numbers vs. words

@Extrain,

Extrain;145824 wrote:

So I fail to see your point entirely.

I see. Well, I dont think that I can express it any more simply, so I guess you'll remain unable to see it.

@ughaibu,

ughaibu;145828 wrote:

I see. Well, I dont think that I can express it any more simply, so I guess you'll remain unable to see it.

How is that something's being so "simply obvious" to you but not to the rest of us somehow supposed to automatically work in your favor? Sorry, it doesn't work that way.

@cws910,

cws910;116375 wrote:

what I am questioning is not the 'beauty' of mathematics. I am questioning whether or not words can be used as a alternative to mathematics.

---------- Post added 01-02-2010 at 12:52 PM ----------

and then again, kennethamy, I am not questioning the beauty and elegance of the equasions, I am stating that they cannot express beauty.

I think we use mathematics to describe mathematical things and words to describe the rest. It's a question of efficiency. You could use words to describe mathematical things but how inefficient would that be? And you could try to reduce non-mathematical things to a formula, I suppose, but to leave any part unaccounted for would be just as inefficient. For example, some would say that a person's beauty is directly related to the symmetry of their features, but I think that this leaves far too many variables unaccounted for. You might be grasping.

@PappasNick,

Numbers are not words. You mix up with Names of numbers. Hope it's helpfull

Pepijn Sweep

@Pepijn Sweep,

Pepijn Sweep;145787 wrote:

[CENTER]Is Hebrew writing a sort of Onto-logic ?[/CENTER]

[CENTER]Does JWH7 make sense ? Probably not, but there are all-ways people grasping at letters & numbers for faith.[/CENTER]

[CENTER]I think a lot. Too much. Not Enough !><![/CENTER]

[CENTER]Pepijn Sweep
Magi-to-be
:bigsmile:[/CENTER]

What are you doing in a philosophy of language thread if you just insist on mocking language itself? That action, itself, doesn't make any sense. You just told us that language has no meaning by your very own use of language to express that thought. Therefore, you haven't actually said anything. If you don't think language is any guide to what reality is really like at all, then you should just stop talking because you won't succeed in making sense anyway about what is actually the case here in the thread. As Wittgenstein said, "Whereof we cannot speak, we must remain silent."

@Pepijn Sweep,

Pepijn Sweep;145870 wrote:

Numbers are not words. You mix up with Names of numbers. Hope it's helpfull

Pepijn Sweep

Thanks. I think I know what you mean. But you're assuming there are nameless / language-less ideas of numbers, no? I'm not sure about that.

@PappasNick,

PappasNick;145891 wrote:

Thanks. I think I know what you mean. But you're assuming there are nameless / language-less ideas of numbers, no? I'm not sure about that.

I don't understand what exactly your view is. Do you think numbers just are words, then?

thanks.

@PappasNick,

PappasNick;145891 wrote:

Thanks. I think I know what you mean. But you're assuming there are nameless / language-less ideas of numbers, no? I'm not sure about that.

Numbers are no more words than cats are words. Numerals are words that name numbers; just as the word "cat" names cats. No one is assuming that there are nameless numbers. But the fact is that numbers are not names. Numbers have names. And, the names of numbers are numerals. You seem to be confusing numbers with numerals.

@kennethamy,

kennethamy;145905 wrote:

Numbers are no more words than cats are words. Numerals are words that name numbers; just as the word "cat" names cats. No one is assuming that there are nameless numbers. But the fact is that numbers are not names. Numbers have names. And, the names of numbers are numerals. You seem to be confusing numbers with numerals.

thanks. you got to it before i did....ha! I wasn't sure if papas was disagreeing or agreeing with what he said.

---------- Post added 03-29-2010 at 07:38 PM ----------

Now that we're on that subject, here's a quiz for everyone:

How many times does the following sentence occur?:

I will not pull Susie's hair in class.
I will not pull Susie's hair in class.
I will not pull Susie's hair in class.

---------- Post added 03-29-2010 at 08:16 PM ----------

student-of-life;145865 wrote:

I think we use mathematics to describe mathematical things and words to describe the rest. It's a question of efficiency. You could use words to describe mathematical things but how inefficient would that be? And you could try to reduce non-mathematical things to a formula, I suppose, but to leave any part unaccounted for would be just as inefficient. For example, some would say that a person's beauty is directly related to the symmetry of their features, but I think that this leaves far too many variables unaccounted for. You might be grasping.

