Sometimes very active discussions about peripheral issues overwhelm a thread, so this is a permanent home for those conversations.
I’ve opened a new “Sandbox” thread as a post as the new “ignore commenter” plug-in only works on threads started as posts.
Talk about smuggling in your assumptions! OK, we know the “true” value how, exactly? We can’t know it by measurement, by your own argument. So how DO we know it? How can we know if there even IS a “true” value, except by presuming it must exist, before we can presume what it is. Your P1 has skipped a good many steps, and you don’t realize it.
Excellent! Flint, too, is now engaging the argument.
Flint, the question of whether length exists is an ongoing argument between you, Neil, and me, but unlike you, Jock hasn’t claimed that there is no such thing as a true length (or true values generally). I’m engaging him right now, so there is no need to spell out our shared premise (or any of the zillion other premises we share).
I promise we’ll get back to the length question, and I am not asking you to agree with P1. For now, my question for you is the hypothetical “if P1 were true, which you don’t believe, would the argument be sound?”
Jock,
This is hilarious. Two hours ago you were trying to refute my argument. Now you’re confirming that I’m correct. What gives?
Why did you challenge my argument if you thought it was correct? And why didn’t you say “yes, your argument is correct” back in January, or at any of the other dozen times I asked you to address it?
Flint,
Having read this comment, do you now understand why “reality is not a theory” is a true statement?
keiths,
You simply failed to notice.
and on this thread, we had an extremely revealing exchange :
in response to your ever-repeated question
I replied as quoted below. HOWEVER, in your haste to rehearse your refutation of what you presumed I was saying, you failed to comprehend my comment about ‘tending the wrong wound’. You filtered that bit out, even going so far as to omit it when you quoted me (I bolded the bits he clipped).
Finally you offered your advice as to how I could correct my erroneous thinking.
Your inability to actually listen leads you astray. Repeatedly.
Jock:
Oh, I noticed all right. I was waiting to see how much further you would go in trying to refute my argument before I sprang that on you. You sprang it on yourself, which is even funnier.
So tell us, this time without dodging the question:
Why did you challenge my argument five hours ago if you knew it was correct? Was it because you couldn’t bear to acknowledge its correctness? Or did you forget that it was correct? What on earth was going on in your head?
And of course, all my answers will be dismissed as evasions.
The theory of reality must include thunderstorms, since we observe them. Recall, if you can, that a theory is a proposed explanation of observations. If our theory of reality disallowed thunderstorms, it would be a lousy theory.
You really do not know what a theory is. So every single one of your questions requires that I pretend that I don’t know what a theory is either, and therefore MUST adopt your error or else I’m evading!. This is not good faith argument.
keiths:
Flint:
A theory can be about thunderstorms, but a theory is not a thunderstorm, and a thunderstorm is not a theory.
Stick with me. I am going to explain the difference.
In a thunderstorm, there is wind and heavy rain. There are lightning flashes and thunderclaps. There can be hail. If you are out in a thunderstorm, you will get wet. Your hair will become tousled. If you are flying an airplane, you can get into serious trouble. Thunderstorms are dangerous for aviators.
Now consider a theory of thunderstorms. When you study a theory of thunderstorms, you don’t get wet. Your hair doesn’t become tousled. You won’t see flashes of light and hear booms coming out of the book. You won’t be pelted with hail. I studied thunderstorms in flight school, and it was perfectly safe. No turbulence, no danger. I was sitting in a chair on a calm day.
A thunderstorm has different attributes from a theory. They are not the same thing. A thunderstorm is not a theory. A theory is not a thunderstorm. A theory of thunderstorms is not a thunderstorm. It’s a theory.
I don’t see how I can make it any clearer, Flint.
Oh, the irony.
No, I suppose you can’t. You have proved yourself unable to distinguish between a theory that explains observations, and the observations themselves, which the theory explains.
