The inference 'If Socrates is a human being, Socrates is an animal' does not hold under uniform substitution (substituting arbitrary species and genus terms need not preserve truth)
A rule whereby a formula of the form A(B/p) is a theorem whenever A is a theorem, provided that B is free for p in A.
animal(Valla's restricted use of 'animal' as a category in his revised ontological classification, explicitly excluding God and angels.)
Creatures that consist of both body and soul; beings with embodied, animate natures.
human being(Second type of group-based account of moral status)
A thick normative concept, grounded in language and social practice, that is not necessarily coextensive with the biological category of Homo sapiens and whose moral content cannot be derived from any descriptive attribute.
inference(Nyāya epistemology)
A component of epistemology in Nyāya philosophy; a veritable inference yields knowledge about the world and must have premises that are themselves known
preserve truth(as used in logic and translation theory)
To keep a statement's truth value the same—if the original sentence is true, the translated version should also be true, and if it's false, it should remain false.
There is another way in which conclusions can be necessary and relevant to their premisses, yet not be formally valid (not be a complete entailment). The necessary connection among the propositions, and the link among their senses, might be a function of non-formal metaphysical truths holding in all possible worlds. For instance, human beings are a kind of animal, so the consequence ‘If Socrates is a human being, Socrates is an animal’ holds of necessity and the sense of the antecedent compels t