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 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)

The tools of logic are used properly or improperly relative to two interrelated purposes. Logic is both a symbolism for the expression of the formal structures of thought and an inference mechanism. Formalization in philosophical logic is justified to the extent that it contributes to our understanding of logical properties and the conceptual problems they may help to state, clarify, or resolve. This view of the value and limits of formalization in logic affords a pragmatic perspective that in (...) principle should selectively support the development of particular formal systems, while excluding others as unjustified. Yet the pragmatic grounds are so liberal as to disallow virtually no exercises in formalization as entirely useless. Logic is abused in another sense, when it is wrongly used, not by violating logical canons generally, but by presupposing that substantive metaphysical, normative, or scientific content can be derived from purely formal logical relations. (shrink)

Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem of first-order logic, namely what (...) is known as geometric logic. (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)

he general theme of this paper is the issue of formalization in philosophy; in a more specific way, it deals with the issue of formalization of arguments in analytic philosophy of religion. One argument in particular – Anselm’s Proslogion II ontological argument – and one specific attempt to formalize it – Robert Adams’ formalization found in his paper “The Logical Structure of Anselm’s Arguments”, published in The Philosophical Review in 1971 – are taken as study cases. The purpose (...) of the paper is to critically analyze Adams’ formalization with the intent to shed some light on the following questions: What are the virtues of formally analyzing arguments and the contributions, if any, of such an enterprise to the debate on Anselm’s argument? Which lessons can Adam’s work teach us about the dangers and limitations of formalization? Do these virtues and dangers teach us something about analysis of arguments in general? (shrink)

Explication is the conceptual cornerstone of Carnap’s approach to the methodology of scientific analysis. From a philosophical point of view, it gives rise to a number of questions that need to be addressed, but which do not seem to have been fully addressed by Carnap himself. This paper reconsiders Carnapian explication by comparing it to a different approach: the ‘formalisms as cognitive tools’ conception. The comparison allows us to discuss a number of aspects of the Carnapian methodology, as well as (...) issues pertaining to formalization in general. We start by introducing Carnap’s conception of explication, arguing that there is a tension between his proposed criteria of fruitfulness and similarity; we also argue that his further desideratum of exactness is less crucial than might appear at first. We then bring in the general idea of formalisms as cognitive tools, mainly by discussing the reliability of so-called statistical prediction rules, i.e. simple algorithms used to make predictions across a range of areas. SPRs allow for a concrete instantiation of Carnap’s fruitfulness desideratum, which is arguably the most important desideratum for him. Finally, we elaborate on what we call the ‘paradox of adequate formalization’, which for the Carnapian corresponds to the tension between similarity and fruitfulness. We conclude by noting that formalization is an inherently paradoxical enterprise in general, but one worth engaging in given the ‘cognitive boost’ it affords as a tool for discovery. (shrink)

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)

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)

The question, what a given statement is “about,” often occurs in philosophic discussion. I shall use this question in the hope of illustrating how a relatively simple application of symbolic logic can clarify a problem which might otherwise turn into a maze of complications.

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

After several decades during which formalization has flourished it now becomes possible to detect its shortcomings. A definition of formalization is given at the outset. It is next shown that the main justification of formalization as making explicit the form of a proof has serious difficulties. An important shortcoming is found in the fact that many validation procedures in logic and mathematics are not adequately represented deductively. Several such procedures relating to the validation of logical and mathematical (...) sentences are examined. It is concluded that formalization is materially inadequate. (shrink)

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...

Three common strategies used by informal logicians are considered: (1) the appeal to standard cases, (2) the attempt to partially formalize so-called "informal fallacies," and (3) restatement of arguments in such a way as to make their logical character more perspicuous. All three strategies are found to be useful. Attention is drawn to several advantages of a "stock case" approach, a minimalist approach to formalization is recommended, and doubts are raised about the applicability, from a logical point of view, (...) of a principle of charitable construal in the reconstruction of arguments. (shrink)

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 argue that the challenge of the formalization of functions not merely consists of analyzing and formalizing yet another concept; the challenge may also consist of formalizing a con...

The purpose of this paper is twofold. First, it aims at introducing the ontological argument through the analysis of five historical developments: Anselm’s argument found in the second chapter of his Proslogion, Gaunilo’s criticism of it, Descartes’ version of the ontological argument found in his Meditations on First Philosophy, Leibniz’s contribution to the debate on the ontological argument and his demonstration of the possibility of God, and Kant’s famous criticisms against the (cartesian) ontological argument. Second, it intends to critically examine (...) the enterprise of formally analyzing philosophical arguments and, as such, contribute in a small degree to the debate on the role of formalization in philosophy. My focus will be mainly on the drawbacks and limitations of such enterprise; as a guideline, I shall refer to a Carnapian, or Carnapian-like theory of argument analysis. (shrink)

We are working on formalizing a proof of the prime number theorem using Isabelle/HOL. In support of this project we formalized a very general notion of O notation.

We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of Meredith. The usual primitive notions of free variable and proper substitution are absent, making it easy to verify proofs in a machine-oriented application. Completeness results are presented. The (...) example of Zermelo-Fraenkel set theory is shown to be finitely axiomatized under the formalization. The relationship with resolution-based theorem provers is briefly discussed. A closely related axiomatization of traditional predicate calculus is shown to be complete in a strong metamathematical sense. (shrink)

Consumer autonomy is a fundamental topic for marketing ethics scholars. Nonetheless, autonomy’s philosophical treatment may have compromised its conceptual clarity. After reviewing the relevant ethics literature on consumer autonomy, the benefits of formally defining consumer autonomy are illustrated, and a novel formalization is adapted from potential performance theory mathematics. The goal is to transfigure a hitherto amorphous topic via a mathematical formalization that defines true autonomy, actual autonomy, reliability of wills, and reliability of product choice. The crucial and (...) surprising result: an action that decreases true autonomy can increase actual autonomy if that action engenders a sufficient increase in one or both types of reliability. Relating the insights from the formalization to the long-standing debates in consumer autonomy suggests fruitful avenues for future research. (shrink)

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.

Structure and organization seems to be at the root of many of the questions raised about institutional behaviour; however, with respect to research on university capacity building, few studies have examined research organizational problems, particularly in developing countries. This study investigates academic reactions to the structure and organization of research at four leading Vietnamese universities. Through document analysis and semi-structured interviews with 55 participants, the study finds that the four case-study Vietnamese universities have accomplished a number of the more visible (...) tasks of research management such as creating research and research management positions; deciding primary organizational units for research delivery; creating a research office; and creating research oversight committees. However, they seem to neglect the other less visible tasks of organizing and structuring research such as developing rules for research integrity; developing a mechanism for evaluating the quality of research outcomes; preparing researchers and research managers for the necessary skills and knowledge; and deciding vertical and horizontal decentralization. The study concludes that even though research has been formally structured and organized, the management of research has not yet been professionalized. The key problem in organizing and structuring research is the lack of an effective system for research behaviour formalization. A more effective system for better formalizing research behaviours should be developed so that Vietnamese universities can integrate more successfully into the global research. (shrink)