This remains an unresolved issue in the philosophy of science. Yet, there are only fallible historical cases of this problem. It doesn't seem to be an issue that prevents scientific progress and new technology. Scientists generally don't consider theories to be true (instead adequate and probable) and instead leave the epistemology to philosophers.
Potter Suppositionalist Adequate? Maybe. Useful? Sure. Probable? I doubt it. There's no way to show that one empirically equivalent theory is more probable than another. How can you show that it is more likely that the universe is moving at a constant velocity than standing still?
Carneades.org *"There's no way to show that one empirically equivalent theory is more probable than another."* A probabilistic argument could be made given (1) how well theory fits the evidence, (2) explains the evidence and (3) the accuracy of it's predictions. But rather than claims about truth, we are dealing with adequate approximations with degrees of uncertainty. In this sense, _verified_ might simply mean confirmed to an accurate model of some aspect of nature. The skeptical proposal that there may be perfectly equivalent theories under strict criteria is hypothetical. But if Occam's Razor genuinely can't slice them, science could probably make use of both. Science is free to use whatever tools are at it's disposal, which is why Newtonian mechanics could still be used for rocketry, despite the fact that Einstein's model of gravity is theoretically more accurate. In the same way, a logician is free to use different logic systems, which have different axioms and domains of application. But to the topic at hand, I would argue that a theory is verified it has met certain criteria, but it doesn't mean it's true. It also doesn't mean it's the only theory available which might accurately fit some aspect of nature. *"How can you show that it is more likely that the universe is moving at a constant velocity than standing still?"* Depending on your definition of _universe_ I'm not sure if that's a coherent question, or if it is a hypothesis which can even be tested. But science can coexist with competing theories and unanswerable questions. This isn't a problem for my view of science. Theories are tools or models, rather than answers to epidemiological questions. There can be competing theories in science, and in the same way there can be competing logics in philosophy. There is no true system of logic, or unquestionable assumption. Paraconsistent logic can be as useful as classical logic. The universe may, in fact, tolerate real paradoxes; such as time travel, or some property being true and not true. I don't know, but I'm curious to find out.
Potter Suppositionalist "A probabilistic argument could be made given (1) how well theory fits the evidence, (2) explains the evidence and (3) the accuracy of it's predictions. " The point of empirically equivalent theories is that they are exactly equal on all of these accounts. They make the same predictions, so the accuracy of their predictions cannot be judged. They are both equally supported by the evidence, so their fit cannot be judged. They both equally explain the evidence, so their explanatory power cannot be judged. There is nothing that can empirically separate them. That's why they are empirically equivalent. . "The skeptical proposal that there may be perfectly equivalent theories under strict criteria is hypothetical. " They are not hypothetical. You have the universe moving at a fixed velocity and the various examples given by Earman in the video (7:33). . ".Science is free to use whatever tools are at it's disposal, which is why Newtonian mechanics could still be used for rocketry, despite the fact that Einstein's model of gravity is theoretically more accurate. In the same way, a logician is free to use different logic systems, which have different axioms and domains of application. " The key here is "use", which is very different from "claim to be true". Under my definition "verification" has to do with truth. looking at the root of the word, this makes sense. When something is verified, it is not shown to be useful, it is shown to be true. . . "I would argue that a theory is verified it has met certain criteria, but it doesn't mean it's true. It also doesn't mean it's the only theory available which might accurately fit some aspect of nature. " What criteria are those? As I note in the video, the argumetn may not apply to all definitions of verified. What exactly is yours? What is necessary and sufficient for something to be verified. . "Depending on your definition of universe I'm not sure if that's a coherent question, or if it is a hypothesis which can even be tested." Remember that notions of testability and falsifiability are also at question here. The problem is that, if we combine the two problems, we see that if you cannot test any one theory without testing the whole set of beliefs, and there are two sets of beliefs that are empirically equivalent, there is no way for you to make either assertion. You must not just suspend belief on the individual cases, but on the set of theories as a whole as they cannot be assessed alone. . ."There can be competing theories in science, and in the same way there can be competing logics in philosophy. There is no true system of logic, or unquestionable assumption. Paraconsistent logic can be as useful as classical logic." This seems like instrumentalism about science, which I am fine with. If you are not asserting that any scientific theory can be shown to be true, simply that we can use different ones, and that different theories are useful in different situations, I'm with you completely. It's asserting that they are likely or true that remains unjustified. . ".The universe may, in fact, tolerate real paradoxes; such as time travel, or some property being true and not true. I don't know, but I'm curious to find out. " Interesting thought. I'm curious to attempt to find out too.
