The ?no???no? paradox (so-called by Sorensen) consists of a pair of propositions each of which says of the other that it is false. It is not immediately paradoxical, since it has a solution in which one proposition is true, the other false. However, that is itself paradoxical, since there is no clear ground for determining which is which. The two propositions should have the same truth-value. The paper shows how a proposal by the medieval thinker Thomas Bradwardine solves not only (...) the Liar paradox, but also symmetric paradoxes like the ?no???no?, the descending ?no???no?, and the Truth-teller paradoxes. (shrink)

This article will explore the pattern of conflicts between secular thinking and religious beliefs from the perspective of critical thinking and analyse the potential that this conflict holds for increasing tolerance inside mixed society such as in Romania. It is often said that the ability of thinking critically deeply erodes the propensity towards religious faith and there are numerous study results that back up this assertion. This article tries to explain that religious faith becomes fully understandable only in some larger (...) pattern that shapes morality, cognitive strategies and social practices and this is true for secular thinking as well. We can name this patterns ascendant, respectively descendant. Ascendant thinking derives and explains higher level practices beginning from lower level entities through progress and emergence and for this kind of thinking, morality and cognition are an open fields that can be indefinitely improved. This kind of thinking embraces novelty and creativity and aims at human beings becoming capable of managing this novelty. The descending model derives from and explains the lower levels through complex and immutable entities and will tend to see novelty as change capable of breaking their models and therefore act towards neutralizing novelty through interpretation. Information and practices that cannot be neutralized will be counted as abnormous. The article comes forward with a comparative analysis between these two opposing patterns, showing that this interpretative frame is valid in retrodiction and that it can fundament concrete predictions. It will also show that critical thinking is permitted and can fundament a space for compromise and dialogue between religious and secular people. (shrink)

The philosophy of loveFor centuries, popular writers and respected scholars have written about and analyzed the phenomenon of love without exhausting its potential for contemporary debate. By representing the three major traditions in the philosophy of love--Platonic eros, Christian agape, and Aristotelian philia--editor Alan Soble has not only examined the intellectual problem of what "love" is, but has designed a dialogue among the three traditions in genuine philosophical style. "Eros is acquisitive, egocentric or even selfish; agape is a giving love. (...) Eros is an unconstant, unfaithful love, while agape is unwavering and continues to give despite ingratitude. Eros is a love that responds to the merit or value of its object; while agape creates value in its object as a result of loving it... Finally, eros is an ascending love, the human's route to God; agape is a descending love, GodÆs route to humans... Philia is caught between eros and agape."--From the Introduction to Eros, Agape and Philia ISSUES EXPLORED: --What is the state of love today as seen through the eyes of Plato, Aristotle, and Paul? --How do relations between the sexes illustrate the difficulties of love? --What are the nature and effects of exclusivity, reciprocity, and constancy? --What are the conceptual and psychological ties between sex and love? --Does it make any sense to think of love in moral terms? (shrink)

As part of an approach to the liar paradox and the other paradoxes affecting truth, I have proposed replacing our concept of truth with two concepts: ascending truth and descending truth.1 I am not going to discuss why I think this is the best approach or how it solves the paradoxes; instead, I concentrate on the theory of ascending and descending truth. I formulate an axiomatic theory of ascending truth and descending truth (ADT) and (...) provide a possible-worlds semantics for it (which I dub xeno semantics). Xeno semantics is a generalization of the familiar neighborhood semantics, which itself is a generalization of the standard relational semantics. Once the details of ADT have been presented, it is easy to show that neither relational semantics nor neighborhood semantics will work for it; thus, the move to a more general framework is required. The main result is a fixed point theorem that guarantees the existence of an acceptable first-order constant-domain xeno model. From this result it follows that ADT is sound with respect to the class of such models. The upshot is that ADT is consistent relative to the background set theory. (shrink)