I will try one more time. We have a theory. This theory holds that there exists an objective, external reality, independent of any limitations of perception. Everything we observe, detect, measure, experience, etc. taken all together are what our theory says exists.
And once again, a theory explains facts. Citing one fact after another and jumping up and down that your facts are not theories, is to completely miss the point. The theory of reality must include thunderstorms. It must include ALL valid observations. The contents of reality are not at issue here. So a tree is not a theory, it’s a tree. But if you reject the theory of reality, the tree is still there and you can still drive into it.
Strangely enough, a great many people DO reject reality, because they find it inconvenient. But good things rarely come from rejecting reality. For example, you might get wet in the thunderstorm, or even struck by lightning!
I would suggest that the theory of reality is so thoroughly accepted and internalized that some people seem utterly unable to accept that it’s a theory at all. They confuse theory with observation.
Flint,
This is getting downright… weird. I refuse to believe that you are unable to agree with my statement:
For the record, is statement #1 true, in your view? False? Both? Neither?
Please answer.
Hint: The correct answer is “true”. A thunderstorm is not a theory, and a theory is not a thunderstorm. Even a theory about thunderstorms is not a thunderstorm. It’s a theory.
Flint,
Assuming that you are still among the sane and are able to agree with statement #1, what about the other numbered statements?
I numbered those statements for a reason. If you actually disagree with any of them, then identifying them by number will help me understand where our differences lie.
I’ll reproduce them here for your convenience:
Please don’t skip over this. It’s important.
Flint:
Lol.
The theory — which is really just the hypothesis that reality exists — isn’t concerned with the limitations of perception, nor is it limited to what we can detect, measure, experience, etc.
We are just talking whether something exists “out there”. When I say that “reality exists”, I am saying that my mind is not the only entity in the universe. Other things exist, and I am referring to those things collectively as “reality”.
Have you been arguing with your intracranial keiths again? Please ignore him and pay attention to me, and to what I actually write.
Absolutely not. As I just explained, the hypothesis that reality exists is simply the claim that something exists “out there”, apart from us. That hypothesis makes no assertions whatsoever about thunderstorms or about whether Gwyneth Paltrow has a mole on her left buttock. Those things are outside the scope of the hypothesis, which merely asserts the existence of reality.
You agreed with that at one point:
I wrote:
You agreed:
Please keep that in mind.
Flint:
Excellent! Can you extend that concept to thunderstorms? If so, you might be able to agree with my statements #1 and #2:
Flint:
Correct. Reality is distinct from any theory of reality. The tree is part of reality, so it continues to exist whether or not there is a theory of reality. That’s what I was getting at in statement #9:
Do you agree with that statement?
I have never thought that your “argument” was correct. Get a grip.
I was contemplating invalid arguments that have (fortuitously) true conclusions.
You really should get out more.
Jock:
Haha. Yeah, right.
But OK, I’ll play along. Let’s pick up where we left off, then.
Flint,
I’m still interested in knowing whether you think my argument would be sound if P1 were true (which you dispute). However, I’ll go ahead and explain why that doesn’t actually matter.
You and Neil disagree with the rest of the world on the definition of measurement error. The consensus is that measurement error is equal to the difference between a measured value and the true value (or “actual value”). Since you and Neil (oddly) dispute the existence of a true value, you can’t use that definition.
That’s awkward, and I pointed it out some time ago, asking how there could be measurement error if there wasn’t a true value for the measurement to deviate from. You have both continued to insist that measurement error does in fact exist, despite the fact that there is no such thing as a “true value”, which presumably means that you have some reference value in mind that can be substituted for “true value” in the equation for measurement error. You (Flint) mentioned deriving a number from a bunch of repeated measurements, via a process similar to what aleta described.
Here’s the key point: If you object to my use of “the true length” in my argument, then simply cross that out and substitute “the reference length”, however you define the latter. The argument still works. Therefore, the conclusion still stands, and exact numbers can be used to express inexact measurements.