Wait a minute. You just repeated the exact same idea behind what this person is saying to whom you think you are objecting. If there are variables unaccounted-for after the reduction of non-mathematical things to all mathematical formulae then, necessarily, those non-mathematical things which have not yet been accounted-for by all those mathematical formulae are potentially not mathematically quantifiable.

@Extrain,

Extrain;145904 wrote:

I don't understand what exactly your view is. Do you think numbers just are words, then?

thanks.

Here's what I originally wrote about this earlier in the thread:

Quote:

I'm still stuck on the notion that numbers are words.

Yes, that begs the question as to what words are. The point for me, however, is that I can't see a hard line difference between numbers and words, which I suspect many people on this forum can see. The word "justice" seems to me to be no different in terms of its status than the word "one", or "1" for that matter. That's all I'm saying.

@PappasNick,

PappasNick;145930 wrote:

Here's what I originally wrote about this earlier in the thread:

Yes, that begs the question as to what words are. The point for me, however, is that I can't see a hard line difference between numbers and words, which I suspect many people on this forum can see. The word "justice" seems to me to be no different in terms of its status than the word "one", or "1" for that matter. That's all I'm saying.

But this doesn't work. Like Kennethamy said, numbers are not numerals; numerals are names of numbers. I will logically prove to you that numbers are not words by a Reductio ad Absurdum argument--that is by supposing that numbers are, in fact, words.

So let's just suppose numbers are words, for the sake of argument, just like you say. Here are some words.

"Bob" is a word--it's a name.

"red" is a word--it's a predicate.

"with" is a word--it's a preposition.

"I" is a word--it's a personal pronoun.

"eat" is a word--it's a verb.

So what kind of word is a number? What else but a name? It doesn't seem to be a predicate, or verb, or a preposition. It seem to be a noun. But all nouns purport to designate an object, or a set objects. And all names, a kind of noun, actually do designate an object, one and only one object at at time. But let's just suppose numbers are not names at all, but merely some unqualified noun or other word.

Here are different instances of the same word mentioned in the quotes: "1."

"1"
"1"
"1"

How many times does the word "1" occur?

The answer is once, because I mentioned the same word three times by using the *quotes*. So suppose,

1<4
1>0
1=1

How many times does the word "1" occur? The answer is four times because I used the word four times.

So let's suppose instead of mentioning the word "1," I decide to use the word instead, when I express addition or equality, as in.

1+1=2

How many times did the same word occur in my use of it here? The answer is twice, because I used it twice.

But wait, now we have the word "2" used here as well. So how many times does the word "2" occur in my use of the word "2" in the expression of this equality? The answer is once.

So how is it that my using the same word twice equal my using the other word once?

It cannot since, if numbers were words, then

1+1=2

would be false,

because I am using, not mentioning, the words in the equality expressed, just as I am using, not mentioning, the equality expressed.

But 1+1=2 is true.

Therefore, numbers are not words.

Q. E. D.

*Further, we can prove the same result with the use/mention distiction in the philosophy of language to prove that numbers cannot be concepts or meanings, or actual physical things either. So numbers can only be abstract entities that don't physically exist, but must exist abstractly.

@Extrain,

Extrain;145799 wrote:

That's right. I can't conceive this. But that's not the point.

The point is that you have no good reason to think that "to believe that p" is something different than "to believe the proposition that P." If you don't have any good reason for thinking this, then why do you think it is even true?

You don't just get to assert something without justification. You need to tell us why you think this.

I've already told you.
If I believe that p and you hope that p, then I beleive the same thing that you hope: that p. But to hope that p is not to hope the proposition that p. So when I beleve that p I am not believing the propositon that p.
Of course, this does not negate the fact that I can also believe the propositon that p.

You've object to that, but I believe your objections have missed the point of that argument. To be honest, I am still trying to make sure that I do understand your objections.

Quote:

So you believe propositions exist then, contrary to the author you quoted? So what are they?

P.M.S Hacker believes that propositions exist. Did you not read carefully what he wrote:

"For believing that p is not the same as believing the proposition that p. To be sure, one can believe propositions, as one can believe stories, rumours, declarations and statements."

And he states earlier, quite clearly, that it is misconceived to view believing as an attitude toward a proposition.

Obviously you don't think that it is a misconception. But you shouldn't construe his rejection of your conception as a denial that there are propositions.

Quote:

If you want to countenance the existence of propositions like it seems you want to do, then you are agreeing, contrary to the author, that propositional attitudes of belief are relations between the really existent person and the really existent proposition.