Telos is in vogue in biosemiotic researches, which present the teleological solution as anti-Darwinian, while it is more often, for biologists, only ante-Darwinian. The assimilation of structuring contents to a “function”, and of the function to a “goal”, in an irreversible temporality, is the most frequent basis of this methodological creepage. The teleology is based on a projective and ascending epistemic orientation, to which we can oppose a retrojective, descending and achronic one, including modal and sensitive interactional semiotics. (...) For semiotics, the challenge lies in the nature of its relationships with other disciplines, particularly biology. Indeed, we see that the temptation is great for semioticians to dwell precisely in the shadows and shams of other disciplines, and to call “sign” or “semiosis” what other sciences seem to have still some trouble to explain, with the risk of only confronting problems that will soon be obsolete. We propose here the theoretical and methodological principles of structural biosemiotics, and precisely attentive to the problems that biologists face, solve and renew. (shrink)

In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply (...) rooted in the tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)

1. Setting off: An introduction. 1.1. A measure of motivation. 1.2. Computable mathematics. 1.3. Reverse mathematics. 1.4. An overview. 1.5. Further reading -- 2. Gathering our tools: Basic concepts and notation. 2.1. Computability theory. 2.2. Computability theoretic reductions. 2.3. Forcing -- 3. Finding our path: Konig's lemma and computability. 3.1. II[symbol] classes, basis theorems, and PA degrees. 3.2. Versions of Konig's lemma -- 4. Gauging our strength: Reverse mathematics. 4.1. RCA[symbol]. 4.2. Working in RCA[symbol]. 4.3. ACA[symbol]. 4.4. WKL[symbol]. 4.5. (...) [symbol]-models. 4.6. First order axioms. 4.7. Further remarks -- 5. In defense of disarray -- 6. Achieving consensus: Ramsey's theorem. 6.1. Three proofs of Ramsey's theorem. 6.2. Ramsey's theorem and the arithmetic hierarchy. 6.3. RT, ACA[symbol], and the Paris-Harrington theorem. 6.4. Stability and cohesiveness. 6.5. Mathias forcing and cohesive sets. 6.6. Mathias forcing and stable colorings. 6.7. Seetapun's theorem and its extensions. 6.8. Ramsey's theorem and first order axioms. 6.9. Uniformity -- 7. Preserving our power: Conservativity. 7.1. Conservativity over first order systems. 7.2. WKL[symbol] and II[symbol]-conservativity. 7.3. COH and r-II[symbol]-conservativity -- 8. Drawing a map: Five diagrams -- 9. Exploring our surroundings: The world below RT[symbol]. 9.1. Ascending and descending sequences. 9.2. Other combinatorial principles provable from RT[symbol]. 9.3. Atomic models and omitting types -- 10. Charging ahead: Further topics. 10.1. The Dushnik-Miller theorem. 10.2. Linearizing well-founded partial orders. 10.3. The world above ACA[symbol]. 10.4. Still further topics, and a final exercise. (shrink)

