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Daniel Barnes

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And the many howlers I find in "Two Kinds of Definition" are so loud they could be heard in Fenway Park right now.

Hi Merlin,

I apologise for a tardy reply to this post but I have been otherwise engaged. While I thank you for your critique of Popper's classic essay "Two Kinds of Definition"(scroll down), I consider it to be clearly mistaken. These mistakes I think are mostly the result of what appears to be a hasty reading and quotation on your part. That’s ok, you didn’t claim to be doing much more. But despite these mistakes I am encouraged by later strong underlying points of agreement between our two positions.

While I will address your criticisms point by point, one general issue seems to be your view of Popper’s incompetence as a philosopher, as you suggest this essay (and his other work) is chockablock with “howlers.” As such, I will try to answer with Popper’s own words and textual references as much as possible, as surely this is the best defence against such an implication. As “Two Kinds of Definition” is a later condensation of Popper’s earlier essay from the OSE (which I seem to recall, perhaps wrongly, you got from the library to better examine) I will use the supporting notes from the OSE Chapter to clarify Popper’s points where necessary. (There are also explanatory notes accompanying “Two Kinds of Definition” in “Popper Selections” but they seem basically the same as the OSE notes. Despite footnote numbering in the online version there are no footnotes)

I apologise for the length of this response, but it is always harder to defend an accusation than to make one, so this is inevitable. I've made it a separate thread, as the original one was getting long enough.

Now, to your first point:

Knowledge, or science, according to Aristotle, may be of two kinds - either demonstrative or intuitive.
This overlooks or dismisses perceptual knowledge. The essentialist method of Aristotle, as Popper describes it, is simply words. Yet when Aristotle wrote anything, his highest authority was reality. Essences pertained to the nature of particulars found by observation

(perception).

We might as well deal with this thoroughly, as it is the basis for your next two points.

First of all, Popper does address the issue of the role of perception in the extensive notes to the original essay. Popper cites George Grote:

“’Aristotle had inherited from Plato his doctrine of an infallible Nous or Intellect, enjoying complete immunity from error.’ (Grote, “Aristotle” 2nd ed, p260). Grote continues to emphasise that, as opposed to Plato, Aristotle does not despise observational experience, but rather assigns to his Nous (i.e. intellectual intuition) ‘a position as terminus and correlate to the process of Induction.’ This is so; but observational experience has apparently only the function of priming and developing our intellectual intuition for its task, the intuition of the universal essence; and indeed, nobody has ever explained how definitions, which are beyond error, can be reached by induction.” (Popper, note 32 Chapter 11, OSE)

It must be said that the topic of Aristotle’s nous and its relation to essentia is a vexed and complex one that will not be solved in this reply (Popper, who used his own translations from the Greek as well as sources, notes the wide divergence between some of his own sources on various points). However we can see from the above that we are very far from a “howler”; Popper is on perfectly reasonable ground with his argument.

Secondly, your claim that “when Aristotle wrote anything, his highest authority was reality” seems itself to be quite a stretch. For if we possess an

infallible nous, how could “reality” be a higher authority than infallibility? Do you argue, contra such common views, that Aristotle thought nous to be fallible? (You are welcome to of course - it is true that some modern intepretations of "nous" look at it differently - but once again we are in the delicate region of scholarly interpretation, not the World Series-sized howlers you suggest). Further, it is hard to deny the overall direction of Aristotle’s thought is away from reality towards pure disembodiment, untainted by real images. After all he regarded the highest of the level of thought as “thinking about thinking”, with even God himself described as merely “thinking thinking about thinking”.

So when you suggest Aristotle appeals to “perceptions” and "reality" as the “ultimate authority” in his thought, you’re skirting some central problems with this yourself.

Moving on:

But the most difficult question is how we can get hold of definitions or basic premisses, and make sure that they are correct - that we have not erred, not grasped the wrong essence. Although Aristotle is not very clear on this point, there can be little doubt that, in the main, he again follows Plato.
Play dough! Forms to Aristotle and Plato were worlds apart.

