The meaning of words

Nate: “The whole problem was that some of the professors in the discussion considered exact measurement to be their standard of truth (following intrincisism or Platonism), when in reality this standard is impossible to achieve.”

But she still insists on using terms such as “absolutely precise”. Yes, the standard is impossible to achieve in practice, but it does exist in the abstract. 1.1 mm is precise as an abstract standard. It’s exactly 1.1, no more, no less, as are 1.2, 1.3 and so on. But when it comes to measuring real-world objects, in practice, one cannot achieve this sort of precision, because nothing is precisely 1.1 mm.

Similarly, for “between 1mm and 2mm”. In the abstract this is a specific range, but real world measurements will conform more or less to that range rather than precisely.

Brendan

Post 61

Sunday, May 22, 2005 - 9:47pm

Hi Daniel,

Thing is, Nate: you haven't got that "something"!. And you can't get it either, other than roughly or approximately. Neither could Ayn Rand or Professor E give it to you - they admit they can only give you something between 0.9 and 1.1 cm (or whatever magnitude you like), and even that attempted solution turned out to be mired in the same difficulty.

Okay, so basically you're objecting to the fact that one cannot make a perfectly precise copy of a standard unit of measurement. That's fair enough-- you're right, since there's no way to judge whether something is exactly the same length as something else (it would require omniscience). However, the means by which this is done is ordinally-- just line the two up and snip the string right along the edge of the ruler. The only thing that I can think of that would be bothering you here is that there may be some extremely small error in length in this copying, but the difference is negligible compared to the measurement being performed.

However, if you feel as though the word "negligible" is too vague, then you can take your copied unit and compare 1,000,000 of them with a kilometer, and then judge your error by multiplication. If the difference is 12 copied units, you've done a very good job, and can be assured that the error based on your centimeter is .000012% of the actual centimeter unit (plus or minus .000001% exactly, of course, since we are counting units here). So long as your measurements do not allow the absolute error to rise past some level of what is appropriate for your particular kind of measurement, you're okay. This is, of course, essentially what people do when they make rulers and other such copies.

So while you can *approach* a centimetre with better and better methods (like measuring light in a vacuum) you cannot actually get to it; and even if you did luckily hit upon it, *you would have no way of knowing you had* (...think about it! What would you physically require to know that you had...?)

You speak here of approaching the length of a "true" centimeter as though it could be done independently of any original unit. What exactly are these scientists comparing these light waves to in order to judge them the length of a meter? Their inherent notion of a meter?

The reason that scientists needed to refer to light in a vacuum to describe the meter is that they had to update their old version of the meter for the microscopic realms that they were investigating; they wanted their macroscopic unit and their microscopic unit to be related, which is the point of measurement, after all. Hence, they picked a certain number of wavelengths of light which measured their old version of the meter and defined that to be the new standard measurement of the meter.

We improve our standards as we add to our knowledge and our abilities, and we do it in a way so that it reduces to our old standards so as not to relate these new units to the old ones at the perceptual level. There is no "perfect centimeter" lying on the altar in the Temple of Science somewhere.

But all is not lost! I would like to contrast this real physical situation for a moment with your "concept" of a centimetre, which is the abstract product of a mental process. Tell me: is that conceptual centimetre as imprecise as the physical object it represents?

Well, a concept is not material, and so it doesn't have extension. As such, even if I could measure things "exactly" (which is impossible anyway), concepts cannot be measured in this way.

If not - if indeed the "concept" centimetre *is* exactly a centimetre, no more and no less, with not even the slightest error - then I think you and I might agree on a fundamental issue, which is always a promising development in a debate!

I appreciate your attempt to solve the problem of the "imperfect centimeter," but this doesn't really do the trick. This is because you can't measure anything with an "ideal centimeter", since such a thing isn't material-- you can't pluck the idea of a centimeter out of your head and measure a block of wood with it. Your unit has to be material-- there's no way around that.

If, however, the concept centimetre *is* as imprecise as the physical situation - if Rand and Professor E would say you could only get between 0.9 and 1.1cm "conceptually" as well as physically - then I'd have to ask:what would you be aiming for in the first place?

The original unit created, of course. Even if there is some very small error in making copies of centimeters, one can still come close enough to make measurements qua centimeter, as mentioned above.

