
41The Logical Status of DiagramsBritish Journal for the Philosophy of Science 48 (2): 290291. 1997.

33Review of Marcus Giaquinto, Visual Thinking in Mathematics: An Epistemological Study (review)Notre Dame Philosophical Reviews 2008 (7). 2008.

71Euler’s visual logicHistory and Philosophy of Logic 19 (1): 129. 1998.The evolution of Euler diagrams is examined from Euler's original system through the modifications made by Venn and Peirce. It is shown that these modifications were motivated by an attempt to increase the expressivity of the diagrams, but that a side effect of these modifications was a loss of the visual clarity of Euler's original system. Euler's original system is reconstructed from a modern, logical point of view. Formal semantics and rules of inference are provided for this reconstruction o…Read more

The Iconic Logic of Peirce's GraphsTransactions of the Charles S. Peirce Society 39 (1): 127133. 2003.

16Peirce's alpha graphs and propositional languagesSemiotica 2011 (186): 333346. 2011.Many do not doubt that Peirce's Existential Graphs are diagrammatic, as opposed to symbolic. However, when we are pressured to draw a distinction between the two different forms of representation, we find ourselves at a loss and our intuition quite vague. In this paper, I locate fundamental differences between two logically equivalent systems, Peirce's Alpha system and propositional languages. Suppose we have only two sentential connectives, ¬ and ^. In spite of its truthfunctional completeness…Read more

23Situationtheoretic account of valid reasoning with Venn diagramsIn Gerard Allwein & Jon Barwise (eds.), Logical Reasoning with Diagrams, Oxford University Press. 1996.

50The Mystery of Deduction and Diagrammatic Aspects of RepresentationReview of Philosophy and Psychology 6 (1): 4967. 2015.Deduction is decisive but nonetheless mysterious, as I argue in the introduction. I identify the mystery of deduction as surpriseeffect and demonstrationdifficulty. 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 …Read more

90The forgotten individual: diagrammatic reasoning in mathematicsSynthese 186 (1): 149168. 2012.Parallelism has been drawn between modes of representation and problemsloving processes: Diagrams are more useful for brainstorming while symbolic representation is more welcomed in a formal proof. The paper gets to the root of this clearcut dualistic picture and argues that the strength of diagrammatic reasoning in the brainstorming process does not have to be abandoned at the stage of proof, but instead should be appreciated and could be preserved in mathematical proofs

4Valid Reasoning and Visual RepresentationDissertation, Stanford University. 1991.This thesis challenges a general prejudice against visualization in the history of logic and mathematics, by providing a semantic analysis of two graphical representation systemsa traditional Venn diagram representation system and an extension of it. While Venn diagrams have been used to solve problems in set theory and to test the validity of syllogisms in logic, they have not been considered valid proofs but heuristic tools for finding valid formal proofs. ;I present Venn diagrams which have…Read more

31Reconstituting beta graphs into an efficacious systemJournal of Logic, Language and Information 8 (3): 273295. 1999.Logicians have strongly preferred firstorder natural deductive systems over Peirce's Beta Graphs even though both are equivalent to each other. One of the main reasons for this preference, I claim, is that inference rules for Beta Graphs are hard to understand, and, therefore, hard to apply for deductions. This paper reformulates the Beta rules to show more finegrained symmetries built around visual features of the Beta system, which makes the rules more natural and easier to use and understan…Read more

57The Iconic Logic of Peirce's GraphsMIT Press. 2002.A case study of multimodal systems and a new interpretation of Charles S. Peirce's theory of reasoning and signs based on an analysis of his system of ...

92Kant's syntheticity revisited by PeirceSynthese 113 (1): 141. 1997.This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theoremproving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peirce…Read more

74Peirce and the logical status of diagramsHistory and Philosophy of Logic 15 (1): 4568. 1994.In this paper, I aim to identify Peirce?s great contribution to logical diagrams and its limit.Peirce is the first person who believed that the same logical status can be given to diagrams as to symbolic systems.Even though this belief led him to invent his own graphical system, Existential Graphs, the success or failure of this system does not determine the value of Peirce?s general insights about logical diagrams.In order to make this point clear, I will show that Peirce?s revolutionary ideas …Read more
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