Now this you have simply misread. For Popper is not even discussing the differences between Aristotle and Plato’s version of “Forms”, but the doctrine of the intellectual intuition thereof. This is what Aristotle "follows" Plato in. This is clear merely from reading the rest of the passage from which you have taken this quote. As Popper makes some other interesting points in passing I will quote at length:

Popper:“But the most difficult question is how we can get hold of definitions or basic premisses, and make sure that they are correct - that we have not erred, not grasped the wrong essence. Although Aristotle is not very clear on this point, there can be little doubt that, in the main, he again follows Plato. Plato taught that we can grasp the Ideas with the help of some kind of unerring intellectual intuition; that is to say, we visualise or look at them with our 'mental eye', a process which he conceived as analogous to seeing, but dependent purely upon our intellect, and excluding any element that depends upon our senses. Aristotle's view is less radical and less inspired than Plato's, but in the end it amounts to the same. For although he teaches that we arrive at the definition only after we have made many observations, he admits that sense experience does not in itself grasp the universal essence, and that it cannot, therefore, fully determine a definition. Eventually he simply postulates that we possess an intellectual intuition, a mental or intellectual faculty which enables us unerringly to grasp the essences of things, and to know them. And he further assumes that if we know an essence intuitively, we must be capable of describing it and therefore of defining it. (His arguments in the Posterior Analytics in favour of this theory are surprisingly weak. They consist merely in pointing out that our knowledge of the basic premisses cannot be demonstrative, since this would lead to an infinite regress, and that the basic premisses must be at least as true and as certain as the conclusions based upon them. 'It follows from this', he writes, 'that there cannot be demonstrative knowledge of the primary premisses; and since nothing but intellectual intuition can be more true than demonstrative knowledge, it follows that it must be intellectual intuition that grasps the basic premisses.' In the De Anima, and in the theological part of the Metaphysics, we find more of an argument; for here we have a theory of intellectual intuition - that it comes into contact with its object, the essence, and that it even becomes one with its object. 'Actual knowledge is identical with its object.')”

So that should clear that up. However, if you are interested Popper’s discussion of the differences between Aristotlean essences and Plationic “forms” see OSE Chapter 11 p8, Routledge edition.

While we may say that the essentialist interpretation reads a definition 'normally', that is to say, from the left to the right, we can say that a definition, as it is normally used in modern science, must be read back to front, or from the right to the left. . . The scientific use of definitions, characterized by the approach 'from the right to the left', may be called its nominalist interpretation, as opposed to its Aristotelian or essentialist interpretation.
Mere verbalism; a distinction without a difference. Yes, there are two kinds of definitions, but Popper misses the boat. The second kind is ostensive.

Now, I contend that it’s you who has missed the boat on this, possibly through again reading the text too hastily and missing a key point. Once again, to demonstrate this all we need do is read the text immediately following what you’ve quoted :

Popper:“While we may say that the essentialist interpretation reads a definition 'normally', that is to say, from the left to the right, we can say that a

definition, as it is normally used in modern science, must be read back to front, or from the right to the left;…”

We then add the part you’ve omitted:

“… for it starts with the defining formula, and asks for a short label for it. Thus the scientific view of the definition 'A puppy is a young dog' would be that it is an answer to the question 'What shall we call a young dog?' rather than an answer to the question 'What is a puppy?'”

We can see the difference quite clearly. To wit, the essentialist or Aristotelian view sees a definition as the answer to the question “what is a puppy?” In contrast, the scientific nominalist view regards a definition as merely the answer to the question “what shall we call a young dog?”

For your assertion that the difference is merely “verbal” to succeed, you would have to argue that the two questions are in fact the same, dressed up in different language. Of course they are not. The difference could not be more marked. As Popper writes:

“There could hardly be a greater contrast than that between this view of the part played by definitions, and Aristotle's view. For Aristotle's essentialist

definitions are the principles from which all our knowledge is derived; they thus contain all our knowledge; and they serve to substitute a long formula

for a short one. As opposed to this, the scientific or nominalist definitions do not contain any knowledge whatever, not even any 'opinion'; they do nothing but introduce new arbitrary shorthand labels; they cut a long story short.”

