the elitist morality to which he himself subscribed. But he was variously a diagnostician, an opponent and a survivor of certain other kinds of nihilism. Schacht argues that Nietzsche cannot have been an error theorist, since meta-ethical nihilism is inconsistent with the moral commitment that Nietzsche displayed. Schacht’s exegetical argument parallels the substantive argument (advocated in recent years (...) by Wright and Blackburn) that Mackie’s error theory can’t be true because if it were, we would have to give up morality or give up moralizing. I answer this argument with a little bit of help from Nietzsche. I then pose a problem, the Doppelganger Problem, for the meta-ethical nihilism that I attribute to Mackie and Nietzsche. (If A is a moral proposition then not-A is a moral proposition: hence not all moral propositions can be false.) I solve the problem by reformulating the error theory and also deal with a variant of the problem, the Reinforced Doppelganger, glancing at a famous paper of Ronald Dworkin’s. Thus, whatever its demerits, the error theory, is not self-refuting, nor does it require us to give up morality. (shrink)
In several recent contributions to the growing literature on slurs, Hedger draws upon Kaplan’s distinction between descriptive and expressive content to argue that slurs are expressions with purely expressive content. The distinction between descriptive and expressive content and the view that slurs are expressions with purely expressive content has been widely acknowledged in prior work, and Hedger aims to contribute to this tradition of scholarship by offering novel arguments in support of his ‘‘pure expressivist’’ account of slurs. But the account (...) that PE offers is explanatorily inadequate, resting on suspect a priori intuitions which also commit one to denying many basic facts about slurs, such as that slurs largely display systematic differential application and that slurs can be used non-offensively between in-group speakers. In this article I provide clear reasons for rejecting PE, arguing particularly against Hedger as one of PE’s most explicit and recent proponents. In showing that PE is inadequate in at least 11 ways, I argue in favor of a mixed or hybrid approach. (shrink)
Our prominent definitions of cognition are too vague and lack empirical grounding. They have not kept up with recent developments, and cannot bear the weight placed on them across many different debates. I here articulate and defend a more adequate theory. On this theory, behaviors under the control of cognition tend to display a cluster of characteristic properties, a cluster which tends to be absent from behaviors produced by non-cognitive processes. This cluster is reverse-engineered from the empirical tests that (...) comparative psychologists use to determine whether a behavior was generated by a cognitive or a non-cognitive process. Cognition should be understood as the natural kind of psychological process that non-accidentally exhibits the properties assessed by these tests (as well as others we have not yet discovered). Finally, I review two plausible neural accounts of cognition's underlying mechanisms?one based in localization of function to particular brain regions and another based in the more recent distributed networks approach to neuroscience?which would explain why these properties non-accidentally cluster. While this notion of cognition may be useful for a number of debates, I here focus on its application to a recent crisis over the distinction between cognition and association in comparative psychology. (shrink)
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