ABSTRACTIn a bilingual educational setting, even when mathematical word problems are presented in one’s first language, students may still perform poorly if cognitive constraints such as working me...

The paper clarifies and defends the orthodox view that counterfactual conditionals with impossible antecedents are vacuously true against recent criticisms. It argues that apparent counterexamples to orthodoxy result from uncritical reliance on a fallible heuristic used in the processing of conditionals. A comparison is developed between such counterpossibles and vacuously true universal generalizations.

This chapter aims to attempt no more than to make some informal and unsystematic remarks on the transformation of analytic philosophy. It deals with a few sketchy remarks on the historiography of recent analytic philosophy. Writing in 1981, David Lewis described “a reasonable goal for a philosopher” as bringing one’s opinions into stable equilibrium. A natural comparison is between Lewis’s Quinean or at least post‐Quinean methodology and the methodology of Peter Strawson, Quine’s leading opponent from the tradition of ordinary language (...) philosophy. Analytic epistemology provides a good case study of the philosophical application of Gricean pragmatics outside the philosophy of language. On Michael Dummett picture of the history of philosophy, Descartes had made epistemology first philosophy, the engine for the rest of philosophy, and then Frege had replaced epistemology by the philosophy of language as first philosophy. The chapter suggests that philosophy sometimes already uses an abductive methodology and ought to use it more in the future. (shrink)

Many advocates of non-classical logic for reasons external to mathematics claim that their proposed revisions are consistent with the use of classical logic within pure mathematics. Doubts are raised about such claims, concerning the applicability of pure mathematics to natural and social science. -/- .

The paper criticizes the truthmaker principle that every truth is made true by something. If we interpret ‘something’ as quantifying into sentence position, we can interpret the principle as a harmless logical truth, but that is not what advocates of the principle intend. They interpret ‘something’ as quantifying into name position, and the principle as requiring the existence of truthmaking individuals. The paper argues that we have no reason to believe the principle on this interpretation. Moreover, the converse Barcan formula (...) is inconsistent with the existence of truthmaking individuals for contingent truths. Considerations about our ability to count possible truthmaking individuals are used to argue that we should prefer the converse Barcan formula. (shrink)

The paper criticizes epistemological conceptions of analytic or conceptual truth, on which assent to such truths is a necessary condition of understanding them. The critique involves no Quinean scepticism about meaning. Rather, even granted that a paradigmatic candidate for analyticity is synonymy with a logical truth, both the former and the latter can be intelligibly doubted by linguistically competent deviant logicians, who, although mistaken, still constitute counterexamples to the claim that assent is necessary for understanding. There are no analytic or (...) conceptual truths in the epistemological sense. The critique is extended to purportedly analytic inference rules. An alternative account is sketched on which understanding a word is a matter of participation in a linguistic practice, while synonymy and concept identity consist in sameness of truth-conditional semantic properties. Although there are philosophical questions about concepts, the idea that philosophical questions in general are conceptual questions generates only an illusion of insight into philosophical methodology. (shrink)

This chapter contains sections titled: The concept of phenomenal character is closely related to that of a phenomenal quality. If phenomenal characters are just maximally specific phenomenal qualities, it would follow that there are no phenomenal characters either. The first section gives reasons for fearing that observational predicates are susceptible to sorites paradoxes, but denies that predicates such as “painful” are perfectly observational. They are instead phenomenal, in a sense developed in the second section. The third section considers and rejects (...) a final attempt to revive a sorites paradox for painful. The fourth section tentatively places these thoughts against a background of a general account of sorites paradoxes, on which they may reflect either speakers' ignorance or semantic indeterminacy or both, depending on the facts of the particular case. The arguments of this chapter therefore have parallels for the paradox of small numbers. (shrink)

According to Gamper, one function of science is to determine how the world is. Science, Gamper continues, rests on a set of basic assumptions, and the gap between basic assumptions and science should be filled by ontological frameworks that accommodates the modal properties of such assumptions. Different frameworks may surely suggest different modal properties. Thus, in so far as we use different basic assumptions, we can have different ontologies with different modal properties. Ontologies affect, in turn, science, which, however, has (...) the power to falsify the ontological frameworks. The aim of this article is to show a possible trouble of Gamper's proposal, here considered as applied to the geographical debate. (shrink)