In modern science, only nominalist definitions occur, that is to say, shorthand symbols or labels are introduced in order to cut a long story short. And we can at once see from this that definitions do not play any very important part in science.
Popperycock. The symbols or labels represent the referents of ostensive definitions. They are extremely important, otherwise we don't know what we are talking about.

Patently false. In studying the effect of wind on a sand dune, to use Popper’s example, no one worries (or argues) over whether they have the “true” or “false” definitions of “wind”, “sand dune”, “effect” etc. So clearly they are not in fact “extremely important”. We know roughly, in shorthand, what we are talking about, and that is more than enough.

In practice, these labels are of the greatest usefulness.
A blatant contradiction to the previous quote. How can they not play an important part and be of the greatest usefulness? .

But there is no “blatant contradiction” on Popper’s part. For, once again, if we look at the very next passage to the one you cite, we find exactly what Popper means by “of the greatest usefulness”

Popper:”In practice, these labels are of the greatest usefulness. In order to see this, we only need to consider the extreme difficulties that would arise if a bacteriologist, whenever he spoke of a certain strain of bacteria, had to repeat its whole description (including the methods of dyeing, etc., by

which it is distinguished from a number of similar species). And we may also understand, by a similar consideration, why it has so often been forgotten, even by scientists, that scientific definitions must be read 'from the right to the left', as explained above.”

So definitions do not play an important part, because we only need rough meanings of “wind” “sand dune” etc in order to grow our knowledge of the effects of the former on the latter; further, nominalist definitions are also of the greatest usefulness because we do not need to cumbersomely repeat whole descriptions. There is not even a slight contradiction, let alone a “blatant” one, between these two statements.

For the nominalist position there is no difficulty which corresponds to the infinite regression. As we have seen, science does not use definitions in order to determine the meaning of its terms, but only in order to introduce handy shorthand labels. And it does not depend on

definitions; all definitions can be omitted without loss to the information imparted. It follows from this that in science, all the terms that are really needed must be undefined terms.

The so-called undefined terms are symbols or labels introduced in ostensive style or by example or refer to things already commonly understood by people in the target audience, e.g. distance, minute, weight, etc. The purpose of a definition is to specify what one is talking about. That can be done by either verbally (verbal definitions) or non-verbally (giving the symbol or label and pointing, or depending on the audience knowing what the referents of the symbol or label are). .

Now in this paragraph it seems you are basically agreeing with Popper. Definitions are not required, and undefined terms are quite sufficient, as you quite correctly suggest because things such as “distance”, “minute”, “weight” etc are “commonly understood.” No further elaboration or precision is needed, nothing need be debated as to the “truth” or “falsity” of such. (Which is just as well, as of course disputes over meaning are not resolvable other than by common agreement)

Of course this stance contrasts most strongly with Rand’s position, where all of man’s knowledge rests on the "truth" or "falsity" of definitions, and where “common understandings” should be rejected as she saw fit. As an example, we might take the term “selfishness”, where she denied the common understanding of the term, and insisted that the “true” or “valid” definition was hers alone.

Hence I suspect there may be an underlying agreement between your view and Popper’s that may become clearer as we examine the situation.

And we continue to cling to this creed in spite of the unquestionable fact that philosophy, which for twenty centuries has worried

about the meaning of its terms, is not only full of verbalism but also appallingly vague and ambiguous, while a science like physics which worries hardly at all about terms and their meaning, but about facts instead, has achieved great precision. This, surely, should be taken as indicating that, under Aristotelian influence, the importance of the meaning of terms has been grossly exaggerated.

The success of physics has relied much on quantification, via numbers and formulas. These are the most precise symbols we have. Philosophy relies on words, rarely quantification (excepting 'all', 'some', and 'none'). So it can't attain the kind of precision that numbers and formulas allow. Also in philosophy key terms used often have very wide application and the different meanings people have for them can vary widely. In physics the opposite is true. (The application may be wide in a spatial sense or cover a wide range of phenomena, but it doesn't pertain to nearly as many aspects of reality and experience as philosophy does.)

