Reply to Merlin

[merjet]

If you think about it carefully I think you will agree that what you call 'toes' are actually abstractions produced in your nervous system. The lightwaves were reflected off "the toes" (in quotes because at this stage the "substance" is unknown to us) and excited the optical nerves resulting in an image in the optical cortex. It is this image that the word 'toe' refers to.

Suppose my 250-pound brother accidentally steps on my toe. I'll try to think about it carefully, like you advise. My toe doesn't really exist; it's the image produced in my optical cortex that hurts. Back to square one.

[tjohnson]

Suppose my 250-pound brother accidentally steps on my toe. I'll try to think about it carefully, like you advise. My toe doesn't really exist; it's the image produced in my optical cortex that hurts. Back to square one.

No, I never said it didn't exist. Also, "your toe hurts" is a gross simplification of what is happening as best we know it. Again, it is the nervous signals originating in that area of your body that is interpreted as "pain" in your cortex.

[merjet]

No, I never said it didn't exist. Also, "your toe hurts" is a gross simplification of what is happening as best we know it. Again, it is the nervous signals originating in that area of your body that is interpreted as "pain" in your cortex.

Pardon me. I'm a novice at thinking your way. But I'm pleased to know my toes exist and they aren't simply an abstraction produced by my nervous system.

[tjohnson]

Pardon me. I'm a novice at thinking your way. But I'm pleased to know my toes exist and they aren't simply an abstraction produced by my nervous system.

"Something" exists, but the word 'toe' refers to an abstraction.

[Brant Gaede]

Pardon me. I'm a novice at thinking your way. But I'm pleased to know my toes exist and they aren't simply an abstraction produced by my nervous system.

"Something" exists, but the word 'toe' refers to an abstraction.

What does the abstraction refer to?

--Brant

[Daniel Barnes]

Your counter is what fails. If I want near 2 pounds of fish, I would not accept 3 pounds or 137 pounds...you seem to be conflating the application of numbers to discrete versus continuous domains (or to count versus measure). How many toes are on each of my feet is exactly 5. It is not 4, 4.9, 5.1, or 6. Weight at the fish market is a continuous domain.

It wasn't me who switched the discussion from 2 as in "two eyes" to 2 as in "near 2 pounds". And as your argument now turns on what you personally will or will not accept as to the meaning of the number 2 there is probably not much point debating it further.

The word was completely meaningless to me -- it had no meaningful content -- until I read your definition.

As I predicted. As was, in fact, the whole basis of my argument laid out above with some care. Nevertheless I will repeat it again. In short, numbers are much simpler in meaning than words, and are almost empty of meaning by comparison. There is a trade off between content and precision. Numbers are content-poor, thus more precise; words are content-rich, thus vaguer.

Further, I find it extremely odd that you claim that something is "empty of meaning" just because it is empty of meaning for you. Next you will be telling us Sanskrit or Swahili are "meaningless" just because you personally can't read them! Er...I don't think so.

You have not explained how 'two' in 'I have two eyes' is "almost completely empty of meaning." Nor have you tried to explain how 'I have two eyes' is any less meaningful than 'I have blue eyes'.

I thought it was obvious from my lengthy explanation, but never mind. Let's go through it step by step then. In this sentence, counting eyes, like your own example to GS with toes, 2 means precisely 2. Not 2.1, not 1.9, nor any of the in fact infinite set of numbers on a continuous scale of measurement that you, personally, may or may not willy-nilly decide to call "near" to two. (After all 137 is near to 2 - compared with 1,000,137!) It's precise, but the cost of that precision is that it is very simple; nearly empty of meaning. Ok? Now, compare the paucity of such simple counting of eyes with the more complex implications a word like "blue" carries: not only in terms of shades of colour, but also emotions (as blue eyes could also mean sad eyes).

When are you going to stop evading this?

As you can see, I am not "evading" this at all. The question should be: when are you going to stop accusing me of such things?

I disagree. A letter of the alphabet is completely symbolic, with no reference to anything beyond itself. Numbers often refer to reality.

While I don't have a strong view on this issue, it seems to me Merlin is wrong in point of fact here. Letters of the alphabet do refer to reality; to the primary, physical sounds of language.

Edited April 18, 2008 by Daniel Barnes

[tjohnson]

What does the abstraction refer to?

