numbers vs. words

@Reconstructo,

Reconstructo;135540 wrote:

It seems to me that negation is something that is not in itself a concept.....It's a hole that needs a donut in which to manifest itself. And addition is perhaps the same as negation, beneath their surface differences....

The concept of being and the non-concept of negation (which can only be spoken of as a concept...)

Negation is an operation we perform on propositions. For example, we can negate the proposition "that the cat is on the mat", and change its truth value. There are, of course, negative numbers, but that is different.

@kennethamy,

kennethamy;135555 wrote:

Negation is an operation we perform on propositions. For example, we can negate the proposition "that the cat is on the mat", and change its truth value. There are, of course, negative numbers, but that is different.

i know that, of course. but i'm talking about what's behind that. is it a learned language game or something deeper in the structuring of our thought. negation is necessary for abstraction as well.

@Reconstructo,

Reconstructo;135557 wrote:

i know that, of course. but i'm talking about what's behind that. is it a learned language game or something deeper in the structuring of our thought. negation is necessary for abstraction as well.

If there is something "behind that" (whatever that means) that does not make it false, or even incomplete. But, what makes you think that there is something behind it (whatever that means)? Sometimes, as Freud said, "a cigar is just a cigar".

@jack phil,

jack;135537 wrote:

Fido,

and what of the words and, or, but, if, then, etc. ?

The word 'and' is quite similar to the symbol for addition, +.

It seems this whole thread begins wrongheaded.

Yes, math and language have a lot in common and can often reach the same result...I read physics, but my math is weak... Fortunately the physicists have the sense to explain the significance of their math...

Even the linking of ideas, the ordering of thought requires a certain conceptual understanding...Does it matter that -and- may mean something different in every instance that it is used??? Well every word is like that, so what is new???Yet, if their meaing were not in some sense conserved, and the value of numbers is, then they could not communicate meaning out of the need always to determine their meaniing...

---------- Post added 03-03-2010 at 05:05 PM ----------

Reconstructo;135557 wrote:

i know that, of course. but i'm talking about what's behind that. is it a learned language game or something deeper in the structuring of our thought. negation is necessary for abstraction as well.

Should not look for truth in words...There is no linguistic or rhetorical truth... Words, sentences, paragraphs, even whole books may be seen as single brush strokes contributing a fraction of a sense of truth that is built up in layers like paint on a canvas...Truth is not what words are, but what people must be, because it is an essential element in all our lives, and we must communicate it, and we must recieve it by communication to have life and the best of life...Truth should be a part of our character, and an element of our nature...

@Fido,

Fido;135310 wrote:

Recon... I can agree with most except to say that knowledge is culture... To have ones culture is to have that knowledge, the aquired knowledge of ones people...

we agree there. a living culture is a shared logos, and this logos or structuring concept is numinous , precisely because it integrates..perhaps logic and coherence are transcendental attractive to us. Is rationality also a passion with all movement toward integration as its object?

Perhaps our concept-imposing function is tied directly into our social instinct, as speech implies its listeners...?

A culture decays as it betrays a living logos for one not so alive?

@Fido,

[QUOTE=Fido;135407]All words are concepts...[/QUOTE]

I have a concept of what words are, but my concept of words and words are not the same thing, and no, my concept of words is not a concept of a concept, for words are not concepts. For example, consider the written word, "orange." It's a word, but it's not a concept, for all concepts are mental, and the written word cannot be mental; how could it be?

So, what is a word, if not a concept? One thing we know about words is that they denote (or stand in place of) meaning, where what is meant might (only might, I say) be considered conceptual, but the important point is that the word is different than what it stands in place of, so even if meanings are concepts, that's not to say the invented words that denote meaning are.

One reason I think you are saying that words are concepts is because they are not physical, and some people have this notion that all of that which is not physical yet exists must somehow therefore be a concept, but I do not believe that is the case.

Here's a scenario that conveys my take:

The word, "sun" is a recent product of humans, but the referent that the word, "sun" refers to (namely, the sun) has been around long before the word. Not only that, but the sun was around long before the human concept of the sun. So, we're dealing with three different things: 1) the sun, 2) the word, "sun" and 3) the concept of the sun.

