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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?

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  • This is Nominalism, i.e. the rejection of universals.
    – Mauro ALLEGRANZA
    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.
    – Mauro ALLEGRANZA
    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.
    – Mauro ALLEGRANZA
    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.
    – Yamar69
    Jan 13, 2020 at 13:38

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Technically speaking, a class or category is defined by a set of criteria, not by a set of particulars. 'Catness' is not a property in its own right; it is a collection of properties that we have associated with the concept 'cat' such that any particular creature which shares those properties will be classed as a cat. That is why such concepts are called universals, because they give us the key to determining cat from not-cat in every case.

Of course, criteria of this sort are adopted by convention, so they may change as our experience grows. but that doesn't change their 'universal' nature; that merely means that what we decide is 'universal' can change.

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Hmm, I might be getting this wrong, but...

If we look at colors, and draw a scale from yellow through orange to red. There will be an infinite variation of shades in between those 3 primary colors. Personally I'm a guy, so I only see primary colors. So a Particular shade in between, will be compared to my Universal definition of yellow, orange and red, and assigned to that category.

So where some may see amber, ocher, honey or gold, I see orange. At least that is the Universal that I put it into.

So where Particulars are physical measurements (whether by instrument or eye) Universals are the idea on your mind, that you compare everything to, in order to classify it. It's an approximate, more than a rule or subset. That witch lies in between, where if you stray to far from it, it becomes something else. Orange is that thing in between yellow and red, where if you get to far from "it"(orangeness) the color becomes red or yellow instead.

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