numbers vs. words

@Extrain,

Extrain;158628 wrote:

So you think "two apples and two apples makes four apples" is false?:rolleyes:

You get another chance to offer a serious response.

@ughaibu,

ughaibu;158633 wrote:

You get another chance to offer a serious response.

That was a serious response. If numbers don't exist outside formal frameworks then the above statement is false. But its true. So numbers exist. It's your turn.

@Extrain,

Extrain;158566 wrote:

Look, no proposition got asserted by someone's saying, "SH is not a detective" on my view. So no one is violating LEM. So technically, it's truth-valueless.

Because you think the sentence "SH is not a detective" implies that SH exists? How then do we say that SH does not exist without implying that he does?

In my view, the sentence is not only meaningful, but it's cognitively meaningful as well.

---------- Post added 04-30-2010 at 11:30 PM ----------

Extrain;158547 wrote:

"Sherlock Holmes is a detective" is false.
"Sherlock Holmes is not a detective" is false.

You got to be kidding!

First off, I can only suppose that you're talking about sentences since you believe no proposition is being expressed.

No sentence that fails to express a proposition is false. Don't confuse "false" with "not true."

@fast,

fast;158649 wrote:

Because you think the sentence "SH is not a detective" implies that SH exists? How then do we say that SH does not exist without implying that he does?

I've already shown you.

~Ex(Sx & Ay (Sx-->y=x) & Dx)

is one way.

I just say, it is not the case that there is something that is Sherlock and is a detective.

fast;158649 wrote:

In my view, the sentence is not only meaningful, but it's cognitively meaningful as well.

Yes, it is very meaningful. I never said it wasn't meaningful. You are confusing meaning with truth, not to mention, meaning with reference.

---------- Post added 04-30-2010 at 09:32 PM ----------

fast;158649 wrote:

You got to be kidding!

First off, I can only suppose that you're talking about sentences since you believe no proposition is being expressed.

No sentence that fails to express a proposition is false. Don't confuse "false" with "not true."

I said in that other post that "Sherlock Holmes is not a detective" is not a proposition that gets expressed on my view so that it is technically truth-valueless.

Here's YOUR probelm. You think "SH is not a detective" is true. But the logical result is this:

"Sherlock Holmes is a not a detective" is true, so

"~Ds" is true, so,

"(Ex) ~Dx" is true.

This is logically valid.

go figure. You think SH exists.

@Extrain,

[QUOTE=Extrain;158651]I've already shown you.

~Ex(Sx & Ay (Sx-->y=x) & Dx)[/QUOTE]

I'm at a disadvantage. I don't speak that language.

[QUOTE]I just say, it is not the case that there is something that that is Sherlock and is a detective.[/QUOTE]I agree with that.

[~(SH and detective)] is true.
[QUOTE]Yes, it is very meaningful. I never said it wasn't meaningful. You are confusing meaning with truth, not to mention, meaning with reference.[/QUOTE]I'm almost afraid to ask, but do you think the sentence, "SH is not a detective" is cognitively meaningful? Everything you've said would lead me to think the answer is no, but stranger things have happened.

---------- Post added 04-30-2010 at 11:40 PM ----------

Quote:

You think SH exists.

I do not think that. I can't make heads or tails of Ds, Ex, and Dx. Sorry.

@fast,

fast;158656 wrote:

I'm at a disadvantage. I don't speak that language.

I agree with that.

[~(SH and detective)] is true.
I'm almost afraid to ask, but do you think the sentence, "SH is not a detective" is cognitively meaningful? Everything you've said would lead me to think the answer is no, but stranger things have happened.

I think it has meaning, yes. So don't misrepresent what I am saying. But technically, I don't think it is cognitively meaningful because a person who truly meant what he said would be saying something very similar to,

"George Bush is no longer the President." This is true. So in logic, the following inference is valid,

(Ex)~Px

This says, there exists something that is not a president.

If "SH is not a detective" is true, the same logical inference is valid,

(Ex)~Dx

But this says, there exists something that is not a detective. So this is true for all those existent things which are not detectives, but it is not true of Sherlock. So there is no sense in saying that "Sherlock is not a detective" anyway.

It's much better if someone said,

"It is not the case there is something that is Sherlock and is a detective."

---------- Post added 04-30-2010 at 09:49 PM ----------

fast;158656 wrote:

I do not think that. I can't make heads or tails of Ds, Ex, and Dx. Sorry.

Ok, look.

If "SH is not a detective" is true, then logic says (by the rule of *existential introduction*) that it is valid to infer that something exists which does not have that property.

So, if "SH is not a detective" is true, then it is also true that,

"There exists at least one thing that is Sherlock, and that thing is not a detective."

But the proposition that this sentence DOES express is literally false. So I don't believe it is true.

Does that make sense?

@Extrain,

[QUOTE=Extrain;158658]I think it has meaning, yes. So don't misrepresent what I am saying. But technically, I don't think it is cognitively meaningful because a person who truly meant what he said would be saying something very similar to,

"George Bush is no longer the President."