What's more, we appear to have an instance of the stolen concept here. By saying that a unit centimeter measures 1.0cm (the extra 0 is significant), you have already agreed to the idea that measurement is possible, and that we are now measuring in tenths of centimeters, which not only is far more precise than the unit of measurement you're claiming has no validity, but is based upon this faulty standard.

Nate T.

Post 62

Sunday, May 22, 2005 - 9:49pm

Brendan,

But when it comes to measuring real-world objects, in practice, one cannot achieve this sort of precision, because nothing is precisely 1.1 mm.

This hits upon the same idea that Daniel brought up, which is once you've chosen a standard, how do you make reliable copies of it. You may want to read my response there, since it will be the same.

Nate T.

(Edited by Nate T. on 5/22, 9:50pm)

(Edited by Nate T. on 5/22, 9:51pm)

Post 63

Monday, May 23, 2005 - 2:09pm

Nate T., your post 61 is spot on.

I certainly enjoy/admire your well-reasoned, well-mannered discussion of the measurement problem.

Ed

Post 64

Monday, May 23, 2005 - 3:51pm

Hi, Ed,

Nate T., your post 61 is spot on.

I certainly enjoy/admire your well-reasoned, well-mannered discussion of the measurement problem.

Thanks, I'm glad you enjoy it! That you admire it means a lot, as I've seen quite a few of your well-reasoned posts, as well.

Even though I'm studying ethics in-depth right now, it never hurts to go back and brush up on metaphysics/epistemology.

Nate T.

Post 65

Monday, May 23, 2005 - 4:31pm

Nate T:

I appreciate your attempt to solve the problem of the "imperfect centimeter," but this doesn't really do the trick. This is because you can't measure anything with an "ideal centimeter", since such a thing isn't material-- you can't pluck the idea of a centimeter out of your head and measure a block of wood with it. Your unit has to be material-- there's no way around that.

True. A "conceptual centimeter" divorced from the material world is devoid of cognitive content.

Space (length and volume) does not come in enumerable units, or at least none that we know of or can presently enumerate. Space is only measurable in terms of motion vs. time.

Daniel:

If, however, the concept centimetre *is* as imprecise as the physical situation - if Rand and Professor E would say you could only get between 0.9 and 1.1cm "conceptually" as well as physically - then I'd have to ask:what would you be aiming for in the first place?

The original unit created, of course. Even if there is some very small error in making copies of centimeters, one can still come close enough to make measurements qua centimeter, as mentioned above.

Daniel, the concept "centimeter" has a precise definition:

A meter is "defined as the length of the path travelled by light in an absolute vacuum during a time interval of exactly 1/299,792,458 of a second." http://en.wikipedia.org/wiki/Metre

It can be measured to an accuracy of one part in about 10,000,000,000,000. This is not absolutely precise.

Daniel asks: "Tell me: is that conceptual centimetre as imprecise as the physical object it represents?"

A concept is a mental representation. It has a REFERENT which is a measurement, but the concept itself is not a measurement, so precision in that sense is inapplicable. You're mixing two kinds of precision.

Conceptual precision might be thought of as whether a concept distinguishes between a thing and all other things not referred to by the concept.

Our concept of "meter" is a precise one, given its assumptions, even if our ability to measure a meter is not.

Our concept of "red," however, is imprecise, as it has no singular frequency of light as a referent, nor does it ordinarily delimit the range of wavelengths which can be called 'shades of red.'

Nathan Hawking

Post 66

Monday, May 23, 2005 - 7:13pm

Nathan,

Space (length and volume) does not come in enumerable units, or at least none that we know of or can presently enumerate. Space is only measurable in terms of motion vs. time.

What do you mean by measuring space here?

Nate T.

Post 67

Monday, May 23, 2005 - 7:55pm

Nate:

Nathan,

Space (length and volume) does not come in enumerable units, or at least none that we know of or can presently enumerate. Space is only measurable in terms of motion vs. time.
What do you mean by measuring space here?

Nate T.

Probably about what you'd imagine.

We can speak of the distance between two points in space, but space is generally thought of an infinitely divisible, devoid of enumerable components.

(If we were to discover that space was composed of irreducible finite units, we might specify the meter in terms of those.)

