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Infinitesimal Calculus as an Epistemic Mediator: A commentary on the use of Squares in Elementary Statistical Theory

Dynneson, Andrew and Alvarez, Aaron (2016) Infinitesimal Calculus as an Epistemic Mediator: A commentary on the use of Squares in Elementary Statistical Theory. [Preprint]

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Abstract

This is a commentary on the use of squares in elementary statistics. One sees an ubiquitous use of squares in statistics, and the analogy of "distance in a statistical sense" is teased out. We conjecture that elementary statistical theory has its roots in classical Calculus, and preserves the notion of two senses described in this paper. We claim that the senses of the differentials dx/dy hold between classical and modern infinitesimal Calculus and show how this sense becomes cashed out in both models. We suggest that the commonalities of both accounts can be used to find a informational realist account of Calculus. This account involves infinitesimal Calculus as acting as an epistemic mediator that expands our conceptual space and enables us to create new measures.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Dynneson, Andrewawdynneson@utep.edu
Alvarez, Aaronaalvarez11@miners.utep.edu
Keywords: Infinitesimal, Leibniz, Informational Realism, Statistics, Calculus, non-standard Calculus, Philosophy of Math, Philosophy of Calculus
Subjects: Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Depositing User: Andrew Dynneson
Date Deposited: 22 May 2016 16:28
Last Modified: 22 May 2016 16:28
Item ID: 12104
Subjects: Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Date: 21 May 2016
URI: http://philsci-archive.pitt.edu/id/eprint/12104

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