That is, the length denialism that you and Neil are engaging in is irrelevant to the question of whether exact numbers can be used to express inexact measurements. If you still dispute my conclusion, you need to come up with something other than the “true length” objection.
In other words, you can change my premises from
…to…
…and the argument still works. Exact numbers can be used to express inexact measurements.
OK, let’s try this another way. I think “reference value” is much better than “true value” because, at least to me, “reference value” carries an implication of precision, accuracy, correct calibration of measurement devices, etc. All of these implications, in turn, imply variability. Which is important, because “exact numbers” as you intend this phrase, imply NO variability under any circumstances. So long as we recognize that, in practice, this implication is not realistic, we’re fine. We can certainly use exact numbers to express inexact measurements, so long as we aren’t tricked into thinking they are also correct numbers, or that our measurements have infinite precision because the numbers describing them are infinitely precise. Personally, I would consider numbers with specified error ranges to be more trustworthy.
Yes, as I said. The theory is that reality exists entirely apart from perception.
Of course, but I don’t see how that’s relevant.
If you prefer the word “claim” to such words as “theory” or “map” or “model”, that’s fine with me. Let’s call it a claim. All theories are claims.
OK, now instead of “claim” you are substituting “hypothesis” or “assertion”.
I’m not sure. Are you saying that if we use the word “claim” (or “assertion” or “hypothesis”) then reality is distinct from the claim that reality exists? How about if we SAY that reality exists because of the overwhelming evidence that it does exist? We even SAY that observation of what exists, of any sort, does not alter what exists.
Much earlier, I said that our theory of reality holds that reality itself, what our theory says exists, cannot tolerate time travel into the past. That’s because such time travel would render reality plastic and local, so that your reality and mine would be qualitatively different depending on what our time traveler altered. But our theory holds that this is not possible. We would need a time machine to test this, and if our theory is correct, such a machine cannot exist.
Flint:
However you go about obtaining it, the “reference value” is a value — a number. The measured value is also a number. My argument shows that the measurement remains inexact even if both the measured value and the reference value are exact numbers. Do you disagree?
The “implication” that exact numbers are exact is realistic. It’s absolutely true. Exact numbers are exact, Flint, with no variability whatsoever. 13.58 is equal to 13.58 ± 0. It has one and only one value. It is infinitely precise. You can use that exact number to express the measurement “13.58 inches”. The measurement is inexact, but the number remains exact. Fully exact. This is not only “realistic”, it’s absolutely true.
My simple argument shows that there is no conflict whatsoever between saying that the number 13.58 is exact — fully exact — and that the measurement “13.58 inches” is inexact. The exactness of the number does not imply that the measurement is exact. Not in the slightest.
By saying “the implication is not realistic”, you are showing me that you are still confused about this.
If you are correct, and I am wrong, there must be a problem with my simple argument. Here it is again, modified to accommodate your “true value” objection:
I am asking for the umpteenth time: Do you see a problem with the argument? If so, please quote the part you think is wrong and explain why. I am asking you to engage my argument in good faith. The actual argument that I just laid out for you.
A number in and of itself cannot be correct or incorrect. Is 13.58 an incorrect number? You can’t say. The question doesn’t make sense. The measurement “13.58 inches” can be incorrect, but the number itself cannot.
Likewise with integers and counts. Is the integer 493 incorrect? You can’t say. The question doesn’t make sense. “493 nurdles”, on the other hand, can be an incorrect count.
You and Jock have been tricking yourselves, literally for months, into thinking that there is something incorrect or unseemly about using exact, infinitely-precise numbers to express inexact, limited-precision measurements. It’s time to stop tricking yourselves.
Your intuition is telling you that there is something wrong, sloppy, or dishonest about using exact numbers in this way. Your intuition is wrong, and it’s been wrong for eight months. I am asking you, at long last, to prioritize reason over intuition. Be rational about this.