So we're forced to quantify space in terms of how much space an object or physical phenomenon requires, such as how far a photon travels in one three-hundred-millionth of a second, and express distance and volume in these indirect terms.

Even a naturalistic derivative like the Planck length uses G and c and another constant (Planck/Dirac) which entails time. So we're always measuring 'what stuff does in space' rather than space itself.

Nathan Hawking

Post 68

Monday, May 23, 2005 - 11:54pm

Nate:
>I appreciate your attempt to solve the problem of the "imperfect centimeter," but this doesn't really do the trick.

I'm not really trying to solve the problem of the "imperfect centimetre"...in fact I agree, as before, with 90% of what you're saying. But your argument is missing my point in a forest-for-the-trees way, and it is probably due to poor explanation on my part. Let's try it this way.

Firstly, I've tried to illustrate that what Ayn Rand calls "exact" or "absolutely precise" everyone else calls "approximate" etc. and that this is likely to be misleading, as she has no better solution to the problem of precision other than swapping the words around (you may call this being more "philosophical" if you like!). I believe I have done this.

This then led to a discussion of the above problem, in which I hoped to highlight the very interesting difference between *abstract standards* and physical ones. Because "centimetre" is merely shorthand for the following formula: "1/100th of the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second". This formulation is of course, an *abstract* standard: that is, a *conscious methodological decision* formulated in *words and numbers*.

Now, we can try to *approximate* the standard set by this formulation, and can do so remarkably precisely - but not *absolutely*. This is because, obviously, the length of the path the light travels is in the first place *measured by an instrument* (a physical ruler), and similarly the time taken to travel it is *measured by an instrument* (a physical clock).

We both accept that there are always limits to the precision of our physical instruments - as you rightly point out, every single one is different, and we can never really be sure even how much by, as we require them to measure each other by! Even our margins of error are themselves only estimates.

Thus we must admit our physical standards can only represent our *best guess* at approaching the standard we have set in our abstract formula, no matter how infinitesimal. So we can never tell *exactly* how far and how fast the light actually travelled - only plus or minus between two other plus or minuses!

So therefore our physical measurements of objects and events are always
1)*an approximation within approximations*- and further, everyone knows what I mean when I say this, so the necessity for redescribing it as "absolutely precise " or "perfectly exact" as Rand does seems, um, dubious.
2) *aiming at achieving an abstract standard*, even if we can never quite know if we have got it!

Does that make my position clearer?

Nate:
>As such, even if I could measure things "exactly" (which is impossible anyway), concepts cannot be measured in this way.

Of course I do not subscribe to Rand's theory of concepts, but I must say this comment makes me curious. How then?

- Daniel

Post 69

Tuesday, May 24, 2005 - 9:59am

Daniel, what a great, illuminative response! Though it was directed to Nathan, I can't help but to comment ...

So therefore our physical measurements of objects and events are always

1)*an approximation within approximations*- and further, everyone knows what I mean when I say this, so the necessity for redescribing it as "absolutely precise " or "perfectly exact" as Rand does seems, um, dubious.

Ok, Ok, Ok ... I ADMIT IT ... I admit to using the phrase "absolutely precise" in somewhat of a dubious mixture of reason and jest--2 very strange bedfellows indeed. But here's the rub:

IF your "approximation within approximations" is DECISIVELY within approximations (let's say an object measured at 10 cm is DECISIVELY within 1 m--which is 100 cm), then doesn't the whole measurement problem reduce down to (please pardon the unintended pun there) Nate T.'s insightful "shut-up-and-count-your-blocks" approach?

Nate T.'s Insightful Approach
If you had blocks, each of them 1 cm long (plus or minus a few microns), and you had to measure something that was, in actuality, an inch long (2.54 cm), then you merely stack the blocks, find that 2 of them didn't capture the length, proceed and find that 3 of them overshoots the length. You have here, by mere counting, DECISIVELY found the length to be between 2 and 3 cms.

Not to put too fine a point on it (again, pardon the pun), but you can also more precisely state the few microns of error inherent in block-making--and, and this is the kicker, you can totally account for this error while making statements about your measurements of reality.

