Can you restate this arugument by Ockham? Can you state in your own words?
No universal is a particular substance, numerically one; for if this were the case, then it would follow that Socrates is a universal; for there is no good reason, why one substance should be a universal rather than another. Therefore no particular substance is a universal; every substance is numerically one and a particular. For every substance is either one thing and not many or it is many things. Now, if a substance is one thing and not many, then it is numerically one; for that is what we mean by “numerically one.” But if, on the other hand, some substance is several things, it is either several particular things or several universal things. If the first alternative is chosen, then it follows that some substance would be several particular substances; and consequently that some substance would be several men. But although the universal would be distinguished from a single particular, it would not be distinguished from several particulars.
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If humanness is a universal that applies to all humans, why can't Socrates also be a universal that applies to all Socrates'? Even though we know of only one Socrates, who's to say what is a universal and what is not? But since Socrates is One thing, he can't be a universal because a universal is a quality, type, property or state of being that applies to more than one thing; such as humanness applies to all humans.
If we look at each substance by itself, it is One and not many. This is common sense. So, if we look at One universal by itself, it should also be one and not many. But some would claim humanness is a several things (applying to all humans); if it is several things it either has to be several particulars (several humans) or several universals (several humannesses). Several humans is logical. This is several particulars.
If some substance is several universals, that is several humannesses, take one of those universals and ask if it is One thing or many things. If one of those universals, is One thing, then it is One thing; a particular. Therefore, it can't be a universal. If one of those universals is several things, whether you call them several particular or several universal things, that substance is several separate things. Being that they are several different things, they are several particular things. Thus, even if you call humanness a universal, and say that it applies to several humans, what you really have is several humans = several particulars.
If humanness exists as something by itself, it is One; a particular. If it exists as many things, it is many. Each of the many is One; each is a particular.
You could distinguish One humanness (universal) from one human (particular), but you could not distinguish One humanness from several humans; because One humanness, again even if you call it a universal, actually means several particulars. So, saying One humannes and several humans would be saying the same thing. Ockham is essentially saying that a universal is a fancy abstract way of saying "many."
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