# On Universals and Particulars

I was thinking about the ontological problem of Universals versus Particulars and there is one thing that I can't understand well about the concept of Universal. If I have a cat (let's call it Steve) I understand that Steve is an Individual but shares several properties with other cats, among which there is also the "Catness". Now "Catness" is a universals, the pure ontological concept of "cat".

What I am trying to understand without result is how such a thing can exist. When our mind thinks about the concept of cat, thought is inevitably accompanied by a shape and a color and other properties. However by definition the universal catness must be devoid of shape or color, otherwise it would be reduced to a Particular.

When I think of this problem, it occurs to me that universals are probably sets while individuals are the elements of sets, for example in the case of cats if we take C ={c1, c2, c3, c4, c5, c6.....} as the set of all cats then C is the universals and c1, c2, c3... are all individuals. From this reasoning it is derived that individuals are only the intersections between sets (Universal).

Is my reasoning right?

• This is Nominalism, i.e. the rejection of universals. Commented Jan 13, 2020 at 13:31
• To say that universals are set of particular means (if we do not beg the question assuming the existence of the abstract object: set) to assume that universals are concept that our mind "abstract from" the knowledge of particulars. Commented Jan 13, 2020 at 13:33
• But, if so, to say "that individuals are only the intersections between sets" is non sense: particulars are ontologically primitive and concepts (sets) are "derived", and thus we have that sets are collections of particulars that are colelcted togetehr by our mind. Commented Jan 13, 2020 at 13:35
• @Thank you. I have an addendum: how can a Particular be red (for example) if red is not an a priori entity? What i was thinking about was the other way around: individuals are intersection of Universals, so for example a red furry cat is the intersection between the universals "redness", "furryness" and "catness" and so on. Commented Jan 13, 2020 at 13:38