On the nature of meaning and its indeterminacy: Davidson''s view in perspective

In order to illustrate the nature of the indeterminacy of meaning, Donald Davidson sometimes compares it to the fact that we can measure length or temperature on different scales. In the following paper I try to explain first why we are supposed to expect such an analogy, given the semantics of the word meaning and of the word length or temperature. In the second part I examine how close the analogy is by distinguishing different forms of indeterminacy of meaning (viz., the indeterminacy of reference and the indeterminacy of truth) and ask whether both forms have an equivalent in a theory of measurement. I shall conclude that this is indeed the case.I would like to thank an anonymous reviewer for his or her detailed comments on a first version of this paper, which helped me to clarify my views considerably.     

Apriority and applied mathematics

I argue that we need not accept Quine's holistic conception of mathematics and empirical science. Specifically, I argue that we should reject Quine's holism for two reasons. One, his argument for this position fails to appreciate that the revision of the mathematics employed in scientific theories is often related to an expansion of the possibilities of describing the empirical world, and that this reveals that mathematics serves as a kind of rational framework for empirical theorizing. Two, this holistic conception does not clearly demarcate pure mathematics from applied mathematics. In arguing against Quine, I present a formal account of applied mathematics in which the mathematics employed in an empirical theory plays a role that is analogous to the epistemological role Kant assigned synthetic a priori propositions. According to this account, it is possible to insulate pure mathematics from empirical falsification, and there is a sense in which applied mathematics can also be labeled as a priori.I am especially indebted to Michael Friedman for his valuable suggestions and criticisms of this paper. I would also like to thank Mark Wilson, Anil Gupta, and Arthur Fine for their comments and encouragement.     

The language dependence of accuracy

David Miller has demonstrated to the satisfaction of a variety of philosophers that the accuracy of false quantitative theories is language dependent (cf. Miller 1975). This demonstration renders the accuracy-based mode of comparison for such theories obsolete. The purpose of this essay is to supply an alternate basis for theory comparison which in this paper is deemed the knowledge-based mode of quantitative theory comparison. It is argued that the status of a quantitative theory as knowledge depends primarily on the soundness of the measurement procedure which produced the theory; such soundness is invariant, on my view, under Milleresque translations. This point is the basis for the linguistic invariance of knowledgelikeness. When the aim of science is not construed simply in terms of the truthlikeness or accuracy of theories, but in terms of the knowledge such theories embody, Miller's language dependence problem is overcome. One result of this analysis is that the possibility of objective scientific progress is restored, a possibility that Miller's analysis has prima facie defeated.I am grateful to Noretta Koertge for numerous comments and criticisms. Thanks are also due to David Miller for clarification of several points in his (1975). Veronica Barnes also made a number of pertinent observations.     

In Defense of Indexicalism:Comments on Davis

Wayne Davis (2004) argues against the thesis that knowledge claims are indexical, and he presents an alternative account of the contextual variability of our use of S knows p. In this commentary I focus on the following three points. First, I want to supplement Daviss considerations about the inability of indexicalism to deal with skeptical paradoxes by considering what the consequence would be if the indexicalists explanation of these paradoxes were satisfactory. Second, I am going to take a brief look at Daviss alternative theory. Third, in the main part of my commentary I try to show that indexicalism may be true in spite of the linguistic evidence Davis presents against it.     

Why we need a relevant theory of conditionals

This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap's system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis' theory of causation, Lewis' dyadic deontic logic, and Chellas' dyadic deontic logic.I am of course deeply indebted to André Fuhrmann, who co-wrote the paper on which the present effort is based. Perhaps I should also thank the Social Sciences and Humanities Research Council of Canada because the original research for this project was funded by them in the form of a post-doctoral fellowship.     

