The Epistemology of Mathematical Necessity

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. Cham, Switzerland: Springer-Verlag. pp. 810-813 (2018)
  Copy   BIBTEX

Abstract

It seems possible to know that a mathematical claim is necessarily true by inspecting a diagrammatic proof. Yet how does this work, given that human perception seems to just (as Hume assumed) ‘show us particular objects in front of us’? I draw on Peirce’s account of perception to answer this question. Peirce considered mathematics as experimental a science as physics. Drawing on an example, I highlight the existence of a primitive constraint or blocking function in our thinking which we might call ‘the hardness of the mathematical must’.

Categories

Keywords

Reprint years

Other Versions

No versions found

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Diagrammatic Representation and Inference10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings.Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz & Francesco Bellucci (eds.) - 2018 - Cham, Switzerland: Springer-Verlag.
Scanning the Invisible: Framing Diagrammatic Cognition in Experimental Particle Physics.Javier Anta - 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. Cham, Switzerland: Springer-Verlag.
The hardness of the iconic must: can Peirce’s existential graphs assist modal epistemology.Catherine Legg - 2012 - Philosophia Mathematica 20 (1):1-24.
Calculus CL as Ontology Editor and Inference Engine.Jens Lemanski - 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. Cham, Switzerland: Springer-Verlag. pp. 752-756.
What the Mathematical Poet Must Abide By: Epistemological Aspects of Charles Peirce's Philosophy of Mathematics.James Edward Willgoose - 2002 - Dissertation, Southern Illinois University at Carbondale
“Things Unreasonably Compulsory”: A Peircean Challenge to a Humean Theory of Perception, Particularly With Respect to Perceiving Necessary Truths.Catherine Legg - 2014 - Cognitio 15 (1):89-112.
Making Sense of Schopenhauer's Diagram of Good and Evil.Jens Lemanski & Amirouche Moktefi - 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. Cham, Switzerland: Springer-Verlag. pp. 721-724.
How to Have True Mathematical Beliefs and Different Mathematical Beliefs at the Same Time.Costanza Brevini - 2018 - Proceedings of the XXIII World Congress of Philosophy 56:11-16.
Peirce on the role of poietic creation in mathematical reasoning.Daniel G. Campos - 2007 - Transactions of the Charles S. Peirce Society 43 (3):470 - 489.
Categories for the working mathematician: making the impossible possible.Jessica Carter - 2008 - Synthese 162 (1):1-13.

Analytics

Added to PP
2019-02-27

Downloads
431 (#64,379)

6 months
83 (#71,331)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Cathy Legg
Deakin University

Citations of this work

No citations found.

Add more citations

References found in this work

Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
What is a Logical Diagram?Catherine Legg - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Basel: Birkhaüser. pp. 1-18.

Add more references