Philosophia Mathematica 20 (1):1-24 (2012)

Authors
Cathy Legg
Deakin University
Abstract
Charles Peirce's diagrammatic logic — the Existential Graphs — is presented as a tool for illuminating how we know necessity, in answer to Benacerraf's famous challenge that most ‘semantics for mathematics’ do not ‘fit an acceptable epistemology’. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the particular structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not merely to individual things but to how those things are related in larger structures, certain aspects of which relations force certain other aspects to be a certain way
Keywords modal epistemology  peirce  existential graphs  benacerraf  necessity  intuition
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Reprint years 2012
DOI 10.1093/philmat/nkr005
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References found in this work BETA

Philosophical Investigations.Ludwig Josef Johann Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell.
On the Plurality of Worlds.David Lewis - 1986 - Wiley-Blackwell.
From a Logical Point of View.W. V. O. Quine - 1953 - Harvard University Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.

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Citations of this work BETA

Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
The Epistemology of Mathematical Necessity.Catherine Legg - 2018 - In Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz & Francesco Bellucci (eds.), Diagrammatic Representation and Inference10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. Berlin: Springer-Verlag. pp. 810-813.

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