My argument shows that you are wrong. If you disagree, then please quote the part you think is wrong and explain why.
You can always change “13.58 inches” to something like “13.58 ± 0.01 inches”, if the situation warrants. However — and this is crucial — the number 13.58 is exact in both cases.
keiths:
Flint:
Here’s the part you got wrong. You wrote:
Reality isn’t limited to things that we can observe, measure, detect, etc. If something exists, it’s part of reality. Whether it can be observed or detected is a separate question.
keiths:
Flint:
I was stressing that my theory of reality does not apply merely to what I can observe, detect, measure, etc. It applies to everything that exists apart from my mind.
I’m not trying to draw fine distinctions between those things. Let X be “the sun appears to rise in the east because of the earth’s rotation”. I believe that X, I accept that X, I assert that X, I claim that X, I hypothesize that X, I theorize that X. My model asserts that X.
Here’s the simple point I was trying to make. You wrote:
But it does not need to include thunderstorms, and it does not need to include all valid observations. As I said:
Flint:
Yes! Reality is reality, and claims are claims. Territories are territories, and maps are maps. Thunderstorms are thunderstorms, and theories are theories.
Reality is not a theory (or a claim, or a hypothesis, or an assertion). A territory is not a map. A thunderstorm is not a theory.
“Reality is not a theory” is a true statement. So are “reality is not a claim”, “reality is not an assertion”, and “reality is not a hypothesis”. Reality is reality.
I have no idea what point you are trying to make here. I believe/claim/assert/accept/hypothesize/theorize that reality exists because I’ve seen overwhelming evidence that it exists. And yes, what exists is independent of my observations. It’s also independent of my beliefs/claims/assertions/hypotheses/theories.
It would really help if instead of sharing your thoughts on time travel, you would tell me which, if any, of my numbered statements you disagree with.
This paragraph simply restates, very clearly, what I have been saying all along. I couldn’t have said it bettter. The theory IS that reality is “independent of my beliefs/claims/assertions/hypotheses/theories.” Just as the theory of evolution (for example) holds that evolution occurs independently of our understanding of it, of our observations of it, or even that we have such a theory. Theories are explanations. They are NOT the things explained. The more overwhelming the evidence, the more likely the theory is correct, but even if the theory were 100% correct, complete, and perfect, it would STILL be a theory. And a damn good one!
I fail to see what you are driving at. Yes, if we divorce numbers from measurements, we can consider them exact although the measurements are not. But if we are actually interested in the measurement itself, it’s important to know the accuracy and precision of the measurement. If I want to know approximately how long something is and you reply “9 feet”, then I have an approximation of the length to the nearest foot. Yes, the “absolute number 9” is part of the reported length, and if I no longer care about the length but only the infinite purity of the number used to describe the length, because it’s now a meaningless number that has nothing to do with the measurement anymore, then we can agree that “9” is an infinitely precise number precisely because it no longer has any context. But so what?
Flint:
YES! You’re so close, Flint. Now I just need you to take the final step. Take that general concept and apply it specifically to reality. Recognize that “reality is not a theory” is a true statement. You’ve been denying it for days, and you’ve been confusing theory with reality even longer. Have you finally seen the light?
Please confirm that you now understand that
a) reality is not a theory;
b) a theory is not reality;
c) a theory can be about reality, but that doesn’t mean that the theory is reality; and
d) in summary, reality and theory are distinct entities.
Agreed?
Flint:
Numbers are exact, period. You don’t need to divorce them from measurements in order to make them exact. The numbers used to express inexact measurements are exact numbers.
13.58 is an exact number, and the 13.58 in “13.58 inches” is the same exact number. Numbers are exact, period.
Of course. But those are attributes of the measurement, not of the number.
