The phrase "a necessary consequent" is correct and usable in written English.
It can be used in discussions about logic, philosophy, or causality to indicate that one event or condition must follow from another.
Example: "In a logical argument, if the premises are true, then a necessary consequent must also be true."
Alternatives: "an essential outcome" or "a required result".
He says that material consequences are those that hold in virtue solely of (the meaning of) their terms (Ockham, Summa Logicae III-3, ch. 1, lines 55 57) but the two examples he gives are of a consequence with an impossible antecedent and a consequence with a necessary consequent.
What is needed in a demonstrative syllogism is not just the necessity of the consequence but a necessary consequent, and this requires that the premises express necessary truths.
But if it is invalid, it is necessarily so, since the premise is a necessary sentence; therefore, we have a consequence with a necessary consequent, thus satisfying the necessary truth-preservation criterion, but which is plainly invalid.
The member of Congress who introduced the Act added: "The power to judge of the legality of the votes is a necessary consequent of the power to count.
Even evil (defined as non-existence or privation) is an object of divine will: it is willed accidentally, i.e., insofar as it is a necessary consequent of the good (Ilāhiyyāt, IX, 6; Steel 2002).
The fragmentation of philosophy and its consequent separation from theology is, according to Rosmini, a necessary consequence of sensationalist thinking.
Thirdly, the existence of these parts involves that of other things as their necessary consequents.
Those events that do not have sufficient power to withstand force are seen as natural and necessary consequents, those events that possess sufficient ability to withstand forces are seen as free acts.
If this consequence is valid, then it has a necessary antecedent and a false consequent (since the consequent says that it is invalid).
One other resource is used, namely, the closure principle which says that the antecedent of a necessary conditional is possible only if the consequent is possible.
Can we use the truth-functional understanding of "if" to propose that the consequent of any conditional (in (i), the consequent is "I used the key") specifies a necessary condition for the truth of the antecedent (in (i), "I opened the door")?