I. An argument is presented for the conclusion that the hypothesis that no one will ever decide a given proposition is intuitionistically inconsistent. II. A distinction between sentences and statements blocks a similar argument for the stronger conclusion that the hypothesis that I have not yet decided a given proposition is intuitionistically inconsistent, but does not block the original argument. III. A distinction between empirical and mathematical negation might block the original argument, and empirical negation might be modelled on Nelson''s (...) strong negation, but only on intuitionistically unacceptable assumptions. IV. Intuitionists may have to accept the original argument, and therefore be committed to a dubious view of time on which there cannot be merely inductive evidence for statements about the infinite future. (shrink)

In this introductory chapter to the volume The Aim of Belief, the editor surveys the fundamental questions in current debates surrounding the aim of belief, and identifies the major theoretical approaches. The main arguments of the ten contributions to the volume are outlined and located in the context of the existing literature.

Robinson argues that by certain threshold criteria, pregnant women qualify for a higher moral status by reason of their pregnancies. While her intention is to make this a status upgrade for women, we worry that it may result in a status downgrade for women as a class, by presupposing and reinforcing women’s value in relation to their reproductive labour. Historically, central to feminist analysis is resistance to reductive accounts of women in relation to their reproductivity. For example, de Beauvoir addressed (...) men’s transcendence and contrasted it with women’s immanence, a status distinction possible because women are mired in expectations that they will marry, produce children and remain in the domestic realm; and for her part, Firestone argued that biological reproduction underlies women’s inferiority to men and that ‘The reproduction of the species by one sex for the benefit of both (should) be replaced by…artificial reproduction’1 2 Her concern was to liberate women from expectations of biological reproduction so their productive value in society is not reduced to their reproductive contributions. A formidable body of analysis in this same vein cautions against collapsing the value of women into their pregnancies, so much so that some commentators even distinguish ‘mothering’ from gestation.3 Robinson’s argument that pregnant women qualify at a higher threshold of personhood emphasises …. (shrink)

The full-text of this article is not currently available in ORA, but the original publication is available at springerlink.com.

The duality of computer programs is characterized, on the one hand, by their physical implementations on physical devices, and, on the other, by the conceptual implementations in programmers’ minds of the objects making up the computational processes they conceive. We contend that central to programmers’ conceptual implementations are (i) the concept of type, at both the programming and the design level, and (ii) metaphors created to facilitate these implementations.

In 1999, Jeffrey Ketland published a paper which posed a series of technical problems for deflationary theories of truth. Ketland argued that deflationism is incompatible with standard mathematical formalizations of truth, and he claimed that alternate deflationary formalizations are unable to explain some central uses of the truth predicate in mathematics. He also used Beth’s definability theorem to argue that, contrary to deflationists’ claims, the T-schema cannot provide an ‘implicit definition’ of truth. In this article, I want to challenge this (...) final argument. Whatever other faults deflationism may have, the T-schema does provide an implicit definition of the truth predicate. Or so, at any rate, I shall argue. (shrink)

The Lowenheim-Skolem theorems say that if a first-order theory has infinite models, then it has models which are only countably infinite. Cantor's theorem says that some sets are uncountable. Together, these theorems induce a puzzle known as Skolem's Paradox: the very axioms of set theory which prove the existence of uncountable sets can be satisfied by a merely countable model. ;This dissertation examines Skolem's Paradox from three perspectives. After a brief introduction, chapters two and three examine several formulations of Skolem's (...) Paradox in order to disentangle the roles which set theory, model theory, and philosophy play in these formulations. In these chapters, I accomplish three things. First, I clear up some of the mathematical ambiguities which have all too often infected discussions of Skolem's Paradox. Second, I isolate a key assumption upon which Skolem's Paradox rests, and I show why this assumption has to be false. Finally, I argue that there is no single explanation as to how a countable model can satisfy the axioms of set theory ;In chapter four, I turn to a second puzzle. Why, even though philosophers have known since the early 1920's that Skolem's Paradox has a relatively simple technical solution, have they continued to find this paradox so troubling? I argue that philosophers' attitudes towards Skolem's Paradox have been shaped by the acceptance of certain, fairly specific, claims in the philosophy of language. I then tackle these philosophical claims head on. In some cases, I argue that the claims depend on an incoherent account of mathematical language. In other cases, I argue that the claims are so powerful that they render Skolem's Paradox trivial. In either case, though, examination of the philosophical underpinnings of Skolem's Paradox renders that paradox decidedly unparadoxical. ;Finally, in chapter five, I turn away from "generic" formulations of Skolem's Paradox to examine Hilary Putnam's "model-theoretic argument against realism." I show that Putnam's argument involves mistakes of both the mathematical and the philosophical variety, and that these two types of mistake are closely related. Along the way, I clear up some of the mutual charges of question begging which have characterized discussions between Putnam and his critics. (shrink)

