numbers vs. words

@Extrain,

Extrain;158725 wrote:

Numerical infinities exist. An infinity of apples doesn't exist.

And you have some non-circular theory to justify this?

@ughaibu,

ughaibu;158727 wrote:

And you have some non-circular theory to justify this?

Do you have an non-circular theory to justify that an infinity of numbers doesn't exist? Or that an infinity of apples does exist?

Whether or not there are actual infinities in the physical world is an open question simply because we can't possibly observe a physical infinity.

It is much more reasonable to believe actual infinities exist in mathematics, however, if infinity is a abstract object.

Though I am not a mathematician, I do know that if you ask any mathematician whether numbers actually exist, and it is very unlikely he will say "no." Though some may have disagreements about what numbers actually are, I know that the prevailing view is that numbers are abstract non-physical sets. Google it online.

@Extrain,

Extrain;158730 wrote:

It is much more reasonable to believe actual infinities exist in mathematics, however, if infinity is a abstract object.

If "four" is an abstract object that can be applied to describe the sum of an addition of apples, then why cant infinity be applied to the result of a supertask involving apples? And, to repeat my question, if those apples dont exist, are they fictional apples?

Extrain;158730 wrote:

I know that the prevailing view is that numbers are sets.

Consider two consistent mathematical systems: Martin-Lof type theory and van Lambalgen's ZFR. In the former the axiom of choice is derivable, in the latter the axiom of choice is provably false. Where do realists about mathematical objects stand in cases like this?

@TuringEquivalent,

TuringEquivalent;158717 wrote:

Not true at all. If there are different categories of existence. The word exist is a quantification over each specific categories.

But there are not different categories of existence. So your antecedent is false. "Existence" is not a predicate. It is place-holder for everything that exists (Ex).

---------- Post added 05-01-2010 at 02:47 AM ----------

ughaibu;158732 wrote:

If "four" is an abstract object that can be applied to describe the sum of an addition of apples, then why cant infinity be applied to the result of a supertask involving apples?

"Four" is not an abstract object. "Four" is a word.

Just because we may have physical limitations applying mathematical infinities to physical apples doesn't suggest anything.

ughaibu;158732 wrote:

And, to repeat my question, if those apples dont exist, are they fictional apples?Consider two consistent mathematical systems: Martin-Lof type theory and van Lambalgen's ZFR. In the former the axiom of choice is derivable, in the latter the axiom of choice is provably false. Where do realists about mathematical objects stand in cases like this?

What does the (dis)provability of "the axiom of choice" in formal systems have to do with the question of whether numbers exist?

@cws910,

If we want to save the LEM in the case of SH, then we don't want to hold that Sherlock Holmes is a detective and Sherlock Holmes is not a detective.

How do we do that?

@Extrain,

Extrain;158733 wrote:

"Four" is not an abstract object. "Four" is a word.

If this reply is serious, it's pretty pathetic. What abstract object, if any, is involved in your story about apples?

Extrain;158733 wrote:

What does the (dis)provability of "the axiom of choice" in formal systems have to do with the question of whether numbers exist?

Should I take it from this that you are not a realist about any mathematical objects? You mentioned the foundational role of set theory, in the standard formulation of numbers. ZF set theory is implied by the axiom of choice.

@kennethamy,

kennethamy;158735 wrote:

If we want to save the LEM in the case of SH, then we don't want to hold that Sherlock Holmes is a detective and Sherlock Holmes is not a detective.

How do we do that?

You do that by denying the surface sentence structure as revealed in "SH is not detective" and "SH is a detective" express the actual truth-valuable proposition being expressed.

@Extrain,

Extrain;158739 wrote:

You do that by denying the surface sentence structure as revealed in "SH is not detective" and "SH is a detective" express the actual truth-valuable proposition being expressed.

Maybe (although I am not sure how you do that). But Russell thought that we had to make a scopic distincition. Otherwise, we allow for truth gaps. And Russell was not a fan of truth gaps (no more than was Quine).

@ughaibu,

ughaibu;158738 wrote:

If this reply is serious, it's pretty pathetic. What abstract object, if any, is involved in your story about apples?