Here I think we have at least one point of continuing agreement, which is also promising: the difference in precision between words and numbers. (I recall you and I agreeing strongly on this point offline a few years back). The two are simply poles apart.

Now, it’s clear Rand does not realise this. In fact in the ITOE she makes comparisons with the precision possible in mathematical formulations and the formulation of concepts, referring to concept formation as being the “algebra” of cognition, and suggests that any “approximation” in the process will result in “all hell” breaking loose.

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. (This is why we need dictionaries for words, but not for numbers)

So Rand’s point is basically fallacious, which I think you and I agree on. Further the natural consequence of accepting the above leads to Popper’s very point:

Popper: “We are always conscious that our terms are a little vague (since we have learnt to use them only in practical applications) and we reach precision not by reducing their penumbra of vagueness, but rather by keeping well within it, by carefully phrasing our sentences in such a way that the possible shades of meaning of our terms do not matter.”

Edit: I think another factor is that physics has dealt with simpler things, whose behavior is easier to describe and far more uniform, than what philosophy deals with. To illustrate compare the complexity and uniformity of the motions of classical physical objects to that of human behavior .

Well it is undoubtedly true that physics deals with simpler things than human behaviour; thus all the more reason, when discussing such complexities, to avoid needless terminological fiddle-faddle. Popper supplies a crucial indication as to how to do this: by lifting our energies away from mere verbalist arguments over terms, and focusing them on plans, proposals, theories etc.

To sum up, it seems that there are no “howlers” to speak of in Popper’s essay, and that other than some hasty misreadings, which I hope I have cleared up, your views appear to have some considerable underlying agreements with mine that you may not have fully considered. As to which Emperor is wearing clothes, it seems Popper at least has his nighshirt and longjohns on, for which we should be grateful. As for Rand, I think she may need some new tailors…;-) I’ll leave Popper with the last word.

The view that the precision of science and of scientific language depends upon the precision of its terms is certainly very plausible, but it is none the less, I believe, a mere prejudice.
Edited by Daniel Barnes
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Knowledge, or science, according to Aristotle, may be of two kinds - either demonstrative or intuitive.

I said this overlooks or dismisses perceptual knowledge. You replied that Popper addressed perceptual knowledge in footnotes. So what? Are such footnotes to the part you call "Two Kinds of Definition" or a different part of OSE? Regardless, if Popper thought perceptual knowledge was important enough to Aristotle, then why did he exclude it from the main text? To make a straw man?

You assert that Aristotle held nous to be infallible. Prove it by citing exactly where Aristotle himself said so. One can find second-hand (or higher) sources claiming all kinds of stuff. I am not going to spend numerous hours to find out what all Aristotle said about nous, especially when he used the term often in different contexts and books.

Play dough! Forms to Aristotle and Plato were worlds apart.
Now this you have simply misread. For Popper is not even discussing the differences between Aristotle and Plato’s version of “Forms”, but the doctrine of the intellectual intuition thereof.

So what? Do you really believe that their different meanings of Form is immaterial? Do you really believe that intellectual intuition is something confined to mystical ends? Scientists never use intellectual intuition when forming hypotheses? It doesn't surprise me that Popper would suggest so, in order to make a straw man.

While we may say that the essentialist interpretation reads a definition 'normally', that is to say, from the left to the right, we can say that a definition, as it is normally used in modern science, must be read back to front, or from the right to the left. . . The scientific use of definitions, characterized by the approach 'from the right to the left', may be called its nominalist interpretation, as opposed to its Aristotelian or essentialist interpretation.
Mere verbalism; a distinction without a difference. Yes, there are two kinds of definitions, but Popper misses the boat. The second kind is ostensive.

You reply with an example of two questions about a puppy. You missed my point. With "mere verbalism" I didn't mean one can't make such a distinction. My point was that (1) the distinction is trivial and (2) it does not reflect a dividing line between modern science and philosophy. Also, you still haven't shown that Popper didn't "miss the boat" on ostensive definitions.

