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  

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Keywords:  Infinitesimal, Leibniz, Informational Realism, Statistics, Calculus, nonstandard Calculus, Philosophy of Math, Philosophy of Calculus  
Subjects:  Specific Sciences > Mathematics Specific Sciences > Probability/Statistics 

Depositing User:  Andrew Dynneson  
Date Deposited:  07 Jul 2016 15:38  
Last Modified:  07 Jul 2016 15:38  
Item ID:  12249  
Subjects:  Specific Sciences > Mathematics Specific Sciences > Probability/Statistics 

Date:  21 May 2016  
URI:  http://philsciarchive.pitt.edu/id/eprint/12249 
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Infinitesimal Calculus as an Epistemic Mediator: A commentary on the use of Squares in Elementary Statistical Theory. (deposited 22 May 2016 16:28)

Infinitesimal Calculus as an Epistemic Mediator: A commentary on the use of Squares in Elementary Statistical Theory. (deposited 05 Jul 2016 15:32)
 Infinitesimal Calculus as an Epistemic Mediator: A commentary on the use of Squares in Elementary Statistical Theory. (deposited 07 Jul 2016 15:38) [Currently Displayed]

Infinitesimal Calculus as an Epistemic Mediator: A commentary on the use of Squares in Elementary Statistical Theory. (deposited 05 Jul 2016 15:32)
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