Bradwardine’s solution to the the logical paradoxes depends on the idea that every sentence signifies many things, and its truth depends on things’ being wholly as it signifies. This idea is underpinned by his claim that a sentence signifies everything that follows from what it signifies. But the idea that signification is closed under entailment appears too strong, just as logical omniscience is unacceptable in the logic of knowledge. What is needed is a more restricted closure principle. A clue can (...) be found in speech act pluralism, whereby indirect speech reports are closed under intersubstitutivity of co-referential terms. The conclusion is that solving the semantic paradoxes does not require revision of logic, thus saving logic from paradox. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Descartes and Method: A Search for a Method in MeditationsPatrick FriersonDaniel E. Flage and Clarence A. Bonnen. Descartes and Method: A Search for a Method in Meditations. New York: Routledge, 1999. Pp. 332. Cloth, $90.00.The book has two parts. The first (Chapters 1-3 and an appendix) outlines Descartes's method of analysis, a method for discovering laws and clarifying ideas. The second (Chapters 4-10) offers a running commentary of (...) the Meditations that can be read on its own and is valuable not only for specialists as a challenging comprehensive account but also for anyone looking for a concise and coherent secondary source.The method is taken from the Discourse and illustrated using the Optics. According to the authors, analysis in the search for laws "is a type of argument to the best explanation" (23) that involves "two different issues, discovery and confirmation" (21). In discovery, one isolates a phenomenon and posits one or more explanations (or causes) for it. In confirmation, one tests this explanation for "material truth" (whether it is recognized as true by the natural light). Then one shows how the phenomenon is "caused" by the explanation, and that it is the best explanation, and that it can be included in a systematic science.The discussion of analysis in the clarification of ideas argues against " 'the epistemic thesis,' that is, the thesis that all innate ideas are (materially) true and known to be true as soon as they are considered"(45). Most of the arguments here address the claim that innate ideas are known to betrue. These arguments are followed by an account of how analysis clarifies ideas through successive refinement, and an illustration of this method from Descartes's clarification of the idea of light in the Optics. The final chapter of the section on method defends the claim that Descartes uses "cause" to refer to formal rather than efficient causation.The authors then turn to the Meditations, offering a virtually line by line treatment of major themes, with attention to showing how the method outlined in part one structures the arguments of the Meditations. Meditations 1-3 "ascend" through discovery and preliminary confirmation, ending with a perfect, non-deceiving God as the best explanation of our idea of God. The final meditations "descend" from that best explanation to its implications. This descent confirms the explanation by showing its place in a system.The second part of the book also includes explanations of the part that conceptual clarifications play in the Meditations. Flage and Bonnen discuss the cogito argument, the account of the wax, the arguments for the existence of God, and the distinction of mind and body, all as examples of conceptual clarification through the method of analysis. In the case of God, for instance, Descartes begins with Hobbes's crude conception of God and clarifies it into the simple, clear, and distinct notion of a "most perfect being."The last chapter addresses the circle ascribed to Descartes by Arnauld: that the argument for the existence of God depends on the truth of clear and distinct ideas, which is only established on the basis of the existence of God. The authors argue that this is not a true circle, since Descartes assumes the material truth of clear and distinct ideas (which is indubitable) in his early argument and draws on their formal truth (in the mind of God) only after he proves the existence of God. They suggest their own circle, however: in his response to other concerns of Arnauld, Descartes suggests that God [End Page 436] stops a causal regress and thus commits himself to the formal truth of the idea of God, which he cannot independently justify.As one would expect in a book that offers a concise and unified interpretation of the Meditations, readers will find unnecessary asides and wish for attention to issues that are passed over. Moreover, though the authors support some views with extensive quotations, they leave others without textual support. The most unfortunate example is the identification of formal truth with actuality. The authors have several accounts of the distinction between formal and material truth and end their book with... (shrink)

Models of cultural evolution need to address not only the organizational aspects of human societies, but also the complexity and structure of cultural idea systems that frame their systems of organization. These cultural idea systems determine a framework within which behaviors take place and provide mutually understood meanings for behavior from the perspective of both agent and recipient that are critical for the coherence of human systems of social organization.

Decay gradients are usually drawn facing the wrong direction. Righting them emphasizes the role of stimuli that mark the response, and leads to different inferences concerning the factors controlling response–reinforcer associations. A simple model of the concatenation of stimulus traces provides some insight to the problems of impulse control relevant to ADHD.

The first truly introductory text on Lyotard, this book situates Lyotard's interventions in the postmodern debate in the wider context of his rethinking of the politics of representation. Bill Readings examines Lyotard's relationship to structuralism, Marxism and semiotics, and contrasts his work with the literary deconstruction of Paul de Man; he positions Lyotard's work so as to draw out the implications of poststructurlaism's attention to _difference_ in reading. Lyotard's willingness to question the political and examine the relationship between art (...) and politics is shown to undermine the charge that deconstruction abdicates political and social articulation. (shrink)

The correspondence theory of truth has experienced something of a revival recently in the form of the Truthmaker Axiom: whatever is true, something makes it true. We consider various postulates which have been proposed to characterize truthmaking, in particular, the Disjunction Thesis (DT), that whatever makes a disjunction true must make one or other disjunct true. In conjunction with certain other assumptions, DT leads to triviality. We show that there are elaborations of truthmaking on which DT holds (which must therefore (...) take steps to avoid the triviality); but that there are more plausible accounts of truthmaking on which DT fails. (shrink)

Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...) be said to exhibit “general-elimination” harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions. (shrink)

