Wolpert, David H. and Kinney, David (2020) Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes. [Preprint]
This is the latest version of this item.
Text
FQXi_Paper.pdf  Accepted Version Download (582kB) 
Abstract
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a matter of certainty, but is instead governed by a probability distribution. We then show that this framework gives a compelling account of several aspects of mathematical practice. These include: 1) the way in which mathematicians generate research programs, 2) the applicability of Bayesian models of mathematical heuristics, 3) the role of abductive reasoning in mathematics, 4) the way in which multiple proofs of a proposition can strengthen our degree of belief in that proposition, and 5) the nature of the hypothesis that there are multiple formal systems that are isomorphic to physically possible universes. Thus, by embracing a model of mathematics as not perfectly predictable, we generate a new and fruitful perspective on the epistemology and practice of mathematics.
Export/Citation:  EndNote  BibTeX  Dublin Core  ASCII/Text Citation (Chicago)  HTML Citation  OpenURL 
Social Networking: 
Item Type:  Preprint  

Creators: 


Additional Information:  Forthcoming in Undecidability, Uncomputability, and Unpredictability. Springer. Ed. Anthony Aguirre, Zeeya Merali, and David Sloan. (Collection of winning essays from FQXi's 2020 Essay Contest)  
Keywords:  mathematical reasoning, mathematical universe hypothesis, abduction, Turing machines.  
Subjects:  General Issues > Confirmation/Induction General Issues > Determinism/Indeterminism Specific Sciences > Probability/Statistics General Issues > Realism/Antirealism 

Depositing User:  Dr David Kinney  
Date Deposited:  26 Nov 2020 05:22  
Last Modified:  26 Nov 2020 05:22  
Item ID:  18451  
Subjects:  General Issues > Confirmation/Induction General Issues > Determinism/Indeterminism Specific Sciences > Probability/Statistics General Issues > Realism/Antirealism 

Date:  28 October 2020  
URI:  https://philsciarchivedev.library.pitt.edu/id/eprint/18451 
Available Versions of this Item
 Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes. (deposited 26 Nov 2020 05:22) [Currently Displayed]
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
View Item 