It's not pathetic. Your fumbling with words will lead to a host of confusions if no one clears that error up--just like it is doing.

The number 4 is involed in our story about apples. What else? Can you frame your question better so that I know what it is that you're asking?

ughaibu;158738 wrote:

Should I take it from this that you are not a realist about any mathematical objects? You mentioned the foundational role of set theory, in the standard formulation of numbers. ZF set theory is implied by the axiom of choice.

Not so. I am a realist about numbers for many reasons, not simply with respect to whether or not they are sets. If you could inform me more about what you are saying, perhaps I would understand. Instead of pulling these conflicting formal systems from the internet, and then mentioning them here without telling me in you words what they say, doesn't do any of us any good. I want to hear you describe to me what you think the "axiom of choice" is all about and what the difficulty is with these two formal systems, otherwise, your alleged rebuttal is an empty objection.

Pretend I am really dumb, and describe to me what these systems say in your own words, please.

@Extrain,

Extrain;158746 wrote:

The number 4 is involed in our story about apples. What else? Can you frame your question better so that I know what it is that you're asking?

Read my recent posts again, if it's still unclear, then you're out of luck.

Extrain;158746 wrote:

Pretend I am really dumb, and describe to me what these systems say in your own words, please.

I just did that. If you lack background, "Google it online".

@kennethamy,

kennethamy;158744 wrote:

Maybe (although I am not sure how you do that). But Russell thought that we had to make a scopic distincition. Otherwise, we allow for truth gaps. And Russell was not a fan of truth gaps (no more than was Quine).

I am not a fan of Russell's description theory of proper names, like I've said--precisely because it does allow for truth-gaps. If proper names are disguised definite descriptions as Russell thought they were, then anything can satisfy that description, and hence make that proposition true or false.

So I personally don't think those sentences express propositions at all. I am much more at ease construing those sentences as embedded within truth-valuable claims about which sentences occur in which stories, not about claims allegedly involving Sherlock Holmes.

---------- Post added 05-01-2010 at 03:15 AM ----------

ughaibu;158751 wrote:

Read my recent posts again, if it's still unclear, then you're out of luck.I just did that. If you lack background, "Google it online".

That's lame. You don't even know what you're talking about. It's not my job to make sense of what you don't even understand....lol. You're just lazy.

Different set-theories that prove contrary results regarding sets does not prove that numbers are not sets. It just shows that there are two different set-theories about sets. I am not even committed to the view that numbers are sets....but I am committed to the view that whatever they are, they exist, and they are not concepts, not ideas, not words, and not apples..but they are abstract.

I've told you my own reason for believing numbers exist. They are indispensible for our scientific theories about the world to be true. They are indispensible for any statement involving numbers to be true. That is a good enough reason for me to believe they exist.

@ughaibu,

ughaibu;158751 wrote:

Read my recent posts again, if it's still unclear, then you're out of luck.I just did that. If you lack background, "Google it online".

Typical ughaibu response. When the discussion gets too hot, and you don't know how to respond, get out of the kitchen by saying that you have already explained what needs explanation (when you have not satisfactorily) and mentioning google irrelevantly.

@kennethamy,

kennethamy;158758 wrote:

Typical ughaibu response. When the discussion gets too hot, and you don't know how to respond, get out of the kitchen by saying that you have already explained what needs explanation (when you have not satisfactorily) and mentioning google irrelevantly.

That's funny. Several times he's told me that my not understanding him was my fault when I ask him to explain to me in plain english what he means. It's not my fault I don't understand him. I don't understand him because he doesn't understand him.

@Extrain,

Extrain;158733 wrote:

But there are not different categories of existence. So your antecedent is false. "Existence" is not a predicate. It is place-holder for everything that exists (Ex).

Do you even know what a category "is"? This is a technical word that occur a lot in metaphysics( not the mystical stuff). When someone say, abstract objects, minds, matter, space-time slice..etc exist. Those are all categories. To say that a triangle exist, means that the category of abstract objects exist, and the triangle in the category of abstract objects exist. I did not use "exist" as a predicate at all. In the language of categories, the existence symbol is used as quantification over the elements of a particular category/domain.