To recap, when the range involved in an approximation (above: the true inch-iness of the inch-long object) IS MUTUALLY EXCLUSIVE TO the ranges involved in approximations dealing with upper/lower bounds (above: the few microns of error per block), then you have contextually-absolute accuracy--with only limited PRECISION (not limited accuracy!), a limitation that is inherent to the measurement tools used, and one that can be entirely accounted for.

2) *aiming at achieving an abstract standard*, even if we can never quite know if we have got it!

Daniel, I honestly don't think this to be of grand importance. In fact, when you say "aiming at achieving" (achieving an abstract standard), I think that what you really mean is "gaining absolute (context-free) precision"--and I charge you with setting up an impossible standard of platonic idealism--just as Jeff had said earlier.

p.s. I think it's fine to use "the distance a photon travels in a vacuum; over a specific time" to calibrate and collaborate (to approach a "conformity" of a given level of precision). Otherwise, some folks may still be using yardsticks (instead of meter-sticks) to measure something 37 inches long--and that can't be good.

Another way to say this is that, as technology improves our level of precision, there is benefit toward sharing the advancements--as there may be some "important" human problems (in the future) that actually REQUIRE the level of precision of which we are, today, capable. Heck, there may even be, in the future, an "important" need to INCREASE on the already-attained level of precision of which we are currently in charge.

In short, imprecision is not a huge deterrent in solving currently important human problems--though inaccuracy is (but these problematic inaccuracies are too far-ranging--e.g. rights, economics, ethics, etc--to be discussed here, alongside the relatively minor issue of "ideal inches" and "centimeters with certitude").

Ed

(Edited by Ed Thompson
on 5/24, 10:12am)

(Edited by Ed Thompson
on 5/24, 10:15am)

(Edited by Ed Thompson on 5/24, 4:33pm)

Post 70

Tuesday, May 24, 2005 - 11:34am

Nathan,

Space is actually a kind of relationship between objects. In order to measure the distance between two things, one must have two things to measure the distance between. As such, there is no way to measure space independently of a material object. So you're right in saying that we can only measure space (and motion) in terms of material objects and time.

Also, know that the objection of reality being unknowable due to its 'continuity' is precisely the main issue that Rand addresses in her discussion "Exact Measurement and Continuity."

In short, I think I agree with you, but I'm not sure since some of the terms you use make me nervous.

Daniel,

Firstly, I've tried to illustrate that what Ayn Rand calls "exact" or "absolutely precise" everyone else calls "approximate" etc. and that this is likely to be misleading, as she has no better solution to the problem of precision other than swapping the words around (you may call this being more "philosophical" if you like!). I believe I have done this.

Yes, I agree with Ed here, that Rand (of all people) knew better than to throw around the term "absolute" too cavalierly. In that sense, it was a poor word choice, since absolute means "irrespective of context," when Rand's entire solution to the problem of measurement is to recognize that measurement is contextual.

This then led to a discussion of the above problem, in which I hoped to highlight the very interesting difference between *abstract standards* and physical ones. Because "centimetre" is merely shorthand for the following formula: "1/100th of the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second". This formulation is of course, an *abstract* standard: that is, a *conscious methodological decision* formulated in *words and numbers*.

You bring up an interesting point here, since I've largely discussed units which are at the perceptual level (i.e., blocks and rods). The question of instruments acting as intermediates never occurred to me. However, you're right that you need some kind of instrument to determine the length of a meter this way. This gets into the special sciences with which I'm unfamiliar.

However, I do know that one must calibrate one's instruments either at the perceptual level or in terms of other, lower level instruments which have been similarly calibrated, to bring them in terms of the perceptual level. This is something akin to what Galileo did with his telescope to be sure that it wasn't tricking him: he observed distant objects through it, and then walked to those objects and verified that they did indeed match what his senses observed.

If we keep discussing in this vein, we may eventually uncover issues in the Realism vs. Instrumentalism debate in the Philosophy of Science.

Now, we can try to *approximate* the standard set by this formulation, and can do so remarkably precisely - but not *absolutely*. This is because, obviously, the length of the path the light travels is in the first place *measured by an instrument* (a physical ruler), and similarly the time taken to travel it is *measured by an instrument* (a physical clock).

Again, I'm not sure how scientists go about making copies of metersticks by this method-- it would be interesting to find out, actually. However, there has to something akin to the 1,000,000 units vs. km test I've written about before to be sure that the meterstick is a valid measuring tool in the context for which it was created.