Popperycock. The symbols or labels represent the referents of ostensive definitions. They are extremely important, otherwise we don't know what we are talking about.
Patently false. In studying the effect of wind on a sand dune, to use Popper’s example, no one worries (or argues) over whether they have the “true” or “false” definitions of “wind”, “sand dune”, “effect” etc. So clearly they are not in fact “extremely important”. We know roughly, in shorthand, what we are talking about, and that is more than enough.

Patently false?? How does the rest of what you say here differ in substance from what I said? Note I said "referents of ostensive definitions", not "essentialist definitions".

But there is no “blatant contradiction” on Popper’s part. For, once again, if we look at the very next passage to the one you cite, we find exactly what Popper means by “of the greatest usefulness”.

What Popper meant by “of the greatest usefulness” is beside the point. He said both (1) these labels "do not play any very important part in science" and (2) these labels "are of the greatest usefulness". One could dissolve the inconsistency by holding that in the following:

In modern science, only nominalist definitions occur, that is to say, shorthand symbols or labels are introduced in order to cut a long story short. And we can at once see from this that definitions do not play any very important part in science.

the 2nd occurrence of "definitions" meant "essentialist definitions". However, that is not what Popper wrote.

Of course this stance contrasts most strongly with Rand’s position, where all of man’s knowledge rests on the truth or falsity of such, and where “common understandings” should be rejected as she saw fit. As an example, we might take the term “selfishness”, where she denied the common understanding of the term, and insisted that the “true” or “valid” definition was hers alone.

Fine, but my post was not to defend Rand's said position. Indeed, I believe that I've expressed my disagreement with it on this forum.

The success of physics has relied much on quantification, via numbers and formulas. These are the most precise symbols we have. Philosophy relies on words, rarely quantification (excepting 'all', 'some', and 'none'). So it can't attain the kind of precision that numbers and formulas allow. Also in philosophy key terms used often have very wide application and the different meanings people have for them can vary widely. In physics the opposite is true. (The application may be wide in a spatial sense or cover a wide range of phenomena, but it doesn't pertain to nearly as many aspects of reality and experience as philosophy does.)
Here I think we have at least one point of continuing agreement, which is also promising: the difference in precision between words and numbers. (I recall you and I agreeing strongly on this point offline a few years back). The two are simply poles apart.

Fine, we agree. But my point remains that Popper said nothing about the success of physics relying on quantification, via numbers and formulas. To the contrary he even says:

The view that the precision of science and of scientific language depends upon the precision of its terms is certainly very plausible, but it is none the less, I believe, a mere prejudice.

In summary and in my view the howlers I claimed still stand.

Edit: The following has little or nothing to do with Popper and definitions.

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???

Edited by Merlin Jetton
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  • 2 months later...
So what? Are such footnotes to the part you call "Two Kinds of Definition" ?

Yes.

Regardless, if Popper thought perceptual knowledge was important enough to Aristotle, then why did he exclude it from the main text? To make a straw man?

Oh, don't be absurd. The OSE must be one of the most extensively footnoted books ever, with some 90 pages of fine print for Vol 2 alone.. Some of Popper's own important arguments are consigned there, where they are peripheral to the thrust of the chapter, as this point is. Recall that the title of the essay is "Two Kinds of Definition", not "Two Kinds of Knowledge." It's about the Aristotelian theory of definition.

You assert that Aristotle held nous to be infallible. Prove it by citing exactly where Aristotle himself said so.

Please stick to the point at issue, which was your allegation that Popper's essay is full of "howlers." I've demonstrated that Popper's assertion (not mine) has perfectly reasonable scholarly support, such as Grote, thus is not a "howler." You're going off on a tangent.

So what? Do you really believe that their different meanings of Form is immaterial? Do you really believe that intellectual intuition is something confined to mystical ends? Scientists never use intellectual intuition when forming hypotheses? It doesn't surprise me that Popper would suggest so, in order to make a straw man.

