Does Science Presuppose the Existence of Regularity in Nature?

A popular criticism of Popper’s scientific method is that he “smuggled induction in through the back door.” Contrary to claims of having done away with it altogether, Popper’s proposed method of science actually presupposes induction. Therefore, critics argue, Popper failed to give an account of the scientific method which avoids the problems of induction.

One such argument has it that Popper’s method of science must presuppose that nature has regularities. If nature has no regularities, then any conjecture positing such must be false. In that case, every conjecture that has so far withstood attempted falsification is just a fluke and may begin yielding false predictions any time. If there are no regularities in nature for scientists discover, then the method of conjecture and falsification is a futile endeavour. Therefore, if Popper’s proposed method of science is to have any success, then one must presuppose there are some regularities in nature.

My responses to this argument are below the fold.

(1) The problem of induction is sometimes identified with the problem of justifying the existence of natural regularities: if their existence could be justified, then inductive inferences would, supposedly, no longer be invalid. However, all attempts to justify the existence of natural regularities using empirical testing assumed that which they were intended to justify and thus begged the question. The existence of natural regularities was unjustifiable.

The association between induction and natural regularities is so strong that they are often equivocated: to posit any natural regularity is often called an “induction.” Thus Popper is said to have smuggled induction back into science by presupposing the existence of natural regularities. However, despite the historical connection with induction, the mere existence of natural regularities is not logically strong enough to validate any inductive inference. Consider the following argument:

Some A are B
Therefore,
All A are B

This is a basic induction; the truth of the conclusion is not entailed by the premise. Now consider the same argument but fortified with the premise that there are some natural regularities:

Some regularities like “All x are y” are true
Some A are B
Therefore,
All A are B

Even with the assumption that nature has regularities, the induction remains invalid. Merely asserting that there are some regularities does not mean any particular regularity must be true. Both premises can be true and the conclusion false without contradiction. The assumption of natural regularities is not strong enough to validate any particular inductive inference. Even if Popper’s method of science must presuppose that nature has regularities, it need not have anything to do with a logic or procedure of induction.

(2) If Popper’s proposed method of science is to have any success, then there must be some regularities in nature. While that much is true, one need not presuppose that there are such regularities. The faulty assumption here is that the methods of science must presuppose their own success; this is not a standard we normally hold for other methods or procedures. For example, if John loses his car keys, then he might

(1) Check his pockets
(2) Retrace his steps
(3) Ask people nearby if they have seen his car keys
(4) Look between sofa cushions
(5) Check the pockets of clothes he wore yesterday

Alternatively, John could

(1) Assault a police officer
(2) Build a spaceship
(3) Whistle Christmas carols
(4) Wait for the keys to materialise in the ignition
(5) Read Das Kapital upside down

While it is conceivable that John will find his car keys by assaulting a police officer (e.g. the police officer previously stole John’s car keys), it is also clear which procedure would normally be a superior method of find lost car keys. But neither procedure need presuppose that John will be successful; it is possible for John to exhaust both procedures and for his keys to be lost forever. Likewise, it is possible that Popper’s method of science is the best method available for discovering natural regularities even if no such regularities are discovered or ever existed in the first place.

Since Popper’s method of science does not presuppose its own success, there is also no presumption that natural regularities exist.

(3) The method of conjecture and falsification turns the inductive vision of science on its head. Rather than proceeding from the results of tests to conjectures, Popper’s method of science places the conjecture first. For example, the induction,

Some A are B
Therefore,
All A are B

Becomes

All A are B
Therefore,
Some A are B

The lower argument is a valid inference (presuming a non-existential interpretation). Popper could do this because he rejected the notion that conjectures must first be justified by sense observation or test results. Falsification of the premise proceeds by searching for counterexamples to the conclusion. The methods of science are entirely deductive. Moreover, the existence of natural regularities becomes a deductive result of conjectures:

All A are B
Therefore,
Some A are B
Some regularities like “All x are y” are true

For Popper’s method of science, one does not have to assume that nature has regularities before making conjectures, because that is just part of what is being conjectured. Natural regularities come along for the ride, so to speak, as a logical consequence of whatever regularities are conjectured. No presumption of induction is involved. That some natural regularities exist is itself a conjecture, albeit one that cannot be falsified.

About Lee Kelly

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23 Responses to Does Science Presuppose the Existence of Regularity in Nature?

  1. Constantius says:

    Excellent argumentation, cheers!!! But one thing Lee Kelly, you must clarify the role (if any) observation statements has on conjecture formulation to ensure that no further confusion ensues from you post. Thank you.

