I'm definitely not a platonist. In fact, I'm a nominalist. I don't buy that any (objective) abstracts exist.

As a platonist, how would you demonstrate that abstracts exist?

Physical objects have properties in common: numbers are a property of objects that are made of separate parts, and then can be counted. Names are possible results of an algorithm that creates all possible strings made from a given alphabet. If something can be defined in a precise way, it means that there exists some kind of "attribute" common to different physical objects that identifies the abstract object. These "attributes" are identifiable information that is contained in physical objects, and information "exists" in reality.

What about uncountably infinite stuff? — Banno

The difference simply is that you cannot count them (duh!), no possibility of putting them in a proper order and hence get the 1-to-1 mapping to natural numbers. This means also that you cannot make a model of them with a function like y = f(x).

However, every uncountable infinite "stuff" does have a proper model of itself, namely itself. You just cannot compute it. And the model is quite useless, actually, because y = y doesn't get you anywhere.

Might sound simplistic or just semantic, but what is important to note that there genuinely is uncountable 'stuff' in mathematics. The best mathematical models for lot of things which we are interested might just be these uncountable/uncomputable 'stuff'.

People wouldn't be actually happy to find it is so.

Names are possible results of an algorithm that creates all possible strings made from a given alphabet — Mephist

If they're just possible, that doesn't imply that they're actual. The claim that they exist whether we count them or not is a claim that they're all actual and not only possible.

If something can be defined in a precise way, it means that there exists some kind of "attribute" common to different physical objects that identifies the abstract object. — Mephist

And that doesn't follow. Our definition could be inaccurate for example.

(I'm also overlooking just how we're using "common" here. Remember that as a nominalist, I don't think that any numerically distinct things, including properties, are actually identical.)

These "attributes" are identifiable information that is contained in physical objects, and information "exists" in reality. — Mephist

In order for the attributes to be actual names, we need to show that they are.

There are integers that have never been thought or said.
— Banno

There are? Where? And how do their names exist prior to being named? — Terrapin Station

Not at all sure what you are saying here. I think we can be confident that there are fifty-digit integers that have not been written down or spoken.

Where do you think that fifty-digit integers that have not been written down or spoken are located?

Between the 49-digit and 51-digit integers.

Very funny.

Well, get to the point.

As a platonist, how would you demonstrate that abstracts exist? — Terrapin Station

As a nominalist how would you demonstrate that abstracts don't exist? To decide either way is to entertain a prejudice.

As I've mentioned many times, I always type my points.

As a nominalist how would you demonstrate that abstracts don't exist? — Janus

By pointing to locations and noting that there are no abstracts there.

SO for you a thing must have a location?

Or perhaps having a location is a prerequisite for having a name?

But why am I trying to guess what you mean?

The notion of a locationless existent (or subsistent, or whatever one would like to propose) is incoherent.

SO - where is the United Nations?

It's obvious that, by the very definition, abstracts do not exist in physical space. So all you are doing here is rehearsing an absurd criterion for existence, or entertaining your prejudice that only the physical; in the narrow sense of determinate physical objects or processes, exists.

In one sense of the UN, it's at 405 East 42nd Street, New York, NY.

"This exists someplace that isn't physical" is what's absurd. The idea of that is completely incoherent. There isn't anything that's nonphysical. It's a completely idiotic idea.

IF you erased that building, would you erase the UN?

No.

In one sense... — Terrapin Station

Special pleading.

It's a fiction that the UN is located at 405 East 42nd Street? lol

Of course it is incoherent to you, as replete with your physicalist prejudices as you are. It is not incoherent per se, in other words, but only when parsed under a particular set of prejudices which rule it out as being absurd.

In any case, even granting your physicalist prejudice which demands that abstracts must have a physical location; you cannot demonstrate their non-existence by pointing to locations where they don't exist, because the locations you are able to point to make up an infinitesimal set that does not even begin to exhaust all possible locations.

Can you explain it, ontologically, in a manner that's coherent to you and that doesn't simply consist of negations ("not physical" etc. )?

Sure, I can simply say that abstracts exist in logical or semantic space. What physical space actually is is really no clearer to us than what logical space is.

Logical or semantic space can be physical, though. So what would be the ontological difference between physical logical or semantic space and nonphysical logical or semantic space that's not simply a negation?

The fact that logical or semantic symbols can be physically instantiated does not entail that logical or semantic space can be physical. How can logical or semantic space be physical according to you?

They can be physical a la an ontological analysis of what they actually are as existents, which is a set of brain states in persons.

So the difference between that and nonphysical claims about them ontologically, where we're not simply stating negations, is?

This is nothing more than another example of you taking your physicalist prejudices for a run. You simply assume what you are being asked to prove; that only the physical, in the narrow sense of observable determinate physical objects and processes, exists. It's OK if that is your preferred prejudice; what is not OK is not seeing and admitting that that is all it is.

You're misunderstanding. This isn't about proving anything. I'm stating an ontological account of how logical and semantic spaces can be physical. In contradistinction to that, your task is state an ontological account of how they can instead be nonphysical, where your account isn't simply a set of negations.

They can be physical a la an ontological analysis of what they actually are as existents, which is a set of brain states in persons. — Terrapin Station

This puzzles me. IS Terra's claim that the number 2 is a brain state?

But that's nonsense, since it would mean that my 2 and your 2, being different brain states, are different numbers.

Looks like cobblers.

And here you are spinning the word "physical".

I dunno. Elsewhere you say clever stuff.