Anti-Realist Truth and Truth-Recognition

I will be concerned with the following question: are there compelling arguments for postulating a distinction between the truth of a statement and the recognition of its truth, when truth is conceived along the lines of a suitable generalization of the intuitionistic idea that it should be characterized as the existence of a proof? I will argue that the distinction is not necessary within the conceptual framework of intuitionism by replying to two arguments to the contrary, one based on the paradox of inference, the other on considerations concerning the content of a statement.     

Anti-Realist Interpretations of Plato: Paul Natorp

The paper considers Paul Natorp's Kantian reading of Plato's theory of ideas, as developed in his monumental work, Platos Ideenlehre, eine Einführung in den Idealismus (1903, 1921). Central to Natrop's reading are, I argue, the following two claims: (1) Plato's ideas are laws, not things; and (2) Plato's theory of ideas in the first instance a theory about the possibility and nature of thought - in particular cognitive and indeed scientific or explanatory thought - and only as a consequence is it a theory about the nature of reality. Natrop thus argues that Plato's theory of ideas is at its heart a transcendental theory, and that Plato's metaphysics is built on this basis. The paper considers these claims - and their textual basis in Plato - in some detail, and attempts an initial evaluation of their plausibility as a reading of Plato. I am on the whole sympathetic to Natorp's reading, though a proper assessment goes beyond the present paper. The wider interest of this idealist or anti-realist reading of Plato ought to be obvious, especially in view of the commonly accepted assumption these days that both Plato and Aristotle, and indeed the Greeks in general, took realism entirely for granted (see e.g. M. Burnyeat). Natorp argues that this is true of Aristotle, but quite untrue of Plato. But he is quite clear that the idealism he ascribes to Plato is not Berkeleyan or metaphysical idealism, but a certain kind of transcendental or epistemological idealism. Natorp, however, is no uncritical follower of Kant, and the version of trascendental idealism that he ascribes to Plato is, I argue, very different from Kant's.     

Kripke Bundle Semantics and C-set Semantics

Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].In this paper, we show that Q-S4.1 is not Kripke bundle complete via C-set models. As a corollary we can give a simple proof showing that C-set semantics for modal logics are stronger than Kripke bundle semantics.     

Wittgensteinian Semantics

Wittgenstein emphasizes two points concerning his notion of family resemblance. One is that the use of a family resemblance expression resists characterization by certain kinds of rules; the other is that due to the prevalence of family resemblance in the philosophical lexicon, philosophical inquiry must in many cases proceed differently from how it traditionally has. This paper develops an interpretation of family resemblance that seeks to do justice to these claims. I argue that what is characteristic about family resemblance expressions is not that they exhibit a basic semantic feature unique to themselves, but that they combine a number of semantic properties that happen not to be coinstantiated elsewhere. These features include (1) content variability (also a property of ambiguous expressions, polysemes, and standard indexicals), (2) a feature I call "topicality" (which is also a characteristic of polysemes), and (3) "semantic openness" (a feature of many ordinary indexicals). The notions of topicality and semantic openness are explained, and certain terms of natural language are shown to be family resemblance expressions. I conclude by indicating some of the potential philosophical ramifications of these results.     

Free Semantics

Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic focussed upon, but the results extend to MC. The semantics is called ‘free semantics’ since it is disjunctively and existentially free in that no disjunctive or existential witnesses are produced, unlike in truth-functional semantics. Such ‘witnesses’ are only assumed in generality and are not necessarily actual. The paper sets up the free semantics in a truth-functional style and gives a natural deduction interpetation of the meta-logical connectives. We then set out a familiar tableau-style system, but based on natural deduction proof rather than truth-functional semantics. A proof of soundness and completeness is given for a reductio system, which is a transform of the tableau system. The reductio system has positive and negative rules in place of the elimination and introduction rules of Brady’s normalized natural deduction system for DW. The elimination-introduction turning points become closures of threads of proof, which are at the points of contradiction for the reductio system.     

Inferentializing Semantics

The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of proof-theoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones.     

Relational Semantics and Domain Semantics for Epistemic Modals

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions.     

Measurement Theoretic Semantics And The Semantics Of Necessity

In the first two sections I present and motivate a formal semantics program that is modeled after the application of numbers in measurement (e.g., of length). Then, in the main part of the paper, I use the suggested framework to give an account of the semantics of necessity and possibility: (i) I show thatthe measurement theoretic framework is consistent with a robust (non-Quinean) view of modal logic, (ii) I give an account of the semantics of the modal notions within this framework, and (iii) I defend the suggested account against various objections.     

Single Scoreboard Semantics

Philosophical Studies -