Earth is the third planet from the sun. Again, there is a difference between 1) Earth, 2) the word, "Earth", and 3) our concept of Earth.

What about the number three? We have 1) the number three, 2) the numeral "three" and 3) our concept of the number three.

Notice the connections: In all examples above, both the words and the concepts are human dependent, but never is it the case that the referent of the words are human dependent. That means that the sun was around before people, the Earth was around before people, and the number three was around before people.

@cws910,

fast wrote:

and the number three was around before people.

I don't mean to imply you are wrong, but what makes you say this? Where does the number three exist in the world to be considered a referent?

What about goblins? We have 1.) The concept of goblins, 2.) The word "goblin" 3.) Goblins...?

But we know goblins do not exist.

@fast,

fast;135905 wrote:

Notice the connections: In all examples above, both the words and the concepts are human dependent, but never is it the case that the referent of the words are human dependent. That means that the sun was around before people, the Earth was around before people, and the number three was around before people.

Sorry, but this appears to me to be obviously false. It is not always the case that what we use a word to refer to is never human dependent. Take the word "chess". Would you claim that the game of chess was around before people?
I would agree with you that the planet earth and the star we call the sun were around before people. But numbers were not around before people since people invented numbers just as they invented the game of chess.

I think you will disagree with my view that numbers were invented rather than discovered. But do you really think that the game of chess was discovered and not invented by humans? Or what about automobiles and houses? We use words to refer to those objects but I would assume you wouldn't claim they were around before humans.

@Zetherin,

Zetherin;135914 wrote:

I don't mean to imply you are wrong, but what makes you say this? Where does the number three exist in the world to be considered a referent?

What about goblins? We have 1.) The concept of goblins, 2.) The word "goblin" 3.) Goblins...?

But we know goblins do not exist.

If the number three is an abstract entity, then it does not exist at any place, at any time. That is what abstract entities are. They have no spatio-temporal properties.

@kennethamy,

kennethamy;135917 wrote:

If the number three is an abstract entity, then it does not exist at any place, at any time. That is what abstract entities are. They have no spatio-temporal properties.

And abstract entities are not dependent on the mind to exist? That is, the number three, being an abstract entity, would exist even if human did not?

---------- Post added 03-04-2010 at 10:27 AM ----------

Ahab;135916 wrote:

Sorry, but this appears to me to be obviously false. It is not always the case that what we use a word to refer to is never human dependent. Take the word "chess". Would you claim that the game of chess was around before people?
I would agree with you that the planet earth and the star we call the sun were around before people. But numbers were not around before people since people invented numbers just as they invented the game of chess.

I think you will disagree with my view that numbers were invented rather than discovered. But do you really think that the game of chess was discovered and not invented by humans? Or what about automobiles and houses? We use words to refer to those objects but I would assume you wouldn't claim they were around before humans.

Yes, I do not understand.

What about justice? We have 1.) A concept of justice 2.) The word "justice" 3.) Justice

But suppose life did not exist, would justice exist? I don't see how. Justice, by the way, is an abstract entity, I think.

@kennethamy,

kennethamy;135917 wrote:

If the number three is an abstract entity, then it does not exist at any place, at any time. That is what abstract entities are. They have no spatio-temporal properties.

If the number three has no spatio-temporal properties (and I agree that it doesn't) than it makes no sense to say that the number three existed before humans did. Which is what Fast claimed earlier.
That would be like saying the number three is round or has the color of a lemon.

@Zetherin,

Zetherin;135918 wrote:

And abstract entities are not dependent on the mind to exist? That is, the number three, being an abstract entity, would exist even if human did not?

---------- Post added 03-04-2010 at 10:27 AM ----------

Yes, I do not understand.

What about justice? We have 1.) A concept of justice 2.) The word "justice" 3.) Justice

But suppose life did not exist, would justice exist? I don't see how. Justice, by the way, is an abstract entity, I think.

