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Journal of Logic, Language and Information
, Volume 21, Issue 2, pp 145161
First online:
The Fall of “Adams’ Thesis”?
 Alan HájekAffiliated withResearch School of Social Sciences, Australian National University Email author
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The socalled ‘Adams’ Thesis’ is often understood as the claim that the assertibility of an indicative conditional equals the corresponding conditional probability—schematically:
The Thesis is taken by many to be a touchstone of any theorizing about indicative conditionals. Yet it is unclear exactly what the Thesis is. I suggest some precise statements of it. I then rebut a number of arguments that have been given in its favor. Finally, I offer a new argument against it. I appeal to an old triviality result of mine against ‘Stalnaker’s Thesis’ that the probability of a conditional equals the corresponding conditional probability. I showed that for all finiteranged probability functions, there are strictly more distinct values of conditional probabilities than there are distinct values of probabilities of conditionals, so they cannot all be paired up as Stalnaker’s Thesis promises. Conditional probabilities are too finegrained to coincide with probabilities of conditionals across the board. If the assertibilities of conditionals are to coincide with conditional probabilities across the board, then assertibilities must be finergrained than probabilities. I contend that this is implausible—it is surely the other way round. I generalize this argument to other interpretations of ‘As’, including ‘acceptability’ and ‘assentability’. I find it hard to see how any such figure of merit for conditionals can systematically align with the corresponding conditional probabilities.
$${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({BA}),{\rm provided}\quad P(A)\neq 0.$$
Keywords
Adams’ Thesis Assertability Assertibility Probabilities of conditionals Conditional probability Triviality results Title
 The Fall of “Adams’ Thesis”?
 Journal

Journal of Logic, Language and Information
Volume 21, Issue 2 , pp 145161
 Cover Date
 201204
 DOI
 10.1007/s1084901291571
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Adams’ Thesis
 Assertability
 Assertibility
 Probabilities of conditionals
 Conditional probability
 Triviality results
 Authors

 Alan Hájek ^{(1)}
 Author Affiliations

 1. Research School of Social Sciences, Australian National University, Canberra, ACT, 0200, Australia