 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 that of the consequent, but it is not formally valid under uniform substitution. Abelard takes such incomplete entailments to hold according to the theory of the topics (to be forms of so-called topical inference). The sample inference above is validated by the topic “from the species”, a set of metaphysical relations one of which is expressible in the rule “Whatever the species is predicated of, so too is the genus” which grounds the inferential force of the entailment. Against Boethius, Abelard maintained that topical rules were only needed for incomplete entailment, and in particular are not required to validate the classical moods of the categorical and hypothetical syllogism mentioned in the preceding paragraph.