If there are abstract entities (and literal wars were fought over this issue in the Middle Ages) Then it is believed they are not mind dependent. A famous instance of this is Plato's theory of Forms. Forms are abstract entities, but not mind-dependent. Some philosophers (Locke, for instance) thought they were mind-dependent. Plato (as I said) thought there was the Form of Justice. He argued that unless there is such a Form of Justice, that justice could not exist, because the existence of justice amounts to what Plato called, "participation" in the Form of Justice. Plato thought that the Form of Justice was independent of whether or not life existed. Platonism is an extreme version of the theory of abstract ideas.

@Ahab,

Ahab;135928 wrote:

If the number three has no spatio-temporal properties (and I agree that it doesn't) than it makes no sense to say that the number three existed before humans did. Which is what Fast claimed earlier.
That would be like saying the number three is round or has the color of a lemon.

Yes, but perhaps there is a belief that abstract entities exist independently of the mind, despite them having no spatio-temporal qualities.

This is what I'm interested in.

---------- Post added 03-04-2010 at 10:43 AM ----------

kennethamy wrote:

If there are abstract entities (and literal wars were fought over this issue in the Middle Ages) Then it is believed they are not mind dependent. A famous instance of this is Plato's theory of Forms. Forms are abstract entities, but not mind-dependent. Some philosophers (Locke, for instance) thought they were mind-dependent. Plato (as I said) thought there was the Form of Justice. He argued that unless there is such a Form of Justice, that justice could not exist, because the existence of justice amounts to what Plato called, "participation" in the Form of Justice. Plato thought that the Form of Justice was independent of whether or not life existed. Platonism is an extreme version of the theory of abstract ideas.

I see. Thanks. And what do you think, and why?

@Zetherin,

Zetherin;135933 wrote:

Yes, but perhaps there is a belief that abstract entities exist independently of the mind, despite them having no spatio-temporal qualities.

This is what I'm interested in.

---------- Post added 03-04-2010 at 10:43 AM ----------

I see. Thanks. And what do you think, and why?

Classes are abstract entities, and Quine has argued that our understanding of math and logic would be impossible unless we posited the existence of classes.

@Zetherin,

Zetherin;135933 wrote:

Yes, but perhaps there is a belief that abstract entities exist independently of the mind, despite them having no spatio-temporal qualities.

Yes, I know that people do believe that. I don't happen to share that belief. In fact I'm not even sure that such a belief even makes sense. I don't really know what it would mean for an abstract entity to exist in some sort of Platonic realm without also attributing some sort of spatio-temporal quality to it. :perplexed:

@Ahab,

Ahab;135957 wrote:

Yes, I know that people do believe that. I don't happen to share that belief. In fact I'm not even sure that such a belief even makes sense. I don't really know what it would mean for an abstract entity to exist in some sort of Platonic realm without also attributing some sort of spatio-temporal quality to it. :perplexed:

I am not familiar with Plato's work, but was it some sort of mysticism of the day? It doesn't make any sense to me either.

kennethamy wrote:

Classes are abstract entities, and Quine has argued that our understanding of math and logic would be impossible unless we posited the existence of classes.

I would be interested in reading his arguments. I will go research them now.

@Zetherin,

Zetherin;135961 wrote:

I would be interested in reading his arguments. I will go research them now.

Here you go: Indispensability Arguments in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

---------- Post added 03-05-2010 at 01:42 AM ----------

At the other extreme: http://philsci-archive.pitt.edu/archive/00001164/00/formfiz_preprint.pdf

@Zetherin,

[QUOTE=Zetherin;135914]I don't mean to imply you are wrong, but what makes you say this? Where does the number three exist in the world to be considered a referent?

What about goblins? We have 1.) The concept of goblins, 2.) The word "goblin" 3.) Goblins...?

But we know goblins do not exist.[/QUOTE]

I said, "the number three was around before people." I could have worded that better. What I mean to say is that the number three exists AND the existence of the number three is mind-independent. The existence of humans is not a requirement for the existence of numbers. We did not invent numbers. We discovered numbers. We invented numerals, and numerals are referring terms, and numerals (what we invented) refer to numbers (what we discovered).

