Direct: an observation statement, or entails an observation statement with an observation statement.
Indirect: S entails with S* an observation statement; No statement in S* can be non-meaningful.
Church's Objection:
3 observation statements: P Q R, neither of which entail the other. S a nonsense statement.
1) (¬P ^ Q) v (R ^ ¬S).
C's argument: whether or not Q is entailed by 1, S ends up true.
This is directly verifiable: (1) + P = R. R an OS; not just entailed by P.
Q not entailed by (1) - Entailed by S + (1), so S is indirectly verifiable.
Q entailed by (1) - by both conjuncts, but in partic. right hand side (2). If (2) is true, then Q. Then we get the negation of S as directly verifiable: and the negation of this is indirectly verifiable...
So S is meaningful, whatever it is.
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