It's much better if someone said,

"It is not the case there is something that is Sherlock and that thing is a detective."[/QUOTE]

Saying "[GB] is no longer the President" implies that GB exists because of "no longer". If he is no longer the President, then he once was, and if he was, then it would be false to say he doesn't exist.

Saying "SH is not a detective" fails to imply anything about SH's existence. A person that does not exist cannot be a detective. SH is not a person. Therefore, SH is not a detective.

I suppose you have a problem with the phrase (or term), "A person that does not exist" because you think it implies 1) that a person exists (because it starts out with "A person") and states 2) "that does not exist (and thus you think this part contradicts the first part)," but why you would think the first part, especially in light of what follows, implies that a person exists, is perplexing, to say the least.

---------- Post added 05-01-2010 at 12:04 AM ----------

Extrain;158658 wrote:

Ok, look.

If "SH is not a detective" is true, then logic says (by the rule of *existential introduction*) that it is valid to infer that something exists which does not have that property.

So, if "SH is not a detective" is true, then it is also true that,

"There is something that is Sherlock, and that thing is not a detective."

But the proposition that this sentence DOES express is literally false. So I don't believe it is true.

Does that make sense?

I'll sleep on it.

SH won't. Smile

(Or if you prefer, it's not true that SH will.)

@fast,

fast;158663 wrote:

Saying "[GB] is no longer the President" implies that GB exists because of "no longer". If he is no longer the President, then he once was, and if he was, then it would be false to say he doesn't exist.

That's right. So does this example:

"George Bush is not president"--this is true if and only if George Bush exists and is not a president.

And so does this example:

"Sherlock Holmes is not a detective"--this is true if and only if Sherlock Holmes exists and is not a detectve.

It's strange to think something exists because I can robustly ascribe a property to it, but then think it doesn't exist because I can robustly deny a property of it. That's just weird to me because it seems that the latter case is the exact opposite.

[QUOTE=fast;158663]Saying "SH is not a detective" fails to imply anything about SH's existence.[/QUOTE]In logic, it DOES imply something exists. It implies that at least one thing exists that is not a detective. And this is false in a world in which the only things that existed are detectives. So to deny that something is a detective is not logically equivalent to deny that something exists and is a detective.

[QUOTE=fast;158663] A person that does not exist cannot be a detective.[/QUOTE]Colloquially, yes.

[QUOTE=fast;158663]SH is not a person. Therefore, SH is not a detective. [/QUOTE]But this is invalid. Surely, some things can be non-persons but detectives. German Shepherds who sniff out narcotics in airports could be detectives (albeit "doggy" detectives). Sherlock is not a detective not merely because Sherlock is not a person, but also because Sherlock doesn't even exist at all and is never purported to be a real person anyway.

[QUOTE=fast;158663] I suppose you have a problem with the phrase (or term), "A person that does not exist" because you think it implies 1) that a person exists (because it starts out with "A person") and states 2) "that does not exist (and thus you think this part contradicts the first part),"[/QUOTE]That's exactly right. "Existence" is not a predicate in logic. It is a quantifier that ranges over existent entities. And you get into a huge logical mess by treating "existence" as a predicate. I think "existence" ranges over all things that exist (number, propositions, people, tables, nations). It doesn't range over non-existent things. If you think it does, then we ARE asserting a literal contradiction by saying "Sherlock Holmes does not exist." I know we talk colloquially that way, but it is not correct. The proposition that gets expressed (assuming there is one) is literally a contradiction. I understand it is hard to convince people without the formal training in logic that it is wrong-headed to think "existence" is a property that some things have and other things don't (Ahab believes this), but it is not obviously true. In fact, it is clearly false that "some things do not exist." I take "existence" to be a very robust notion. That's why I think that if it is possible to refer to imaginary beings, then those beings exist, and they exist in only one way. All things that exist, exist, and they exist in the same way that everything else exists. There are not "kinds" of existence.

Immanuel Kant was the first person who said this two hundred years ago. He noticed how many logical problems treating "existence" like a predicate created in philosophy. So he said we shouldn't be treating "existence" that way. I happen to agree, and so do most philosophers. You get into strange theories like Ahab's theory when you do. It's a mess.

@Extrain,

fast;158549 wrote:

See, this is where you have it wrong. I'm talking about the proposition (the proposition, I say). The proposition being expressed is not what you think it is. You cannot read the sentence and determine the proposition being expressed without considering the context in which the sentence is used. The context helps determine what is being expressed by the sentence, and what you think is literally being expressed isn't what's being expressed.

The boy does not think it's actually George Washington, nor is he meaning to convey that it is. If the boy was severely mentally challenged such that he could not distinguish between a real live person and a portrait, then maybe he is meaning to convey what you think he is. Don't take things literally when context demands of us to do otherwise. Speaking in shorthand can sometimes make determining the proposition problematic, but context usually help to dissolve any present ambiguity.