Keep in mind that numbers is a class, and the number class is a class of all numbers. For example, the number three is a particular that belongs to the class of numbers. Furthermore, and this bears keeping in mind as well, the number three itself is a class, but the question is, what is it a class of?

The answer is that the number three is the class of all triples. But, what in the heck is a triple? Think of a triple as the physical relationship between a group of three objects. For example, three people standing next to each other. Three trees clustered together. Isn't it so that the relationship between the sun and the other planets is such that Earth is the third from the sun? That physical relationship is fact, and it was a fact prior to our discovery.

In regards to Goblins:

There are 1) referring terms and 2) non-referring terms. Some referring terms 1) successfully refer and some referring terms 2) fail to refer.

However, there is a difference between 1) a referring term that fails to refer and 2) a non-referring term.

"Goblin" is a referring term, but it fails to refer since there are no goblins. If we are mistaken and find that there are goblins, then "Goblin" will still be a referring term, but instead of it failing to refer, it will succeed at referring. Same with unicorns.

A non-referring term would be terms that simply cannot have referents (not to be confused with meaning, of course). A few examples include words like, "however", "but" and "although." Never could there be something in our universe to instantiate them.

---------- Post added 03-04-2010 at 12:43 PM ----------

Ahab;135916 wrote:

Sorry, but this appears to me to be obviously false. It is not always the case that what we use a word to refer to is never human dependent. Take the word "chess". Would you claim that the game of chess was around before people?

I was only talking about the examples I gave. Sorry for the confusion.

Pencils were invented by humans, but if all humans dropped dead, pencils would not cease to exist.

@fast,

fast;135983 wrote:

I said, "the number three was around before people." I could have worded that better. What I mean to say is that the number three exists AND the existence of the number three is mind-independent.

One can acknowledge the existence of three without taking the further step of claiming it is mind-independent.

Quote:

The existence of humans is not a requirement for the existence of numbers. We did not invent numbers. We discovered numbers. We invented numerals, and numerals are referring terms, and numerals (what we invented) refer to numbers (what we discovered).

Obviously, we disagree on this. Humans invented the numbering system. They invented mathematics. Mathematical propositions are rules for the transformation of empirical propositions. Rules are not discovered, but invented.

Quote:

The answer is that the number three is the class of all triples. But, what in the heck is a triple? Think of a triple as the physical relationship between a group of three objects. For example, three people standing next to each other. Three trees clustered together. Isn't it so that the relationship between the sun and the other planets is such that Earth is the third from the sun? That physical relationship is fact, and it was a fact prior to our discovery.

I think we can agree that the planets existed long before humans did. After all, that is part of our conception of what a planet is: a physical substance that enjoys independent existence.

We could have chosen to number all planetary objects in pairs. That would mean that Mercury and Venus would be considered as one (the first pair), Earth and Mars as two (the second pair), etc. Although this sort of way of classifying the spatial relationships of the planets does not at first glance appear usefu, it is not too difficult to think of scenarios in which it could have arisen. Are you going to argue that this other way of classifying the planetary relationships also existed before humans were around?

Isn't classification arbitrary? We classify things accoring to our needs and interests.

---------- Post added 03-04-2010 at 11:36 AM ----------

fast;135983 wrote:

IThere are 1) referring terms and 2) non-referring terms. Some referring terms 1) successfully refer and some referring terms 2) fail to refer.

However, there is a difference between 1) a referring term that fails to refer and 2) a non-referring term.

"Goblin" is a referring term, but it fails to refer since there are no goblins. If we are mistaken and find that there are goblins, then "Goblin" will still be a referring term, but instead of it failing to refer, it will succeed at referring. Same with unicorns.

That is a stipulated use of the word "refer". It is part of a theory of how language should work.
Based on my understanding of English language and my observation of how others use it, I don't think most people would agree with that stipulation or even find it useful. Leastways, I don't ever recall being told in grammar school that I couldn't use words to refer to imaginary beings because those beings don't actually exist.

@cws910,

Ahab wrote:

Isn't classification arbitrary? We classify things accoring to our needs and interests.

That was exactly my first thought. But have you read Quine's arguments?

Philosophy Forum

numbers vs. words

Quick Links

My Account

able2know