Carneades.org *"The key here is "use", which is very different from "claim to be true". Under my definition "verification" has to do with truth. looking at the root of the word, this makes sense. When something is verified, it is not shown to be useful, it is shown to be true..."* It would be a problem if scientists made the claim that various competing mathematical and conceptual models were _true_. But they generally don't make this claim and such models are provisionally held, even when they've been well substantiated. So this is a problem with semantics in the Philosophy of Science, rather than an issue in the practice of science. *"What criteria are those? As I note in the video, the argument may not apply to all definitions of verified. What exactly is yours? What is necessary and sufficient for something to be verified..."* That is a question for a philosopher of Science to solve. But everything in science is provisionally held, even after it has been confirmed by experiment and observation; and theories are never proven only disproven. It makes sense that verification, if such a word is ever used, should be taken to mean a provisionally held confirmation that some _T_ has passed the criteria for a scientific theory, withstood peer review and is scientifically fruitful. Verified as a scientific _theory_, rather than verified as absolute _truth_. *"They are not hypothetical. You have the universe moving at a fixed velocity and the various examples given by Earman in the video (7 :33)"* That's a hypothesis, which is defined as a potentially testable idea. But scientists cannot pear beyond the universe to make such a measurement, nor don't we have an indirect method of conducting such a test. So it's not a scientific theory, which is some tested and well-substantiated explanation of the evidence. But I'll grant you this example. *"This seems like instrumentalism about science, which I am fine with. If you are not asserting that any scientific theory can be shown to be true, simply that we can use different ones, and that different theories are useful in different situations, I'm with you completely. It's asserting that they are likely or true that remains unjustified..."* When I talk about probability I'm referring to degrees of likelihood given our models and data. But my contention is that no matter how accurate some scientific understanding becomes, it will never be absolute, so it's never true in a strict sense. However, there are methods of calculating probability with variable uncertainty (Bayesian probability, ect). *"Interesting thought. I'm curious to attempt to find out too."* Good conversation, thank you. Additionally, I'd be curious to hear what you think about paraconsistent logics sometime.
3:00 I feel that Zeno's paradox is at the heart of what you talk and the resolution the same. In Zeno's case, the *existence* of infinite number of half-steps to the finish line prevented him, _conceptually_, from reaching the finish line. But because in every other context but conceptual there is always a smallest step involved, including reality, and thus the slowest racer on a Non-Zeno, non-contextual team will always beat out the fastest racer on a Zeno, contextual team. 9:50 Wouldn't we have to be equally skeptical of Modens Ponens as well? After all, if p>q, it is also the case that p>(qvr) by addition, ... but also p>(qvrv~r), and so on and so on. Thus, since p>q doesn't just imply q but qv(...), with an infinite number of trivial additions, then doesn't that make MP underdetermined and thus we should be skeptical of it just as we should any other theory? If so, I can't help but think that being skeptical about MP is itself an irrational position to hold since it's hard for me to imagine a system where one could discard MP and still be rational. Otherwise, if we aren't comfortable with dismissing MP as saying *a* cause implies *all* effects, not just *an* effect... ... then why are we comfortable with dismissing theories as saying *a* piece of evidence (a cause) will imply *all* hypothesis (all effects) and not just *an* hypothesis? The key, as I see it, is recognizing and removing trivial additions. In your example, the state of the universe, as being static or moving at constant velocity, is a trivial addition to the theory because it was trivially added to the fact that we already know q (Newtonian gravity) is true. Thus, we could just as soon say that because we can't distinguish between Newtonian Gravity & Unicorns versus Newtonian Gravity & No Unicorns, then we are justified in saying that Newtonian Gravity and the very framework upon which it's built are all irrational.
Yes. No one can know anything. There is and there is not reality. This is where philosophy and religion join hands and jump down the rabbit hole. When you can prove any point on any side of an argument or issue by reference to an equally valid tenet of a discipline, I think that all meaning, usefulness and relevance of that discipline evaporate.
lreadlResurrected So ethics have no relevance? Logic has no relevance? Truth? Beauty? Just because you can't find a way to know something, doesn't mean that there isn't one. Why would you give up on a pursuit just because you have failed now? My skepticism does not assert that nothing can be known, it just seems that we haven't figured out how to know something yet.
