next up previous
Next: About this document ...

Pollock Part II

Selmer Bringsjord
Philosophy of AI

Lottery Paradox Diagnosis



Since we ought never to believe both p and $\neg p$, and since we know that a certain ticket will win, we must conclude (since the reasoning itself is unexceptionable) that it's not the case that we ought to believe that tk will win. We must replace this belief with a defeasible belief based on that fact that we have but a prima facie reason for believing that tk will win.

Lottery Paradox Case of Collective Defeat



Suppose that we are warranted in believing r and that we have equally good prima facie reasons for

\begin{displaymath}p_1, \ldots, p_n\end{displaymath}

where $\{p_1, \ldots, p_n\} \cup \{r\}$ is inconsistent but no proper subset of $\{p_1, \ldots, p_n\}$ is inconsistent with r. Then, for every pi:

\begin{displaymath}r \wedge
p_1 \wedge \ldots p_{i-1} \wedge p_{i+1} \wedge \ldots p_n\} \vdash \neg p_i\end{displaymath}

In this case we have equally strong support for each pi and each $\neg p_i$, so they collectively defeat one another.

The Paradox of the Preface





 
next up previous
Next: About this document ...
Selmer Bringsjord
2000-11-27