Sentence examples for be logically valid from inspiring English sources
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.
In this formal system, sentences can be logically valid, even if they express contingent propositions.
(When we embed (2) within the necessity operator '□' we get a truth; and any claim of the form AS → □AS will be logically valid).
Given these kinds of considerations, it is natural to wonder whether there are better interpretations of Proslogion II according to which the argument in question turns out NOT to be logically valid.
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.
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.
