The traditional view of lying holds that this phenomenon involves two central components: stating what one does not believe oneself and doing so with the intention to deceive. This view remained the generally accepted view of the nature of lying until very recently, with the intention-to-deceive requirement now coming under repeated attack. In this article, I argue that the tides have turned too quickly in the literature on lying. For while it is indeed true that there can be lies where (...) there is no intention on the part of the speaker to deceive the hearer, this does not warrant severing the connection between lying and deception altogether. Thus, I defend the following account of lying: A lies to B if and only if (1) A states that p to B, (2) A believes that p is false, and (3) A intends to be deceptive to B in stating that p. (shrink)

The main result of this paper is Theorem 3.1 which is a criterion for weak o-minimality of a linearly ordered structure in terms of realizations of 1-types. Here we also prove some other properties of weakly o-minimal structures. In particular, we characterize all weakly o-minimal linear orderings in the signature $\{ . Moreover, we present a criterion for density of isolated types of a weakly o-minimal theory. Lastly, at the end of the paper we present some remarks on the Exchange (...) Principle for algebraic closure in a weakly o-minimal structure. (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of (...) the connectives or the best logic outside of a specified context are not legitimate questions. (shrink)

The aim of this paper is to sketch a theory of musical experience which takes the empirical research seriously without abandoning or neglecting music’s transcendental features. The tension between the recent empirical approach, as represented particularly by Huron’s ITPRA theory, and the transcendental fact that music as an instance of art is something one can understand and, moreover, can understand oneself through, should be overcome by elaborating on the concept of emotion and the role it can play in musical understanding. (...) This will be done against the narrower background of the pragmatists’ theories of meaning, as represented by the semantic work of Meyer and Brandom, and their broader link to the philosophy of Hegel and the great systems of German idealism. (shrink)

This paper further develops the system of illocutionary logic presented in ?Propositional logic of supposition and assertion? (Notre Dame Journal of Formal Logic 1997, 38, 325-349) to accommodate an ?I believe that? operator and resolve Moore's Paradox. This resolution is accomplished by providing both a truth-conditional and a commitment-based semantics. An important feature of the logical system is that the correctness of some arguments depends on who it is that makes the argument. The paper then shows that the logical system (...) can be expanded to resolve the surprise execution paradox puzzle. The prisoner's argument showing that he can't be executed by surprise is correct but his beliefs are incoherent. The judge's beliefs (and our beliefs) about this situation are not incoherent. (shrink)

We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.

The sorites paradox is the name given to a class of paradoxical arguments, also known as little by little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap (...) and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion. (shrink)

Many logicians have tried to formalize a modal logic from the Prior Analytics, but the general view is that Aristotle has failed to offer a consistent modal logic there. This paper explains that Aristotle is not interested in modal logic as such. Modalities for him pertain to the relations of predication, without challenging the assertoric system of deductions simpliciter. Thus, demonstrations or dialectical deductions have modal predicates and yet are still deductions simpliciter. It is a matter of distinguishing inferential necessity (...) that applies to every deduction from the modal predicates in the two premises and conclusion. The modality of demonstrations can be either necessary or possible. The necessity is predicative, i.e., independent of inferential necessity. While the possible demonstration challenges the predicative necessity of the necessary demonstration, it preserves the inferential necessity of the deduction simpliciter. (shrink)

This paper shows that Aristotle's De Interpretatione does not separate syntax from semantics. Linguistic sentences are not syntactic entities, and non-linguistic meanings are not semantic propositions expressed by linguistic sentences. In fact, Aristotle resorts to a mental conception of meaning, distinguishing linguistic meanings in a given language from non-linguistic mental contents in relation to actual things: while the former are not the same for all, the latter are shared by everyone. Aristotle is not a modern logician, like Boole, Frege, or (...) Russell, in so far as a mental conception of meaning does not reveal an abstract semantics for a syntactic language. (shrink)

Logic isn’t special. Its theories are continuous with science; its method continuous with scientific method. Logic isn’t a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in Maddy, Priest, Russell, and Williamson. Although these authors agree on many methodological issues about logic, (...) they disagree about which logic anti-exceptionalism supports. Williamson uses an anti-exceptionalist argument to defend classical logic, while Priest claims that his anti-exceptionalism supports nonclassical logic. This paper argues that the disagreement is due to a difference in how the parties understand logical theories. Once we reject Williamson’s deflationary account of logical theories, the argument for classical logic is undercut. Instead an alternative account of logical theories is offered, on which logical pluralism is a plausible supplement to anti-exceptionalism. (shrink)

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given (...) class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings ; integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. This allows us to show that several theorems about degree spectra of relations on computable structures, nonpreservation of computable categoricity, and degree spectra of structures remain true when we restrict our attention to structures in any of the classes on this list. The codings we present are general enough to be viewed as establishing that the theories mentioned above are computably complete in the sense that, for a wide range of computability-theoretic nonstructure type properties, if there are any examples of structures with such properties then there are such examples that are models of each of these theories. (shrink)