I did not really get an addressing of ethics out of my view of this piece, but maybe I need to watch it again. The point I got was along the notion that the scientific method is substantially invalidated by its arbitrary(?) methodology. When, as you seem to assert here, philosophy of equally valid authority can be used to prove both sides of a logical issue, yea, even the validity of logic itself, then it (philosophy, not logic) is rendered inert. Regarding the pursuit you describe above: Ah, but isn't that more or less a distinction without a difference? What holy grail is it for which you search? What tool is necessary for the job? Is it one that exists but is not being used correctly? Or perhaps one that has yet to be conceived? Is this not sounding more and more circular and almost starting to border on, if you'll excuse the expression, woo?
Carneades.org «My skepticism does not assert that nothing can be known, it just seems that we haven't figured out how to know something yet. » Does it seem that we will ever figure out? Does it not seem to be a fruitless quest?
The article at stanford about underdetermination is really amazing. But as regards the argument you made using Kukla, notice that we cannot conclude from "there is no purely empirical way we can decide between T and T' " to "there is no way we can rationally decide between T and T' ". If we simply apply Bayes theorem to calculate the probabilities of both given some evidence E, assuming that both entail the evidence (i.e. P(E|T) = P(E|T') = 1), and considering that T' = not-T and E, we would have the conditional probabilities P(T|E) = P(T)/P(E) and P(T'|E) = P(E|not-T)*P(not-T)/P(E) = P(not-T|E). Now, if we have P(E) < 1, (i.e. if the evidence is not a COMPLETELY UNDOUBTABLE NECESSARY FACT, that we can know even purely a priori and prior to experimentation) this yields P(T|E) > P(T), which in turn yields P(not-T|E) < P(not-T) and subsequently P(T'|E) < P(not-T). As such, upon learning E, the probability of T rises, and of not-T lowers. In particular, if we assume P(T) = 0.5, this proves that P(T|E) > P(not-T|E) = P(T'|E), and as such we can say that T is better than T'. Of course, you may object to the choice of prior for T, but considering that T is a theory formalized in some logical calculus, we should be able to give an objective probability semantics to this calculus and find at least an uniquely rational lower bound for the probability of T. (for instance, if its algebraization by the Lindenbaum-Tarksi method yields a free Boolean algebra, giving 50% chance to its generators and assuming them to be independent, already determines uniquely a probability for all molecular formulas and gives upper and lower bounds to several quantified expressions, if the language allows quantifiers at all). If we do that, at least some theories may have prior probabilities bigger than or equal to 50%, and in this case even the anti-realist skeptical arguments will fail against them.
Fascinating comment! Thanks for sharing. I have a great deal of objections to Bayesian Epistemology many of which are drawn from the argument that I'm skeptical that you can create an objective system to identify the prior for T, I see no reason to assign 50% to each generator or to assume that they are independent without argument, but some very interesting ideas! Here's the intro video on my series on Bayesian Epistemology (th-cam.com/video/rWb7up_MoZc/w-d-xo.html).
weird question but im reading the comments to learn other perspectives do you think this is worthwile and actually betters my thinking or im better off reading from professionals?
No. Okay so this one is going to get mathy. So for a dataset, there are only a finite number of theories to explain the data. We can explain it with a first degree polynomial - the nest fit line. There is no need for any other line, because the best fit line is best. We are able to explain the data better by curving the line and finding the best fit two degree polynomial to fit the data. We can increase the degrees of polynomials until the number of degrees equals the number of observations in yue dataset. A best fit polynomial with degrees equal to the number of observations in the dataset will pass through every point of data. There is no need to increase polynomials beyond that degree Now, the best fit polynomial with degrees equal to the number of observations will only explain that dataset. It will be useless when the next set of observations is collected. So, the goal is to find what degree of polynomial will best explain new datasets. If there are multiple degrees of polynomials that equally explain newly gathered data, here is where we will use occcum's razor and pick the lowest degree of polynomial that can explain the data best. Thus, we can get exact verification and econ beats philosophy again.
This remains an unresolved issue in the philosophy of science. Yet, there are only fallible historical cases of this problem. It doesn't seem to be an issue that prevents scientific progress and new technology. Scientists generally don't consider theories to be true (instead adequate and probable) and instead leave the epistemology to philosophers.
Potter Suppositionalist Adequate? Maybe. Useful? Sure. Probable? I doubt it. There's no way to show that one empirically equivalent theory is more probable than another. How can you show that it is more likely that the universe is moving at a constant velocity than standing still?
