It's often hypothesized that the structure of mental representation is map-like rather than language-like. The possibility arises as a counterexample to the argument from the best explanation of productivity and systematicity to the language of thought hypothesis—the hypothesis that mental structure is compositional and recursive. In this paper, I argue that the analogy with maps does not undermine the argument, because maps and language have the same kind of compositional and recursive structure.

Responding to the paradox of inference and the related problems in philosophy of logic, this paper argues for the necessity of distinguishing between two different objects of justification: logica utens and logica docens. Then, equipped with Peirce’s critical common-sensist conception of logica utens and his classification of sciences, I propose a diagnosis of and a solution to the problem of justification of logic. I argue that this alternative approach successfully avoids circularity in which most attempts in philosophy of logic have (...) been inescapably trapped. I also anticipate and respond to possible objections to taking a Peircean turn in justifying logic. (shrink)

In this article, we try to trace the relationship between semiotics and theory of legal reasoning using Peirce’s idea that all reasoning must be necessarily in signs: every act of reasoning/argumentation is a sign process, leading to “the growth of knowledge. The broad scope and universal character of Peirce’s sign theory of reasoning allows us to look for new conciliatory paradigms, which must be presented in terms of possible synthesis between the traditional approaches to argumentation. These traditional approaches are strongly (...) affected by either the dialectical (logical) perspective or the rhetorical perspective on argumentation, while Peirce’s approach tends to reconcile the rhetorical and methodological aspects of reasoning. This reconcilation is best illustrated by Peircean analysis of argument’s logical and rhetorical structure; while the diagrammatic (iconic) analysis of arguments is performed in the system of Existential Graphs (which is Peirce’s major methodological system, designed for the expressions of propositions in point of their relational structure). Obviously, Peirce’s original division of argument parts offered only the characterisation of the sign activity (involved in the process of reasoning), and thus left much to be desired in terms of practical explication. (shrink)

Deduction is decisive but nonetheless mysterious, as I argue in the introduction. I identify the mystery of deduction as surprise-effect and demonstration-difficulty. The first section delves into how the mystery of deduction is connected with the representation of information and lays the groundwork for our further discussions of various kinds of representation. The second and third sections, respectively, present a case study for the comparison between symbolic and diagrammatic representation systems in terms of how two aspects of the mystery of (...) deduction – surprise-effect and demonstration-difficulty – are handled. The fourth section illustrates several well-known examples to show how diagrammatic representation suggests more clues to the mystery of deduction than symbolic representation and suggests some conjectures and further work. (shrink)

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a (...) corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic. (shrink)

Throughout its long history, mathematics has involved the use ofsystems of written signs, most notably, diagrams in Euclidean geometry and formulae in the symbolic language of arithmetic and algebra in the mathematics of Descartes, Euler, and others. Such systems of signs, I argue, enable one to embody chains of mathematical reasoning. I then show that, properly understood, Frege’s Begriffsschrift or concept-script similarly enables one to write mathematical reasoning. Much as a demonstration in Euclid or in early modern algebra does, a (...) proof in Frege’s concept-script shows how it goes. (shrink)

In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or (...) localized a faculty to register them. We defend the perception of necessity against such Humeanism, drawing on examples from mathematics. (shrink)

This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how to extend his (...) method to a subset of first-order formulas, namely, formulas that do not contain dyadic sentential connectives within the scope of any quantifier. (shrink)

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. The structure of mental models is iconic as far as possible. The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. Individuals tend to construct only a single, typical model. They spontaneously develop their own strategies for relational reasoning. Regardless of strategy, the difficulty of an inference depends (...) on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle. (shrink)

Abstract.Stuart Kauffman's proposal in Investigations to ground a “general biology” in the laws of self‐organization governing systems of autonomous agents runs up against the methodological problem of how to integrate formal mathematical with semantic and semiotic approaches to the study of evolutionary development. Gilles Deleuze's concept of the virtual and C. S. Peirce's system of existential graphs provide a theoretical framework and practical art for answering this problem of method by modeling the creative event of collective self‐organization as both represented (...) and practiced in the scientific community. (shrink)

This paper suggests that reference to phenomenal qualities is best understood as involving iconicity, that is, a passage from sign-vehicle to object that exploits a similarity between the two. This contrasts with a version of the ‘phenomenal concept strategy’ that takes indexicality to be central. However, since it is doubtful that phenomenal qualities are capable of causally interacting with anything, indexical reference seems inappropriate. While a theorist like David Papineau is independently coming to something akin to iconicity, I think some (...) of the awkwardness that plagues his account would be remedied by transitioning to a more inclusive philosophy of signs. (shrink)

While the topic of assertion has recently received a fresh wave of interest from Peirce scholars, to this point no systematic account of Peirce’s view of assertion has been attempted. We think that this is a lacuna that ought to be filled. Doing so will help make better sense of Peirce’s pragmatism; further, what is hidden amongst various fragments is a robust pragmatist theory of assertion with unique characteristics that may have significant contemporary value. Here we aim to uncover this (...) theory, and to show that assertion for Peirce is not a mere corollary of pragmatic conceptions of truth, judgement, and belief, but is rather a central aspect of his philosophy. (shrink)

I develop an account of scientific representations building on Charles S. Peirce's rich, and still underexplored, notion of iconicity. Iconic representations occupy a central place in Peirce's philosophy, in his innovative approach to logic and in his practice as a scientist. Starting from a discussion of Peirce's approach to diagrams, I claim that Peirce's own representations are in line with his formulation of iconicity, and that they are more broadly connected to the pragmatist philosophy he developed in parallel with his (...) scientific work. I then defend the contemporary relevance of Peirce's approach to iconic representations, and specifically argue that Peirce offers a useful ‘third way’ between what Mauricio Suárez has recently described as the ‘analytical’ and ‘practical’ inquiries into the concept of representation. As a philosophically minded scientist and an experimentally inclined philosopher, Peirce never divorced the practice of representing from questions about what counts as a representation... (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)