Here is something about categories.
Categories (Stanford Encyclopedia of Philosophy)

@kennethamy,

kennethamy;158758 wrote:

mentioning google irrelevantly.

Rubbish, I was returning a patronising jab.

---------- Post added 05-01-2010 at 06:47 PM ----------

Extrain;158762 wrote:

I don't understand him because he doesn't understand him.

I understand myself, so your excuse fails. Getting to a level from which you can understand is not my responsibility, it is something that only you can do. Alternatively, you could adopt Kennethamy's approach, and remain not understanding.

@TuringEquivalent,

TuringEquivalent;158768 wrote:

Do you even know what a category "is"? This is a technical word that occur a lot in metaphysics( not the mystical stuff). When someone say, abstract objects, minds, matter, space-time slice..etc exist. Those are all categories.

You don't have to be pedantic.

Those are all categories of types of things that exist, yes. But they are not categories of types of existence. "Existence" is univocal (a la Quine).

TuringEquivalent;158768 wrote:

To say that a triangle exist, means that the category of abstract objects exist, and the triangle in the category of abstract objects exist.

Sure. That sounds right.

TuringEquivalent;158768 wrote:

I did not use "exist" as a predicate at all. In the language of categories, the existence symbol is used as quantification over the elements of a particular category/domain.

Yes, and "existence" has one meaning.

@Extrain,

Extrain;158762 wrote:

That's funny. Several times he's told me that my not understanding him was my fault when I ask him to explain to me in plain english what he means. It's not my fault I don't understand him. I don't understand him because he doesn't understand him.

Yes, I call it "the ughaibu ploy". Actually, it works maybe the first time or so. But he really overuses it. People catch on. He really has to find a new one. Or, failing that, try to answer the question if he can.

Ughaibu is English, and Englishmen of a certain age and background were raised on the famous Stephen Potter books on gamesmanship.

[Stephen Potter] published The Theory and Practice of Gamesmanship: Or the Art of Winning Games Without Actually Cheating., illustrated by Frank Wilson, in 1947.[3] the first of his books that purport to teach "ploys" for manipulating one's associates, especially making them feel inferior and thereby gaining the status of being "one-up" on them.

From Wiki.

If you have never read the Stephen Potter gamesmanship books you should. They are really meant to be funny, but, of course, like many funny books, they make a serious point about some people.

@ughaibu,

ughaibu;158771 wrote:

Rubbish, I was returning a patronising jab.

---------- Post added 05-01-2010 at 06:47 PM ----------

I understand myself, so your excuse fails. Getting to a level from which you can understand is not my responsibility, it is something that only you can do. Alternatively, you could adopt Kennethamy's approach, and remain not understanding.

This would be the case if what you are talking about are mathematical equations, but in philosophy, simple premises with some reference to wikipedia will do just fine.

@ughaibu,

ughaibu;158771 wrote:

Rubbish, I was returning a patronising jab.

I didn't intend for it to be patronizing. I simply intended to refer you to mathematicians who thought numbers were sets since I thought it was clear I wasn't actually committed to that view, and you seemed to want to know more about it.

---------- Post added 05-01-2010 at 06:47 PM ----------

ughaibu;158771 wrote:

I understand myself, so your excuse fails.

No you don't. Then you tell me again in plain English what the axiom of choice is, why two different set theories arrive at contrary results with respect to it, and why this means numbers don't exist. You don't just introduce an objection without even telling me what your objection is. What's your objection again?

@TuringEquivalent,

TuringEquivalent;158785 wrote:

This would be the case if what you are talking about are mathematical equations, but in philosophy, simple premises with some reference to wikipedia will do just fine.

Okay:
The Axiom of Choice (Stanford Encyclopedia of Philosophy)
http://staff.science.uva.nl/~michiell/docs/JSL92.pdf
http://www.math.kth.se/~kurlberg/colloquium/2005/MartinLooef.pdf
Anything else that they're incapable of googling?

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numbers vs. words

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