Online research in philosophy

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)

Is the restricted, consistent, version of the T-scheme sufficient for an ‘implicit definition’ of truth? In a sense, the answer is yes (Haack 1978 , Quine 1953 ). Section 4 of Ketland 1999 mentions this but gives a result saying that the T-scheme does not implicitly define truth in the stronger sense relevant for Beth’s Definability Theorem. This insinuates that the T-scheme fares worse than the compositional truth theory as an implicit definition. However, the insinuation is mistaken. For, as (...) Bays rightly points out, the result given extends to the compositional truth theory also. So, as regards implicit definability, both kinds of truth theory are equivalent. Some further discussion of this topic is mentioned (Gupta 2008 , Ketland 2003 , McGee 1991 ), all in agreement with Bays’s analysis. (shrink)

On the difficulty of extracting the logical form of a seemingly simple sentence such as ‘If Andy went to the movie then Beth went too, but only if she found a taxi cab’, with some morals and questions on the nature of the difficulty.

This paper examines E. W. Beth’s work in the philosophy of physics, both from a historical and a systematic point of view. Beth saw the philosophy of physics first of all as an opportunity to illustrate and promulgate a new and modern general approach to the philosophy of nature and to philosophy tout court: an approach characterized negatively by its rejection of all traditional metaphysics and positively by its firm orientation towards science. Beth was successful in defending (...) this new ideology, and became its leading Dutch representative in the first two decades after the second world war. Beth also contributed importantly to the method of the philosophy of physics in a narrower sense, by proposing and promoting the semantic approach in the formal analysis of physical theories. Finally, he worked on several specific foundational questions; but he was probably too much of a logician to leave his mark in this area. (shrink)

This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definability to arbitrary logics, formalised as institutions, and we develop three general definability results. One generalises the classical Beth theorem by relying on the interpolation properties of the institution. Another relies on a meta Birkhoff axiomatizability property of the institution and constitutes a source for many new actual definability (...) results, including definability in (fragments of) classical model theory. The third one gives a set of sufficient conditions for 'borrowing' definability properties from another institution via an 'adequate' encoding between institutions. The power of our general definability results is illustrated with several applications to (many-sorted) classical model theory and partial algebra, leading for example to definability results for (quasi-)varieties of models or partial algebras. Many other applications are expected for the multitude of logical systems formalised as institutions from computing science and logic. (shrink)

The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.

A basic aim of E. Beth's work in philosophy of science was to explore the use of formal semantic methods in the analysis of physical theories. We hope to show that a general framework for Beth's semantic analysis is provided by the theory of semi-interpreted languages, introduced in a previous paper. After developing Beth's analysis of nonrelativistic physical theories in a more general form, we turn to the notion of the 'logic' of a physical theory. Here we (...) prove a result concerning the conditions under which semantic entailment in such a theory is finitary. We argue, finally, that Beth's approach provides a characterization of physical theory which is more faithful to current practice in foundational research in the sciences than the familiar picture of a partly interpreted axiomatic theory. (shrink)

All extensions of the modal Grzegorczyk logic Grz possessing projective Beth's property PB2 are described. It is proved that there are exactly 13 logics over Grz with PB2. All of them are finitely axiomatizable and have the finite model property. It is shown that PB2 is strongly decidable over Grz, i.e. there is an algorithm which, for any finite system Rul of additional axiom schemes and rules of inference, decides if the calculus Grz+Rul has the projective Beth property.

A few results generalizing well-known classical model theory ones have been obtained in institution theory these last two decades (e.g. Craig interpolation, ultraproduct, elementary diagrams). In this paper, we propose a generalized institution-independent version of the Beth definability theorem.

We prove that if ℵα is uncountable and regular, then the Beth-closure of Lωω(Qα) is not a sublogic of L∞ω(Qn), where Qn is the class of all n-ary generalized quantifiers. In particular, B(Lωω(Qα)) is not a sublogic of any finitely generated logic; i.e., there does not exist a finite set Q of Lindstrom quantifiers such that B(Lωω(Qα)) ≤ Lωω(Q).