I'm glad you've written this last post, since it presents your views very nicely. It has helped clarify this issue that we've bounced around in the last few posts:

Of course I do not subscribe to Rand's theory of concepts, but I must say this comment makes me curious. How then?

Concepts, as defined by Rand, are mental integrations of existents which have some similar characteristic. Its purpose is to allow one to recognize a certain kind of existent and to categorize one's knowledge abstractly, instead of storing one's knowledge as facts about concretes. As such, a concept is a mental entity, not a material one, and therefore it cannot be measured in units of length, as it has no material extension. It would be like trying to measure mass in inches-- it cannot be measured in that way.

However, I think by "concept of centimeter," you are referring to the "abstract standard" of the light-based definition of the meter, is that right?

Nate T.

Post 71

Tuesday, May 24, 2005 - 12:41pm

Nate T:

Space is actually a kind of relationship between objects.

That's the way some define it. There is probably no universally accepted definition, though.

In order to measure the distance between two things, one must have two things to measure the distance between. As such, there is no way to measure space independently of a material object. So you're right in saying that we can only measure space (and motion) in terms of material objects and time.

Ironically, we can only measure time in terms of space and material objects, too. A tidy little vicious circle if ever there was one. But reality is what it is.

Also, know that the objection of reality being unknowable due to its 'continuity' is precisely the main issue that Rand addresses in her discussion "Exact Measurement and Continuity."

In short, I think I agree with you, but I'm not sure since some of the terms you use make me nervous.

Which terms? To my knowledge I'm not employing language outside general English useage unless I stipulate a special meaning in a context. Why should that make you nervous?

Nathan Hawking

Post 72

Tuesday, May 24, 2005 - 1:16pm

Nathan,

That's the way some define it. There is probably no universally accepted definition, though.

Is there another way to legitimately define space other than what I've already introduced?

Ironically, we can only measure time in terms of space and material objects, too. A tidy little vicious circle if ever there was one. But reality is what it is.

That's not true-- we can measure time much as we do length: by dividing it into units. It's a little trickier here, because you have to make sure you choose a unit which is repeatable and does not vary in duration (the time it takes for the earth to rotate, the swing of a pendulum, the vibration of a quartz crystal or an atom). However, once one has a unit of time, one can count units of time just as one counts units of length, and the same kinds of principles hold. In order to compare units, one can use simultaneity for time instead of ordinal measurement for length.

Moreover, this kind of time measurement depends not on being able to measure the length of an object, but upon recognizing the beginning and end of some periodic event.

Which terms? To my knowledge I'm not employing language outside general English usage unless I stipulate a special meaning in a context. Why should that make you nervous?

Saying things like "space is infintely divisible." Unless you mean something specific, this implies (1) space can be divided somehow, and (2) it can be done so infinitely finely. I'm not sure what you mean by (1), and (2) postulates exactly what I have been arguing against this whole time, a measurement of zero error.

The only way that you can "divide" space is by attempting to measure the length between two objects (in some suitable context, of course). However, this division is ten epistemological, not metaphysical-- there is no actual cutting up of space happening when you measure the distance between two objects.

You could say that space is "infinitely divisible" in that the size of the unit chosen can potentially be as small as one pleases (relative to some other fixed unit). If all of this is all you meant by the above, I have no problem with it.

Nate T.

Post 73

Tuesday, May 24, 2005 - 3:05pm

Nate T:

That's the way some define it. There is probably no universally accepted definition, though.
Is there another way to legitimately define space other than what I've already introduced?

As I said, "relationship between objects" is one way. This mentions some others:

http://en.wikipedia.org/wiki/Space

(I have no interest in debating this--I just mention it FYI.)

Ironically, we can only measure time in terms of space and material objects, too. A tidy little vicious circle if ever there was one. But reality is what it is.
That's not true-- we can measure time much as we do length: by dividing it into units.

But the point is: HOW do we divide it into units? So far as I know, every known method involves material objects and their periodic MOTION through space.

If you know another way, there's doubtless a Nobel prize in it for you.

