Justificationist Semantics

The paper begins with a conceptual discussion of Michael Dummett's proof-theoretic justification of deduction or proof-theoretic semantics, which is based on what we might call Gentzen's thesis: 'the introductions constitute, so to speak, the "definitions" of the symbols concerned, and the eliminations are in the end only consequences thereof, which could be expressed thus: In the elimination of a symbol, the formula in question, whose outer symbol it concerns, may only "be used as that which it means on the basis (...) of the introduction of this symbol".' The intuitive philosophical content of Dummett's notions of harmony and stability is that harmony obtains if the grounds for asserting a proposition match the consequences of accepting it, and stability obtains if the converse also holds. Rules of inference define the meanings of a logical constant they govern if and only if they are stable. Gentzen observed that 'it should be possible to establish on the basis of certain requirements that the elimination rules are functions of the corresponding introduction rules.' One of the objectives of this paper is to specify such a function: I will specify a process by which it is possible to determine the elimination rules of logical constants from their introduction rules, and conversely, to determine the introduction rules from the elimination rules. I'll give the general forms of rules of inference and generalised reduction procedures for the normalisation of deduction. I'll give a formally precise characterisations of harmony and stability and show that deductions in logics that contain only constants governed by stable rules always normalise. (shrink)

Discursive pluralism, recently fostered by anti-representationalist views, by stating that not all assertions conform to a descriptive model of language, poses an interesting challenge to representationalism. Although in recent years alethic pluralism has become more and more popular as an interesting way out for this issue, the discussion also hosts other interesting minority approaches in the anti-representationalist camp. In particular, the late stage of contemporary expressivism offers a few relevant insights, going from Price's denunciation of “placement problems” to Brandom's inferentialism. (...) This paper attempts to show how these expressivist ideas combine well together, composing a unitary and metaphysically sober metaphilosophical framework. (shrink)

We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati and Schlöder 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic S5 modulo an appropriate translation. The logical framework developed provides the (...) basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve. (shrink)

This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from (...) rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguish it from Francez's. (shrink)

The article explains on the two-year experiment after the author’s finalization of dissertation. The thesis of the dissertation was hidden in the last chapter with analytical linguistics. It was done so with the fascist development of the Chinese Communist regime with neo- Nazi characteristics. Since numerous prior warnings on the political downshifts & coup d’état in China was willfully ignored by the university, the linguistic innovations in dissertation found a balance between multilateralism and outer space (security). The experiments were conducted (...) with a combination of physical unit analysis & thermonuclear dynamics analysis. It describes the experiment process in terms of gravitation as gravitational singularity and Bekenstein-Penrose singularity. Detailed research process is elaborated in the article concerning the sociopolitical interactions the research involved. (shrink)

This essay is about the conception of second person in Donald Davidson. For Davidson, what characterizes a significant act and the possibility of the content of an attitude is the interaction between two agents driven by a primary intention: the speaker has the intention that his utterances be understood by another person. The essay is organized in three sections: in the first section, I present the specific meaning of the second person as a creature with whom the speaker currently interacts, (...) regardless of whether they share a rule or linguistic convention beforehand. In the second section I present Davidson’s thesis of triangulation, which is that the individualization of beliefs and thoughts is established from systematic causal connections in triangulation between the individual, another speaker with whom he interacts, and objects or events in the world. Finally, in the third section, I present the idea of the “norm of conversation” as a theoretical tool to address epistemological issues: in conversation, when interlocutors intend to understand each other, speakers engage in a kind of investigation about the meaning and content of the sentences, beliefs, and intentions in dispute. (shrink)