Firstly, Popper did not, as you wrongly claimed, say that Plato and Arisotle's notion of the Forms was the same. He said that Aristotle follows Plato "in the main" in the doctrine that the Forms/Essences are grasped by intellectual intuition. I've already quoted the passage in question at exhaustive length here. I do not know how I can express this obvious point any more clearly. If you have evidence that this is some kind of "howler", rather than an absolutely commonplace interpretation, please present it.

Secondly, you claim to be familiar with Popper's work. Yet you say that Popper, in order to "make a straw man", would suggest that "scientists never use intellectual intuition when forming hypotheses." This is frankly incredible. Popper has always embraced intuition (along with imagination, among other things) as a potential source of hypotheses. (For example, I refer you to your copy of Objective Knowledge p134, where you will find Popper saying "Everything is welcome as a source of inspiration,including intuition...") So there's a howler and a straw man here alright - but unfortunately they're both yours.

You reply with an example of two questions about a puppy. You missed my point. With "mere verbalism" I didn't mean one can't make such a distinction. My point was that (1) the distinction is trivial and (2) it does not reflect a dividing line between modern science and philosophy.

I admit the difference between "what is a puppy" and "what shall we call a puppy" appears trivial. But as Popper argues in his essay, I think correctly, the former conceals some serious logical errors that the latter entirely escapes; therefore the more philosophy dwells on the former, and science the latter, so much the worse for philosophy and so much the better for science. Of course, if you consider such logical problems "trivial" that is up to you.

Also, you still haven't shown that Popper didn't "miss the boat" on ostensive definitions.

You may simply use the "puppy" example as follows: I say "puppy" and point to a young dog; you say "puppy" and point to an arrogant young man. Who then is pointing to "true" ostensive definition, and how do you come to that conclusion?

Patently false?? How does the rest of what you say here differ in substance from what I said? Note I said "referents of ostensive definitions", not "essentialist definitions".

So let me get this straight. Do you agree with Rand's (and/or Aristotle's) essentialist theory of definitions or not?

What Popper meant by “of the greatest usefulness” is beside the point. He said both (1) these labels "do not play any very important part in science" and (2) these labels "are of the greatest usefulness". One could dissolve the inconsistency by holding that in the following:
In modern science, only nominalist definitions occur, that is to say, shorthand symbols or labels are introduced in order to cut a long story short. And we can at once see from this that definitions do not play any very important part in science.

the 2nd occurrence of "definitions" meant "essentialist definitions". However, that is not what Popper wrote.

This seems to be a very trivial criticism. Surely the overall thrust of Popper's piece is perfectly clear?

Fine, but my post was not to defend Rand's said position. Indeed, I believe that I've expressed my disagreement with it on this forum.

Well this is news to me. Your ire has been, AFAICS, entirely directed at Popper. Where have you disagreed with Rand's doctrine of definitions? That would be most useful.

Fine, we agree. But my point remains that Popper said nothing about the success of physics relying on quantification, via numbers and formulas.

Well you know this essay is not infinite in scope. It's a criticism of the Arisotelian "essentialist" methodology of definition. If you want Popper on the importance of numbers and formulas and the success of physics, there's plenty - try "Conjectures and Refutations", for example the essay "Why is Logic Applicable to Reality?".

]In summary and in my view the howlers I claimed still stand.

In my view they certainly do not. But we will have to agree to disagree.

Edit: The following has little or nothing to do with Popper and definitions.
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???

How many shades of "two" are there?

- D

Edited by Daniel Barnes
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  • 1 month later...

Actually "two" can have three meanings -- a count, a measure, and ordinally.

In response to Barnes' question, "two" can have several shades of meaning. Suppose I go to the fish market wanting two pounds of fish, which comes in large pieces. The seller may offer me and I may accept between, say, 1.9 and 2.1 pounds.

By the way, Barnes' question was evasion, after I challenged him on his assertion that numbers are "almost completely empty of meaning."