Not sure if this is a serious question but....normally we say a symbol stands for something else - that's more or less what being a symbol means. The word 'toe', as a symbol, stands for a mental image, an abstraction if you will. The abstraction was manufactured in our nervous system from the stimuli picked up by our "sensors", or nerve endings. To answer your question the abstraction doesn't refer to anything, it's not considered a symbol.

[Michael Stuart Kelly]

GS,

That abstraction you are talking about is called percept and concept in Objectivism. A word symbolizes the abstraction and gives it concrete form so we can do things with it like communicate it.

Michael

[merjet]

It wasn't me who switched the discussion from 2 as in "two eyes" to 2 as in "near 2 pounds".

That was in response to you asking 'How many shades of "two" are there?' here (as if there couldn't be any) rather than answering my question.

While I don't have a strong view on this issue, it seems to me Merlin is wrong in point of fact here. Letters of the alphabet do refer to reality; to the primary, physical sounds of language.

The phrase "refer to reality" is a huge stretch, obviously so regarding a deaf person. Letters "correlate to sounds" is far better.

[Daniel Barnes]

That was in response to you asking 'How many shades of "two" are there?' here (as if there couldn't be any) rather than answering my question.

Yes, and the "shades" of "two", which in that sentence by your own insistence refers to counting, are precisely nil. 2, in this sense, is 2, just as I have said all along, not 2.1 or 1.9 or anything "near". This is the very point I made with my remark. You've then conflated the issue by then switching from counting to a continuous scale of measurement, amusingly having just mocked General Semanticist for making the self-same argument only a few posts earlier!

The phrase "refer to reality" is a huge stretch, obviously so regarding a deaf person.

This is rather like your earlier attempted rebuttal that if a word has no meaning to you, it therefore has no meaning. Look, just because a deaf person can't relate an abstract alphabetical letter to a physical sound, this doesn't mean that the alphabet doesn't refer to physical sound. Go to a primary school and see how they teach young children the alphabet, then get back to me. But I see you have backed off from your initial claim anyway with your below:

Letters "correlate to sounds" is far better.

Yes. Unfortunately your previous sweeping claim was that a letter of the alphabet "is completely symbolic, with no reference to anything beyond itself." Now you say it in fact "correlates to sounds."

You try to make out that the difference between "refer to" and "correlate to" is some kind of "huge stretch." This seems a retreat to mere pedantry. It's a minor blunder, why not just admit it?

[Jonathan]

Just a technical point, but there are no more "shades of blue" than there are "shades of two," a fact which is easily illustrated by referring to colors by their numerical wavelength values rather than by any individual's vague opinion of how large a portion of the visible spectrum he is willing to call "blue." Those who use color professionally (artists, photographers, scientists, etc.) recognize blue as having a wavelength of 475 nanometers. Cyan has a wavelength of 492 nm. A color with the wavelength of 475.1 nm is not "blue," but is a color between blue and cyan. Perhaps it's "ultramarine," or "evening shade" or "polar ice," but whatever one might choose to call it, it's no more "blue" than 2.1 is 2.

J

[Daniel Barnes]

Just a technical point, but there are no more "shades of blue" than there are "shades of two," a fact which is easily illustrated by referring to colors by their numerical wavelength values rather than by any individual's vague opinion of how large a portion of the visible spectrum he is willing to call "blue." Those who use color professionally (artists, photographers, scientists, etc.) recognize blue as having a wavelength of 475 nanometers. Cyan has a wavelength of 492 nm. A color with the wavelength of 475.1 nm is not "blue," but is a color between blue and cyan. Perhaps it's "ultramarine," or "evening shade" or "polar ice," but whatever one might choose to call it, it's no more "blue" than 2.1 is 2.

Fine, but in that sense almost nobody has blue eyes.

Added: Also note that now we have simply defined the meaning of the word as being a particular number (itself representing a physical wavelength). Note how in doing so, we have "emptied it out" of the multiple shades of meaning, demonstrating the precision/meaning tradeoff.

Edited April 19, 2008 by Daniel Barnes

[Alfonso Jones]

Just a technical point, but there are no more "shades of blue" than there are "shades of two," a fact which is easily illustrated by referring to colors by their numerical wavelength values rather than by any individual's vague opinion of how large a portion of the visible spectrum he is willing to call "blue." Those who use color professionally (artists, photographers, scientists, etc.) recognize blue as having a wavelength of 475 nanometers. Cyan has a wavelength of 492 nm. A color with the wavelength of 475.1 nm is not "blue," but is a color between blue and cyan. Perhaps it's "ultramarine," or "evening shade" or "polar ice," but whatever one might choose to call it, it's no more "blue" than 2.1 is 2.