Clearly neither I nor anyone will ever read any substantial part of this massive tome so I will discuss the one article that interests me most and which I think provides the framework necessary for the understanding of all the rest. I refer to the one on Ludwig Wittgenstein (W). Even were I to try to discuss others, we would not get past the first page as all the issues here arise immediately in any discussion of behavior. The differentiation of (...) pragmatics and semantics is largely meaningless. It is defensible that one might subtitle this work ‘Developments of Wittgenstein’s Contextualism’, but of course this term has inevitably been corrupted by philosophers. One might then say that pragmatics and semantics are parts of or coextensive with epistemology and ontology and the descriptive psychology of higher order thought (Searle’s Logical Structure of Rationality) or that they describe how we use noises in specific contexts to give them meaning --i.e., a true or false (propositional) use which Searle calls their Conditions of Satisfaction. Adding the Wittgenstein/Searle work to modern research on thinking provides a framework for pragmatics, semantics and all other human behavior. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

This paper assesses the prospects of a pragmatist theory of content. I begin by criticising the theory presented in D.H. Mellor’s essay ‘Successful Semantics’. I then identify problems and lacunae in the pragmatist theory of meaning sketched in Chapter 13 of Dummett’s The Logical Basis of Metaphysics. The prospects are brighter, I contend, for a tempered pragmatism, in which the theory of content is permitted to draw upon irreducible notions of truth and falsity. I sketch the shape of such a (...) theory and illustrate the role of its pragmatist elements by showing how they point towards a promising account of the truth conditions of indicative conditionals. A feature of the account is that it validates Modus Ponens whilst invalidating Modus Tollens. (shrink)

The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, I (...) shall grant Dummett his general bias towards verificationism, encapsulated in the slogan 'meaning is use'. The second general assumption I see no need to question is Dummett's particular breed of molecularism. Some of Dummett's assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inference in the Dummettian framework. (shrink)

I here argue for a particular formulation of truth-deflationism, namely, the propositionally quantified formula, (Q) “For all p, <p> is true iff p”. The main argument consists of an enumeration of the other (five) possible formulations and criticisms thereof. Notably, Horwich’s Minimal Theory is found objectionable in that it cannot be accepted by finite beings. Other formulations err in not providing non-questionbegging, sufficiently direct derivations of the T-schema instances. I end by defending (Q) against various objections. In particular, I argue (...) that certain circularity charges rest on mistaken assumptions about logic that lead to Carroll’s regress. I show how the propositional quantifier can be seen as on a par with first-order quantifiers and so equally acceptable to use. While the proposed parallelism between these quantifiers is controversial in general, deflationists have special reasons to affirm it. I further argue that the main three types of approach the truth-paradoxes are open to an adherent of (Q), and that the derivation of general facts about truth can be explained on its basis. (shrink)

Virtual environments engage millions of people and billions of dollars each year. What is the ontological status of the virtual objects that populate those environments? An adequate answer to that question requires a developed semantics for virtual environments. The truth-conditions must be identified for “tree”-sentences when uttered by speakers immersed in a virtual environment (VE). It will be argued that statements about virtual objects have truth-conditions roughly comparable to the verificationist conditions popular amongst some contemporary antirealists. This does not mean (...) that the virtual objects lack ontological standing. There is an important sense in which virtual objects are no less real for being mind-dependent. (shrink)

I argue for a kind of logical pluralism on the basis of a difficulty with defining the meaning of negation in the framework of Dummett's and Prawitz' proof-theoretic semantics.

This paper is divided into four sections. -/- The first section contains an informal characterization of what may, for the purposes of this discussion, be referred to as the standard interpretation of theological statements. -/- Then, in the second section, I mention two challenges to the commonsense view that theological statements have cognitive content: the quote “falsifiability challenge” and the “ translatability challenge”. -/- Both of these challenges involve an appeal to an empiricist criterion of cognitive content, but I contend (...) that they are nonetheless very different arguments and that clarity about the fundamental issues involved in the question of theology and verificationism cannot be achieved unless these two lines are argument are carefully distinguished. -/- The third section is concerned with the question of the possibility of an empiricist criterion of cognitive significance. The underlying purpose of the discussion will be to arrive derive at an evaluation of the commonly advanced claim that verificationist objections to the meaningfulness of theological language can be refuted by simply arguing that is not possible to formulate an adequate confirmability criterion of cognitive significance. -/- I then conclude by suggesting some responses that seem more promising. (shrink)