Pollock Part II

Selmer Bringsjord
Philosophy of AI

• Back Up to the Problem of Ordinary Non-Defeasible Inference$\ldots$
• Suppositional Reasoning
  • (Schubert Steamroller)

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 t_k 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 t_k 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

$$p_1, \ldots, p_n$$

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 p_i:

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

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

The Paradox of the Preface