The so-called New Theory of Reference (Marcus, Kripke etc.) is inspired by the insight that in modal and intensional contexts quantifiers presuppose nondescriptive unanalyzable identity criteria which do not reduce to any descriptive conditions. From this valid insight the New Theorists fallaciously move to the idea that free singular terms can exhibit a built-in direct reference and that there is even a special class of singular terms (proper names) necessarily exhibiting direct reference. This fallacious move has been encouraged by a (...) mistaken belief in the substitutional interpretation of quantifiers, by the myth of thede re reference, and a mistaken assimilation of direct reference to ostensive (perspectival) identification. Thede dicto vs.de re contrast does not involve direct reference, being merely a matter of rule-ordering (scope).The New Theorists' thesis of the necessity of identities of directly referred-to individuals is a consequence of an unmotivated and arbitrary restriction they tacitly impose on the identification of individuals. (shrink)

The ontological argument fails because of an operator order switch between (1) “necessarily there is an perfect being” and (2) “there is a being which necessarily is perfect”. Here (1) is trivially true logically but (2) problematic. Since Kant's criticisms were directed at the notion of existence, not at the step from (1) to (2), they are misplaced. They are also wrong, because existence can be a predicate. Moreover, Kant did not anticipate Frege's claim that “is” is ambiguous between existence, (...) predication, identity, and class‐inclusion. To restore the ontological argument, an extra premise is needed to the effect that it is known who the existentially perfect being is. The question is raised whether Kant could have meant the failure of this extra premise by his thesis that existence is not a real predicate. (shrink)

In a recent paper, Sven Danielsson argued that the ‘original paradoxes' of deontic logic, in particular Ross's paradox and Prior's paradox of derived obligation, can be solved by restricting the modal inheritance rule. I argue that this does not solve the paradoxes.

According to the semantic view of scientific theories, theories are classes of models. I show that this view -- if taken seriously as a formal explication -- leads to absurdities. In particular, this view equates theories that are truly distinct, and it distinguishes theories that are truly equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view -- as currently formulated -- threatens to (...) undermine scientific structuralism. (shrink)

In this paper, it is argued that the most fruitful approach to developing normative models of argument quality is one that combines the argumentation scheme approach with Bayesian argumentation. Three sample argumentation schemes from the literature are discussed: the argument from sign, the argument from expert opinion, and the appeal to popular opinion. Limitations of the scheme-based treatment of these argument forms are identified and it is shown how a Bayesian perspective may help to overcome these. At the same time, (...) the contributions of the standard scheme-based approach are highlighted, and it is argued that only a combination of the insights of different traditions will yield a complete normative theory of argument quality. (shrink)

In this article, we argue for the general importance of normative theories of argument strength. We also provide some evidence based on our recent work on the fallacies as to why Bayesian probability might, in fact, be able to supply such an account. In the remainder of the article we discuss the general characteristics that make a specifically Bayesian approach desirable, and critically evaluate putative flaws of Bayesian probability that have been raised in the argumentation literature.

We continue the investigations initiated in the recent papers where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using the Bayes rule. In this paper we take the more general Jeffrey formula as a conditioning device and study the corresponding modal logics that we call Jeffrey logics, focusing mainly on the countable case. The containment relations among (...) these modal logics are determined and it is shown that the logic of Bayes and Jeffrey updating are very close. It is shown that the modal logic of belief revision determined by probabilities on a finite or countably infinite set of elementary propositions is not finitely axiomatizable. The significance of this result is that it clearly indicates that axiomatic approaches to belief revision might be severely limited. (shrink)

In the article [2] a hierarchy of modal logics has been defined to capture the logical features of Bayesian belief revision. Elements in that hierarchy were distinguished by the cardinality of the set of elementary propositions. By linking the modal logics in the hierarchy to the modal logics of Medvedev frames it has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. However, the infinite case (...) remained open. In this article we prove that the modal logic of Bayesian belief revision determined by standard Borel spaces is also not finitely axiomatizable. (shrink)

Mainstream epistemology is a highly theoretical and abstract enterprise. Traditional epistemologists rarely present their deliberations as critical to the practical problems of life, unless one supposes—as Hume, for example, did not—that skeptical worries should trouble us in our everyday affairs. But some issues in epistemology are both theoretically interesting and practically quite pressing. That holds of the problem to be discussed here: how laypersons should evaluate the testimony of experts and decide which of two or more rival experts is most (...) credible. It is of practical importance because in a complex, highly specialized world people are constantly confronted with situations in which, as comparative novices, they must turn to putative experts for intellectual guidance or assistance. It is of theoretical interest because the appropriate epistemic considerations are far from transparent; and it is not clear how far the problems lead to insurmountable skeptical quandaries. This paper does not argue for flat-out skepticism in this domain; nor, on the other hand, does it purport to resolve all pressures in the direction of skepticism. It is an exploratory paper, which tries to identify problems and examine some possible solutions, not to establish those solutions definitively. (shrink)

Recent work on conditional reasoning argues that denying the antecedent [DA] and affirming the consequent [AC] are defeasible but cogent patterns of argument, either because they are effective, rational, albeit heuristic applications of Bayesian probability, or because they are licensed by the principle of total evidence. Against this, we show that on any prevailing interpretation of indicative conditionals the premises of DA and AC arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather (...) depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

Substructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0.1]. In this paper, we introduce Uninorm logic UL as Multiplicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom ((A → B) ∧ t) ∨ ((B → A) ∧ t). Axiomatic extensions of UL include known fuzzy logics such as Monoidal t-norm logic MTL and Gödel logic G, and new weakening-free logics. Algebraic semantics for these logics are (...) provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0, 1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0, 1]. (shrink)

It has been noted before in the history of logic that some of Frege's logical and semantic views were anticipated in Stoicism. In particular, there seems to be a parallel between Frege's Gedanke (thought) and Stoic lekton; and the distinction between complete and incomplete lekta has an equivalent in Frege's logic. However, nobody has so far claimed that Frege was actually influenced by Stoic logic; and there has until now been no indication of such a causal connection. In this essay, (...) we attempt, for the first time, to provide detailed evidence for the existence of this connection. In the course of our argumentation, further analogies between the positions of Frege and the Stoics will be revealed. The classical philologist Rudolf Hirzel will be brought into play as the one who links Frege with Stoicism. The renowned expert on Stoic philosophy was Frege's tenant and lived in the same house as the logician for many years. In der Geschichte der Logik ist häufig bemerkt worden, dass einige der logischen und semantischen Auffassungen Freges in der Stoa antizipiert worden sind. Genannt wurden insbesondere die Parallelen zwischen dem Fregeschen Gedanken und dem stoischen Lekton sowie die Unterscheidung zwischen vollständigen und unvollständigen Lekta, die bei Frege ihre Entsprechung hat. Ein Wirkungszusammenhang ist allerdings nicht behauptet worden. Dazu gab es bislang auch keinen Anlass. Der vorliegende Beitrag versucht erstmalig, einen detaillierten Indizienbeweis für das Bestehen eines solchen Zusammenhangs vorzulegen. Dabei werden weitere charakteristische Übereinstimmungen zwischen Frege und der Stoa aufgewiesen. Als Mittelsmann wird der Altphilologe Rudolf Hirzel vorgestellt. Er wohnte lange Jahre als Mieter zusammen mit Frege im selben Haus und war ein anerkannter Experte der stoischen Philosophie. (shrink)

The use of “levels of abstraction” in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section “Some Definitions and Preliminary Examples” the nature and applicability of the epistemological method of levels of abstraction is clarified. In section “A Classic Application of the Method ofion”, the philosophical fruitfulness of the new (...) method is shown by using Kant’s classic discussion of the “antinomies of pure reason” as an example. In section “The Philosophy of the Method of Abstraction”, the method is further specified and supported by distinguishing it from three other forms of “levelism”: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems. (shrink)

Contemporary science seems to be caught in a strange predicament. On the one hand, it holds a firm and reasonable commitment to a healthy naturalistic methodology, according to which explanations of natural phenomena should never overstep the limits of the natural itself. On the other hand, contemporary science is also inextricably and now inevitably dependent on ever more complex technologies, especially Information and Communication Technologies, which it exploits as well as fosters. Yet such technologies are increasingly “artificialising” or “denaturalising” the (...) world, human experiences and interactions, as well as what qualifies as real. So the search for the ultimate explanation of the natural seems to rely upon, and promote, the development of the artificial, seen here as an instantiation of the non-natural. In this article, I would like to try and find a way out of this apparently strange predicament. I shall argue that the naturalisation of our knowledge of the world is either philosophically trivial, or mistaken. First, I shall distinguish between different kinds of naturalism. Second, I shall remind the reader that the kinds of naturalism that are justified today need to be protected and supported pragmatically, but they are no longer very interesting conceptually. We know how to win the argument. We just have to keep winning it. Whereas the kind of naturalism that is still interesting today is now in need of revision in order to remain acceptable. Such a kind of naturalism may be revised on the basis of a realistic philosophy of information, according to which knowing is a constructive activity, through which we do not merely represent the phenomena we investigate passively, but create more or less correct informational models of them, proactively and interactively. I shall conclude that the natural is in itself artefactual, and that the information revolution is disclosing a tension not between the natural and the non-natural, but a deeper one between a user’s and a producer’s interpretation of knowledge. The outcome is a philosophical view of knowledge and science in the information age that may be called constructionist and a revival of philosophy as a classic, foundationalist enterprise. (shrink)

In this paper we define an augmentation mHC of the Heyting propositional calculus HC by a modal operator ?. This modalized Heyting calculus mHC is a weakening of the Proof-Intuitionistic Logic KM of Kuznetsov and Muravitsky. In Section 2 we present a short selection of attractive (algebraic, relational, topological and categorical) features of mHC. In Section 3 we establish some close connections between mHC and certain normal extension K4.Grz of the modal system K4. We define a translation of mHC into (...) K4.Grz and prove that this translation is exact, i. e. theorem-preserving and deducibility-invariant. We have established (however, in this note we do not present a proof of this) that the lattice of all extensions of mHC is isomorphic to the lattice of normal extensions of K4.Grz (a generalization of the Kuznetsov and Muravitsky theorem). (shrink)