Though E. W. Beth is famous for his contributions to logic aspects of his philosophical reflections and details of its development are almost unknown. In his work four periods can be distinguished: the neo-kantian, the anti-kantian, the anti-irrationalist and the logical one. Within this framework it is possible to individuate a core around which Beth developed his reflections: it is the interplay between philosophy and the sciences. His philosophy was always linked to the sciences in two ways: He (...) steadily checked his philosophical ideas against the current situation in foundational research and he occupied himself with the general question of the relationship between philosophy and the sciences. (shrink)

In this paper it will be shown that the Beth definability property corresponds to surjectiveness of epimorphisms in abstract algebraic logic. This generalizes a result by I. Németi (cf. [11, Theorem 5.6.10]). Moreover, an equally general characterization of the weak Beth property will be given. This gives a solution to Problem 14 in [20]. Finally, the characterization of the projective Beth property for varieties of modal algebras by L. Maksimova (see [15]) will be shown to hold for (...) the larger class of semantically algebraizable logics. (shrink)

In response to Mader's and Deutscher's questions, the author defends her approach to reading Irigaray and Butler, which entails extending the ideas of these thinkers into areas of thought with which they do not engage directly themselves. This involves relating Irigaray's ideas to the tradition of the philosophy of nature and interpreting Butler as offering, in spite of her focus on the genealogy of claims about sex, also a theory of sex itself, a theory of sex as an effect entirely (...) of gender. This approach to reading differs from Irigaray's own reading method of expanding and transforming philosophies in light of their constitutive exclusions. An example of this, explored here, is Irigaray's expansion and transformation of Merleau-Ponty's late ontology of flesh in light of its constitutive exclusion, the "maternal sojourn." This article also asks whether rhythmic sexual difference, which the author has attempted to differentiate from biological sex difference, ultimately remains tied to biological sex difference. This commentary suggests that it does but that reference to biological sex difference need not be politically problematic. Finally, the author asks whether the metaphysics of potentials and tendencies that she attributes to Irigaray impedes social change by inevitably reinstalling the actual as the horizon of possibility. Irigaray's strategy of reading texts and cultures for their constitutive exclusions offers a solution to this problem. (shrink)

The debate over foundationalism, the viewpoint that there exists some secure foundation upon which to build a system of knowledge, appears to have been resolved and the antifoundationalists have at least temporarily prevailed. From a firmly historical approach, the book traces the foundationalism/antifoundationalism controversy in the work of many important figures Animaxander, Aristotle and Plato, Augustine, Descartes, Hegel and Nietzsche, Habermas and Chisholm, and others throughout the history of philosophy. The contributors, Joseph Margolis, Ronald Polansky, Gary Calore, Fred and Emily (...) Michael, William Wurzer, Charlene Haddock Siegfried, Sandra B. Rosenthal, Kathleen Wallace, and the editors present well the diversity, interest, and roots of antifoundationalism. Tom Rockmore is Professor and Chairman in the Department of Philosophy at Duquesne University. Beth J. Singer is Professor of Philosophy at Brooklyn College of the City University of New York. (shrink)

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. (...) Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism. (shrink)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones (each shared with some other authors) are: (i): I defend the traditional Nagelian conception of reduction (Section 3}); (ii): I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' (Section 4); (iii): I stress the collapse of supervenience into deduction via Beth's theorem (Section 5.1); (iv): I adapt some examples already in the literature to show supervenience without emergence and vice versa (Section 5.2). (shrink)

Function theorists routinely speculate that a viable function theory will be equally applicable to biological traits and artifacts. However, artifact function has received only the most cursory scrutiny in its own right. Closer scrutiny reveals that only a pluralist theory comprising two distinct notions of function--proper function and system function--will serve as an adequate general theory. The first section describes these two notions of function. The second section shows why both notions are necessary, by showing that attempts to do away (...) with one of them fail. This demonstration draws on examples from the artifactual realm to motivate major points of the argument. The third section is an outline of artifact function. It confirms the conclusions of the second section, and also begins the task of describing some of the special features of artifact function needing accommodation within the general theory. (shrink)

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...) propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)

: Recent work in the area of ethics and animals suggests that it is philosophically legitimate to ascribe emotions to nonhuman animals. Furthermore, it is sometimes argued that emotionality is a morally relevant psychological state shared by humans and nonhumans. What is missing from the philosophical literature that makes reference to emotions in nonhuman animals is an attempt to clarify and defend some particular account of the nature of emotion, and the role that emotions play in a characterization of human (...) nature. I argue in this paper that some analyses of emotion are more credible than others. Because this is so, the thesis that humans and nonhumans share emotions may well be a more difficult case to make than has been recognized thus far. (shrink)

The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) and prove for it (...) results which correspond to many major classical model theories, taken from Shoenfield [5]. In particular we prove counterparts of the theorems of o-Tarski and Chang-o-Suszko, Craig-Robinson and the Beth definability theorem. (shrink)

