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(H9) Proof of Incompatibilism1

Selmer Bringsjord
Philosophy of AI

Here, first, is the basic setup:

Now here is the proof:

1.
$\Box$((P$_0 \wedge$ L) $\rightarrow$ P) (definition of determinism)
2.
$\Box$(P $_0 \rightarrow$ (L $\rightarrow$ P)) (from 1)
3.
N(P $_0 \rightarrow$ (L $\rightarrow$ P)) (from 2 by $\alpha$)
4.
NP0 (premise)
5.
N(L $\rightarrow$ P) (from 3 and 4 by $\beta$)
6.
NL (premise)
7.
NP (from 5 and 6 by $\beta$)

Since P can stand for any true proposition, let it stand for your decision to vote for the candidate of your choice. The proof shows that no one has, or ever had, any choice about whether you voted this way or not.



 
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Selmer Bringsjord
2000-11-09