Formal semantics is an enterprise which accounts for meaning in formal, mathematical terms, in the expectation of providing a helpful explication1 of the concept of the meaning of specific word kinds (such as logical ones), or of words and expressions generally. Its roots go back to Frege, who proposed exempting concepts, meanings of predicative expressions, from the legislation of psychology and relocating them under that of mathematics. This started a spectacular enterprise, fostered at first within formal logic and later moving (...) into the realm of natural languages, and featuring a series of eminent scholars, from Tarski and Carnap to Montague and David Lewis. Partly independently of this, Frege set the agenda for a long-term discussion of the question of what a natural language is, his own contribution being that language should be seen not as a matter of subjective psychology, but rather as a reality objective in the sense in which mathematics is objective. His formal semantics, then, was just an expression of this conception of language. And many theoreticians now take it for granted that formal semantics is inseparably connected with a Platonist conception of language. Moreover, the more recent champions of formal semantics, Montague and David Lewis, took for granted that natural language is nothing else than a structure of the very kind envisaged by the theories of formal logicians. While Montague claims quite plainly that there is no substantial difference between formal and natural languages ("I reject the contention," he says, 1974, p. 188, "that an important theoretical difference exists between formal and natural languages"), Lewis states that it is fully correct to say that a linguistic community entertains a language in the form of a mathematical structure ("we can say", states Lewis, 1975, p.. (shrink)

Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...) considering a Sheffer function for intuitionistic logic. (shrink)

The basic idea of logical expressivism in the Brandomian tradition is that logic makes inferential relations explicit and thereby accessible to critical discussion. But expressivists have not given a convincing explanation of what the point of logical theories is. Peregrin provides a starting point by observing a distinction between making explicit and explication in Carnap’s sense of replacing something unclear and vague by something clear and exact. Whereas logical locutions make inferential relations explicit within a language, logical theories use formal (...) languages to explicate inferential roles and meanings of ordinary-language expressions. But Peregrin also holds that the whole point of logical theories is to provide perspicuous models of inferential structures in ordinary language practice. This turns explication into a mere continuation of making explicit by other means, and it leads to a one-sided conception of logic which has no room for evaluating inferential practice in light of logical theories. As a more convincing alternative, I suggest that expressivists rely on the method of reflective equilibrium. This approach is closely related to Carnapian explication, but it has the potential of correcting informal inferential practice without dubious ambitions to replace ordinary languages by logical formalisms. (shrink)

Various attempts at demarcating logic were undertaken, many of them based on specific understanding of how logical knowledge is formal and not material. MacFarlane has persuasively shown that general idea of formality of logic can be understood in various ways. I take two of the accounts of formality, namely the requirement of conservativity and the requirement of schematicity of logical vocabulary, into consideration as promising candidates to make the all too unclear notion of formality more precise and study to what (...) degree they could be considered as either necessary or sufficient conditions for logicality of some piece of vocabulary. Finding both notion unsatisfactory, as they stand, I propose combining them and envisage a hierarchy of logicality of expressions of a given language. Such a hierarchy is complicated and not linear, yet still offers a valuable explication of both the range and pragmatic significance of logic, if we combine it with logical expressivism. (shrink)

Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...) battle over the ‘one true logic’ is conceptually talking past each other. The theory of logics-as-formalizations is presented as a conceptually open theory of logic which is Carnapian in flavour and grounding. Rudolf Carnap’s notions surrounding ‘external’ and ‘pseudo-questions’ about linguistic frameworks apply to formalizations, thus logics, as well. An account of what formalizations are, a more structured sub-set of modelling, is given to ground the claim that logics are formalizations. Finally, a novel account of correctness, the COFE framework, is developed which allows the notions of logical monism, pluralism and nihilism to be more precisely formulated than they currently are in the discourse. (shrink)