When Cool finally realized that false memories had been planted, she sued the psychiatrist for malpractice. In March 1997, after five weeks of trial, her case was settled out of court for $2.4 million. Nadean Cool is not the only patient to develop false memories as a result of questionable therapy. In Missouri in 1992 a church counselor helped Beth Rutherford to remember during therapy that her father, a clergyman, had regularly raped her between the ages of seven and (...) 14 and that her mother sometimes helped him by holding her down. Under her therapist's guidance, Rutherford developed memories of her father twice impregnating her and forcing her to abort the fetus herself with a coat hanger.The father had to resign from his post as a clergyman when the allegations were made public. Later medical examination of the daughter revealed, however, that she was still a virgin at age 22 and had never been pregnant. The daughter sued the therapist and received a $1-million settlement in 1996. (shrink)

There is a thriving debate over what aspects of our capacity to produce and understand language are special. My concern here is a key part of this wider debate: Is speech special? In particular, my focus is on speech perception, and whether it is special. This isn’t just one but a number of different questions. Too frequently, these very different questions are not clearly distinguished and kept apart. I discuss a framework for distinguishing various versions of the question, Is speech (...) perceptually special? Focusing on a particular class of questions, I make a proposal about the sense in which speech is perceptually special. According to this account, the capacity to perceive speech is an acquired perceptual skill, and involves learning to hear language-specific types of biologically-significant sounds. This account illuminates the significance of interlocution in understanding what makes the perception of speech distinctive. (shrink)

Tool use rivals language as an important domain of cognitive phenomena, and so as a source of insight into the nature of cognition in general. But the favoured current definition of tool use is inadequate because it does not carve the phenomena of interest at the joints. Heidegger's notion of equipment provides a more adequate theoretical framework. But Heidegger's account leads directly to a non-individualist view of the nature of cognition. Thus non-individualism is supported by concrete considerations about the nature (...) of tools and tool use. (shrink)

Behaviorism and mentalism are commonly considered to be mutually exclusive and conjunctively exhaustive options for the psychological explanation of behavior. Behaviorism and mentalism do differ in their characterization of inner causes of behavior. However, I argue that they are not mutually exclusive on the grounds that they share important foundational assumptions, two of which are the notion of an innerouter split and the notion of control. I go on to argue that mentalism and behaviorism are not conjunctively exhaustive either, on (...) the grounds that dropping these common foundational assumptions results in a distinctively different framework for the explanation of behavior. This third alternative, which is briefly described, is a version of non-individualism. (shrink)

The paper treats several ontological questions about certain nineteenth-century and contemporary medical and scientific conceptualizations of hereditary relation. In particular, it considers the account of mid-nineteenth century psychiatric thought given by Foucault in Psychiatric Power: Lectures at the Collège de France, 1973–1974 and Abnormal: Lectures at the Collège de France, 1974–1975 . There, Foucault argues that a fantastical conceptual prop, the ‘metabody,’ as he terms it, was implicitly supposed by that period’s psychiatric medicine as a putative ground for psychiatric pathology. (...) After presenting the heart of Foucault’s thought on the ‘metabody,’ the paper investigates the possibility that a contemporary version of a ‘metabody’ may operate today as a conceptual analog of the nineteenth-century psychiatric theory and practice that Foucault began to expose in the texts examined here. It speculates that we might identify a contemporary genetic version of a ‘metabody’ in a particular current conception of the gene as replicator, an item marked by an ambiguous temporal ontology. (shrink)

A god is a cosmic designer-creator. Atheism says the number of gods is 0. But it is hard to defeat the minimal thesis that some possible universe is actualized by some possible god. Monotheists say the number of gods is 1. Yet no degree of perfection can be coherently assigned to any unique god. Lewis says the number of gods is at least the second beth number. Yet polytheists cannot defend an arbitrary plural number of gods. An alternative is (...) that, for every ordinal, there is a god whose perfection is proportional to it. The n -th god actualizes the best universe(s) in the n -th level of an axiological hierarchy of possible universes. Despite its unorthodoxy, ordinal polytheism has many metaphysically attractive features and merits more serious study. (shrink)

Agency can be construed as both the manner in which autonomous individuals embark on particular courses of action (or inaction), and the relationship between such agents and the outcomes of the courses of action on which they embark. A promising strategy for understanding both senses of agency consists in the combination of a modal logic of agency and branching time semantics. Such is the strategy behind stit theory, the theory of agentive action developed by Nuel Belnap and others. However, stit (...) theoretic evaluations of the agentive relationship between agents and outcomes that are uncertain—due to either the presence of indeterminism, or the possible intervention of other agents—yield counterintuitive results. This paper develops a pair of alternative operators (the “act” operators) for modeling agency with respect to uncertain outcomes. Unlike the stit-theoretic model, the act-theoretic model of agency with respect to a particular state of affairs does not require that the state of affairs be realized in every possible history. If the state of affairs in fact obtains in the actual history, and its obtaining was dependent on the agent’s pursuing a particular course of action, then the agent is deemed agentive under act theory. (shrink)