I am sure this is at least the 20th time — no exaggeration — that I am telling you this, but numbers are distinct from measurements. Because they are distinct, they can have different attributes. Numbers are exact; measurements are inexact. Numbers are infinitely precise; measurements are limited in accuracy and precision. It’s crucial that you keep numbers separate from measurements in your mind. I’ve lost track of how many times you’ve learned the distinction, only to forget it again.
I think it’s time for you to start keeping a TSZ notebook. As you learn things, record them in the notebook. Review the notebook periodically. Please include the following, to start:
1) numbers are distinct from measurements;
2) numbers are exact, but measurements are inexact;
3) numbers are distinct from their representations;
4) integers are real numbers;
5) integers are distinct from counts;
6) a map is distinct from the territory it represents;
7) a model is distinct from the things it models;
8) reality is not a theory; it’s reality.
I’m serious, Flint. We’ve wasted a lot of time re-educating you about things that you previously learned during our discussions, but then forgot. I think the notebook will help.
No. This is another example of something you keep learning and then unlearning, over and over. I am 6′ 0″ tall. When people ask, I tell them I’m “6 feet tall”. That is not an approximation to the nearest foot. The people who hear me say that know perfectly well that I am not merely saying that I’m somewhere between 5.5 and 6.5 feet tall. You know it too, yet you’ve somehow acquired the belief that the precision of a measurement can always be inferred from the way it is expressed. That isn’t right. Please add this to your notebook:
9) The precision of a measurement can sometimes be inferred from the way the measurement is expressed, but only sometimes.
The choice is yours: you can continue to believe the same stupid shit that you and Jock have believed for eight months, out of sheer spite, or you can act like a grownup and pay attention to what logic and reason have been telling you.
The number 9, both on its own and within the context of the measurement “9 feet”, is exact, infinitely precise, with one and only one value: 9 ± 0. The measurement is inexact, but the number is exact. My argument shows it, you know that it does, and after eight months you are still unable to refute it. Reason is telling you that you are wrong, but you are stamping your feet, covering your ears, and squeezing your eyes shut because you don’t like what reason is telling you. It’s pitiful.
The challenge remains:
Okay, keiths, so long as you agree that, were I to ask you to tell me the roots of x^5 – 4.x^3 – x^2 + 3 = 0, you would provide me with three measurements.
It’s a strange use of the word “measurement”.
Jock,
Is that your “Look! A squirrel!” attempt to deflect attention away from the following?
You wrote:
I called your bluff. Where’s your refutation?
May I again request that keiths or Jock start an OP and leave the sandbox for its original purpose.
Sometimes very active discussions about peripheral issues overwhelm a thread, so this is a permanent home for those conversations.
ETA: It looks like your bolding has spilled over into this comment. Did you forget to close an HTML tag, by any chance?
Alan,
You are asking us not to use the Sandbox for its stated purpose.
Flint started this discussion in the “A Natural Afterlife” thread, and I moved it here because it was off-topic there. That’s precisely why Lizzie created the Sandbox:
Yup, missed a caret. Odd that WordPress didn’t close it automatically.
I’m suggesting it as a way to focus on a topic. It would hardly have mattered had you continued in the “Natural Afterlife” thread as that has died a natural death anyway.
I see we are holding at around 100 unique visitors daily. Come on, folks, you are all welcome to chip in with a comment or an OP.
Alan:
In effect, you’re saying “Don’t use the Sandbox for its stated purpose. Keep off-topic discussions in the threads where they don’t belong.”
That doesn’t make sense to me. What’s the problem with using the Sandbox the way Lizzie intended?
I’m not seeing any evidence that people are confused and unable to focus on the topics. Why not just let things proceed as they are?
Just seems simpler to follow a thread that is focused on a topic. Never mind, it’s no big deal.
Errr, you yourself linked to it, keiths, with your “Two hours ago, you were trying to refute my argument” bit. You didn’t find it compelling, of course, but pretending it didn’t happen makes you look bad. Try to keep up.
Jock,
That’s pathetic.