In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the logical constants to be given by their elimination rules. I then consider the question: given a set of introduction rules \, what are the strongest elimination rules that are validated by an assertability (...) conditional meaning-theory based on \? I prove that the intuitionistic introduction rules are the strongest rules that are validated by the intuitionistic elimination rules. I then prove that intuitionistic logic is the strongest logic that can be given either an assertability-conditional or consequence-conditional meaning-theory. In “Grounding Grounding” I discuss the notion of grounding. My discussion revolves around the problem of iterated grounding-claims. Suppose that \ grounds \; what grounds that \ grounds that \? I argue that unless we can get a satisfactory answer to this question the notion of grounding will be useless. I discuss and reject some proposed accounts of iterated grounding claims. I then develop a new way of expressing grounding, propose an account of iterated grounding-claims and show how we can develop logics for grounding. In “Is the Vagueness Argument Valid?” I argue that the Vagueness Argument in favor of unrestricted composition isn’t valid. However, if the premisses of the argument are true and the conclusion false, mereological facts fail to supervene on non-mereological facts. I argue that this failure of supervenience is an artifact of the interplay between the necessity and determinacy operators and that it does not mean that mereological facts fail to depend on non-mereological facts. I sketch a deflationary view of ontology to establish this. (shrink)

Can we base the whole of logic solely on the concept of incompatibility? My motivation for asking this is two-fold: firstly, a technical interest in what a minimal foundations of logic might be; and secondly, the existence of philosophers who have taken incompatibility as the ultimate key to human reason (viz., e.g., Hegel's concept of determinate negation). The main aim of this contribution is to tackle two related questions: Is it possible to reduce the foundations of logic to the mere (...) concept of incompatibility? and Does this reduction lead us to a specific logical system? We conclude that the answers, respectively, are YES and a qualified NO (qualified in the sense that basing semantics on incompatibility does make some logical systems more natural than others, but without ruling out the alternatives.) A search for the bare bones of logic generally leads one to the relation of inference (or consequence). This way is explored meticulously by Koslow (1992). He defines an implication structure as, in effect, an ordered pair , where S is a set and | f Pow(S)HS fulfilling certain (relatively simple) restrictions. And obviously if we reduce incompatibility to inference, which is achievable by the well known ex contradictione quodlibet principle, we reach a logic based on incompatibility. The kind of logic flowing most straightforwardly from this setting is the intuitionist one. However, there is also the approach taken by R. Brandom and A. Aker (2008), who have set up a logic based directly on incompatibility. They define an incompatibility structure as an ordered pair such that S is a set and z f Pow(S) (again fulfilling certain restrictions). The authors introduce logical operators in such a way that they reach classical logic. Does this mean that inference 'naturally' leads to intuitionist logic, whereas incompatibility leads to the classical one? Myself, I have argued that it is indeed intuitionist logic that is the logic of inference (see Peregrin, 2008).. (shrink)

According to traditional logical expressivism, logical operators allow speakers to explicitly endorse claims that are already implicitly endorsed in their discursive practice — endorsed in virtue of that practice’s having instituted certain logical relations. Here, I propose a different version of logical expressivism, according to which the expressive role of logical operators is explained without invoking logical relations at all, but instead in terms of the expression of discursive-practical attitudes. In defense of this alternative, I present a deflationary account of (...) the expressive role of vocabulary by which we ascribe logical relations. (shrink)

Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis has also (...) had an influence on the philosophy of language: some prominent writers in that area, notably Dummett and Robert Brandom, have taken it to be a special case of a more general requirement that the grounds for asserting a statement must cohere with its consequences. This essay considers various ways of making the Harmony Thesis precise and scrutinizes the most influential arguments for it. The verdict is negative: all the extant arguments for the Thesis are weak, and no version of it is remotely plausible. (shrink)

O nějaké činnosti v rámci nějakého lidského společenství říkám, že je řízená pravidly , jsou‐li určité způsoby provozování této činnosti systematicky brány členy tohoto společenství, nebo nějakou jeho podskupinou, za správné, a jiné za nesprávné. Braní za správné či nesprávné (neboli normativní postoje ) beru v podstatě za dále neanalyzovatelné behaviorální vzorce, není to tedy pojem, který by primárně odkazoval k něčemu jako je kognitivní výbava účastníků, rozhodně nepředpokládá nic takového, jako že jsou tyto postoje věcí něčeho jako jsou plnohodnotná (...) přesvědčení. Hlavními symptomy těchto vzorců jsou určité typy reakcí na to, co dělají druzí; v extrémním případě snaha jim v děláním určitých věcí za každou cenu zabránit či je k němu naopak přimět. Často jde ale o mnohem subtilnější projevy "souhlasu" či "nesouhlasu" (od různých forem "odměn" a "trestů" po všelijaké náznaky "souznění" a "nevole") – projevy, které se člověk v rámci začleňování do lidských společenství učí rozpoznávat jako jisté "společenské tření", které ho v tom, co by měl a neměl dělat, usměrňuje. (shrink)