Signification and supposition

The via antiqua conception http://plato.stanford.edu/entries/universals-medieval/#8

Signification is the relation on the left-hand-side, connecting a common term to individualized natures, or forms. For example, the signification of the English word 'white' is the relation that connects this term to individualized whitenesses of individual white things. (If they are actually white, then to their actual whitenesses, if they are merely potentially white, then to their potential whitenesses.) But, obviously, this relation between this utterance (or the corresponding inscription in written English) and those actual or potential whitenesses is established by the common convention of English that this utterance is associated with that concept of our minds by means of which we conceive of white things in a universal manner. So this utterance in English is subordinated to (or immediately signified by) this concept (just as the word 'album' is in Latin, or 'blanc' is in French, etc.). But this concept, insofar as it is formed in my mind, is an act of my mind, and insofar as it is formed in your mind, is an act of your mind. These distinct acts of our minds are what we call the ‘subjective’ or ‘formal’ concepts of individual human minds. But these individual acts have the same representational content: both represent individualized whitenesses in a universal manner. It is this same content that we call the objective concept. The word is primarily subordinated to this objective concept (but then, as a consequence, it becomes subordinated to my subjective concept, as soon as I learn the language, and to yours as you do, etc.). The absolute nature is in fact nothing other than the objective concept, for the objective concept is just the absolute nature regarded as the object of the abstractive human mind. Read carefully what Aquinas says about this in c. 2 of "On Being and Essence". (I also quote the relevant text here: http://plato.stanford.edu/entries/universals-medieval/index.html#7) But apart from the niceties of distinguishing subjective concepts/objective concepts/absolute natures, the whole semantic point is simply this, namely, that the word 'white' will ultimately signify individualized whitenesses on account of being subordinated to the concept by which we conceive of white things in a universal, abstract manner. It is this relation of ultimate signification that is represented by the arrow pointing from the common term to individualized natures.   On the other hand, the supposita of the term 'white', given its signification in English, are those things that actually have these individualized natures at the time indicated by the tense of the verb of the proposition in which the term occurs. So, supposition, indicated by the dashed arrow connecting the common term to singulars is another semantic relation, which connects the word of a given signification to the things that actually have the significata of the word at the time indicated by the verb of the proposition in which the term occurs. Thus, if I say, "The white balls on my balcony last year were snowballs", in this proposition the term 'white' supposits for those balls on my balcony that had whiteness last year (but not for the black bowling balls, for example). Now clearly, these things are no longer there, since by now they have melted away, and so they could not be supposited for by the same term in the proposition "The white balls on my balcony this year are snowballs". The point is that the term ‘white’ has the same signification in both sentences (it signifies whitenesses), but it has different supposition, for in the first sentence it supposits for the snowballs I had on my balcony last year, but in the second it supposits for nothing (for now there are no white balls on my balcony).