  2. Lee Kelly says:

    Constantius,

    Part of the miscommunication between you are others on this blog is that we are making a sharp distinction between logic and psychology. For example, an observation-statement is not the same thing as some experience; it is not even the same thing as an observation-proposition. To be pedantic, experiences are not something which can actually be true or false: the proposition that someone had an experience may be true, but the experience that proposition is about cannot itself be true. The distinction here is one of events or occurrences and propositions about those events or occurrences: the latter are the only things it is proper to describe as true or false.

    Experiences are events that cause other events. Sometimes we might describe the discovery of a new hypothesis as the effect of prior psychological events; we might describe the discovery of new conjecture as the consequence of past experiences. However, this is not a logical consequence, but rather a chain of psychological or physical causes and effects. There is no sense in which those experiences are the premises of a logical inference with their effects as the conclusion: that would be a confusion of the logical and psychological (or perhaps physical, if we described the events in terms of neurons and brain states).

  3. 1Z says:

    (1) If the principle of the Uniformity of Nature is stated as something like “observed regularities will probably continue” then a valid syllogism can be obtained.

    Several instances of B’s succeeding on A’s have been observed
    Regularities observed in the past will probably continue.
    therefore, B’s will continue to follow on A’s.

    (2) The uniformity of nature need to be posited to explain how science
    works. It also needs to be posited to for conjectures to make sense.
    If it conjecture C is true of all things of type T, things of type T have to behave in a stable manner, or the conjecture is meaningless.

  4. d says:

    1Z,

    I see at least two problems with your approach:

    1. The syllogism may be valid, but that does not entail that they will be sound. What use, then, is the syllogism when it cannot tell apart sound from unsound inductive inferences? In other words, you’re tacking on an assumption that does not make inductive inferences more grounded, more probable, more certain, for it applies equally to sound and unsound syllogisms.

    2. The uniformity of nature you demand is already present within the logical content of the conjecture. If, for instance, I conjecture that all emeralds are grue (“all x are y” when expressed as Goodman predicates), the ‘uniformity’ I posit is the grue-ness of emeralds; if I conjecture that all emeralds are green (“all x are y” in English) the ‘uniformity’ I posit is the green-ness of emeralds.

  5. Lee Kelly says:

    1Z,

    What d said, plus:

    (1) Even if the principle of natural uniformity is merely probable, then the problem of induction remains: the new principle cannot be justified without begging the question. How probable is the conclusion of your argument? It has the same probability as the premise that observed regularities will continue, and how probable is that premise? Since it is a regularity, it must have the same probability as the premise that observed regularities will continue, i.e. the premise must have the same probability as itself. Therefore, the conclusion of your argument has whatever probability we initially assigned to the premise that observed regularities will continue, but we have no way of determining that probability inductively.

    (2) Your argument is actually invalid. The conclusion should be “‘it is probable that all Bs will continue to follow As.” This modified version of your argument reduces induction to a subset of deduction.

    (3) Read section 3 of my response again. Our conjectures imply that nature has uniformities; the methods of science don’t need to presuppose that uniformity. It is logically possible that such uniformities do not exist or will never be found, but the scientific method might still have been a good method for trying to find uniformities.

  6. Lee Kelly says:

    1Z,

    Suppose you wanted to falsify some scientific hypothesis. So you observe the initial conditions, use the hypothesis to derive observable consequences, and then measure the results. But after many experiments, the hypothesis remains unfalsified: every single prediction has been corroborated by the evidence. Suppose there aren’t even any anomalous or inconclusive results. Of course, none of this means the hypothesis is true, but suppose its competitors have not fared so well. The hypothesis you have been trying to falsify is the only competitor left on the table, and so, in the absence of any unfalsified alternative, you tentatively conjecture that it is true.

    Now, just because you have failed to discover anything to falsify the hypothesis, does it follow that your methods were bad? Did your methods presuppose that you would succeed? Let’s go one further and suppose the hypothesis is actually true and no falsifier is ever discovered: no falsifier ever existed in the first place. Now, just because you were doomed to failure from the outset, again, does it follow that your methods of searching for a potential falsifier were bad or presupposed their own success?

    By the way, thank you for commenting!

  7. 1Z says:

    2. The uniformity of nature you demand is already present within the logical content of the conjecture. If, for instance, I conjecture that all emeralds are grue (“all x are y” when expressed as Goodman predicates), the ‘uniformity’ I posit is the grue-ness of emeralds; if I conjecture that all emeralds are green (“all x are y” in English) the ‘uniformity’ I posit is the green-ness of emeralds.

