In the document Historical individuum, Here-and-now individuum (Critical Series) in First Part of Website we said the following (some small alterations being made) :
If Nominalism wishes to say that Socrates is (a) Quantity, then Nominalism should express this as : " Socrates is quantitative " (because it must put emphasis on Socrates), in the sense of " Socrates is quantitatively determined ". But in fact Nominalism cannot assert this, because Socrates is after all not (as such) quantitatively determined : His length is variable in time, its value constantly being replaced by other values during the course of his individual existence, albeit often very little. So Nominalism should express Socrates being quantitative as : " Socrates is 1.70 meter long " (without letting this imply that the proposition in fact means : " Socrates has a length of 1.70 meter "). But then the reference can only be to something-here-and-now. Only Socrates-here-and-now is quantitatively determined. This implies that Nominalism must refer to (individual) Substance as a here-and-now individuum (because, again, Socrates’ length varies, i.e. is being replaced, during his life-time), i.e. Nominalism's concept of individuality should relate to a here-and-now individuum, and not to a historical individuum (= all the successive stages of Socrates, taken together). Such a view of individuality is however problematic, and constitutes a weak point in Nominalism.Thomism, on the other hand, does not say that Socrates is a quantity, but only that, for example, 1.70 meter length is a quantity (and also it needs not to say that Socrates is quantitatively determined. It allows for indeterminateness with respect to his quantity).
Thomism, as has been said, applies, say, the term QUANTITY to any individual being that is subsumed under the type (type of being) QUANTITY (again : for example, the being (or 'thing') : 1.70 meter lenght). In this way it can leave out of consideration the Substance itself (it only involves the Substance itself as soon as it uses the term 1.70 meter long ). So even if there were quantities existing all by themselves it could still apply the term QUANTITY to them.
Not so in Nominalism.
Nominalism always applies the term QUANTITY to one or another individual Substance. It says that every individual Substance is quantified. But it must be specific and definite, using for example the term 2.5 cm long, and then it says : " This crystal is 2.5 cm long ". The concrete term 2.5 cm long of this proposition is (in Nominalism) connotative. It signifies primarily the Substance involved, and secondarily the truth of a certain proposition (So here we do not have a substance + determination (accident), but a substance + a true proposition about that substance). Hence that which is connoted does not refer to something (existing) in Reality. This connoted proposition poses that the conditions, necessary for the attribution of the term 2.5 cm long, are met, based for example on an observation.
Nominalism only accepts real individual beings to exist in extramental reality. And for something to be such a real being it must be totally determined, that is not, for instance as regards quantity, by this being or thing being quantitative, or being long, but by being 1.70 meter long (as the case may be). The same holds for all accidents and also for substance itself. And this indeed implies that Nominalism can only deal with the here-and-now individual (and not with the usual individual, that is, the historical individual).