J

Would you attempt to sustain an ordinary conversation like this? Unable to refer to anything having a specific color? No blue eyes, no green grass, etc.?

Alfonso

[Brant Gaede]

Just a technical point, but there are no more "shades of blue" than there are "shades of two," a fact which is easily illustrated by referring to colors by their numerical wavelength values rather than by any individual's vague opinion of how large a portion of the visible spectrum he is willing to call "blue." Those who use color professionally (artists, photographers, scientists, etc.) recognize blue as having a wavelength of 475 nanometers. Cyan has a wavelength of 492 nm. A color with the wavelength of 475.1 nm is not "blue," but is a color between blue and cyan. Perhaps it's "ultramarine," or "evening shade" or "polar ice," but whatever one might choose to call it, it's no more "blue" than 2.1 is 2

Then what are we looking at? What is the point of your technical point? There are, btw, "shades of two." Two girls, two boys, two guns, two cars, two people, two airplanes, two posters, etc. There are also three, four and many more!

Back to the drawing board! Sheesh!

--Brant

--Brant (two Brants?)

[Jonathan]

Fine, but in that sense almost nobody has blue eyes.

I agree. And almost nobody gets precisely two pounds of fish from their butcher despite calling it "two pounds."

Added: Also note that now we have simply defined the meaning of the word as being a particular number (itself representing a physical wavelength).

Right, but identifying "blue" as a wavelength number was only meant to illustrate the idea that accepting a fairly random range of hues that we are willing to call "blue" is no less arbitrary than accepting a range of 1.9 to 2.1 as being "two."

The same is true when using names of colors rather than their wavelength numbers. The precision we use depends on the context. We have all probably been told numerous times throughout our lives that mixing blue and yellow paint will give us green paint. I don't know how many teachers I had who insisted that I (and all of the other students in my classes) should be able to take some random hue within the teacher's arbitrary range of "blue," such as this

and mix it with yellow

and that we should end up with green.

Well, what we ended up with was this

...a slightly greenish tinted dark gray, because actual pure blue and yellow don't make green, they cancel each other out and result in a neutral tone. The two colors that actually make green are cyan and yellow.

+ =

If our teachers had told us that 1 plus "2" (which they defined as a number within the range of 0.75 to 1.3) equaled three, it would be pretty clear that the standard of precision that they were using was too sloppy for the context of teaching math.

Btw, one of my art teachers once gave me a failing grade on a color-wheel assignment because I didn't follow her instructions on how to make secondary colors from primaries. I used cyan instead of the blue that she had told the class to use, and magenta instead of red, and although I was the only student to end up with brilliant greens, oranges and violets instead of grays and browns, the moron gave me a failing grade because I "cheated." Heh.

Note how in doing so, we have "emptied it out" of the multiple shades of meaning, demonstrating the precision/meaning tradeoff.

Understood, but numbers can have shades of meaning if we choose to be as arbitrary or metaphorical in using them as we are in accepting ranges of hues or meanings which are "blue."

Would you attempt to sustain an ordinary conversation like this? Unable to refer to anything having a specific color? No blue eyes, no green grass, etc.?

It would depend on the context. All I'm saying is that if someone believes that there are "shades of blue" but there are no "shades of two," then they are using different standards of precision. It's a minor technical point and nothing to get too upset about.

Then what are we looking at? What is the point of your technical point?

The point is that choosing an arbitrary range of hues to call "blue" is no less arbitrary than accepting an arbitrary range of numerical values to call "two."

There are, btw, "shades of two."

I agree. Here are shades of two in shades of blue:

Edited April 19, 2008 by Jonathan

[tjohnson]

As I keep saying, we can only do exact analysis with numbers when doing mathematics. As Jonathan's (very nice!) example shows that in real life the lines of membership in a group are often blurred and so we lose the exactness of numbers. In pure mathematics, however, we can say for sure if the element is a member to be counted or not. In other words Aristotelian, 2-valued logic works in mathematics absolutely but only relatively well in natural language.

[merjet]

Unfortunately your previous sweeping claim was that a letter of the alphabet "is completely symbolic, with no reference to anything beyond itself." Now you say it in fact "correlates to sounds."

You try to make out that the difference between "refer to" and "correlate to" is some kind of "huge stretch." This seems a retreat to mere pedantry. It's a minor blunder, why not just admit it?