Edited by Merlin Jetton
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Numbers were created by man in order to express exact, symmetric and asymmetric relations. Although we find symmetric and asymmetric relations in nature we do not find exact relations - these we only have in mathematics. Even if Merlin wanted exactly 2 pounds of fish this is, in principle, impossible - it may say 2 on one scale but not on another. This is why we have policies in place like a property description by a Land Surveyor which the court accepts as a description not because it is exact, but because at some point we have to accept the measurements and call them final.

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general semanticist,

Are you trying to tell me I don't have exactly five toes on each of my feet?

But what if one toe was defective in some way, does it still count as a toe? Counting depends on being able to put objects into categories without question and we all know the world is not always black and white. If there is no dispute about categories then we can agree on the count so there is still some condition to this relation. In mathematics set theory there is no possibility of dispute as when an element may be in a set according to one person but not by another. So even though counting works most of the time in establishing exact relations it doesn't always.

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Although we find symmetric and asymmetric relations in nature we do not find exact relations - these we only have in mathematics.
general semanticist,

Are you trying to tell me I don't have exactly five toes on each of my feet?

So even though counting works most of the time in establishing exact relations it doesn't always.

Sounds contradictory.

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So even though counting works most of the time in establishing exact relations it doesn't always.

Sounds contradictory.

Well if you can't always agree exactly how many elements are in a set then what do you call that? The counting part is exact, the classifying part isn't.

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I am aware of your vew that counting and ordering in a hierarchy according to a standard is not measurement. After mulling it over, I find them to be types of measurements.

I will stay with Rand's view.

You are free to use terms as vaguely as you wish.

But here is an experiment. Find a child who can correctly say that a pencil is bigger than a match, but the child does not know how to count or read. Ask that child how many inches long the pencil is.

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Merlin,

Why should I do that? I don't understand the point.

How many types of measurement does your concept of measurement allow, anyway? I personally don't think saying that counting or ordinal relationahisp are kinds of measurement is a vague statement. On the contrary, they separate measurement into smaller categories of types of measurement.

But if this is vague, it is vague in the same manner Rand was vague. So at least I am in good company. :)

Michael

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How many types of measurement does your concept of measurement allow, anyway? I personally don't think saying that counting or ordinal relationahisp are kinds of measurement is a vague statement. On the contrary, they separate measurement into smaller categories of types of measurement.

There are many kinds of measurements in my concept of measurement. Ones of length, weight, volume, temperature, velocity, population per square mile, etc. Every one of them is or embeds a numerical value one obtains using a physical, hand-controlled gauge -- a tape measure, thermometer, timer, etc. The resulting numerical values are real numbers. Counting does not use such a gauge and the resulting numerical values are integers only (zero and positive).

Calling anything that uses numbers "measurement" is like calling cars, trikes, tractors, tanks and wagons the same thing because they have wheels. There is a better and more common term to mean what you do by "measurement" in the wider sense. It is "quantification". Indeed, it doesn't even require using numbers. I leave you the exercise of thinking of examples.

But if this is vague, it is vague in the same manner Rand was vague. So at least I am in good company. :)

That's nothing to preen about when it comes to math. :)

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  • 2 weeks later...
In response to Barnes' question, "two" can have several shades of meaning. Suppose I go to the fish market wanting two pounds of fish, which comes in large pieces. The seller may offer me and I may accept between, say, 1.9 and 2.1 pounds.

And he calls my reply "an evasion"!....;-)

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And he calls my reply "an evasion"!....;-)

At least I tried to answer your question. You have yet to explain how numbers are "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'.

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And he calls my reply "an evasion"!....;-)

At least I tried to answer your question. You have yet to explain how numbers are "almost completely empty of meaning."

Well, I believe I have already explained this to you in a personal email some time ago. However, I'm happy to repeat my argument.

To demonstrate the difference in meaning content between numbers and words, let me take a number you have (probably!) never heard of before:

17,383,838,940,394.26353879986

Now, if you know the basic rules of how our number system operates you will know what this number means; you will be able to infer it simply from your previous experience. Thus its content is so slight as to be perfectly comprehensible via mere inference. You do not need to know any more to use it perfectly successfully in an equation or similarly.

