This paper seeks to identify and defend an approach to inquiry dubbed ‘metaphysical optimism’, particularly as it is evidenced at crisis points in the fields of physics, mathematics and logic. That the practice of metaphysical optimism at such moments, wherein it has appeared that there is no clear way to proceed or understand where we have arrived, is both reasonable and useful suggests it is to be taken seriously as capable of progressing fields and increasing knowledge. Given this, the paper (...) then looks in more depth at what such an approach involves and why it might be useful both as a methodological approach in general and to help clarify positions along the realism/anti-realism spectrum in philosophy. From here, the paper arrives at a possible argument in defence of the realist attitude to transcendence. (shrink)

An account of the distinction between singular and general propositions should reflect the core ideas that have motivated the distinction. Those core ideas can be appreciated independently of many commitments regarding the metaphysics of propositions, but theorists with differing views on the latter have given quite different explanations of what it is for a proposition to be singular or general. Many of those explanations turn out not to reflect the core ideas adequately after all, either by misclassifying certain propositions or (...) by failing to be sufficiently informative. A more satisfactory account can be formulated by more directly elaborating on the background ideas motivating the distinction. The resulting account not only does better than its competitors, but is compatible with various views on the metaphysics of propositions. (shrink)

According to Michael Friedman’s theory of explanation, a law X explains laws Y1, Y2, …, Yn precisely when X unifies the Y’s, where unification is understood in terms of reducing the number of independently acceptable laws. Philip Kitcher criticized Friedman’s theory but did not analyze the concept of independent acceptability. Here we show that Kitcher’s objection can be met by modifying an element in Friedman’s account. In addition, we argue that there are serious objections to the use that Friedman makes (...) of the concept of independent acceptability. (shrink)

It is often argued that by assuming the existence of a universal language, one prohibits oneself from conducting semantical investigations. It could thus be thought that Tarski’s stance towards a universal language in his fruitful Wahrheitsbegriff differs essentially from Carnap’s in the latter’s less successful Untersuchungen zur allgemeinen Axiomatik. Yet this is not the case. Rather, these two works differ in whether or not the studied fragments of the universal language are languages themselves, i.e., whether or not they are closed (...) under derivation rules. In Carnap’s case, axiom systems are not closed under derivation rules, which enables him to adopt a substitutional concept of models. His approach is directly rooted in the tradition of formal axiomatics, we argue, and in this contrary to Tarski’s. In comparing these works by Carnap and Tarski, our aim will be to qualify the connection between Tarski’s approach and the tradition of formal axiomatics, which has been overemphasized in the literature. (shrink)

We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. (...) This point is illustrated by Carnap’s early semantics and model theory, which he developed within a type theoretical framework and which stand out both for their universalistic treatment and for certain idiosyncratic technicalities by which the construction is supported. One special property is that individuals are context relative in Carnap’s system. This leads to a model theory in which the model domains are more flexible than has been suggested in the literature. (shrink)

This paper scrutinizes Everett Nelson's conception of consistency by comparing it with the “standard” account of C. I. Lewis. This conflict surprisingly resembles a related controversy between the ancient logicians Chrysippus and Diodorus. Nelson's intuitions behind his peculiar conception of consistency are analysed and certain features of his logical system are critically examined. In particular, his objections against the law of the transitivity of implication and against the laws of conjunction and disjunction have to be discussed. Although Nelson's considerations contain (...) interesting ideas in favour of a relevantist conception of logic, they fail to convincingly support the hardcore connexive thesis that even a selfcontradictory proposition doesn't entail its own negation. (shrink)

Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to (...) an argument when it contributes to the validity of that argument. I then argue that the sequents which best embody this ideal of relevance are the so-called perfect sequents—that is, sequents which are valid but have no proper subsequents that are valid. Church’s theorem entails that there is no recursively axiomatizable proof-system that proves all and only the perfect sequents, so the project that emerges from studying perfection in classical logic is not one of finding a perfect subsystem of classical logic, but is rather a comparative study of classifying subsystems of classical logic according to how well they approximate the ideal of perfection. (shrink)

This paper contributes to the calculization of evocation and erotetic implication as defined by Inferential Erotetic Logic (IEL). There is a straightforward approach to calculizing (propositional) erotetic implication which cannot be applied to evocation. First-order evocation is proven to be uncalculizable, i.e. there is no proof system, say FOE, such that for all X, Q: X evokes Q iff there is an FOE-proof for the evocation of Q by X. These results suggest a critique of the represented approaches to calculizing (...) IEL. This critique is expanded into a programmatic reconsideration of the IEL-definitions of evocation and erotetic implication. From a different point of view these definitions should be seen as desiderata that may or may not play the role of a point of orientation when setting up "rules of asking". (shrink)