I made a minor blunder, but not the one Barnes alleges. I stick with my original claim. A letter has both visual and auditory forms. So, except in algebra and set theory, any reference is only to itself. To say like Barnes does that a visual form of a letter refers to its sound(s) makes about as much sense as saying one side of a dime refers to other side.

Edited April 20, 2008 by Merlin Jetton

[william.scherk]

Unfortunately your previous sweeping claim was that a letter of the alphabet "is completely symbolic, with no reference to anything beyond itself." Now you say it in fact "correlates to sounds."

[ . . . ]

To say like Barnes does that a visual form of a letter refers to its sound(s) makes about as much sense as saying one side of a dime refers to other side.

I am officially lost in this thread. I went off the rails around here:

But we already know that words can only be approximate by comparison to numbers – that there is a trade off between meaning and precision, in that numbers are precise because they are almost completely empty of meaning; whereas words are meaning-saturated, with a consequent loss of precision.

I disagree with said trade-off and that numbers are "almost completely empty of meaning."

1. I have blue eyes.

2. I have two eyes.

The 2nd has far less meaning than the 1st???

I think I went off the rails because the implicit comparison of "2" and "blue" is corrupted by the addition of "eyes." The referents of 2 are simple and precise. Precisely 2 versus precisely blue. 2 points to a place on the spectrum of number and blue points to a smear. One quantifies in a simple way, one in a fuzzy way. The difference is obvious.

Blue covers one part of the waterfront of wavelengths of light, but is also used in metaphor to colour all manner of things, from 'blue moods' to 'the blues' to 'blue states" and "blue laws" . . . numeral 2 merely cannot do this duty. 2 does not carry connotations of sadness, or liberalism or prudery. Blue is flexible as a word whereas 2 bears little weight but as a marker.

So I am kinda with Daniel on this point. Which may or may not have answered Merlin's complaints:

You have not explained how 'two' in 'I have two eyes' is "almost completely empty of meaning." Nor have you tried to explain how 'I have two eyes' is any less meaningful than 'I have blue eyes'. When are you going to stop evading this?

But back to the latest twist on the path of this thread:

If you want to make a relationship between numbers and words, I think equating a number with a letter of the alphabet would be more accurate than equating it with a word.

I disagree. A letter of the alphabet is completely symbolic, with no reference to anything beyond itself. Numbers often refer to reality.

Ah, this has been amended:

Letters of the alphabet do refer to reality; to the primary, physical sounds of language.

So, I agree with Merlin rather than Michael and Daniel that comparing numbers and words is best accomplished by comparing numbers to words, rather than to the constituents of words, letters. Now remaining is:

A letter has both visual and auditory forms. So, except in algebra and set theory, any reference is only to itself. To say like Barnes does that a visual form of a letter refers to its sound(s) makes about as much sense as saying one side of a dime refers to other side.

I am off track again! What is at issue? Yes to 'letters of the alphabet do refer to . . . sound' but no to 'visual form of a letter refers to its sound'?

I confessed to being stupefied by this kind of discussion.

[Daniel Barnes]

I think I went off the rails because the implicit comparison of "2" and "blue" is corrupted by the addition of "eyes." The referents of 2 are simple and precise. Precisely 2 versus precisely blue. 2 points to a place on the spectrum of number and blue points to a smear. One quantifies in a simple way, one in a fuzzy way. The difference is obvious.

Blue covers one part of the waterfront of wavelengths of light, but is also used in metaphor to colour all manner of things, from 'blue moods' to 'the blues' to 'blue states" and "blue laws" . . . numeral 2 merely cannot do this duty. 2 does not carry connotations of sadness, or liberalism or prudery. Blue is flexible as a word whereas 2 bears little weight but as a marker.

You got it...;-)

I am off track again! What is at issue? Yes to 'letters of the alphabet do refer to . . . sound' but no to 'visual form of a letter refers to its sound'?

I confessed to being stupefied by this kind of discussion.

Yawn. Me too. It's one of those obtuse little alleyways that threads often drift into.

To summarise the topic at hand: do Merlin's accusations about this important Popper essay "Two Kinds of Definition" have any weight? Is it really as chock-a-block with "howlers" as he claims? I argue no. I argue that it is in fact Merlin's comments which are half-baked. He's an extremely smart guy, with much to contribute on a variety of subjects, but on this one he's completely struck out. I don't think he makes a single good point. Nevertheless Merlin's sticking to his guns - no matter how much they're misfiring - so that's fine for now. I've replied in as much detail as I think I can, at this point it's up to the interested reader to decide.