You will also note that this number is perfectly precise. It means no more or no less than 17,383,838,940,394.2635387998! (Your previous argument, where you attempt to argue that 2 can also mean 1.9 or even 2.1 just because you personally might "accept" it I think must fail; for why not just say then 2 can also mean 3? Or 137 or whatever, just because you might "accept" it? For here you have conflated the problem of meaning with the problem of the application of abstract systems to physical reality. I note with some irony that only a few posts ago you criticize General Semanticist for making the exact same argument you are now making to me...;-))

Continuing on, now let us take a word you've (probably!) never heard of before:

Epitrachelion

Now, even with a good knowledge of language and its rules, I would wager it very difficult to infer what the meaning of this word is from your past experience with words (it is in fact "the stole of an Orthodox priest or bishop"). This is because it has more meaningful content. Unlike the number, you would struggle to use it meaningfully without the aid of a dictionary. Similarly, it is also less precise than the number, in that it could mean different stole designs, colours sizes etc. Whereas 17,383,838,940,394.2635387998 means 17,383,838,940,394.2635387998, no more no less. So we see a tradeoff of meaning and precision between words and numbers.

In simple terms, this is why you need a dictionaries to find the meanings of words, but you don't need dictionaries to find the meanings of numbers!

Hopefully that answers your question.

Edited by Daniel Barnes
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In simple terms, this is why you need a dictionaries to find the meanings of words, but you don't need dictionaries to find the meanings of numbers!

Daniel,

Actually you do need a dictionary if you use numbers for coding computer software.

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.

Michael

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Your previous argument, where you attempt to argue that 2 can also mean 1.9 or even 2.1 just because you personally might "accept" it I think must fail; for why not just say then 2 can also mean 3? Or 137 or whatever, just because you might "accept" it?

Your counter is what fails. If I want near 2 pounds of fish, I would not accept 3 pounds or 137 pounds.

For here you have conflated the problem of meaning with the problem of the application of abstract systems to physical reality. I note with some irony that only a few posts ago you criticize General Semanticist for making the exact same argument you are now making to me...;-))

Not at all. However, 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.

Continuing on, now let us take a word you've (probably!) never heard of before:

Epitrachelion

Now, even with a good knowledge of language and its rules, I would wager it very difficult to infer what the meaning of this word is from your past experience with words (it is in fact "the stole of an Orthodox priest or bishop"). This is because it has more meaningful content.

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

Hopefully that answers your question.

No. You gave one number that you regard as "almost completely empty of meaning." 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?

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.

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Merlin, I think you are evading yourself. Counting is nothing more than establishing a 1-to-1 correspondence between a set and the natural numbers. This process is capable of exact treatment, but, the process of establishing membership in the set to be "counted" is by no means exact. Your example of toes is a trivial one but what about some more complex ones, like how many votes did Bush get in Florida in the last election? Or how many "black" people are there in your neighborhood? The difficulties and compromises we have to deal with arise from the classification process, not the counting process.

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Merlin, I think you are evading yourself. Counting is nothing more than establishing a 1-to-1 correspondence between a set and the natural numbers. This process is capable of exact treatment, but, the process of establishing membership in the set to be "counted" is by no means exact. Your example of toes is a trivial one but what about some more complex ones, like how many votes did Bush get in Florida in the last election? Or how many "black" people are there in your neighborhood? The difficulties and compromises we have to deal with arise from the classification process, not the counting process.

What exactly is it you believe I'm evading? You say nothing here (after the first sentence) I disagree with. On the other hand here you said "Although we find symmetric and asymmetric relations in nature we do not find exact relations - these we only have in mathematics." I say the (exactly) five toes on each of my feet are in nature.

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What exactly is it you believe I'm evading? You say nothing here (after the first sentence) I disagree with. On the other hand here you said "Although we find symmetric and asymmetric relations in nature we do not find exact relations - these we only have in mathematics." I say the (exactly) five toes on each of my feet are in nature.

Ah, I see, it's back to metaphysics. 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.

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