Nope. I'm simply agreeing with the author that it is misconceived to view belief as an attitudinal relationship towards a proposition. And that view does not entail that propositions do not exist.

Quote:

I agree, and so does Kenneth.

Why do you think it matters whether or not Kenneth agrees with you? I completely understand that the view I am taking is the minority position among philosophers.

Quote:

So now the burden is on you to tell us what a proposition actually is.

So you can't just say propositions exist, deny propositions are abstract entities, but then not tell us what you think propositions actually are.

Are they atomic facts in the world, or states of affairs in the world that are combinations of atomic facts, like Russell thought they were?

I already told you that a proposition is something that can be expresssed by the use of a sentence. That doesn't entail that it is an abstract object.

And even if I can't provide a satifactory answer to what a propositon is, it doesn't follow that I need adopt a concept of propositions that appears deeply flawed to me.

Sorry if I seem a little snappish in this post. But I was a little surprised at you response to what was basically a 'I need time to think some of this over' post. I don't claim to understand all th points you have made so far. Until I do, I can't see if they really are adequate to justifying the abandonment of views that I already hold.

I have over the past decade made some big changes in the views I hold and believe that I am still capable of making more changes if callled for.

@kennethamy,

kennethamy;145658 wrote:

But I agree with you. What makes you believe I don't? But that does not mean that that p, and the proposition that p are not identical. Isn't that what you were claiming?

Just as the fact that I can fear the postman, but not fear my father, does not mean that the postman and my father are not identical.

I'm sorry, Kennethamy, but I still don't see how this applies to the question as to whether or not we can legitimately construe 'A believes that p' as 'A believes the proposition that p'.
If you suspect that that there will be too many guests coming for dinner and I believe that there will be too many guests for dinner, there is no question as to what is being believed or being suspected. Could what is being believed or suspected in this case be anything other than the number of guests coming for dinner?
I can see that if A knows what C said and B believes what C said, it does not follow that A knows what B believes. But I don't see a similar ambiguity in the case I just presented.

@Ahab,

Ahab;146006 wrote:

I've already told you.
If I believe that p and you hope that p, then I beleive the same thing that you hope: that p.But to hope that p is not to hope the proposition that p. So when I beleve that p I am not believing the propositon that p.
Of course, this does not negate the fact that I can also believe the propositon that p.
You've object to that, but I believe your objections have missed the point of that argument. To be honest, I am still trying to make sure that I do understand your objections.

P.M.S Hacker believes that propositions exist. Did you not read carefully what he wrote:

"For believing that p is not the same as believing the proposition that p. To be sure, one can believe propositions, as one can believe stories, rumours, declarations and statements."

And he states earlier, quite clearly, that it is misconceived to view believing as an attitude toward a proposition.

Obviously you don't think that it is a misconception. But you shouldn't construe his rejection of your conception as a denial that there are propositions.

Nope. I'm simply agreeing with the author that it is misconceived to view belief as an attitudinal relationship towards a proposition. And that view does not entail that propositions do not exist.

Why do you think it matters whether or not Kenneth agrees with you? I completely understand that the view I am taking is the minority position among philosophers.

I already told you that a proposition is something that can be expresssed by the use of a sentence. That doesn't entail that it is an abstract object.
And even if I can't provide a satifactory answer to what a propositon is, it doesn't follow that I need adopt a concept of propositions that appears deeply flawed to me.

Sorry if I seem a little snappish in this post. But I was a little surprised at you response to what was basically a 'I need time to think some of this over' post. I don't claim to understand all th points you have made so far. Until I do, I can't see if they really are adequate to justifying the abandonment of views that I already hold.

I have over the past decade made some big changes in the views I hold and believe that I am still capable of making more changes if callled for.

Ok, wait a minute! Something very very duplicitous is going on here with this alleged account on several levels. I hear both you and Hacker simultaneously asserting and denying the existence of propositions. Here's why:

(1) The article is titled "The Ontology of Belief," not "On the Relational Analysis of Belief," or even better "On Cognitive Attitudes" or "On the non-Existence of Propositional-Attitude of Beliefs." I take beliefs to be propositional attitudes, nothing more, nothing less. And so do most others. And so why is he calling it an ontology of belief if he were not discussing the ontological status of propositions themselves? That is, whether they exist or not? Obviously, (a) Hacker (like you) is unwilling to discuss the Nature of propositions themselves. (b)Nor do either of you find their very existence in any way shape or form contestable at all (at least you claim to). So why did Hacker call his Article the "an ontology of belief" anyway, if he wasn't intending to discuss whether propositions did, or did not, exist??--Catch my drift?

