 Consider the following pair of valid inferences: Fido is a brown dog, so Fido is a dog; Fido is not a dog, so Fido is not a brown dog. As illustrated with the first example, replacing a predicate (or general term) like ‘brown dog’ with a less restrictive predicate like ‘dog’ is often valid. But sometimes—paradigmatically, in cases involving negation—replacing a predicate like ‘dog’ with a more restrictive predicate like ‘brown dog’ is valid. Plausibly, the first pattern reflects the default direction of valid replacement: removing a restriction preserves truth, except in special cases like those involving negation. Suppose we take it as given that poodles are dogs of a particular sort, and hence that every poodle is a dog. Then replacing‘poodle’ with ‘dog’ in ‘Fido is P’ is valid, regardless of what ‘Fido’ names. This can be viewed as a special case of ‘n is P, and every P is D; so n is D’. But the validity of this inference form can also be viewed as symptom of a basic principle that came be called dictum de omni: whatever is true of every P is true of any P. Or as Aristotle might have put it, if the property of being a dog belongs to every poodle, then it belongs to any poodle. In which case, Fido is a dog if Fido is a poodle. And since the property of being a dog surely belongs to every brown dog, any brown dog is a dog. The flip side of this point is that negation inverts the default direction of inference. Anything that isn’t a dog isn’t a brown dog; and similarly, if Fido isn’t a dog, then Fido isn’t a poodle. So in special cases, adding a restriction to a general term like ‘dog’ can preserve truth.