Berka I 18/19
Deduction/Bolzano: if one of the sentences A, B, C does not include any of the latter, we can also omit it, and assert the derivability of the conclusions from the remaining B, C,... For under these circumstances, the sentence A must be true, and it must remain at all times, no matter what is chosen for ideas. As often as the sentences B, C, D ... become all true, also the sentences A,B,C,D... become true and hence also the conclusions M, N, O ...
If certain conclusions M, N, O... are to be derivable from certain premisses A, B, C...it follows that among them must be a false one. If all A, B, C, D were true, then all M, N, O ... would have to be true. Because otherwise it would not be true that every epitome (unity of) makes ideas true in the place of i,j,... that A, B, C... makes true (namely the ideas i,j,... themselves) also makes the M, N, O ... true.
If all the propositions which are derivable are true, the propositions A, B, C ... must themselves be true, for to the different propositions, which can be derived from A, B, C, belong certainly also the sentences A is true, B is true, etc.
(1)
1. B. Bolzano, Wissenschaftslehre, Sulzbach 1837 (gekürzter Nachdruck aus Bd. II S. 113-115, S. 191 – 193; § 155; §162)