    Quite. Uniformity is involved in all conjectures and attempted falsifications, so in itself it the best corroborated of all conjectures. Since a well corroborated conjecture can be treated as true enough to make deductions from by Popperians, the probablistic deduction which you have called a syllogism is not only valid but sound.

  8. 1Z says:

    d,

    “1. The syllogism may be valid, but that does not entail that they will be sound. What use, then, is the syllogism when it cannot tell apart sound from unsound inductive inferences? In other words, you’re tacking on an assumption that does not make inductive inferences more grounded, more probable, more certain, for it applies equally to sound and unsound syllogisms”

    The Uniformity principle is well corroborated, so sound. It is not a question
    of sound versus unsound syllogisms: the deductions is *probablistic* and
    so expected to fail in some case. All contemporary inductivists regard inductions as probablistic, so putting forward a number of non-probablistic syllogisms
    as examples of how it might work is not really trying.

    “Until about the middle of the previous century induction was treated as a quite specific method of inference: inference of a universal affirmative proposition (All swans are white) from its instances (a is a white swan, b is a white swan, etc.) The method had also a probabilistic form, in which the conclusion stated a probabilistic connection between the properties in question. It is no longer possible to think of induction in such a restricted way; much synthetic or contingent inference is now taken to be inductive; some authorities go so far as to count all contingent inference as inductive. “–SEP

  9. Lee Kelly says:

    1Z,

    Just because the existence of regularities in nature is a logical consequence of all scientific theories, it does not follow that it is a well-corroborated conjecture. Corroboration is not transmitted from premises to conclusion in a valid argument. A trivial example would be a member of the set of tautologies. A tautology is a logical consequence of all scientific theories, but tautologies cannot be corroborated, by definition, because they don’t predict anything.

    Falsifiable hypotheses have some unfalsifiable logical consequences. Sometimes these are metaphysical assumptions of the hypothesis, such as that nature has regularities or is deterministic. For example, Newtonian physics conjectured a clockwork universe of strict causal laws; metaphysical determinism was an implicit assumption that could be deduced from the theory. However, it would be mistaken to conclude that determinism must be scientific because it can be derived from a scientific theory.

  10. Lee Kelly says:

    1Z,

    What I think d is getting at is that the conclusion of your syllogism does not increase in probability with repeated observations of Bs succeeding on As. The probability of the conclusion is equal to whatever arbitrary probability is assigned to the premise that observed regularities will continue. Any and all “inductions,” regardless of how many repeated instances of Bs succeeding As are observed, will have exactly the same probability. Your premises don’t help us identify true theories, because they arbitrarily assign the same probability to all theories consistent with the evidence. That is, falsified theories get eliminated, but after that, all competing theories are equally “inductively probable.”

  11. 1Z says:

    Lee,

    “What I think d is getting at is that the conclusion of your syllogism does not increase in probability with repeated observations of Bs succeeding on As”

    Of course not. No syllogism could do that. Induction can only be a calculus of probabilities, which classical, bivalent logic, can only hint at it.

  12. 1Z says:

    d,

    I see at least two problems with your approach:

    “2. The syllogism may be valid, but that does not entail that they will be sound. What use, then, is the syllogism when it cannot tell apart sound from unsound inductive inferences?”

    I can see at least two problems with your approach. For one thing , syllogistic form ever says anything at all about soundness as opposed to validity.
    For another, the syllogistic form advertised as preferable, ie:

    All A are B
    therefore, some A are B.

    suffers from a worse version of the same problem. It is impeccably valid, but since “All A are B”
    is raw conjecture, and conjecture per se has no particular truth value or probability the soundness is of the syllogism is imponderable (it can’t even be said to be unsound). On the other hand, the Uniformity Principle is a well corroborated conjecture and can therefore found a (FAPP) sound syllogism,
    even by Popperian standards.

    “The uniformity of nature you demand is already present within the logical content of the conjecture. If, for instance, I conjecture that all emeralds are grue (“all x are y” when expressed as Goodman predicates), the ‘uniformity’ I posit is the grue-ness of emeralds; if I conjecture that all emeralds are green (“all x are y” in English) the ‘uniformity’ I posit is the green-ness of emeralds.”

    Grue can’t be a natural law, since it is specific to time. Unformity is a metaphysical principle. Not everything with the logical form “for all..”
    counts as a Uniformity principle.