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration (...) of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen's. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic. (shrink)

I discuss the debate between dynamical versus geometrical approaches to spacetime theories, in the context of both special and general relativity, arguing that the debate takes a substantially different form in the two cases; different versions of the geometrical approach—only some of which are viable—should be distinguished; in general relativity, there is no difference between the most viable version of the geometrical approach and the dynamical approach. In addition, I demonstrate that what have previously been dubbed two ‘miracles’ of general (...) relativity admit of no resolution from within general relativity, on either the dynamical or ‘qualified’ geometrical approaches, modulo some possible hints that the second ‘miracle’ may be resolved by appeal to recent results regarding the ‘geodesic principle’ in GR. (shrink)

Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a (...) contradictory pair, in which one statement affirms what the other denies of the same thing, Aristotle himself gave counterexamples to the rule. This gives some credence to Swyneshed’s claim that his solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Insolubles are false, he said, because they falsify themselves; and their contradictories are false because they falsely deny that the insoluble itself is false. Swyneshed’s solution depends crucially on the revision he makes to the acount of truth and falsehood, brought out in his first thesis: that a false proposition can signify as it is, or as Paul of Venice, who took up and developed Swyneshed’s solution some sixty years later, puts it, a false proposition can have a true significate. Swyneshed gave a further counterexample to when he claimed that some insolubles, like future contingents, are neither true nor false. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. Consequently, Swyneshed’s logical heresy is very different from that found in dialetheism. (shrink)

Jan Lukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle's logical systems. However, Lukasiewicz's interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to non-empty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition.

Re-reads Marx in light of the contemporary critical interrogation of subjectivity.

Ideologies, worldviews, or simply personal theories, often acquire a distorted and pathological character, and become a factor of alienation rather than an epistemic resource and an aid for personal existence. This paper attempts to better define the limits and characteristics of this experience, which we call distorted intellectual beliefs, or general conceptual beliefs (GB), while trying to highlight both its sometimes dramatic background and its personal and social consequences, which are no less potentially deleterious. We believe that such experiences should (...) not be confused tout court with a broader and more complex phenomenon, such as extremism and politico-religious radicalism, but are a specific typology of that broader and multifaceted fact that is self-deception. We hypothesize that the self-deception implicit in experiences of intellectual distortion produces a cognitive dissonance of which the subject is normally, though with varying intensity, aware (or may become aware through honest introspection). The phenomenon occurs in two extreme forms: one is normal (sporadic), the other is exceptional (systematic). The passage from one to the other is a complex process of escalation and de-escalation, on which multiple external and internal variables act. In its ascending path, it essentially coincides with a process of psychological polarization and cognitive "de-pluralization", while its descending phase marks a return to reality and a "re-pluralization", where the subject returns to being what he basically is, namely, an active and tireless meaning seeker. In the central part of the chapter, similarities and differences between processes of deradicalization and phenomena of religious deconversion are analyzed, with reference, among others, to the case of the Austro-Hungarian writer Arthur Koestler. -/- An abridged version of this text has been delivered for the Workshop "Explaining Extreme Belief and Extreme Behavior", September 15-16, 2022, Vrije Universiteit Amsterdam. I am grateful to David Konstan (NYU) for reading and commenting on a first version of this chapter and to Rik Peels (VUA) for his comments and questions during the Workshop. I would also like to thank my bachelor's and master's students at UDG, who discussed these topics at length with during semester 2022-B. (shrink)

In this book, Stephen Read sets out to rescue logic from its undeserved reputation as an inflexible, dogmatic discipline by demonstrating that its technicalities and processes are founded on assumptions which are themselves amenable to philosophical investigation. He examines the fundamental principles of consequence, logical truth and correct inference within the context of logic, and shows that the principles by which we delineate consequences are themselves not guaranteed free from error. Central to the notion of truth is the beguiling issue (...) of paradox. Its philosophical value, Read shows, lies in exposing the invalid assumption on which the paradox is built. Thinking About Logic also discusses logical puzzles which introduce questions relating to language, the world, and their relationship. (shrink)