It's a little trickier here, because you have to make sure you choose a unit which is repeatable and does not vary in duration (the time it takes for the earth to rotate, the swing of a pendulum, the vibration of a quartz crystal or an atom). However, once one has a unit of time, one can count units of time just as one counts units of length, and the same kinds of principles hold. In order to compare units, one can use simultaneity for time instead of ordinal measurement for length.

Moreover, this kind of time measurement depends not on being able to measure the length of an object, but upon recognizing the beginning and end of some periodic event.

Yes, but don't you see that periodic events like vibrating quartz use "space and material objects" as I stated? The quartz crystal is in motion.

Space and time are inextricably commingled. So far as I know, each can only be measured, ultimately, in terms of the other. If you think you're measuring time independent of space, it's probably because you're smuggling it into the method unbeknownst.

Which terms? To my knowledge I'm not employing language outside general English usage unless I stipulate a special meaning in a context. Why should that make you nervous?
Saying things like "space is infinitely divisible."

Unless you mean something specific, this implies (1) space can be divided somehow, and (2) it can be done so infinitely finely.

(1) It should be obvious that I'm talking about the conceptual act of specifying distance between two points. (2) In practice, measuring real space runs into quantum limits.

I'm not sure what you mean by (1), and (2) postulates exactly what I have been arguing against this whole time, a measurement of zero error.

Ignoring quantum limits to measurement, saying that space is infinitely divisible does not imply that humans can afford the time for infinite precision, since "forever" is a lot of overtime.

The only way that you can "divide" space is by attempting to measure the length between two objects (in some suitable context, of course). However, this division is ten epistemological, not metaphysical-- there is no actual cutting up of space happening when you measure the distance between two objects.

The word "divisible" has many meanings.

You could say that space is "infinitely divisible" in that the size of the unit chosen can potentially be as small as one pleases (relative to some other fixed unit). If all of this is all you meant by the above, I have no problem with it.

You may recall my original statement: "Space (length and volume) does not come in enumerable units, or at least none that we know of or can presently enumerate." In other words, there are no quantum units of space. We can measure the length of a beam of coherent light in the number of waves, but this has no counterpart in space itself.

So, yes, "the unit chosen can potentially be as small as one pleases," at least in superficial theory.

Nathan Hawking

Post 74

Tuesday, May 24, 2005 - 7:12pm

Nathan,

But the point is: HOW do we divide it into units? So far as I know, every known method involves material objects and their periodic MOTION through space.

I was mostly just concerned with your statements here:

Ironically, we can only measure time in terms of space and material objects, too. A tidy little vicious circle if ever there was one.

It's true that all of the methods I give for measuring time involve involve material things in space which change-- if they did not, one would not be measuring that which one is ultimately trying to measure, which is change (motion) in relationship (between existents). However, one need not measure time to realize that something is changing-- just as one need not know the length in centimeters of two objects to realize that one is longer than the other. There is no vicious circle here.

Nate T.

Post 75

Tuesday, May 24, 2005 - 9:28pm

Nate: “This hits upon the same idea that Daniel brought up, which is once you've chosen a standard, how do you make reliable copies of it. You may want to read my response there, since it will be the same.”

Since the standard is abstract, you can’t make material “copies” of it. Take the standard for centimetre mentioned by Daniel: “1/100th of the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second”. This standard is not justified by measuring objects in the external world. It’s justified by doing the numbers: the speed of light x the relevant time interval, divided by 100.

The answer is as precise as you can get. But when it comes to the world of material objects, they don’t precisely match the numbers. Even if they did, you still couldn’t “copy” the standard, since it’s not a material object.

Where we differ is most likely in our view of concepts. If you believe that the meaning of a concept is its referents, you’re going to have difficulty in arguing for precision in measurement, since you won’t find precise measurements in material objects. But if you believe that the meaning of a concept is found in its definition, you can accept lack of precision in material objects, while still claiming that abstract measurement can be precise.

Brendan

Post 76

Wednesday, May 25, 2005 - 12:35am

Nate T.:

But the point is: HOW do we divide it into units? So far as I know, every known method involves material objects and their periodic MOTION through space.
I was mostly just concerned with your statements here:

Ironically, we can only measure time in terms of space and material objects, too. A tidy little vicious circle if ever there was one.
It's true that all of the methods I give for measuring time involve involve material things in space which change-- if they did not, one would not be measuring that which one is ultimately trying to measure, which is change (motion) in relationship (between existents). However, one need not measure time to realize that something is changing-- just as one need not know the length in centimeters of two objects to realize that one is longer than the other. There is no vicious circle here.

