The article addresses two closely related questions: What are the criteria of adequacy of logical formalization of natural language arguments, and what gives logic the authority to decide which arguments are good and which are bad? Our point of departure is the criticism of the conception of logical formalization put forth, in a recent paper, by M. Baumgartner and T. Lampert. We argue that their account of formalization as a kind of semantic analysis brings about more problems (...) than it solves. We also argue that the criteria of adequate formalization need not be based on truth conditions associated with logical formulas; in our view, they are better based on structural (inferential) grounds. We then put forward our own version of the criteria. The upshot of the discussion that follows is that the quest for an adequate formalization in a suitable logical language is best conceived of as the search for a Goodmanian reflective equilibrium. (shrink)

Traditional logical reconstruction of arguments aims at assessing the validity of ordinary language arguments. It involves several tasks: extracting argumentations from texts, breaking up complex argumentations into individual arguments, framing arguments in standard form, as well as formalizing arguments and showing their validity with the help of a logical formalism. These tasks are guided by a multitude of partly antagonistic goals, they interact in various feedback loops, and they are intertwined with the development of theories of valid inference and adequate (...) formalization. This paper explores how the method of reflective equilibrium can be used for modelling the complexity of such reconstructions and for justifying the various steps involved. The proposed approach is illustrated and tested in a detailed reconstruction of the beginning of Anselm’s De casu diaboli. (shrink)

The paper offers a historical survey of the emergence of logical formalization in twentieth-century analytically oriented philosophy of religion. This development is taken to have passed through three main ?stages?: a pioneering stage in the late nineteenth and early twentieth centuries (led by Frege and Russell), a stage of crisis in the 1920s and early 1930s (occasioned by Wittgenstein, logical positivists such as Carnap, and neo-Thomists such as Maritain), and a stage of rehabilitation in the 1930s, 1940s, and 1950s (...) (led by the Cracow Circle and Quine). (shrink)

This paper contains a careful derivation of principles of Interpretability Logic valid in extensions of I0+1.

This article summarizes the main ideas for formalizing categorial languages genrated by classical categorial grammar originated by K. Ajdukiewicz [1935,1960].This formalization is presented in detail in the author's monographs in Polish "Teorie Języków Syntaktycznie Kategorialnych" ("Theories of Syntactically Categorical Languages"), PWN, Warszawa-Wrocław 1985 and in English "Theory of Language Syntax, Categorial Approach", Kluwer Academic Publishers, Boston-London-Dordrecht 1991.

This paper deals with Tarski's first axiomatic presentations of the syntax of deductive system. Andrzej Grzegorczyk's significant results which laid the foundations for the formalization of metalogic, are touched upon briefly. The results relate to Tarski's theory of concatenation, also called the theory of strings, and to Tarski's ideas on the formalization of metamathematics. There is a short mention of author's research in the field. The main part of the paper surveys research on the theory of deductive systems (...) initiated by Tarski, in particular research on the axiomatization of the general notion of consequence operation, axiom systems for the theories of classic consequence and for some equivalent theories, and axiom systems for the theories of nonclassic consequence. In this paper the results of Jerzy Supecki's research are taken into account, and also the author's and other people belonging to his circle of scientific research. Particular study is made of his dual characterization of deductive systems, both as systems in regard to acceptance and systems in regard to rejection . Comparison is made, therefore, with axiomatizations of the theories of rejection and dual consequence, and the theory of the usual consequence operation. (shrink)

Within a weak subsystem of second-order arithmetic , that is -conservative over , we reformulate Kreisel's proof of the Second Incompleteness Theorem and Boolos' proof of the First Incompleteness Theorem.

The idea at the basis of this special issue is that reopening the old debate about the logical status of Hegel’s dialectics is extremely interesting, for various reasons.1 The first reason is that...

Wilfred Sieg. “Church's Thesis”, “Consistency”, “Formalization”, “Proof Theory”: Dictionary Entries.

In the last decade, philosophers have offered a number of proposals concerning the logical form of hypothetical cases, or thought experiments, as these are used for purposes of testing philosophical claims. In this paper, I discuss what the desiderata for a formal proposal are. Employing a comparison with general philosophy of science, I suggest that one important desideratum is to highlight recurrent patterns of disagreement surrounding cases. I advocate a proposal in propositional modal logic which, I argue, better meets this (...) desideratum than competing proposals. I also sketch how this proposal may be extended into more fine grained analyses, employing counterfactual conditionals yet avoiding certain problems due to so-called "deviant realizations". (shrink)

In this paper, we provide a logical formalization of the emotion triggering process and of its relationship with mental attitudes, as described in Ortony, Clore, and Collins’s theory. We argue that modal logics are particularly adapted to represent agents’ mental attitudes and to reason about them, and use a specific modal logic that we call Logic of Emotions in order to provide logical definitions of all but two of their 22 emotions. While these definitions may be subject to debate, (...) we show that they allow to reason about emotions and to draw interesting conclusions from the theory. (shrink)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the (...) standard meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

This paper can be treated as a simplification of the Gentzen formalization of SCI-tautologies presented by A. Michaels in [1].

Deontic logic, as traditionally conceived, provides only a deductive theory that constrains the states or possible worlds within which an agent should try to remain.

This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the reconstruction offered by Hamami is premised on a strong and controversial epistemological thesis and a strong and controversial thesis in the philosophy of mind. Secondly, we will argue that Hamami’s reconstruction of the standard view robs it of its original philosophical rationale, i.e. making sense of the notion of rigor in mathematical practice.

We propose a new dynamic hybrid logic to reason about social networks and their dynamics building on the work of “Logic in the Community” by Seligman, Liu and Girard. Our framework distinguishes between the purely private sphere of agents, namely their mental states, and the public sphere of their observable behavior, i.e., what they seem to believe. We then show how such a distinction allows our framework to model many social phenomena, by presenting the case of pluralistic ignorance as an (...) example and discussing some of its dynamic properties. (shrink)

This paper discusses six formalization techniques, of varying strengths, for extending a formal system based on traditional mathematical logic. The purpose of these formalization techniques is to simulate the introduction of new syntactic constructs, along with associated semantics for them. We show that certain techniques (among the six) subsume others. To illustrate sharpness, we also consider a selection of constructs and show which techniques can and cannot be used to introduce them. The six studied techniques were selected on (...) the basis of actual practice in logic and computing. They do not form an exhaustive list. (shrink)