Ideologies, worldviews, or simply personal theories, often acquire a distorted and pathological character, and become a factor of alienation rather than an epistemic resource and an aid for personal existence. This paper attempts to better define the limits and characteristics of this experience, which we call distorted intellectual beliefs, or general conceptual beliefs (GB), while trying to highlight both its sometimes dramatic background and its personal and social consequences, which are no less potentially deleterious. We believe that such experiences should (...) not be confused tout court with a broader and more complex phenomenon, such as extremism and politico-religious radicalism, but are a specific typology of that broader and multifaceted fact that is self-deception. We hypothesize that the self-deception implicit in experiences of intellectual distortion produces a cognitive dissonance of which the subject is normally, though with varying intensity, aware (or may become aware through honest introspection). The phenomenon occurs in two forms: one is normal (sporadic), the other is exceptional (systematic). The passage from one to the other is a complex process of escalation and de-escalation, on which multiple external and internal variables act. In its ascending path, it essentially coincides with a process of psychological polarization and cognitive "de-pluralization", while its descending phase marks a return to reality and a "re-pluralization", where the subject returns to being what he basically is, namely, an active and tireless meaning seeker. In the central part of the chapter, similarities and differences between processes of deradicalization and phenomena of religious deconversion are analyzed, with reference, among others, to the case of the Austro-Hungarian writer Arthur Koestler. -/- An abridged version of this text has been delivered for the Workshop "Explaining Extreme Belief and Extreme Behavior", September 15-16, 2022, Vrije Universiteit Amsterdam. I am grateful to David Konstan (NYU) for reading and commenting on a first version of this chapter and to Rik Peels (VUA) for his comments and questions during the Workshop. I would also like to thank my bachelor's and master's students at UDG, who discussed these topics at length with during semester 2022-B. (shrink)

Debates about empathy's role in morality are notoriously complex. On the one hand, proponents of empathy argue that it plays a crucial role in the process of making moral judgments, moral motivation, moral development, and the cultivation of meaningful personal relationships. On the other hand, critics of empathy warn that it is especially susceptible to a number of morally troubling biases and motivational shortcomings. Yet there is little consensus about what empathy is or what it might be good for from (...) a moral point of view. As a result, critics and proponents of empathy alike often wind up talking past each other and debates about empathy's role in morality reach an impasse. This paper proposes a typology of empathy's affective, cognitive, and motivational dimensions and the different forms that empathy can take depending on the nature and degree of prominence of these. It argues that different forms of empathy are well equipped to handle some moral tasks as well as ill‐equipped to handle others. Its aim in doing so is to clarify an otherwise conceptually thorny set of debates and to amplify future research on empathy and its role in the moral life. (shrink)

Ecological Psychology and Enactivism both challenge representationist cognitive science, but the two approaches have only begun to engage in dialogue. Further conceptual clarification is required in which differences are as important as common ground. This paper enters the dialogue by focusing on important differences. After a brief account of the parallel histories of Ecological Psychology and Enactivism, we cover incompatibility between them regarding their theories of sensation and perception. First, we show how and why in ecological theory perception is, crucially, (...) not based on sensation. We elucidate this idea by examining the biological roots of work in the two fields, concentrating on Gibson and Varela and Maturana. We expound an ecological critique of any sensation-based approach to perception by detailing two topics: classic retinal image theories and perception in single-celled organisms. The second main point emphasizes the importance of the idea of organism-environment mutuality and its difference from structural coupling of sensations and motor behavior. We point out how ecological - phenomenological methods of inquiry grow out of mutualism and compare Gibson’s idea of visual kinesthesis to Merleau-Ponty’s idea of the lived body. Third, we conclude that Ecological Psychology and varieties of Enactivism are laying down different paths to pursue related goals. Thus, convergence of Ecological Psychology and Enactivism is not possible given their conflicting assumptions, but cross-fertilization is possible and desirable. (shrink)

We approach the physics of \emph{minimal coupling} in general relativity, demonstrating that in certain circumstances this leads to violations of the \emph{strong equivalence principle}, which states that, in general relativity, the dynamical laws of special relativity can be recovered at a point. We then assess the consequences of this result for the \emph{dynamical perspective on relativity}, finding that potential difficulties presented by such apparent violations of the strong equivalence principle can be overcome. Next, we draw upon our discussion of the (...) dynamical perspective in order to make explicit two `miracles' in the foundations of relativity theory. We close by arguing that the above results afford us insights into the nature of special relativity, and its relation to general relativity. (shrink)

This article examines Michel Foucault’s critical investigation of neoliberalism in the course published as Naissance de la biopolitique: Cours au Collège de France, 1978-1979. Foucault’s lectures are interrogated along two axes. First, examining the way in which neoliberalism can be viewed as a particular production of subjectivity, as a way in which individuals are constituted as subjects of “human capital.” Secondly, Foucault’s analyses is augmented and critically examined in light of other critical work on neoliberalism by Wendy Brown, David Harvey, (...) Christian Laval, Maurizo Lazzarato, and Antonio Negri. Of these various debates and discussions, the paper argues that the discussion of real subsumption in Marx and Negri is most important for understanding the specific politics of neoliberalism. Finally, the paper argues that neoliberalism entails a fundamental reexamination of the tools of critical thought, an examination of how freedom can constitute a form of subjection. (shrink)

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion of semantics into syntax. The charge is shown to be mistaken. It is argued on inferentialist grounds that labelled deductive systems are as syntactically (...) pure as any formal system in which the rules define the meanings of the logical constants. (shrink)

We analyze the axiomatic strength of the following theorem due to Rival and Sands [28] in the style of reverse mathematics. Every infinite partial order P of finite width contains an infinite chain C such that every element of P is either comparable with no element of C or with infinitely many elements of C. Our main results are the following. The Rival–Sands theorem for infinite partial orders of arbitrary finite width is equivalent to $\mathsf {I}\Sigma ^0_{2} + \mathsf {ADS}$ (...) over $\mathsf {RCA}_0$. For each fixed $k \geq 3$, the Rival–Sands theorem for infinite partial orders of width $\leq \!k$ is equivalent to $\mathsf {ADS}$ over $\mathsf {RCA}_0$. The Rival–Sands theorem for infinite partial orders that are decomposable into the union of two chains is equivalent to $\mathsf {SADS}$ over $\mathsf {RCA}_0$. Here $\mathsf {RCA}_0$ denotes the recursive comprehension axiomatic system, $\mathsf {I}\Sigma ^0_{2}$ denotes the $\Sigma ^0_2$ induction scheme, $\mathsf {ADS}$ denotes the ascending/descending sequence principle, and $\mathsf {SADS}$ denotes the stable ascending/descending sequence principle. To the best of our knowledge, these versions of the Rival–Sands theorem for partial orders are the first examples of theorems from the general mathematics literature whose strength is exactly characterized by $\mathsf {I}\Sigma ^0_{2} + \mathsf {ADS}$, by $\mathsf {ADS}$, and by $\mathsf {SADS}$. Furthermore, we give a new purely combinatorial result by extending the Rival–Sands theorem to infinite partial orders that do not have infinite antichains, and we show that this extension is equivalent to arithmetical comprehension over $\mathsf {RCA}_0$. (shrink)

There exists a common view that for theories related by a ‘duality’, dual models typically may be taken ab initio to represent the same physical state of affairs, i.e. to correspond to the same possible world. We question this view, by drawing a parallel with the distinction between ‘interpretational’ and ‘motivational’ approaches to symmetries.

In recent years, speech-act theory has mooted the possibility that one utterance can signify a number of different things. This pluralist conception of signification lies at the heart of Thomas Bradwardine’s solution to the insolubles, logical puzzles such as the semantic paradoxes, presented in Oxford in the early 1320s. His leading assumption was that signification is closed under consequence, that is, that a proposition signifies everything which follows from what it signifies. Then any proposition signifying its own falsity, he showed, (...) also signifies its own truth and so, since it signifies things which cannot both obtain, it is simply false. Bradwardine himself, and his contemporaries, did not elaborate this pluralist theory, or say much in its defence. It can be shown to accord closely, however, with the prevailing conception of logical consequence in England in the fourteenth century. Recent pluralist theories of signification, such as Grice’s, also endorse Bradwardine’s closure postulate as a plausible constraint on signification, and so his analysis of the semantic paradoxes is seen to be both well-grounded and plausible. (shrink)

The surge of interest in Jean-Francois Lyotard's writings has pushed him into the centre of debate on the postmodern.