  13. 1Z says:

    Lee,

    “(1) Even if the principle of natural uniformity is merely probable, then the problem of induction remains: the new principle cannot be justified without begging the question.”

    I don’t see what you mean. If the new principle is merely a special case of general
    uniformity, then the argument it no more question begging than:
    All As are B
    therefore,
    Some As are B.

    “How probable is the conclusion of your argument?”

    A syllogism can never tell you that. It is only a place-holder for some probability
    calculus.

    “It has the same probability as the premise that observed regularities will continue, and how probable is that premise? Since it is a regularity, it must have the same probability as the premise that observed regularities will continue, i.e. the premise must have the same probability as itself. Therefore, the conclusion of your argument has whatever probability we initially assigned to the premise that observed regularities will continue, but we have no way of determining that probability inductively.”

    We can calculate the probability of the conclusion relative to
    the premise. I don’t think anyone puts a low value on the premise, or
    Popperians would never board planes, in case the Bernoulli effect suddenly
    failed. Quantising Uniformity is a profound theoretical problem, but
    a non-issue For All Practical Purposes. Doing any kind of relativistic
    probability calculation, you would treat it as 1. Doing anything practical,
    you would treat is as very close to 1.

    “(2) Your argument is actually invalid. The conclusion should be “‘it is probable that all Bs will continue to follow As.” ”

    True. That is what I meant to write.

    “This modified version of your argument reduces induction to a subset of deduction.”

    So?It is unfair to complain that induction should be, but cannot be justified deductively, and then to complain that., if it can, it is no longer induction.

    “(3) Read section 3 of my response again. Our conjectures imply that nature has uniformities; the methods of science don’t need to presuppose that uniformity.”

    If uniformity is presupposed, and withstands falsification, then it founds what
    is , FAPP, induction. IOW, only one conjecture ever nneed be made.

    “It is logically possible that such uniformities do not exist or will never be found, but the scientific method might still have been a good method for trying to find uniformities”

    And they have been found. Why doesn’t that support the Uniformity priciple abductively?

  14. 1Z says:

    Lee,

    “What I think d is getting at is that the conclusion of your syllogism does not increase in probability with repeated observations of Bs succeeding on As. ”

    Again: only a probability calculation could be expected to do that.

  15. 1Z says:

    Lee.

    “Let’s go one further and suppose the hypothesis is actually true and no falsifier is ever discovered: no falsifier ever existed in the first place. Now, just because you were doomed to failure from the outset, again, does it follow that your methods of searching for a potential falsifier were bad or presupposed their own success?”

    I am not clear what you are getting at. I don’t reject attempted falsification
    or anything else in the Popperian canon. Popperians reject something I
    accept, that is the difference.

  16. Lee Kelly says:

    d,

    Look what 1Z wrote!

    All A are B
    therefore, some A are B.

    suffers from a worse version of the same problem. It is impeccably valid, but since “All A are B” is raw conjecture, and conjecture per se has no particular truth value or probability the soundness is of the syllogism is imponderable (it can’t even be said to be unsound).

    Isn’t that familiar?

    I have encountered the same assumption elsewhere, normally implicit, that supplying justification is part of what it means to make a logically valid argument. My first logic textbook explicitly stated that the purpose of the premises in a valid argument were to justify the conclusion. In a very weak sense this may be so, but then “justify” is merely a synonym for “entails” or “implies” — words already being used by the author. The intuition appears to be that without justification, one has no right to assign truth to any of the premises and, therefore, no right to deduce the truth of any consequence. Since “{A} entails {}” is false, logic without justification is incoherent.

    According to 1Z, the premises have no truth-value (or probability) because they are conjectured: the “soundness of the syllogism is imponderable.” Since one cannot deduce true consequences from premises with no truth-values, and only justified premises are permitted to have a truth-values, it follows that justification is necessary to make a coherent logical argument.

    We have no epistemic right to assign truth-values as we please. The right is granted to us by an authority, whether sense experience, the intellect, or maybe religious texts. Allowing any conjecture to be assigned a truth-value would create epistemological anarchy: how can we reconcile disagreements without an authority that tells everyone what it is proper to believe?

  17. 1Z says:

    The “authority” of the senses is fine by me, by all scientists. and by most people in general.

    It is just silly to compare empiricism to an ad hominem kind of authority.

  18. d says:

    Lee,

    Upon reading 1Z’s comments, I was struck by a serious case of deja vu as well.