Carneades.org
*"There's no way to show that one empirically equivalent theory is more probable than another."*
A probabilistic argument could be made given (1) how well theory fits the evidence, (2) explains the evidence and (3) the accuracy of it's predictions. But rather than claims about truth, we are dealing with adequate approximations with degrees of uncertainty. In this sense, _verified_ might simply mean confirmed to an accurate model of some aspect of nature. The skeptical proposal that there may be perfectly equivalent theories under strict criteria is hypothetical. But if Occam's Razor genuinely can't slice them, science could probably make use of both.
Science is free to use whatever tools are at it's disposal, which is why Newtonian mechanics could still be used for rocketry, despite the fact that Einstein's model of gravity is theoretically more accurate. In the same way, a logician is free to use different logic systems, which have different axioms and domains of application. But to the topic at hand, I would argue that a theory is verified it has met certain criteria, but it doesn't mean it's true. It also doesn't mean it's the only theory available which might accurately fit some aspect of nature.
*"How can you show that it is more likely that the universe is moving at a constant velocity than standing still?"*
Depending on your definition of _universe_ I'm not sure if that's a coherent question, or if it is a hypothesis which can even be tested. But science can coexist with competing theories and unanswerable questions. This isn't a problem for my view of science. Theories are tools or models, rather than answers to epidemiological questions. There can be competing theories in science, and in the same way there can be competing logics in philosophy. There is no true system of logic, or unquestionable assumption. Paraconsistent logic can be as useful as classical logic.
The universe may, in fact, tolerate real paradoxes; such as time travel, or some property being true and not true.
I don't know, but I'm curious to find out.
Potter Suppositionalist "A probabilistic argument could be made given (1) how well theory fits the evidence, (2) explains the evidence and (3) the accuracy of it's predictions. " The point of empirically equivalent theories is that they are exactly equal on all of these accounts. They make the same predictions, so the accuracy of their predictions cannot be judged. They are both equally supported by the evidence, so their fit cannot be judged. They both equally explain the evidence, so their explanatory power cannot be judged. There is nothing that can empirically separate them. That's why they are empirically equivalent. . "The skeptical proposal that there may be perfectly equivalent theories under strict criteria is hypothetical. " They are not hypothetical. You have the universe moving at a fixed velocity and the various examples given by Earman in the video (7:33). . ".Science is free to use whatever tools are at it's disposal, which is why Newtonian mechanics could still be used for rocketry, despite the fact that Einstein's model of gravity is theoretically more accurate. In the same way, a logician is free to use different logic systems, which have different axioms and domains of application. " The key here is "use", which is very different from "claim to be true". Under my definition "verification" has to do with truth. looking at the root of the word, this makes sense. When something is verified, it is not shown to be useful, it is shown to be true. . . "I would argue that a theory is verified it has met certain criteria, but it doesn't mean it's true. It also doesn't mean it's the only theory available which might accurately fit some aspect of nature. " What criteria are those? As I note in the video, the argumetn may not apply to all definitions of verified. What exactly is yours? What is necessary and sufficient for something to be verified. . "Depending on your definition of universe I'm not sure if that's a coherent question, or if it is a hypothesis which can even be tested." Remember that notions of testability and falsifiability are also at question here. The problem is that, if we combine the two problems, we see that if you cannot test any one theory without testing the whole set of beliefs, and there are two sets of beliefs that are empirically equivalent, there is no way for you to make either assertion. You must not just suspend belief on the individual cases, but on the set of theories as a whole as they cannot be assessed alone. . ."There can be competing theories in science, and in the same way there can be competing logics in philosophy. There is no true system of logic, or unquestionable assumption. Paraconsistent logic can be as useful as classical logic." This seems like instrumentalism about science, which I am fine with. If you are not asserting that any scientific theory can be shown to be true, simply that we can use different ones, and that different theories are useful in different situations, I'm with you completely. It's asserting that they are likely or true that remains unjustified. . ".The universe may, in fact, tolerate real paradoxes; such as time travel, or some property being true and not true.
I don't know, but I'm curious to find out. " Interesting thought. I'm curious to attempt to find out too.
