A Pragmatic Interpretation of Quantum Logic

Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be interpreted as a pragmatic language of assertive formulas which formalize statements about physical systems that are empirically justified or unjustified in the framework of quantum mechanics. According to this interpretation, QL formalizes properties of the metalinguistic notion of empirical justification within quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic. By the way, some elucidations of the standard notion of quantum truth are also obtained. Key words: pragmatics, quantum logic, quantum mechanics, justifiability, global pluralism.Comment: Third version: 20 pages. Sects. 1, 2, and 4 rewritten and improved. Explanations adde

The Logical Burdens of Proof. Assertion and Hypothesis

The paper proposes two logical analyses of (the norms of) justification. In a first, realist-minded case, truth is logically independent from justification and leads to a pragmatic logic LP including two epistemic and pragmatic operators, namely, assertion and hypothesis. In a second, antirealist-minded case, truth is not logically independent from justification and results in two logical systems of information and justification: AR4 and AR4¢, respectively, provided with a question-answer semantics. The latter proposes many more epistemic agents, each corresponding to a wide variety of epistemic norms. After comparing the different norms of justification involved in these logical systems, two hexagons expressing Aristotelian relations of opposition will be gathered in order to clarify how (a fragment of) pragmatic formulas can be interpreted in a fuzzy-based question-answer semantics

On an Intuitionistic Logic for Pragmatics

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justications and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the S4 modal translation, we give a denition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is dened and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, dened as a hypothesis that in some situation the truth of p is epistemically necessary

Hakikat Kebenaran; Perspektif Pengetahuan, Ilmu, Agama dan Filsafat

This research is to find out the nature of truth; perspectives of knowledge, science, religion and philosophy. This research uses a library research method with a qualitative approach. The research results show that: 1) The nature of truth. The emergence of a theory of truth can build knowledge from the views and understanding obtained through existing processes. In order to emphasize theory as a benchmark for truth, we can look at the theory of truth from two very common perspectives, namely: the western-based theory of truth and the theory of truth. The nature of truth is rational, empirical and pragmatic. 2) Knowledge includes reasoning and logic, 3) The characteristics of knowledge are that it is arranged methodically, systematically and coherently about a particular field and reality and can be used to explain certain phenomena in the field (knowledge). 4) Religion is human belief or belief in a teaching that comes from God, the bearer of truth, and 5) philosophy is a science that seriously studies the nature of the truth of all things

A pragmatic logic for the expressive conception of norms and values and the Frege-Geach problem

Abstract: In this paper I intend to overcome the incompatibility -basically expressed by the Frege-Geach problem- between the expressive conception of norms and values and the applicability of logic to them, as well as the widespread scepticism about a possible "logic of attitudes" (Hale). To this end, I present a logic for the expressive conception of norms and values providing a solution to the Frege-Geach problem, that is immune to the ambiguities affecting two previous attempts by Blackburn (1984 and [1988] 1993). In particular, I use and extend a pragmatic language Lp, that is an extension of the language of standard propositional logic L, which is obtained by adding two categories of logical-pragmatic signs to the vocabulary of L: the signs of pragmatic mood („¥, O and H, standing for 'assertion', 'obligation' and 'approval', respectively) and the pragmatic connectives (~, ∩, ∪, ⊃, ≡). The wffs of L are called radical formulas (rf) of Lp. By applying the signs of pragmatic mood to the rfs, we obtain elementary sentential formulas (sf) (assertive, normative, evaluative) of Lp, that can be connected by means of the pragmatic connectives, so obtaining complex sfs. Every rf of Lp has a truth value and every sf has a justification value, which is defined in terms of the intuitive notion of proof and which depends on the truth value of its radical subformulas. In this language, the notions of pragmatic validity, compatibility, satisfiability and inference are defined and some criteria of pragmatic validity are given. Therefore, in Lp, it is possible to carry out inferences between norms and values expressively understood and, thus, to adequately formalize Geach's problematic inferences

The Notion of Eikos Within Conspiracy Theories. A Rhetorical Analysis

Based on the analysis of one specific conspiracy theory, this paper will explore, from the rhetorical framework, the antic concept of likelihood [eikos]. Indeed, we believe that the rhetorical approach could allow us, on a larger scale, to (re)question, in the light of contemporary challenges, the complex relationship we have with the notions of rationality and truth. More precisely, to proceed with the rhetorical analysis, we will mobilise two types of logical reasoning: first, “the logic of the pot” argument from pragmatic logic and second, the logic of amplification and poetization of discourse. This will allow us to draw some comparisons between conspiracist speeches and, respectively, the rhetorical genres of judicial and epideictic discourses. The comparisons will be based on the criteria of likelihood, eikos, in order to propose a first definition of this notion in conspiracist discourses

Some Logical Notations for Pragmatic Assertions

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems

Gestalt Shifts in the Liar Or Why KT4M Is the Logic of Semantic Modalities

ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why -- and how -- truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M (= S4M). Drawing on the structure of KT4M (=S4M), the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable