(September 13, 2018 at 8:02 pm)polymath257 Wrote: Let me put it this way. If everyone agrees what it is to be the number 4, what is it, precisely?

Here here Poly 

And just like Stuntedsteve Roadkill just dances around your responses .

(September 13, 2018 at 8:09 pm)RoadRunner79 Wrote:

(September 13, 2018 at 8:02 pm)polymath257 Wrote: Let me put it this way. If everyone agrees what it is to be the number 4, what is it, precisely?

You seem to be talking about the nature of language here.  If everyone agrees what a tree is, then what is it?  It would seem ridiculous to say that trees don’t exist that they are subjective, because we agree to call them trees.

But there is nothing about the real trees that dictate that the English word 'tree' be used for it. There is nothing that dictates the language used.

We can, given language, define generally what it means to be a tree (a wooden plant with certain other characteristics).

And generally, people agree what it means to be a tree.

But what does it mean to be the number 4? NOT, mind you, what does it mean to have 4 apples. But what actually *is* the number 4?

By the way, there are answers to this question. But there are several, mutually exclusive answers.

(September 13, 2018 at 8:59 pm)polymath257 Wrote:

(September 13, 2018 at 8:09 pm)RoadRunner79 Wrote: You seem to be talking about the nature of language here.  If everyone agrees what a tree is, then what is it?  It would seem ridiculous to say that trees don’t exist that they are subjective, because we agree to call them trees.

But there is nothing about the real trees that dictate that the English word 'tree' be used for it. There is nothing that dictates the language used.

We can, given language, define generally what it means to be a tree (a wooden plant with certain other characteristics).

And generally, people agree what it means to be a tree.

But what does it mean to be the number 4? NOT, mind you, what does it mean to have 4 apples. But what actually *is* the number 4?

By the way, there are answers to this question. But there are several, mutually exclusive answers.

You seem to be starting to get it, but then are drifting to epistemology. I’m not talking about epistemology. Would you agree that the number 4 is descriptive, and what it describes, is not changed, whether you and I agree or not?

(September 13, 2018 at 9:01 pm)RoadRunner79 Wrote:

(September 13, 2018 at 8:59 pm)polymath257 Wrote: But there is nothing about the real trees that dictate that the English word 'tree' be used for it. There is nothing that dictates the language used.

We can, given language, define generally what it means to be a tree (a wooden plant with certain other characteristics).

And generally, people agree what it means to be a tree.

But what does it mean to be the number 4? NOT, mind you, what does it mean to have 4 apples. But what actually *is* the number 4?

By the way, there are answers to this question. But there are several, mutually exclusive answers.

You seem to be starting to get it, but then are drifting to epistemology. I’m not talking about epistemology. Would you agree that the number 4 is descriptive, and what it describes, is not changed, whether you and I agree or not?

No. In fact, I deny that specifically. The number 4 comes up in several places, even within mathematics and has different meanings in each.

So even within math, the number is NOT objective. And, if anything, it gets worse as you from the abstract realm of math and into the real world.

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(September 13, 2018 at 2:52 pm)SteveII Wrote:

(September 13, 2018 at 12:53 pm)polymath257 Wrote: On the contrary, I have studied these things most of my adult life (and i am 55 years old). You are simply wrong in claiming that no rational person sees the number 4 as subjective.

Let's ask this: are language constructs 'objective' under your definition? It seems that they are, which in turn says that your definition is faulty. Language constructs certainly *shouldn't* be objective, even if they are independent of any particular person.

Language is subjective. The concept of 4 objects is the very opposite of subjective. It is more than three and less than 5. Never any different. Would have the same meaning in all possible languages, all corners of the universe and would have the same meaning in all possible worlds (as in possible world semantics used in modal logic claims). If these facts are true, it follows necessarily that the concept of 4 objects is not just a language construct and has an entirely separate ontological status. 

Well, more than 3 and less than 5 doesn't uniquely determine the number 4: the number 3.5 works also.

But, more of a problem, you haven't defined what 3, 5, 'more' or 'less' mean. Those have meanings in specific situations, but the issue here is whether there is a *general* 'object' that is the number 4 that is objective.

(September 13, 2018 at 9:14 pm)polymath257 Wrote:

(September 13, 2018 at 9:01 pm)RoadRunner79 Wrote: You seem to be starting to get it, but then are drifting to epistemology. I’m not talking about epistemology. Would you agree that the number 4 is descriptive, and what it describes, is not changed, whether you and I agree or not?

No. In fact, I deny that specifically. The number 4 comes up in several places, even within mathematics and has different meanings in each.

So even within math, the number is NOT objective. And, if anything, it gets worse as you from the abstract realm of math and into the real world.

How is the number 4 different in mathematics? Are you saying that if their are 4 trees in reality, that is subjective? Do you believe in the basic principle; the law of identity?

(September 13, 2018 at 9:19 pm)RoadRunner79 Wrote:

(September 13, 2018 at 9:14 pm)polymath257 Wrote: No. In fact, I deny that specifically. The number 4 comes up in several places, even within mathematics and has different meanings in each.

So even within math, the number is NOT objective. And, if anything, it gets worse as you from the abstract realm of math and into the real world.

How is the number 4 different in mathematics?  Are you saying that if their are 4 trees in reality, that is subjective?  Do you believe in the basic principle; the law of identity?

I'd suggest reading some Frege or Russell. That will get you started.

There is a difference between saying 'there are four trees' is objective (which I will agree to: it is a publicly observable situation) and saying the number 4 is objective (no publicly observable situation exists for this).

Once again, the use of 4 is a language construct. The number itself doesn't exist as something separate.

And, in math, there are several different mutually exclusive *models* for the natural numbers. Russell proposed one (so four would be the class of all sets with four elements--which can be defined in terms of logic and equality). But there are other definitions that don't have the logical issues that Russell's definition does (being a proper class is problematic--see Russell's paradox).

Von Neumann gave a different definition that is often used in set theory today, but it is far from being the only possible one: see discussions of the difficulty by Hillary Putnam.

When you say the number 4 is 'objective', I think you are missing any number of subtleties concerning how that concept is, or can be, defined. At best, it is an equivalence class of concepts, but that also fails to capture the intuitions many have.

And that is part of the point: we have intuitions, but those intuitions are self-contradictory. The upshot is that '4' is a *language* construct, not something that exists out of a language.

I have also found that people that emphasize the 'law of identity' tend to have not thought very much about these things. Might I suggest a bit of modern model theory as a subject of utility?

(September 13, 2018 at 9:30 pm)polymath257 Wrote:

(September 13, 2018 at 9:19 pm)RoadRunner79 Wrote: How is the number 4 different in mathematics?  Are you saying that if their are 4 trees in reality, that is subjective?  Do you believe in the basic principle; the law of identity?

I'd suggest reading some Frege or Russell. That will get you started.

There is a difference between saying 'there are four trees' is objective (which I will agree to: it is a publicly observable situation) and saying the number 4 is objective (no publicly observable situation exists for this).

Once again, the use of 4 is a language construct. The number itself doesn't exist as something separate.

And, in math, there are several different mutually exclusive *models* for the natural numbers. Russell proposed one (so four would be the class of all sets with four elements--which can be defined in terms of logic and equality). But there are other definitions that don't have the logical issues that Russell's definition does (being a proper class is problematic--see Russell's paradox).

Von Neumann gave a different definition that is often used in set theory today, but it is far from being the only possible one: see discussions of the difficulty by Hillary Putnam.

When you say the number 4 is 'objective', I think you are missing any number of subtleties concerning how that concept is, or can be, defined. At best, it is an equivalence class of concepts, but that also fails to capture the intuitions many have.

And that is part of the point: we have intuitions, but those intuitions are self-contradictory. The upshot is that '4' is a *language* construct, not something that exists out of a language.

I have also found that people that emphasize the 'law of identity' tend to have not thought very much about these things. Might I suggest a bit of modern model theory as a subject of utility?

Indeed 4 is a description of a quantity not a separate magic thing in it's own right .

Why do you think that the law of identity is not thought through very well? It would seem that without it; we cannot have a rational conversation. Tree is a language concept as well.

As Neo pointed out, you seem to be assuming the answer to your question in your argument (that if you cannot observe the number it ildoesnt exist). In any case the number as a description is not dependent on the subject. It is describing an external part of reality, not giving information about the person who holds the view.

(September 13, 2018 at 11:53 am)RoadRunner79 Wrote:

(September 13, 2018 at 11:48 am)Neo-Scholastic Wrote: LOL, so in a debate about the existence of non-physical objects, of which the number 4 is an example, you'll only be satisfied if someone produces the number 4 as a physical object. Yeah...that sounds reasonable.

It seems to me, that the number or quantity of something is the same, no matter if you call it four or quatro. Whether you are talking about dollars,  pesos or euros; apples or oranges. Unless you are talking bolivars in which case four is essentially equal to zero.

Does it? why does the "4" in 408 equal 32?

(September 14, 2018 at 5:27 am)Abaddon_ire Wrote:

(September 13, 2018 at 11:53 am)RoadRunner79 Wrote: It seems to me, that the number or quantity of something is the same, no matter if you call it four or quatro. Whether you are talking about dollars,  pesos or euros; apples or oranges. Unless you are talking bolivars in which case four is essentially equal to zero.

Does it? why does the "4" in 408 equal 32?

Different way of explaining or referencing the same thing.