(2) It is understood by philosophers far and wide in the discipline that if you deny a relational account of propositional attitudes as consisting of a belief-relation between the person and what is believed by that person, then by default, you've denied the existence of propositions altogether, (not simply denied their status as abstract entities), or at least made them completely unknowable, because you, Ahab, no longer stand in any relation to a propostion whatsoever when you believe it. So how would you have epistemic access to what it was that you believed anyway if you didn't stand in any relation at all to what it was that you believed? Make sense? You're completely disconnected. There needs to be some account of how you are standing in the relation to contents of your own thoughts, and what that relation is if it is not a cognitive relation or a propositional-belief kind of relation.

(3) And what is it, anyway, that is true or false of the world, if it not some entity (presumably abstract) that is true or false of that world? If it is not abstract, then what is it? The question really does deserve an answer in spite of your insistence that it doesn't, because whatever answer we give is going to change alot of things about what it is that we take ourselves to be doing when we believe these things called "propositions," what we are doing when we are asserting these things called "propositions," or debating over their truth values, etc. Because if we can't answer this, then quite honestly it seems we are just hiding our heads in the sand concerning these real problems at stake.

After all, you can hold a relational account of propositional attitudes and then countenance that a propostion is NOT an abstract entity, but as set of some kind of atomic facts, or a set of constituents of facts, or real world states of affairs (Russellian, Wittgensteinian), or as a sentence-type existing within one's own linguistic framework and not outside that framework (Quine), as if shared by all languages. Or as modal realists construe propositions as functions from possible worlds to truth values (Lewis, Stalnaker). So I'm going to get back to you, and hold my tongue regarding the many things I would like to say, but I am not even sure what Hacker really thinks anymore. It just hope this account is not one of those accounts collapsing one's belief with the object of one's belief so that what I believe just is my act of believing it. So I'm confused.

Alot of things are VERY unclear to me, and you think I am misunderstanding Hacker. But I don't think that's fair at all. I suspect something is deeply problematic here.

@Extrain,

Extrain;145761 wrote:

Ahab wrote:

Again I am not denying that people can believe the proposition that x.

But that's what this passage is actually denying below! Read it again. It is saying that propositional attitudes, (such as believing and knowing), if construed as "an attitude toward a proposition," then this relational analysis (which people like myself are advancing) between the person standing in the belief-relation to the proposition p believed, is false. So, therefore, propositions don't exist.

It is saying that to construe belief as an attitudinal relationship toward a propostion is misconceived. If someone critiques your concept of reference does that mean he thinks there is no such thing as being able to refer to things?

Quote:

Why do you think the article is titled "The Ontology of Belief"? It is not merely titled "The Linguistics of Belief." So it is denying the existence of propositions as abstract entities, just as you have done before.

The title is Of the Ontolgy of Belief.

The article is concerned with giving a conceptual analysis of belief.

@PappasNick,

PappasNick;145930 wrote:

Here's what I originally wrote about this earlier in the thread:

Yes, that begs the question as to what words are. The point for me, however, is that I can't see a hard line difference between numbers and words, which I suspect many people on this forum can see. The word "justice" seems to me to be no different in terms of its status than the word "one", or "1" for that matter. That's all I'm saying.

But "one" is not a number, "one" is a word, more specifically, it is a numeral, just like, "1". Bot are the name of the number, one. Just exactly as "cat" is not a cat. "Cat" is a word. And the word, "cat" is the name of the animal, cat.

Your confusion is between what philosophers call, "use" and "mention".

Use?mention distinction - Wikipedia, the free encyclopedia

@Extrain,

Extrain;146133 wrote:

Ok, wait a minute! Something very very duplicitous is going on here with this alleged account on several levels. I hear both you and Hacker simultaneously asserting and denying the existence of propositions. Here's why:

(1) The article is titled "The Ontology of Belief," not "On the Relational Analysis of Belief," or even better "On Cognitive Attitudes" or "On the non-Existence of Propositional-Attitude of Beliefs." I take beliefs to be propositional attitudes, nothing more, nothing less. And so do most others. And so why is he calling it an ontology of belief if he were not discussing the ontological status of propositions themselves? That is, whether they exist or not? Obviously, (a) Hacker (like you) is unwilling to discuss the Nature of propositions themselves. (b)Nor do either of you find their very existence in any way shape or form contestable at all (at least you claim to). So why did Hacker call his Article the "an ontology of belief" anyway, if he wasn't intending to discuss whether propositions did, or did not, exist??--Catch my drift?