Carneades.org
*"The key here is "use", which is very different from "claim to be true". Under my definition "verification" has to do with truth. looking at the root of the word, this makes sense. When something is verified, it is not shown to be useful, it is shown to be true..."*
It would be a problem if scientists made the claim that various competing mathematical and conceptual models were _true_. But they generally don't make this claim and such models are provisionally held, even when they've been well substantiated. So this is a problem with semantics in the Philosophy of Science, rather than an issue in the practice of science.
*"What criteria are those? As I note in the video, the argument may not apply to all definitions of verified. What exactly is yours? What is necessary and sufficient for something to be verified..."*
That is a question for a philosopher of Science to solve. But everything in science is provisionally held, even after it has been confirmed by experiment and observation; and theories are never proven only disproven. It makes sense that verification, if such a word is ever used, should be taken to mean a provisionally held confirmation that some _T_ has passed the criteria for a scientific theory, withstood peer review and is scientifically fruitful.
Verified as a scientific _theory_, rather than verified as absolute _truth_.
*"They are not hypothetical. You have the universe moving at a fixed velocity and the various examples given by Earman in the video (7 :33)"*
That's a hypothesis, which is defined as a potentially testable idea. But scientists cannot pear beyond the universe to make such a measurement, nor don't we have an indirect method of conducting such a test. So it's not a scientific theory, which is some tested and well-substantiated explanation of the evidence. But I'll grant you this example.
*"This seems like instrumentalism about science, which I am fine with. If you are not asserting that any scientific theory can be shown to be true, simply that we can use different ones, and that different theories are useful in different situations, I'm with you completely. It's asserting that they are likely or true that remains unjustified..."*
When I talk about probability I'm referring to degrees of likelihood given our models and data. But my contention is that no matter how accurate some scientific understanding becomes, it will never be absolute, so it's never true in a strict sense. However, there are methods of calculating probability with variable uncertainty (Bayesian probability, ect).
*"Interesting thought. I'm curious to attempt to find out too."*
Good conversation, thank you.
Additionally, I'd be curious to hear what you think about paraconsistent logics sometime.
3:00
I feel that Zeno's paradox is at the heart of what you talk and the resolution the same.
In Zeno's case, the *existence* of infinite number of half-steps to the finish line prevented him, _conceptually_, from reaching the finish line. But because in every other context but conceptual there is always a smallest step involved, including reality, and thus the slowest racer on a Non-Zeno, non-contextual team will always beat out the fastest racer on a Zeno, contextual team.
9:50
Wouldn't we have to be equally skeptical of Modens Ponens as well?
After all, if p>q, it is also the case that p>(qvr) by addition, ... but also p>(qvrv~r), and so on and so on.
Thus, since p>q doesn't just imply q but qv(...), with an infinite number of trivial additions, then doesn't that make MP underdetermined and thus we should be skeptical of it just as we should any other theory? If so, I can't help but think that being skeptical about MP is itself an irrational position to hold since it's hard for me to imagine a system where one could discard MP and still be rational.
Otherwise, if we aren't comfortable with dismissing MP as saying *a* cause implies *all* effects, not just *an* effect...
... then why are we comfortable with dismissing theories as saying *a* piece of evidence (a cause) will imply *all* hypothesis (all effects) and not just *an* hypothesis?
The key, as I see it, is recognizing and removing trivial additions. In your example, the state of the universe, as being static or moving at constant velocity, is a trivial addition to the theory because it was trivially added to the fact that we already know q (Newtonian gravity) is true.
Thus, we could just as soon say that because we can't distinguish between Newtonian Gravity & Unicorns versus Newtonian Gravity & No Unicorns, then we are justified in saying that Newtonian Gravity and the very framework upon which it's built are all irrational.
godam u crazy as hell but good ideas but kinda sussy but cool
also like imo this does call it irrational but in practically we off course know this does not matter
Yes. No one can know anything. There is and there is not reality. This is where philosophy and religion join hands and jump down the rabbit hole. When you can prove any point on any side of an argument or issue by reference to an equally valid tenet of a discipline, I think that all meaning, usefulness and relevance of that discipline evaporate.
lreadlResurrected So ethics have no relevance? Logic has no relevance? Truth? Beauty? Just because you can't find a way to know something, doesn't mean that there isn't one. Why would you give up on a pursuit just because you have failed now? My skepticism does not assert that nothing can be known, it just seems that we haven't figured out how to know something yet.
I did not really get an addressing of ethics out of my view of this piece, but maybe I need to watch it again. The point I got was along the notion that the scientific method is substantially invalidated by its arbitrary(?) methodology.
