Sentence examples for a valid consequence from inspiring English sources

The principles of propositional modal logic, found in Prior Analytics I.15, were generally expressed as follows: if the antecedent of a valid consequence is possible/necessary, the consequent is possible/necessary (Abelard, Dialectica 202.6 8).

According to Buridan, this example should not count as a valid consequence, and one reason he gives for this is that its contrapositive 'Some donkey is running, therefore some sentence is negative' is not a valid consequence.

'No sentence is negative, therefore no donkey is running' comes out as a valid consequence according to the criterion thus formulated, because 'No sentence is negative' can never be true: its mere existence falsifies itself whenever it is produced.

While they differed in particular in the various definitions given to the formal vs. material consequence distinction, they all agreed that necessary truth-preservation (TP) is a necessary condition for something to count as a (valid) consequence (Dutilh Novaes 2008).

Alongside with this more technical layer, medieval authors also discussed extensively the very nature of the notion of consequence: what counts as appropriate grounds for a valid consequence, adequate definitions, subdivisions of kinds of consequence etc.

'God does not exist, therefore you are a donkey' counts as a valid consequence according to (TP) ('God does not exist' is considered to be an impossible sentence), but the consequent is not contained in the antecedent in the same way as in 'Socrates is a man, therefore Socrates is an animal'.

Burley explicitly says that all valid consequences are based on dialectical Topics (On the purity, p. 158 and 162).

Humans often falsely report having seen a causal link between two dynamic scenes if the second scene depicts a valid logical consequence of the initial scene.

Whereas the algebraic values are elements of an algebraic structure and referents of formulas, the logical value true is used to define valid consequence: If every premise is true, then so is (at least one of) the conclusion(s).

Our definition of logical consequence also sanctions the common thesis that a valid argument is truth-preserving--to the extent that satisfaction represents truth.

These are typically enthymematic consequences, i.e. consequences with a 'missing premise' (with the additional premise, they become a valid syllogism).