I would say so. Just that all things do not necessarily have opposites. I’ve made the case for existence almost as best as I can (existence has no opposite; non-existence does not exist[sub]I don’t even like saying it, haha[/sub]).
It is possible that a case could be made for opposites not existing in fact, from the nominalist case where universals also do not exist in any way shpe or form. “Oppositeness” then, as a universal, doesn’t exist. How easy was that!
But if we accept universals as existing in some sense then we are indeed faced with a problem. Platonic: universals exist independant of the rest of stuff. “Whiteness” exists in and of itself, or oppositeness as the case may be. Never felt comfortable with that.
Realists might posit that universals only exist conceptually. “Whiteness” is there, but as a concept. A measurement, as Rand would pose. Their existence is contingent on existence of objective reality, and the objects contained therein. (not that platonists don’t believe in an objective reality, just that we aren’t getting the whole picture—Plato’s Forms, Kant’s noumenal reality, etc)
If we take universals as existing as concepts then surely oppositenes exists. The question now becomes, is this concept formation/abstraction valid? That is, can the concept of whiteness or oppositeness be said to be an unescapable conclusion in abstraction? Are this white envelope and my white coffee mug (forget the stains :p) really alike in some way or is the concept artificial (dependent on my personl abstraction)?
I’d say it is unartificial. But then, you say, didn’t you just switch from a realist argument to a platonic one (where universals exist)? Nah. The crucial distinction is that “whiteness” is a part of the object which is white. One cannot remove the whiteness from it and pass it around, much to the dismay of many acid heads I’m sure
So, then, are opposites always tautological/definitional in nature? Again, I would distinguish a “true” opposite from an artificial one.
A true opposite would be one where we may take either A or ~A as the starting point and then define the other, ~A or A, from it.
A false opposite would be purely artificial in nature, where we can only take A and get to ~A; were we to take ~A we could not get to A.
ALL OF THIS, of course, assumes the law of the excluded middle, and that things are either true or false, and that their opposites are then false or true. We run into some problems in mathematics here if we also go on to say that mathematics is true. Here is where the happy formalists come in and say math isn’t true or false, there is no true or false about math, only in math. But I’m not prepared to get into formalism Vs intuitionism Vs constuctionism, logical positivisism, mathematical platonism, blah blah blah. That is outside the scope of this book
[sub]Enter spiritus mundi to destroy everything I’ve said[/sub]