Philosophical Aspects of an Alleged Connection Between the Axiom of Choice and Predicting the Future

2017 ◽  
pp. 213-220
Author(s):  
Pawel Pawlowski
Keyword(s):  
Axiom Of Choice ◽  
The Future ◽  
The Axiom Of Choice

A Peculiar Connection Between the Axiom of Choice and Predicting the Future

2008 ◽  
Vol 115 (2) ◽  
pp. 91-96 ◽  
Author(s):  
Christopher S. Hardin ◽  
Alan D. Taylor
Keyword(s):  
Axiom Of Choice ◽  
The Future ◽  
The Axiom Of Choice

The Axiom of Choice Machine

2018 ◽  
Author(s):  
Alexander R. Pruss
Keyword(s):  
Set Theory ◽  
Laws Of Nature ◽  
Axiom Of Choice ◽  
Dutch Book ◽  
The Axiom Of Choice

This is a mainly technical chapter concerning the causal embodiment of the Axiom of Choice from set theory. The Axiom of Choice powered a construction of an infinite fair lottery in Chapter 4 and a die-rolling strategy in Chapter 5. For those applications to work, there has to be a causally implementable (though perhaps not compatible with our laws of nature) way to implement the Axiom of Choice—and, for our purposes, it is ideal if that involves infinite causal histories, so the causal finitist can reject it. Such a construction is offered. Moreover, other paradoxes involving the Axiom of Choice are given, including two Dutch Book paradoxes connected with the Banach–Tarski paradox. Again, all this is argued to provide evidence for causal finitism.

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