Listening to a different voice: A feminist critique of Gilligan

A critical examination of Carol Gilligan's study of psychological theory and women's development, this essay begins by exploring her concerns about malebiased developmental theorizing. I consider in detail Gilligan's criticisms of Sigmund Freud and her own empirical studies of moral development, as they relate to the work of L. Kohlberg. After defending Freud to some degree, I propose various (less theoretical but intuitively plausible) alternative interpretations of her data-interviews with males and females about hypothetical ethical dilemmas and with females about actual abortion decisions. I contend that Gilligan is too willing to concede the adequacy of Kohlberg's categories for fathoming the moral reasoning of males and that she may, in consequence, exaggerate differences between males and females. Noting the ironic similarities between Gilligan's claims and Schopenhauer's misogyny, I suggest that there may be something undesirably self-limiting about the different course of development she sketches. To move toward a morally preferable, feminism-compatible version of an ethic of care, I recommend that it be extended — by the imagination — beyond the here and now and that it not be restricted to existing webs of personal relationships.     

The logical study of science

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4).I would like to thank David Pearce and Veikko Rantala for their helpful comments.     

A measure for the distance between an interval hypothesis and the truth

The problem of distance from the truth, and more generally distance between hypotheses, is considered here with respect to the case of quantitative hypotheses concerning the value of a given scientific quantity.Our main goal consists in the explication of the concept of distance D(I, ) between an interval hypothesis I and a point hypothesis . In particular, we attempt to give an axiomatic foundation of this notion on the basis of a small number of adequacy conditions.Moreover, the distance function introduced here is employed for the reformulation of the approach to scientific inference — developed by Hintikka, Levi and other scholars — labelled cognitive decision theory. In this connection, we supply a concrete illustration of the rules for inductive acceptance of interval hypotheses that can be obtained on the basis of D(I, ).Lastly, our approach is compared with other proposals made in literature about verisimilitude and distance from the truth.I am grateful for the possibility of spending a period of some months at the Department of Philosophy of University of Gröningen. I profited there a lot from the supervision by Dr. Theo Kuipers. I am also grateful to Prof. Ilkka Niiniluoto who gave rise to my interest in this kind of research during a period spent at Department of Philosophy of University of Helsinki, and who made a number of useful suggestions in the final stage of this paper. Moreover, I would like to thank Dr. Carlo Buttasi for suggesting a better formulation of the proof of (T.24).     

On some structural aspects of physical problems

Bachelard's concept of the problématique is used in order to classify physical problems and their interrelations. This classification is effectuated along two dimensions. Along the horizontal dimension, physical problems are divided into the kinds that the different modes of physics' development define. These modes are themselves determined by the interplay among the conceptual system, the object and the experimentation transactions specific to physics. Along the vertical dimension, physical problems are classified according to the different stages of maturation they have to undergo before the process of their solution is effectively undertaken. To determine these maturation stages, the Althusserian conception of ideology is used. The interrelations between physical problems are examined through the introduction and elaboration of the notion interdependence network.It is a pleasure to thank Marcello Pera and Kostas Gavroglou for their very helpful comments and criticisms.     

Conceptual issues in the reunion of development and evolution

Recently a growing number of biologists have begun to consider the causal role that processes of embryonic development may play in evolution. This constitutes a reunion of these phenomena which had been linked in the nineteenth century through Haeckel's biogenetic law. This reunion may result in a new subdiscipline of biology, if there is a set of unique concepts and methods which tie the various research approaches together. Such concepts as bauplan, canalization, and developmental constraint, may serve in such a capacity. The methods employed must combine comparative and experimental analyses, with special attention paid to the range of variation in developmental events within each taxon. These concepts and methods are also applicable to the problem of how development evolved, thus the evolution of development may also be considered part of the reunion. The reunion is discussed in terms of the potential participation of various schools of thought found in the current literature.This work was supported by the NEH and undertaken as part of an NEH summer seminar entitled Philosophy of Biology in a Cultural Context, which was directed by Richard Burian and Marjorie Grene in the summer of 1989 at Blacksburg, Virginia. The author wishes to thank Professors Burian and Grene and all the participants of the seminar for the tremendous intellectual stimulus afforded by that summer experience. Conversations with K. Elizabeth Atkinson, M. Balaban, and M. Zelditch have also contributed greatly in the preparation of this paper. Whatever shortcomings may exist within it are, of course, my responsibility.     