No, you have it wrong. It doesn't matter what the boy thinks, or what he is intending to convey. "George Washington" refers to George Washington, not the picture of George Washington. And it's always been this way as soon as someone gave him that name. So what the boy literally says is literally false. But what he implied "there is a picture of George Washington" is true.

This is exactly the problem: Your theory of reference (whatever it is) is all messed up because you keep saying different things. In some places you say a term X refers to Y regardless of someone's intentions. In other places you say the exact same term X refers to Z--to something completely different--precisely because of someone's intentions. Proper Names are not indexicals that shift their referents dependent on context. Only the referent of pronouns such as "you," "me," "it," "he," "I," and "that" shift depending on context. "Here" and "there" are indexicals whose referents shift depending on the context, too...same with "now" and "later." But proper names don't do this. What shifts depending on context is which name is being used. There is not one name "George Washington" simply because there are hundreds and thousands people people with that type of name "George Washington."

@Extrain,

Extrain;158636 wrote:

That was a serious response. If numbers don't exist outside formal frameworks then the above statement is false. But its true. So numbers exist. It's your turn.

Apples aren't mathematical objects, your story was about apples, were they fictional apples?

@ughaibu,

ughaibu;158700 wrote:

Apples aren't mathematical objects, your story was about apples, were they fictional apples?

"The number of apples is 4" is true because there are 4 apples.

Things don't both exist and not exist. If you think numbers exist "only" in formal frameworks but don't "really" exist, then you are asserting a contradiction.

@Extrain,

Extrain;158707 wrote:

"The number of apples is 4" is true.

I'll assume they're fictional apples. Your original statement, getting rid of the apples, is true in Peano arithmetic, in bases greater than three. In short, within a specific set of formalisms.

@ughaibu,

ughaibu;158709 wrote:

I'll assume they're fictional apples. Your original statement, getting rid of the apples, is true in Peano arithmetic, in bases greater than three. In short, within a specific set of formalisms.

There are not different "kinds" of existence

Things don't both exist and not exist. If you think numbers exist "only" in formal frameworks but don't "really" exist, then you are asserting a contradiction. Same goes for apples.

@Extrain,

Extrain;158710 wrote:

If you think numbers exist "only" in formal frameworks but don't "really" exist, then you are asserting a contradiction. Same goes for apples.

Are you saying that fictional apples do exist?
There are four apples, is a statement in which "four" is an adjective, how does this imply realism about numbers?
Consider a walker with an even pace strolling from A to B:
A------------B
Rearrange the paces: llllllllllll and you have a number in base one. What about this suggests any kind of abstract object to conjecture realism about?

@ughaibu,

ughaibu;158709 wrote:

I'll assume they're fictional apples. Your original statement, getting rid of the apples, is true in Peano arithmetic, in bases greater than three. In short, within a specific set of formalisms.

Not so! A formalization of numbers do not at all eliminate the need for numbers. You are confusing our models of reality to reality itself.

@TuringEquivalent,

TuringEquivalent;158713 wrote:

Not so! A formalization of numbers do not at all eliminate the need for numbers. You are confusing our models of reality to reality itself.

Are you espousing realism about mathematical objects as abstract objects? Or are you pointing out that measuring things, with ratios, is useful?

@Extrain,

Extrain;158710 wrote:

There are not different "kinds" of existence

.

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

---------- Post added 05-01-2010 at 03:09 AM ----------

ughaibu;158715 wrote:

Are you espousing realism about mathematical objects as abstract objects? Or are you pointing out that measuring things, with ratios, is useful?

I mean what i say. It seems you think that just because we have a nice formalism of the integers, then mathematical Platonism is false. This is ridiculously absurd.

@ughaibu,

ughaibu;158712 wrote:

Are you saying that fictional apples do exist?
There are four apples, is a statement in which "four" is an adjective, how does this imply realism about numbers?
Consider a walker with an even pace strolling from A to B:
A------------B
Rearrange the paces: llllllllllll and you have a number in base one. What about this suggests any kind of abstract object to conjecture realism about?

Just because the word "four" functions as an adjective doesn't mean 4 is an adjective. You confuse the use/mention distinction in linguistics--thus confusing numbers with numerals. And your view ends up in a contradiction. I had proved this logically over a month ago in this same thread when someone said the exact same thing as you.

Again, either numbers exist, or they don't. Either apples exist, or they don't.

It is just as silly to think physical apples exist in abstract formal frameworks as to think abstract numbers exist as physical things in physical frameworks. Just because the one kind of thing doesn't exist in the other framework doesn't mean it exists any more or less than the other kind of thing. Existence doesn't come in degrees or kinds.

@Extrain,

Extrain;158721 wrote:

either numbers exist, or they don't. Either apples exist, or they don't.

Infinity is a mathematical object, consider an infinite number of apples, are these apples fictional? If so, do they exist?

@ughaibu,

ughaibu;158723 wrote:

Infinity is a mathematical object, consider an infinite number of apples, are these apples fictional? If so, do they exist?

You are confusing two different infinities.

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

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