Confident people, when they are debating, will actually engage each other. It’s like a tennis rally: a back-and-forth in which each side responds to the claims and arguments of the other. Back and forth. Confident players don’t just flee the court.
You’re full of bravado:
And:
But now that I’ve called your bluff, you’re looking for excuses to bail out. Your bravado has evaporated.
What is it with you and Flint? You’ve had eight months to find a flaw in my argument. You avoided it for that entire time, without offering an explanation for your silence. You (Jock) finally responded two days ago, with a failed refutation. I showed you why your refutation failed. The ball’s in your court. If you’ve never believed that my argument was correct, why didn’t you respond to it in January? If you are confident in your refutation, why are you fleeing the court instead of continuing the rally?
It couldn’t be clearer. The reason you dodged the argument for eight months, and the reason you are running away after one failed attempt at refutation, is because you know the argument is correct. It’s an extremely simple argument, and it’s clearly sound.
You know it. I know it. The readers are watching you pretend a confidence that you don’t actually possess. Why are you doing this? Why not simply acknowledge what everyone already knows, by saying something like “That’s a good argument. I can’t see a flaw in it”? Would a bit of honesty kill you?
This is just a blog on the internet, dedicated to discussion and debate. That’s all. Just a blog. You took a position that turned out to be false. Your interlocutor explained your error. No big deal. You could have acknowledged that back in January, when I first presented the argument.
It obviously wasn’t in TSZ’s interest for you to obstruct the discussion for eight months, but here’s what I can’t figure out: it wasn’t in your interest, either. If you had simply said “You’re right” back in January, you wouldn’t be in this situation. It would have stung for a couple of hours, perhaps, but then it would have blown over. We would have moved on. What was the point of prolonging your misery for eight months? What is the point of prolonging it now by pretending to believe that my argument is flawed?
This is just a frikkin’ blog in one corner of the internet. That’s all it is. What is the big deal about simply admitting your mistake?
Given F&J’s continued evasion, I should probably present the argument, Jock’s attempted refutation, and the reason his refutation failed.
The argument, in compact form:
Flint objects to the use of “true value”, so in his case, imagine the same argument but with “true value” replaced with “reference value”. It works just as well.
Jock’s attempted refutation:
The flaw in Jock’s attempted refutation is that he is reasoning circularly:
So OK, we start with a true value which is not known and cannot be known, but which CAN be specified to an infinite precision! How can we assign infinite precision to an unknown and unknowable value? Simple: we assume it!
Next, we perform a measurement. We know this value to the limits of precision of our measuring technique, and we know that our technique is nowhere near infinitely precise. Nonetheless, we assign this measurement an infinitely precise value. How can we do this? Simple, we SAY that it’s infinitely precise. Or rather, the measurement itself isn’t infinitely precise, but the number produced by our measurement IS infinitely precise. Let’s not think too hard about that.
Finally, we calculate the difference between the unknown but infinitely precise “true” value and the approximate but infinitely precise measured value, and we get an error which is infinitely precise. Our calculator says so, but only to 9 decimal digits because the calculator, just like our measurement technique, is limited. But so what? We know the true and measured values are being expressed with infinite precision because we SAID so.
This is, of course, entirely unrelated to the fact that both our “true” (or reference) value and our measurement are wrong because of our limitations in determining either one. But that’s not the point. The great thing about infinite precision is that there is no implication that it’s correct, or even close. It’s just precise.
Flint:
You’ve been telling us that true values don’t exist, but now you’re telling us that they are merely unknown and unknowable. Please spend some time thinking about this and come up with a consistent position on whether they do, or don’t, exist.
My own position is that they do exist, but that they are unknown and unknowable. The fact that they can’t be known precisely, however, doesn’t mean that they are entirely unknowable. I can confidently say just by looking at the photo below that the true length of object A is greater than the true length of object B, even though I can’t specify either length precisely.