I'd rather not bandy words to the point of tediousness, but it is circular indeed. It is just like a definition which defines A in terms of B and B in terms of A.

We define length in terms of how far light travels in a unit of time, and we define time in terms of how a particular physical object repeats its motion through a particular length.

The two are so intimately related that at high velocities they both, time and length, contract--but the relationships remain exactly the same. If you can't see some sense in which there is circularity in the nature of these existents, mutual and irreducible interdependence of nature, then you are using the word "circular" in an excessively rigid or narrow manner.

Take it or leave it--I don't feel like debating such a trivial point any further.

Nathan Hawking

Post 77

Wednesday, May 25, 2005 - 1:27am

Ed writes:
>IF your "approximation within approximations" is DECISIVELY within approximations (let's say an object measured at 10 cm is DECISIVELY within 1 m--which is 100 cm), then doesn't the whole measurement problem reduce down to (please pardon the unintended pun there) Nate T.'s insightful "shut-up-and-count-your-blocks" approach?

The first problem is that adding the word "decisively" to the above formulation adds nothing to its meaning, and courts absurdity by calling the situation "decisively approximate". If you're going to say that, you might as well say it is "absolutely precisely approximate!" (And of course you are welcome to say that if you wish). The second problem is...

Ed continues:
>If you had blocks, each of them 1 cm long (plus or minus a few microns), and you had to measure something that was, in actuality, an inch long (2.54 cm), then you merely stack the blocks, find that 2 of them didn't capture the length, proceed and find that 3 of them overshoots the length.

OK Ed. Go back and re-read my previous post a couple of times. Think it through carefully, and then see if you can see what is utterly and fundamentally wrong with this idea. (Nate T. has now spotted it I think).

I wrote:
>2) *aiming at achieving an abstract standard*, even if we can never quite know if we have got it!

Ed replied:
>Daniel, I honestly don't think this to be of grand importance. In fact, when you say "aiming at achieving" (achieving an abstract standard), I think that what you really mean is "gaining absolute (context-free) precision"--and I charge you with setting up an impossible standard of platonic idealism--just as Jeff had said earlier.

You say that like it's a bad thing!

OK, I think I'm going to have to say a few words about kneejerk anti-Platonism. Guys, I'm a Popperian. If anyone should be a kneejerk anti Platonist it should be me! Karl Popper wrote possibly the most comprehensive and intellectually devastating attack on Plato of all time. Beside his volume 1 of "The Open Society And Its Enemies:The Spell of Plato", Ayn Rand's occasional muttered ad hominems are like a child's pop gun sitting next to a bazooka. Where she disagreed with Plato she offered no sound arguments that I am aware of, and where she was strongly influenced by him she is utterly silent. For example, Rand is regularly credited (within Objectivism at least) with being the first to identify individualism with selfishness, and collectivism with altruism. Unfortunately, Plato beat her to this formulation only by a millenia or two! (It turns out that this is an error anyway...but we'll save that for another thread).

For all his manifold errors, I believe Plato's basic insight is of a great deal of importance. So just belay all that chatter for a few moments, and start to think about the glimmer of the issue as I have begun to put it to you. Because the first thing you have to realise is that Plato wasn't just sitting coming up with evil theories like Darth Vader in a toga. He was actually *trying to solve a problem*, or in Objectivist speak, observing a curious *fact of reality*. Just like you hopefully just have...

- Daniel

Post 78

Wednesday, May 25, 2005 - 5:25am

Hi Ed
I think I was probably a bit too sweeping in my earlier post. It's not so much "utterly and fundamentally" wrong as just *seemingly* wrong, and also an issue I dealt with earlier.

The crux is this:
Ed:
>You have here, by mere counting, DECISIVELY found the length to be between 2 and 3 cms

Just so long as you haven't slipped back into Rand and Prof E's mistake in this - which is what I took it to be at first.
If not, I have typed in haste, and will repent at my leisure...;-)(Of course, my first objection, the linguistic one, still holds)

Thanks for your kind remarks earlier also.

- Daniel

Post 79

Wednesday, May 25, 2005 - 1:41pm