litewave

Because a collection is something different than its elements, yet it is also something that is common to the elements.

Well, I'm trying to describe the concept of set in some intuitive terms. You may say that the concept of set is extra-logical but I wouldn't be able t...

I said instances of redness have the property of redness. The property of redness itself doesn't seem to be red, hence it doesn't instantiate itself.

Ok, I haven't studied fuzzy logic, it may be a useful way of dealing with uncertainties, but ontologically I regard every set as completely specified,...

We can agree on many things that should be included as elements in the set of red things (instances of redness), for example ripe tomatoes and their v...

That's what I am saying the property of redness is - the set of all red things (the set of all instances of redness).

The extra property (the set) is a thing that is the result of the unification of the elements into one thing (while keeping the elements distinct from...

Shades and hues of red are instances of redness, so they all have the property of redness.

When I say that a property is identical to the set of all objects that have this property, I mean that the property is completely specified and thus t...

Aha, I think I see what you mean. The singleton set is distinct from the element it contains and so it is something additional to the element. The ele...

Collections or sets are not just mental or linguistic abstractions though. As I am typing this I am actually holding a collection called "smartphone".

But that's exactly what I am arguing - there is a fourth object and this fourth object is identical to the set of the three objects. The set as a sing...

Even the extravagant set that @"Moliere" has mentioned above is something in addition to the pebble and the sentence, and this something is a property...

Order of elements of a set doesn't matter, I agree. But I think it is important to emphasize the identity of a set as a single thing, distinct from it...

When we identify some thing extensionally/by substitution, it doesn't mean that we identify the thing with its extension. It means that we identify th...

Different versions of the same property are actually different properties (although they are similar in some way significantly enough to call them "ve...

I really don't think that a set is identical to its elements. A single object is not identical to many objects. We can write that the set S = {a,b,c} ...

A set is a single object. Elements are multiple objects. So a set is not identical to its elements. Even in set theory, a set is an object in its own ...

Thanks. Not on an academic level. As long as it is possible (logically consistent) for an organism to have a heart without a kidney, or vice versa, th...

Yes, all instances of a property, in all possible worlds, constitute the set that I indentify with the property. It can. And with such a specification...

Is it possible (logically consistent) for the property of being the king of France to be instantiated? If yes, then it is instantiated in some possibl...

I mean that the property is the set. But knowing only that justice is the set of all just acts will not help you know which acts belong to this set or...

A set is a different object than any of its elements. But if the box is black then it also contains instances of blackness, not just redness. For exam...

Numbers are properties (universals/general entities) too, so defining a number n as a collection of all things that instantiate the number n would be ...

Consciousness is a weird thing. I wouldn't be so surprised if it experienced a static structure as moving, especially if the structure is a smooth seq...

Which means that life would exist, but it wouldn't.

Why would it only happen in our mind? The cookie is out there, it is a part of collection E, then a part of collection F. Collections E and F are out ...

In other words, reality consists of collections of collections of collections... Welcome to set theory, the instantiation of abstract mathematics in c...

It may be logically possible in some possible world but not in ours. Since "the present King of France" has a logically inconsistent definition (in ou...

It would be logically inconsistent for an entity to exist at a place and time where it doesn't exist. The present king of France doesn't exist on our ...

In such cases, a "unicorn" can exist as an image on the movie screen or as an encoding of that image on a tape or a digital device, or as a printed wo...

He doesn't exist because he's logically inconsistent. Same for the present unicorns on this planet.

I think that is still too narrow a definition. For me, an existent is that which is not nothing. This might include particular things like a particula...

And for me a possible world is a logically consistent one, so I see no difference between metaphysical and logical possibility. A mile high unicycle w...

But it must be logically consistent too, otherwise it wouldn't exist. Logically inconsistent water cannot exist, for example water that is not water, ...

But what is the difference between logical and metaphysical possibility? If such a unicycle is logically possible why is it not metaphysically possibl...

And what is the difference between them? I can't imagine the difference.

I asked you whether you can imagine a difference between a logically consistent object and a real object. Are you saying that if you were totally igno...

So what is the difference between a logically consistent object and a real object? Can you imagine that? What do you mean by 'following relations'? Di...

According to ontic structural realism, relations are the only things that exist. I am not so extreme though, I just think that relations and non-relat...

But that doesn't mean that relations don't exist, if that's what you were getting at. It also doesn't mean that when we make sense of an object by its...

Circularity doesn't bother me in ontology, it's like in mathematics where all mathematical objects are consistently interrelated and all of them exist...

Relata cannot exist without their relations and relations cannot exist without their relata. Relata and relations are inseparable, and I don't see why...

By "possibility" I mean logical consistency, that is an object that is logically consistently defined in relations to all other possible (logically co...

MWI interpretation is not deterministic in the sense that in a parallel world later events logically follow from earlier events and from the laws of p...

Ok, I didn't know this is used as an argument against causation. Of course in our life as humans we single out a particular cause or a small number of...

You would not be the sole cause though. For example, planet Earth would participate in the causality too. If planet Earth didn't exist you would not b...

For me, the (deductive) inferential theory of causation seems the most elegant. It says that the structure of our spatio-temporal world contains regul...

Empty set? Emptiness is a property, which is something. And so is that which has it. Is that a problem? As long as all things are consistently defined...

In point-set topology, a point of space can be any set. The simplest set is the empty set, which is not nothing but something that has no parts.