You and Neil can’t say that, because you have put yourselves in the weird position of denying that true lengths exist. If true lengths don’t exist, then they can’t be compared to each other, and there is no way to determine that object A is truly longer than object B. This is an example of why I roll my eyes at some of the stuff you guys claim.
Question: Are you really unwilling to say that object A is truly longer than object B? Or do you say that A is longer than B, but that neither has a true length? Or what? It looks like a mess to me. How do you resolve it?
For now, I’ll take your paragraph as written. It refers to an true value that actually exists, albeit one that is unknown and unknowable.
You wrote:
Value (singular) means infinite precision, so if there is a true value (singular), it is infinitely precise. We know that it’s infinitely precise, but we don’t know the value and so we cannot specify it infinitely precisely. If we could specify it infinitely precisely, we would know the value, and we wouldn’t need to bother with the measurement!
We don’t have to assume it. If it is a true value (singular), then it is automatically infinitely precise.
Are you following?
Flint:
No, no, please do think! I need you to think instead of blindly following your intuition. You will never understand this stuff if you keep prioritizing your intuition over reason.
Recall item #1 in your notebook:
The measurement is inexact, but the number is exact. There is no contradiction, because numbers are distinct from measurements. Exactness is an attribute of the number, and inexactness is an attribute of the measurement.
The number 13.58 is exact. The measurement “13.58 inches” is inexact. Your intuition is screaming at you that the second 13.58 cannot be exact since the measurement isn’t exact. Your intuition is wrong. Tell it to STFU, and please continue to think. Both the first and the second 13.58 are exact. 13.58 ± 0.
How does the act of measuring produce an inexact measurement that nevertheless is expressed using an exact number? I explain that in the second part of my argument:
Are you still with me?
Flint:
No! We don’t know the true value, so we cannot determine the measurement error. Think about it.
Measurement error = measured value – true value. By simple algebra, that means that true value = measured value – measurement error. If we knew both the measured value and the measurement error, we could calculate the true value! We would use that instead of the measured value.
Obviously, that isn’t possible. We don’t know what the measurement error is for a particular measurement. We can get an idea of the possible values of measurement error, and their relative probabilities, but we cannot say what the error is on a given measurement. If we knew the error, we would know the true value. That’s not how it works.
We don’t determine the true value. Ever. It’s unknown and unknowable. We do know that it is infinitely precise, however, because that’s what the word “true” indicates in this context. It’s a true value (singular). One and only one value. Infinitely precise.
“Infinitely precise” means “single-valued” means “exact”. A number in and of it itself is infinitely precise, single-valued, and exact. A number in and of itself cannot be “correct” or “close”.
Is 13.58, in and of itself, infinitely precise? Yes. Single-valued? Yes. Exact? Yes.
Is 13.58, in and of itself, correct? The question doesn’t make sense. Is it close? Again, the question doesn’t make sense? “Correct” and “close” don’t apply to numbers per se. They are relational properties: Correct as an answer to what? Close to what, and by what criteria?
Are you still with me?
Flint,
Let me emphasize a point and address a potential objection.
You wrote:
To assert that a value is infinitely precise isn’t the same as specifying it to an infinite precision. I have no idea what the 45th root of Avogadro’s number is, so I can’t specify it at all, much less infinitely precisely. However, I can assert that it is infinitely precise.
It’s the same with true values. They aren’t knowable, so you can’t specify them to an infinite precision, but you can assert that they are infinitely precise. The “true” in “true value” means that the value (singular) is correct. Single-valued means infinitely precise.
One objection that you and Neil have tried to raise is to assert (weirdly) that there is no such thing as length (which presumably extends to other quantities such as mass). I’ve addressed that elsewhere and may return to it.
Another potential objection is to concede that length exists but to assert that true length doesn’t exist. Length can change to due to thermal expansion, for example, so you might argue that it doesn’t make sense to speak of an object’s single true length.
