# The Fall of “Adams’ Thesis”?

Article

- First Online:

DOI: 10.1007/s10849-012-9157-1

- Cite this article as:
- Hájek, A. J of Log Lang and Inf (2012) 21: 145. doi:10.1007/s10849-012-9157-1

- 7 Citations
- 183 Downloads

## Abstract

The so-called ‘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

$${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({B|A}),{\rm provided}\quad P(A)\neq 0.$$

*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 finite-ranged 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 fine-grained 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 finer-grained 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.### Keywords

Adams’ Thesis Assertability Assertibility Probabilities of conditionals Conditional probability Triviality results## Copyright information

© Springer Science+Business Media B.V. 2012