(2) It is understood by philosophers far and wide in the discipline that if you deny a relational account of propositional attitudes as consisting of a belief-relation between the person and what is believed by that person, then by default, you've denied the existence of propositions altogether, (not simply denied their status as abstract entities), or at least made them completely unknowable, because you, Ahab, no longer stand in any relation to a propostion whatsoever when you believe it. So how would you have epistemic access to what it was that you believed anyway if you didn't stand in any relation at all to what it was that you believed? Make sense? You're completely disconnected. There needs to be some account of how you are standing in the relation to contents of your own thoughts, and what that relation is if it is not a cognitive relation or a propositional-belief kind of relation.

(3) And what is it, anyway, that is true or false of the world, if it not some entity (presumably abstract) that is true or false of that world? If it is not abstract, then what is it? The question really does deserve an answer in spite of your insistence that it doesn't, because whatever answer we give is going to change alot of things about what it is that we take ourselves to be doing when we believe these things called "propositions," what we are doing when we are asserting these things called "propositions," or debating over their truth values, etc. Because if we can't answer this, then quite honestly it seems we are just hiding our heads in the sand concerning these real problems at stake.

After all, you can hold a relational account of propositional attitudes and then countenance that a propostion is NOT an abstract entity, but as set of some kind of atomic facts, or a set of constituents of facts, or real world states of affairs (Russellian, Wittgensteinian), or as a sentence-type existing within one's own linguistic framework and not outside that framework (Quine), as if shared by all languages. Or as modal realists construe propositions as functions from possible worlds to truth values (Lewis, Stalnaker). So I'm going to get back to you, and hold my tongue regarding the many things I would like to say, but I am not even sure what Hacker really thinks anymore. I'm confused.

Alot of things are VERY unclear to me, and you think I am misunderstanding Hacker. But I don't think that's fair at all. I suspect something is deeply problematic here.

Have you actually read the article?

Edited comment:

And you seem to be referring to early Wittgenstien. Have you studied his later philsophy? If you had then you would know that he thinks that the concept of a 'proposition' is a family-resemblence concept.

@Ahab,

Ahab;146138 wrote:

It is saying that to construe belief as an attitudinal relationship toward a propostion is misconceived. If someone critiques your concept of reference does that mean he thinks there is no such thing as being able to refer to things?

The title is Of the Ontolgy of Belief.

The article is concerned with giving a conceptual analysis of belief.

Wait. So it IS a relational account then, because reference is a kind of relation. It is the relation of reference, right?

Look:
For any two given objects, nothing is going to happen between them, or some type of connection be instantiated between them without that connection being some kind of relation. Even if you dont' specify what that relation is, it is still a relational account if you think there are two objects involved that have some kind of connection with one another, right? That connection is going to be a relation.

This is the real question then:

Does Hacker collapse the object of my belief with my belief itself? So that what I believe just is my act of believing it?

---------- Post added 03-30-2010 at 07:33 AM ----------

Ahab;146140 wrote:

Have you actually read the article?

No, not yet. Sorry. Apparently I'll have to.

But I'm not liking it at all so far, to tell you truth. So I guess I'm more curious than ever now...lol..

@Ahab,

Ahab;146132 wrote:

I'm sorry, Kennethamy, but I still don't see how this applies to the question as to whether or not we can legitimately construe 'A believes that p' as 'A believes the proposition that p'.
If you suspect that that there will be too many guests coming for dinner and .

It doesn't. But it does show that it isn't true that we cannot.

@Extrain,

Extrain;146142 wrote:

Wait. So it IS a relational account then, because reference is a kind of relation. It is the relation of reference, right?

For any two given objects, nothing is going to happen between them, or some type of connection instantiated between them without some kind of relation. Even if you dont' specify what that relation is, it is still a relational account it there are two objects involved that have some kind of connection with one another, right? That connection is going to be a relation.

This is the real question then:

Does Hacker collapse the object of my belief with my belief itself? So that what I believe just is my act of believing it?

We express our beliefs through language. Of course, we can also express them through our behavior, but lanaguage is another form of behavior.

Generally speaking, the later Wittgenstein questioned the claim that a belief is an inner mental state.

This is very brief and don't know if any of the above provides helpful clues. Have to get ready for work.

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