My response would be that even if length varies over time, an object still has a true length at any given moment. The fact that kids grow over the years, for instance, doesn’t mean that you can’t speak of a kid’s true height.
You might instead argue that objects have multiple true lengths at any given moment (on quantum-mechanical grounds, perhaps). Even if that were true, my argument would still work. Multiple true lengths would mean that the measurement error wasn’t single-valued, but there would still be measurement error, and that’s enough to establish that a measurement is inexact.
Dunno if there are any members of the American Political Science Association here–or if anybody here cares what they think–but I just posted a review of their new study on political parties in the U.S. There’s an introduction and a link to it at luckorcunning.blogspot.com
[I will also apologize in advance for the almost completely random paragraphing utilized by my editor at 3:16 AM Magazine (the publisher of the review). That’s been a regular practice with my reviews for several months now. I don’t understand enough about html to know if this is typical when word docs are converted, but alas……]
Jock:
It sure is, so why are you using the word that way? Have I said something that makes you think I regard the roots of polynomials as measurements?
ETA: Don’t use my question as an excuse to avoid responding to this.
keiths,
Re your purported ‘flaw‘, your P1 carries (by equivocation) the same implicit assumption that you are trying to prove. You in fact have the same circularity problem that you think I have. You don’t see this, and never will: I am uninterested in beating you over the head with this point, since I agree with the specific conclusion you are claiming.
Re the roots of that quintic [Q(x)], we have discussed this previously: aleta understood just fine, but I guess it whooshed with you. I tried to direct you to Wildeberger on this topic, but you seemed unwilling to educate yourself. It’s not just measurements that suffer from the “insuperable inexactness” problem.
walto,
Thoroughly enjoyed your review, walto.
For my beach reading next week, I bought Levitsky & Ziblatt’s “Tyranny of the Minority”.
Did I err?
Jock:
No, it doesn’t. Here are the premises:
P1 doesn’t specify or imply that the measured value and true value are exact, nor does it specify or imply that they are inexact. That’s quite deliberate.
It is the argument that shows that exact numbers can be used to express inexact measurements, not the premise.
Don’t bail out, Jock! Keep the rally going. I’ve shown that your circularity objection fails. What is your response?
This is how debate is supposed to work. I made an argument. You offered a refutation. I showed that your refutation was circular, so you tried a different approach and claimed that it is the argument that is circular. I’ve shown that it isn’t circular. Back and forth. It’s your move. Keep the rally going!
Yes, and I’m glad you agree. It took a while to get you there, but you made it. That’s progress!
No, you didn’t. This is the first time you’ve linked to that video. You merely mentioned Wildberger, and when I asked you to quote him in support of your position, you bailed out, in typical Jockian fashion.
Better late than never, I guess. So now that I’ve seen the Wildberger video, tell me how it led you to your weird statement about measurements being the roots of that polynomial:
I responded:
Please answer this time. Why are you using the word “measurement” in that weird way?
A comment on that video.
Wildberger is standing in front of a graph of a polynomial that shows it crossing the x-axis in three places. Places where the graph crosses the x-axis are known as ‘roots’, or ‘zeros’. That polynomial therefore has three zeros. It’s obvious, right?
Guess what Wildberger says about those zeros:
So standing in front of a graph that shows the polynomial crossing the x-axis at three points, he is saying that no such points exist.
You picked the wrong horse to back, Jock.
I will give a read when I’ve got through the Guardian.
An evil demon has created a room. It is divided into two by a clear screen which allows everything to pass between the two spaces: light, sound, smell etc except people or objects they might hurl. The spaces are equipped with all basic needs bathroom, food arrives regularly, air quality, temperature and humidity are maintained at comfort levels but there is no contact or communication with the outside world. (Ok it’s the Sartre scenario).
You, fellow interlocutor, get put in one half. and someone else gets put in the other half. Assume it is for quite a while. Who would you least like to be your companion ?
Answers on a postcard.