When, as you seem to assert here, philosophy of equally valid authority can be used to prove both sides of a logical issue, yea, even the validity of logic itself, then it (philosophy, not logic) is rendered inert.
Regarding the pursuit you describe above: Ah, but isn't that more or less a distinction without a difference? What holy grail is it for which you search? What tool is necessary for the job? Is it one that exists but is not being used correctly? Or perhaps one that has yet to be conceived? Is this not sounding more and more circular and almost starting to border on, if you'll excuse the expression, woo?
Carneades.org «My skepticism does not assert that nothing can be known, it just seems that we haven't figured out how to know something yet. »
Does it seem that we will ever figure out? Does it not seem to be a fruitless quest?
@@yunoewig3095 Does that not seem to be fallacious? There's no entailment from what's been stated so far that therefore it's fruitless.
this tread is so depressing omg
This was outstanding. I got a lot out of this. Loved the idea that different theories could use the same evidence.
The article at stanford about underdetermination is really amazing. But as regards the argument you made using Kukla, notice that we cannot conclude from "there is no purely empirical way we can decide between T and T' " to "there is no way we can rationally decide between T and T' ". If we simply apply Bayes theorem to calculate the probabilities of both given some evidence E, assuming that both entail the evidence (i.e. P(E|T) = P(E|T') = 1), and considering that T' = not-T and E, we would have the conditional probabilities P(T|E) = P(T)/P(E) and P(T'|E) = P(E|not-T)*P(not-T)/P(E) = P(not-T|E). Now, if we have P(E) < 1, (i.e. if the evidence is not a COMPLETELY UNDOUBTABLE NECESSARY FACT, that we can know even purely a priori and prior to experimentation) this yields P(T|E) > P(T), which in turn yields P(not-T|E) < P(not-T) and subsequently P(T'|E) < P(not-T). As such, upon learning E, the probability of T rises, and of not-T lowers. In particular, if we assume P(T) = 0.5, this proves that P(T|E) > P(not-T|E) = P(T'|E), and as such we can say that T is better than T'.
Of course, you may object to the choice of prior for T, but considering that T is a theory formalized in some logical calculus, we should be able to give an objective probability semantics to this calculus and find at least an uniquely rational lower bound for the probability of T. (for instance, if its algebraization by the Lindenbaum-Tarksi method yields a free Boolean algebra, giving 50% chance to its generators and assuming them to be independent, already determines uniquely a probability for all molecular formulas and gives upper and lower bounds to several quantified expressions, if the language allows quantifiers at all).
If we do that, at least some theories may have prior probabilities bigger than or equal to 50%, and in this case even the anti-realist skeptical arguments will fail against them.
Fascinating comment! Thanks for sharing. I have a great deal of objections to Bayesian Epistemology many of which are drawn from the argument that I'm skeptical that you can create an objective system to identify the prior for T, I see no reason to assign 50% to each generator or to assume that they are independent without argument, but some very interesting ideas! Here's the intro video on my series on Bayesian Epistemology (th-cam.com/video/rWb7up_MoZc/w-d-xo.html).
Ok, I will watch and see if I can give a comment on those. Thanks for the reply!
weird question but im reading the comments to learn other perspectives do you think this is worthwile and actually betters my thinking or im better off reading from professionals?
So where is the next video? Or the previous videos come to that?
Here's the full playlist: th-cam.com/play/PLz0n_SjOttTenxXXdML7fOu1og3D9LaME.html
Thanks. I actually eventually found it.
That doesn't seem to be the case for pragmatists, ESR's and holistic verificationists.
No.
Okay so this one is going to get mathy.
So for a dataset, there are only a finite number of theories to explain the data. We can explain it with a first degree polynomial - the nest fit line. There is no need for any other line, because the best fit line is best.
We are able to explain the data better by curving the line and finding the best fit two degree polynomial to fit the data. We can increase the degrees of polynomials until the number of degrees equals the number of observations in yue dataset. A best fit polynomial with degrees equal to the number of observations in the dataset will pass through every point of data. There is no need to increase polynomials beyond that degree
Now, the best fit polynomial with degrees equal to the number of observations will only explain that dataset. It will be useless when the next set of observations is collected. So, the goal is to find what degree of polynomial will best explain new datasets.
If there are multiple degrees of polynomials that equally explain newly gathered data, here is where we will use occcum's razor and pick the lowest degree of polynomial that can explain the data best. Thus, we can get exact verification and econ beats philosophy again.