Frege’s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel’s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ‘complete’ it is clear from Dedekind’s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical or (...) complete, there are logical extensions of these theories into second-order and by the addition of generalized quantifiers which are categorical. Frege’s project really found success through Gödel’s completeness theorem of 1930 and the subsequent development of first- and higher-order model theory. (shrink)

The Oxford Calculator Roger Swyneshed put forward three provocative claims in his treatise on insolubles, written in the early 1330s, of which the second states that there is a formally valid inference with true premises and false conclusion. His example deployed the Liar paradox as the conclusion of the inference: ‘The conclusion of this inference is false, so this conclusion is false’. His account of insolubles supported his claim that the conclusion is false, and so the premise, referring to the (...) conclusion, would seem to be true. But what is his account of validity that can allow true premises to lead to a false conclusion? This article considers Roger’s own account, as well as that of Paul of Venice, writing some sixty years later, whose account of the truth and falsehood of insolubles followed Roger’s closely. Paul endorsed Roger’s three claims. But their accounts of validity were different. The question is whether these accounts are coherent and support Paul’s claim in his Logica Magna that he endorsed all the normal rules of inference. (shrink)

For Knox, ‘spacetime’ is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays theoperationalrole of spacetime—i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields—we identify in this paper important limitations of her approach: these limitations are based upon the fact that there is a (...) gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox’s spacetime functionalism might be amended in light of these issues. (shrink)

Anti-exceptionalism about logic is the doctrine that logic does not require its own epistemology, for its methods are continuous with those of science. Although most recently urged by Williamson, the idea goes back at least to Lakatos, who wanted to adapt Popper's falsicationism and extend it not only to mathematics but to logic as well. But one needs to be careful here to distinguish the empirical from the a posteriori. Lakatos coined the term 'quasi-empirical' `for the counterinstances to putative mathematical (...) and logical theses. Mathematics and logic may both be a posteriori, but it does not follow that they are empirical. Indeed, as Williamson has demonstrated, what counts as empirical knowledge, and the role of experience in acquiring knowledge, are both unclear. Moreover, knowledge, even of necessary truths, is fallible. Nonetheless, logical consequence holds in virtue of the meaning of the logical terms, just as consequence in general holds in virtue of the meanings of the concepts involved; and so logic is both analytic and necessary. In this respect, it is exceptional. But its methodologyand its epistemology are the same as those of mathematics and science in being fallibilist, and counterexamples to seemingly analytic truths are as likely as those in any scientic endeavour. What is needed is a new account of the evidential basis of knowledge, one which is, perhaps surprisingly, found in Aristotle. (shrink)

A series of essays on film and philosophy whose authors - philosophers or film studies experts - write on a wide variety of films: classic Hollywood comedies, war films, Eastern European art films, science fiction, showing how film and watching it can not only illuminate philosophy but, in an important sense, be doing philosophy. The book is crowned with an interview with Wittgensteinian philosopher Stanley Cavell, discussing his interests in philosophy and in film and how they can come together.

Critics of empathy—the capacity to share the mental lives of others—have charged that empathy is intrinsically biased. It occurs between no more than two people, and its key function is arguably to coordinate and align feelings, thoughts, and responses between those who are often already in close personal relationships. Because of this, critics claim that empathy is morally unnecessary at best and morally harmful at worst. This paper argues, however, that it is precisely because of its ability to connect people (...) by coordinating and aligning their feelings, thoughts, and responses, that empathy is especially well suited to perform one particular moral task that has been largely overlooked in moral philosophical discussions. That is, helping people, including those who are antagonistically opposed on matters of moral, social, and political importance—what I call antagonistic moral opponents—find common ground: a set of shared beliefs, attitudes, values, or experiences that lays the requisite ground for even minimally positive relationships. Doing so can contribute to a number of morally, practically, and epistemically important outcomes, including resolving fraught disagreements, mitigating antagonism, promoting cooperation, learning from differences, and even forging positive relationships of various sorts. Contra critics, I therefore maintain that empathy is important for at least one area of the moral life. (shrink)

