an "Instance" is something you can perceive with your senses

Far, far, far be it for me to throw a (conceptual) "spanner" into the (conceptual) "machinery", but ....

a (conceptual) "instance", which I conceive that the (conceptual) "Paolo" may have been alluding to can also be a thing beyond our perception. Putting that another way, can an instance be imaginary?

YMMV, but personally, I certainly hope so. Because if not, then the (classifier) "set of imaginary numbers" could not exist. Therefore, the square root of -1 could not exist. Therefore a great deal of the mathematics of quantum physics could not exist. Thus it follows that a great deal of semiconductor technology could not etc etc. Etc, ad absudium, until this "thing" that I perceive that I am banging my fingers on cannot exist. Which is a bit of a problem, because then, none of you exist. (Others have discussed this in detail.) Ahem, to get back on track..

"Why is a raven like a writing desk?" is a question posed by a mathematician of the 19th century who did a bit of work on set theory a wrote a certain book. Or at least I conceive that he was and did, for I have never met the fellow. His generally accepted identifying attribute was (and still is) "Lewis Carroll". He had other identifying attributes as well, but that would depend on the "classification scheme" that could be used. (You see where I am going here?) The one I will use in this

~~instance~~ discussion is (let's just accept, for the sake of sanity) "The set of all English writers, mathematicians, logicians, Anglican deacons, and photographers born in a parsonage at Daresbury, Cheshire in January 1832 and resident at Christ Church College, Oxford in 1862". Hopefully then, one could construct a

Carroll diagram where the cardinality of the set of instances in the "Yes" box is 1. However, that is not important.

What is important is that at that time "set theory" or the "mathematics of categorization" had just begun to be formalized (or at least in the so-called "western hemisphere" of this planet). Now, "a set" is unfortunately just a concept, you cannot pick up (touch) "a set", nor can you see, hear, smell or taste "a set". But it is a good thing that instances of "a set" exist, because if not then Dr Codd could not have invented relational theory and then...

(and don't even think about, let alone mention, "the set of all sets" at this point. It's been done.)

Which in my usual obtuse fashion, brings me back to the point.

Set theory is is the science of categorization. To keep this short, in a Venn diagram the rectangle is the universe of all physical and conceptual "things", the circles are classifiers which abstract a set into which one can put or not put (or partially put!) "things". (Deep breath) A class, as we use the term here, is a description of such an abstraction of a set. And an instance is one, and only one, of those "things".

All "things" exist, physical and conceptual, invented and not-yet invented. They are in Venn's rectangle. Out job is to decide whether they are also inside this or that circle or both or neither (or partially). To be successful, we must define the circles properly such that they adequately describe their membership.

So, qwerty, I agree with you entirely or at least 99%. For sure, there are Cars and Customers and Cabbages and Kings. But there are also Accounts and Payments and Messages and Ratios and other kinds of things.

BTW, regarding ravens etc, just like the Hatter and Dodgson, I have no idea either.

b

(I think I might go and have a little lie down now.)