Pollock Part I

Selmer Bringsjord
Philosophy of AI

• The Design Stance$\ldots$
• Artilects
• Agents
• Two Paradoxes at the Beginning
  • The Liar Paradox
  • The Lottery Paradox

function
SIMPLE-REFLEX-AGENT(percept) returns action
static: rules, a set of condition-action rules

state $\leftarrow$ INTERPRET-INPUT(percept)
rule $\leftarrow$ RULE-MATCH(state, rules)
action $\leftarrow$ RULE-ACTION(rule)
return action

Suppose you hold one ticket (t_k, for some $k \ge 1$) in a fair lottery consisting of 1 million tickets, and suppose it is known that one and only one ticket will win. Since the probability is only .000001 of t_k's being drawn, it seems reasonable to believe that t_k will not win. By the same reasoning it seems reasonable to believe that t₁ will not win, that t₂ will not win, $\ldots$, that t_1000000 will not win. Therefore it is reasonable to believe

$$\neg \exists t_i \mbox{($t_i$ will win)}.$$

But we know that

$$\exists t_i \mbox{($t_i$ will win)}.$$

So we have an outright contradiction.