There have been many ingenious attempts to find an argument which can be expressed in modern logical formalism, which is logically valid, and which might plausibly be claimed to be the argument which is expressed in this passage.
Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the "logical constants" of a language from its nonlogical expressions.
This is the principle stating that, if a formula A is logically valid, i.e., a logical truth, then its necessitation, that is, the formula obtained by prefixing to it a box or necessity operator, is logically valid, too.
Therefore exactly two of the 24 valid Aristotelian syllogisms (namely the modi CAMENES — or CALENTES in Bolzano's terminology — and CAMENOP of form IV) are invalid in Bolzano's logic as he himself proved by means of counter-examples (WL II, 415, 558), whereas all other Aristotelian modi (including the weakened ones) are logically valid also in Bolzano's logic.
The formal validity of an inference was checked against the laws of formal logic that allows to exactly determine what is logically valid.
There is a tradition in logic that holds that in order for an argument to be logically valid, the conclusion must be true in all cases in which the premises are true.
And \(A\) is logically valid or a tautology iff it is valid under all valuations.
(For details, see Rickless (2007, 138 187).) It appears that every Argument of D2 is logically valid.
It appears that every Argument of D1 other than D1A9 is logically valid.
In this formal system, sentences can be logically valid, even if they express contingent propositions.
Then, if the argument is logically valid, and the conclusion genuinely unacceptable, the assertions must be false after all.
