Mario Gomez-Torrente

Among the influential contributions of Alfred Tarski to logic and philosophy, and close in importance to his widely applied and discussed definition of truth, one finds his definition of logical consequence for formal languages. Like his definition of truth, Tarski's definition of logical consequence has been widely and fruitfully applied. Unlike the definition of truth, that of logical consequence has been rarely discussed philosophically. The main aim of this dissertation is to offer a thorough discussion of some philosophical issues arising from the neglected definition. ;The point of departure is an interpretative reading of the relevant writings by Tarski. This reading yields historically interesting data that refute other recent readings. It also provides philosophical illumination, by clarifying how Tarski thought that his definition satisfied some pretheoretic desiderata. ;Next it is discussed whether Tarski's definition satisfies other pretheoretic desiderata, not stated by Tarski and in some cases not endorsed by him, but which are desiderata nonetheless from reasonable standpoints. These include the desiderata that all instances of logical consequence in Tarski's defined sense be instances of analytical implication, and that they be instances of valid implication. The conclusion of this part of the dissertation is that, under reasonable assumptions regarding the field of applicability of the definition and the concepts used in it, there are reasons to believe that these desiderata are met, and none to believe they are not. ;Finally, the problem of logical constants is examined. The concept of a "logical constant" is the only concept not taken from logic and mathematics that appears in Tarski's definition. The problem of logical constants is that of replacing the primitive 'logical constant' with a defined, better understood concept, and in a such a way that the resulting defined concept of logical consequence meets the previously discussed desiderata. The main conclusion of this part is that some attempts to do this replace the obscure with the more obscure, while other attempts that seem to be in the right spirit have shortcomings of their own

I argue that recent defenses of the view that in 1936 Tarski required all interpretations of a language to share one same domain of quantification are based on misinterpretations of Tarski’s texts. In particular, I rebut some criticisms of my earlier attack on the fixed-domain exegesis and I offer a more detailed report of the textual evidence on the issue than in my earlier work. I also offer new considerations on subsisting issues of interpretation concerning Tarski’s views on the logical correctness of certain omega-arguments, on the Tarskian proof that Etchemendy took to be modal and fallacious, and on Tarski’s appeals to the “common concept of consequence”.

The pretheoretical notions of logical consequence and of a logical expression are linked in vague and complex ways to modal and pragmatic intuitions. I offer an introduction to the difficulties that these intuitions create when one attempts to give precise characterizations of those notions. Special attention is given to Tarski’s theories of logical consequence and logical constancy. I note that the Tarskian theory of logical consequence has fared better in the face of the difficulties than the Tarskian theory of logical constancy. Other theories of these notions are explained and criticized.

I offer a new objectivist theory of the contents of color language and color experience, intended especially as an account of what normal intersubjective variation in color perception and classification shows about those contents. First I explain an abstract account of the contents of color and other gradable adjectives; on the account, these contents are certain objective properties constituted in part by contextually intended standards of application, which are in turn values in the dimensions of variation associated with the adjectives. Then I propose an explanation of normal variations in linguistic color classification; these are postulated to be effects of differences in intended standards for the color adjectives appearing in the classifying predicates. Next, I consider a potential objection to this explanation, based on the suggestion that contextual content should be more accessible than the explanation predicts. In reply, I point out that contextual content is occasionally opaque to unsophisticated reflection. Finally, I present a companion account of the contents of color experiences on which these represent an object as lying on certain salient intervals in the chromatic dimensions, and I show how the account accommodates intersubjective variation in color perception

There have been several different and even opposed conceptions of the problem of logical constants, i.e. of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these ideas and from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory.

Timothy Williamson’s potentially most important contribution to epistemicism about vagueness lies in his arguments for the basic epistemicist claim that the alleged cut-off points of vague predicates are not knowable. His arguments for this are based on so-called ‘margin for error principles’. This paper argues that these principles fail to provide a good argument for the basic claim. Williamson has offered at least two kinds of margin for error principles applicable to vague predicates. A certain fallacy of equivocation seems to underlie his justification for both kinds of principles. Besides, the margin for error principles of the first kind can be used in the derivation of unacceptable consequences, while the margin for error principles of the second kind can be shown to be compatible with the falsity of epistemicism, under a number of assumptions acceptable to the epistemicist