    1Z,

    You say, “Grue can’t be a natural law, since it is specific to time. Unformity is a metaphysical principle. Not everything with the logical form “for all..”
    counts as a Uniformity principle.”

    By prohibiting a priori the maturation of emeralds, acorns, grapes, children, &c., you’ve just forbidden them by your say-so. But why?

    Furthermore, I need not even bring up Goodman predicates for the objection to stand–it’s merely the most ‘outlandish’ example. Think of all sorts of possible ‘natural laws’ that are invariant to time that are unsound after assuming a Uniformity of Nature and collecting a finite number of corroborations.

    In short, you’ve just begged the question in order to solve the problem of induction, but your begging the question cannot tell the difference between a true or strictly universal statement that has been presently corroborated. It does nothing but (1) push the problem back one more step while (2) not solving the initial problem (even after assuming a Uniformity of Nature, a false strictly universal statement may have a high probability assigned to it, no?).

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  21. DS says:

    Hello Lee,
    I’m not sure if you or anyone else is monitoring this post or not, but I do not quite understand (& yet would like to!) our second response to the objection that falsificationism relies on nature being uniform in some relevant ways:

    “(2) If Popper’s proposed method of science is to have any success, then there must be some regularities in nature. While that much is true, one need not presuppose that there are such regularities. The faulty assumption here is that the methods of science must presuppose their own success”

    Isn’t this issue with falsificationism (about it having to assume that the future will resemble the past in the relevant ways, that is, with respect to the single falsifying instances observed) about whether or not falsificationism is *justified* as a scientific method (any more so than one based induction), and not about whether or not falsificationism needs to be able to *predict* its own success? And isn’t it only justified in its principle of single negative instances being able to falsify a universal hypothesis, if that negative instance continues to be such tomorrow just as it was in today’s experiment?
    What I mean is, by taking any empirical observation (whether it negates or seems to support a given hypothesis) as true, for any time after the experiment is conducted, imply that we believe there to be some sort of relevant uniformity to the world with respect to that observation?

    And anyway I also wonder how someone advocates falsificationism without believing (let alone knowing) it will have any success, why would they be driven to advocate it in the first place?

    Hopefully someone sees and responds to this post. I would greatly appreciate an elaboration of (2) in light of these questions…

  22. Lee Kelly says:

    Hi DS,

    I apologise for not responding sooner. I began a response earlier this week, but it transformed into my most recent post, Science: An Effective Method?.

    In any case, before responding to the criticism you mention, let me offer a comment and clarification.

    First, the term ‘falsificationism’ is misleading. I’ve used it before, but I’ve never been satisfied doing so. It’s used almost exclusively by critics and is associated with ‘naive falsification’ or positivist criteria of meaning. In my experience, the term is good only for sowing confusion.

    Second, I originally intended to follow this post with another to address the particular criticism you mention, but I never got around to it for some reason. While the issues here are related, I believe they are logically distinct.

    Okay, the matter at hand: when we assume that an experiment that falsified a theory in the past will continue to falsify it in the future, is this an implicit inductive inference?

    Of course, my answer is a resounding no! For one, this assumes that induction is possible, but that is just part of what is in dispute. However, let’s put that matter aside, since there is a simpler response.

    A falsification occurs when theories clash. Each predicts that, for a given experiment, the other will be falsified. So, why do we think that falsifying experiments of the past will continue to falsify in the future? Because that is what the surviving theory predicts!

    For example, why do we expect Newtonian physics to continue to be falsified by experiments that falsified it in the past? It’s because Einsteinian physics not only predicts those experimental results, it also explains why Newtonian theory gets them wrong. That is, if we conjecture that Einsteinian physics is true, then it follows that Newtonian physics will fail experimental tests where Einsteinian physics predicts it will. There is no need to induce anything about future experiments from past experiments, because we can deduce all we need to about such future experiments from the rival (unfalsified) theory.

    Hopefully, this response if clear enough. If not, I'm happy to clarify.

  23. Vagif says:

    Hi everybody. Hello Lee.
    The last comment has been made long time ago.
    The discussion over here is interesting. I want to add.
    What about regularity in…….Fortune’s “behaviour” which means PREDICTABILITY, as You all know. Can’t be?
    I found it can!!! After my everyday observations for the last 7 months.
    All I can say now is that this “behaviour” is chaotic, as expected. But inside this chaos I found pure regularity.
    Will be happy to share the results of my observations.
    agasanov74@gmail.com

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