In response to Paul Boghossian's objections in ‘Inferentialism and the epistemology of logic’, this paper defends counterexamples offered by Paolo Casalegno and the author to an inferentialist account of what it is to understand a logical constant, on which Boghossian had relied in his explanation of our entitlement to reason according to basic logical principles. The importance for understanding is stressed of non-inferential aspects of the use of logical constants. Boghossian's criteria for individuating concepts are also queried.

Can we turn the screw on counter-examples to the KK principle (that if one knows that P, one knows that one knows that P)? The idea is to construct cases in which one knows that P, but the epistemic status for one of the proposition that one knows that P is much worse than just one’s not knowing it. Of course, since knowledge is factive, there can’t be cases in which one knows that P and knows that one doesn’t know (...) that P (we can’t strengthen ¬KKp to K¬Kp)! If we can construct such cases, we may be able to use them to understand some puzzling epistemic phenomena. (shrink)

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

What role does religious transcendence play in liberal democracies? In Jürgen Habermas’s early political theory of the bourgeois public sphere, religion was downplayed if not dismissed completely. In the past several years however, he has developed a greater interest in religion. Habermas seems to like the positive solidarity-forming effects religion can have on communities that mediate in a public sphere between private individuals and state authority. However, in light of continuing terrorist activity, he is deeply critical of any sort of (...) other worldly transcendence that is too open to violent cooption. Nonetheless, Habermas relates his renewal of a critically engaged public sphere of debate to universalized rational procedures which he discusses in light of a philosophical notion of “detranscendentalization.” However, if it is the case that the solidarity of communities is being eroded by the influences of mass media and free market globalization as Habermas claims, then a further reflection on the way religious communities form around shared transcendent beliefs is required. Are his detranscendentalized rational procedures of critical debate adequate in inspiring the critical power communities need to solidify themselves against state authority? It is in light of this questions that I will develop the thought of Karl Barth. (shrink)

“Thin concepts” are dubious entities. Careful analysis of the usual examples of thick and thin raises serious doubts about both their conceptuality and their thinness. Confusions aside, there is little obvious use for them in ethics or metaethics. The very idea that there could be a naturally-occurring purely evaluative moral concept, with no descriptive content, no cultural setting, and no capacity for distanced or ironic use, is as chimerical as any other ahistorical illusion. Our concentration on thick and thin has (...) distracted us from thinking about other interesting and important ethical distinctions—evidential/ verdictive, evaluative/ prescriptive, determinable/ determinate, Zangwill’s because-relation, Anscombe’s brute-relative-to relation—which have something genuine and non-illusory on both sides of them. (shrink)

Consider the following two passages. I apologise for their length, but this is necessary to bring out what I want to bring out.

In this dissertation we study two-cardinal phenomena—both of the admitting cardinals variety and of the Chang’s Conjecture variety—under the assumption that all our models have stable theories. All our results involve two, relatively widely accepted generalizations of the traditional definitions in this area. First, we allow the relevant subsets of our models to be picked out by (perhaps infinitary) partial types; second we consider δ-cardinal problems as well as two-cardinal problems.

The main result of this paper is that KT is closed under a cancellation principle. This result extends to KTG1, but it does not extend to modal systems associated with the provability interpretation of L, such as KW and KT4Grz. Following Williamson, these results are applied to philosophical concerns about the proper form for theories of meaning, via the interpretation of L as some kind of veriflability. The cancellation principle can then be read as saying that verifilability conditions and falsiflability (...) conditions jointly determine truth conditions. (shrink)

Gilbert (2015) warns us that advisory brain implant systems—neural implants that predict brain activity and give the user advice based on those predictions—could threaten the user's autonomy. If th...

This chapter explores the limits on what can be known that are revealed by an argument first published by Fitch, sometimes known as the Paradox of Knowability. The argument shows that if some truths are unknown then some truths are unknowable. This represents an important challenge to verificationism and anti‐realism. Objections to the argument by Edgington, Kvanvig, Melia, and others are considered and projected. Thus, knowledge turns out to have structural limits.