Logical pluralism is the claim that different accounts of validity can be equally correct. Beall and Restall have recently defended this position. Validity is a matter of truth-preservation over cases, they say: the conclusion should be true in every case in which the premises are true. Each logic specifies a class of cases, but differs over which cases should be considered. I show that this account of logic is incoherent. Validity indeed is truth-preservation, provided this is properly understood. Once understood, (...) there is one true logic, relevance logic. The source of Beall and Restall’s error is a recent habit of using a classical metalanguage to analyse non-classical logics generally, including relevance logic. (shrink)

In this book, Rupert Read offers the first outline of a resolute reading, following the highly influential New Wittgenstein 'school', of the Philosophical Investigations. He argues that the key to understanding Wittgenstein's later philosophy is to understand its liberatory purport. Read contends that a resolute reading coincides in its fundaments with what, building on ideas in the later Gordon Baker, he calls a liberatory reading. Liberatory philosophy is philosophy that can liberate the user from compulsive patterns of (...) thought, freeing one for possibilities that were previously obscured. Such liberation is our prime goal in philosophy. This book consists in a sequential reading, along these lines, of what Read considers the most important and controversial passages in the Philosophical Investigations 1, 16, 43, 95 & 116 & 122, 130-3, 149-151, 186, 198-201, 217, and 284-6. Read claims that this liberatory conception is simultaneously an ethical conception. The PI should be considered a work of ethics in that its central concern becomes our relation with others. Wittgensteinian liberations challenge widespread assumptions about how we allegedly are independent of and separate from others. Wittgenstein's Liberatory Philosophy will be of interest to scholars and advanced students working on Wittgenstein, and to scholars of the political philosophy of liberation and the ethics of relation. (shrink)

Affective polarization is characterized by deep antagonism between political opponents and is an issue of growing concern. Some philosophers have recently suggested empathy as a possible remedy. In particular, it has been suggested that empathy might mitigate the harm resulting from affective polarization by helping us find common ground across our differences. While these discussions provide a helpful starting point, important questions regarding the conditions under which empathizing and finding common ground are morally appropriate and likely to be useful, given (...) the many risks associated with taking this approach, remain unaddressed. In this paper, I therefore give an account of the risks that we must reckon with if empathy and common ground are to help remedy affective polarization and repair damaged relations between political opponents. Far from suggesting that empathy is morally unimportant or intrinsically harmful, my goal is thus to extend and amplify previous discussion to promote a more nuanced understanding of empathy's role in this important aspect of the moral life and to ensure that our efforts to empathize are appropriate and fruitful. (shrink)

‘You can’t stop progress’, we are endlessly told. But what is meant by “progress”? What is “progress” toward? We are rarely told. Human flourishing? And a culture? That would be a good start – but rarely seems a criterion for ‘progress’. Rather, ‘progress’ is simply a process, that we are not allowed, apparently, to stop. Or rather: it would be futile to seek to stop it. So that we are seemingly-deliberately demoralised into giving up even trying.Questioning the myth of ‘progress’, (...) and seeking to substitute for it the idea of real progress – progress which is actually assessed according to some independent not-purely-procedural criteria – is a vital thing to do, at this point in history. Literally: life, or at least civilisation, and thus culture, may depend on it.Once we overcome the myth of ‘progress’, we can clear the ground for a real politics that would jettison the absurd hubris of liberalism and of most ‘Leftism’. And would jettison the extreme Prometheanism and lack of precaution endemic to our current pseudo-democratic technocracy. The challenge is to do so in a way that does not fall into complete pessimism or into an endorsement of the untenable and unsavoury features of conservatism. The challenge, in other words, is to generate an ideology or philosophy for our time, that might yet save us, and ensure that we are worth saving.This paper is then a kind of reading of Wittgenstein’s crucial aphorism on this topic: ‘Our civilization is characterized by the word progress. Progress is its form rather than making progress being one of its features.’. (shrink)