Taking mathematical fictions seriously

I argue on the basis of an example, Fourier theory applied to the problem of vibration, that Field's program for nominalizing science is unlikely to succeed generally, since no nominalistic variant will provide us with the kind of physical insight into the phenomena that the standard theory supplies. Consideration of the same example also shows, I argue, that some of the motivation for mathematical fictionalism, particularly the alleged problem of cognitive access, is more apparent than real.I would like to thank Mark Wilson, who first suggested that I look at the literature on applied Fourier theory, and whose paper Honorable Intensions (1993) helped me understand it better. I would also like to acknowledge gratefully support from a UWM Graduate School Research Committee Award.     

A Coalgebraic View of Heyting Duality

We give a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. More precisely, we show that the category of Heyting spaces is isomorphic to a full subcategory of the category of all -coalgebras, based on Boolean spaces, where is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets. As an appendix, we include a proof of the characterization of Heyting spaces and the morphisms between them.     

Formalization of functionally complete propositional calculus with the functor of implication as the only primitive term

The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments.To the memory of Jerzy Supecki     

Some problems concerning the logic of grammatical modifiers

This paper consists principally of selections from a much longer work on the semantics of English. It discusses some problems concerning how to represent grammatical modifiers (e.g. slowly in x drives slowly) in a logically perspicuous notation. A proposal of Reichenbach's is given and criticized; then a new theory (apparently discovered independently by myself, Romain Clark, and Richard Montague and Hans Kamp) is given, in which grammatical modifiers are represented by operators added to a first-order predicate calculus. Finally some problems concerning applications of adjectives to that-clauses and gerundive-clauses are discussed.     

Group beliefs

It is argued in this paper that there can be both normative and nonnormative, merely factual group beliefs. The former involve the whole social group in question, while the latter only relate to the distributions of personal beliefs within the group. The paper develops a detailed theory, called the positional account of group beliefs, to explicate normative, group-involving group beliefs. Normative group beliefs are characterized within this approach in terms of joint acceptances of views by the group members — or their representatives — acting in their right positions and tasks, and in a sense creating group commitments for all the members to accept (and keep accepting) the view in question. Also aggregate accounts of group belief are considered in the paper, especially the shared we-belief approach. Such aggregate accounts purport to account for merely factual group beliefs.I wish to thank Kaarlo Miller and Philip Pettit for critical comments.     

Three views of demonstrative reference

Three views of demonstrative reference are examined: contextual, intentional, and quasi-intentional. According to the first, such reference is determined entirely by certain publicly accessible features of the context. According to the second, speaker intentions are criterial in demonstrative reference. And according to the third, both contextual features and intentions come into play in the determination of demonstrative reference. The first two views (both of which enjoy current popularity) are rejected as implausible; the third (originally proposed by Kaplan in Dthat) is argued to be highly plausible.     

On the definability of the quantifier “there exist uncountably many”

In paper [5] it was shown that a great part of model theory of logic with the generalized quantifier Q x = there exist uncountably many x is reducible to the model theory of first order logic with an extra binary relation symbol. In this paper we consider when the quantifier Q x can be syntactically defined in a first order theory T. That problem was raised by Kosta Doen when he asked if the quantifier Q x can be eliminated in Peano arithmetic. We answer that question fully in this paper.I would like to thank Kosta Doen and Zoran Markovi who made valuable suggestions and remarks on a draft of this paper.     

Warranting reconsidered: Response to Feldman

Summary The examples presented by Professor Feldman underscore the need to distinguish several of the notions of warranting examined in Counterfactuals. It is tempting to apologize for the complexity of the above considerations. But this complexity reflects the truth of the matter, that our intuitions concerning warranting require a variety of warranting notions. The aim of Counterfactuals was to make this complexity manageable by providing a unified method, the method of e-systems and contractions, for distinguishing and explaining the types of warranting.