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Inductive Reasoning In Science

by Steven Novella, Apr 13 2009

Recently I received the following question from an SGU listener named Marty:

I’ve been debating with a friend about the nature of science, and he brought up the following argument:

“1. All inferences from experience to conclusions about the future presuppose the principle that the future will resemble the past. (Principle of the Uniformity of Nature)
a. If we suspect that the course of nature may change and that the past is no guide to the future, then all experience becomes useless and does not support any conclusion about the future.
2. Therefore, no argument from experience can support the principle that the future will resemble the past.
3. No deductive argument can establish the principle that the future will resemble the past.
4. Therefore, the Principle of the Uniformity of Nature cannot be rationally justified.
5. If the Principle of the Uniformity of Nature cannot be rationally justified, then inductive reasoning in science cannot be rationally justified.
6. Therefore, inductive reasoning in science cannot be rationally justified. ”

Your thoughts?

This type of question comes up frequently – they essentially are attempts to use philosophy to argue that science cannot lead to objective truth, therefore  science is not valid (or at least I can ignore it whenever I choose, which is typically how such arguments are applied). The problem with all such arguments is that science is not about objective metaphysical truth, but rather it is a collection of methods for making abstract models of nature and then testing those models against reality.

Inductive Logic

First a word on inductive reasoning, which is one of the types of reasoning in science (but not the only one). Induction is the process of going from the specific to the general, or forming a conclusion about the nature of the universe from a limited set of observations. One classic example is the fact that, so far, it has always been observed that the sun rises each day in the East. Therefore we can infer that the sun always rises each day in the East.

Induction is distinguished from deduction, which can be summarized as going from the general to the specific. If we take as a premise that the sun always rises each morning in the East, then we can deduce that the sun will rise tomorrow morning in the East. In valid deduction, if the premises are true then the conclusion must be true.

Induction is different – the observations may be true but because they are limited the conclusion may still be false. The classic example here is the observation that all swans ever observed are white, leading to the conclusion through induction that all swans are white. This was a reasonable conclusion until black swans were discovered in Australia.

Induction and Science

Science certainly involves induction, but it is not limited to it. But because much of scientific reasoning is inductive that has lead to the philosophical question of how valid are conclusions in science. This is not a new question, and Marty’s friend would do well to investigate some of the extensive discourse on this question.

Philosopher Karl Popper had an interesting answer to this question – inductive reasoning does not exist, and therefore science is not induction. Rather he focused on verification and falsification. He argued that science comes up with hypotheses and theories that make predictions and therefore can be tested. He also noted that there is an asymmetry to this in that thousands of verifications cannot prove a theory correct, but one falsification can prove it wrong. Therefore the ability to be falsified is a necessary feature of any truly scientific idea.

This also means that no theory can be absolutely validated – only tentatively validated. Therefore science never arrives at absolute certainty. There may always be a black swan to be discovered out there. But scientific induction can lead to conclusions that have been validated to such a degree that we can comfortably act as if they are true. I don’t think anyone should waste any time or resources preparing for the possibility that the sun will not rise tomorrow.

Much time has also passed since Popper, and his ideas have been greatly extended. I will ignore for this post what I consider to be a huge diversion into post modernism but rather fast forward to a more contemporary vision of the nature of science.

While Popper, in my opinion, was essentially correct his view was incomplete. For example, science does not only consider one hypothesis at a time. Rather collections of theories are evaluated together over time by a community of scientists. Each theory must not only survive falsification it must also be consistent with other established theories – it must fit into the web of evolving scientific theories.

There are also other processes to consider in science, such as causal inference. Science does not just describe what exists or what happens in nature, it tries to explain how things happen – what causes what. For example, we may investigate genetic causes of the color of swans, or even the effects of various pigments on the absorption and reflection of various frequencies of light and how they affect the cones in our retinas.

Causal inferences often also require triangulation from multiple independent lines of evidence. Evolution, for example, cannot be established by one line of evidence, but requires many – the fossil record, genetic homology, developmental biology, population genetics, etc.

The Principle of Uniformity

The reasoning employed by Marty’s friend does not seem to take into account the actual nature of scientific conclusions. What they are saying, essentially, is that science does not yield philosophically certain truth – conclusions that must be true. This is correct but irrelevant, since that has never been part of science. Rather science comes up with models of nature and then tests those models. It retains those that are validated, but only for as long as they are validates, while continuing to try to falsify even previously validated ideas. It rejects or modifies falsified ideas. Scientists also try to infer causality in order to develop an increasingly complex abstraction of nature which makes predictions that can be further tested. And all the independent threads of scientific ideas must weave together into one seamless web.

The notion that there is temporal uniformity in nature – that the future will resemble the past is not really a premise of scientific induction but rather one thread in the tapestry of science. It itself is a hypothesis that makes predictions and can be tested. For example, we have been measuring the speed of light very accurately for decades. If the speed of light were not constant and changed over time we could detect it. Therefore the constancy of the speed of light is falsifiable, but so far has been verified.

The same is true of all constants and laws so far discovered in nature. The laws of nature do not appear to change over time, and they also appear to exist throughout the universe. The principle of uniformity has been verified so far.

The only refuge for someone denying the utility of scientific induction and scientific reasoning more generally is to say that nature is so capricious and inscrutable that we cannot even reason about the principle of uniformity, or any other basic law or constant. However, such arguments, as the one above, generally take the form of using logic to demonstrate that science cannot reach conclusions that must be true – logically, 100%, metaphysically true. They then conclude that science is not valid, or “cannot be rationally justified.” But this is a false premise, because science has never been about logical truth, as I described above.

The real question is – is science pragmatically valid. Does it do what it claims to do. Here we have the metaexperiment of science itself. Over the last few centuries of formalized scientific investigation, what has science produced? If nature were inscrutable and the laws and constants that we infer from it of no utility, then science should not have progressed much or at all over the last few hundred years.

And by progress I do not mean just the ability to weave explanations of how the world works – any system can potentially do that. Rather I mean has science given us an increasing ability to make predictions about nature that are later validated. Here the answer is clearly yes. If the principle of uniformity and all of our abstractions about gravity, mechanics, electricity, and the structure of the solar system were of no utility, then we could not send a hunk of metal from the earth and guide it to a distant planet and receive as reward stunning pictures of Saturn.


I may not be able to prove philosophically that the sun must rise tomorrow, but I can infer from observation and induction that it is overwhelmingly probable that the sun will rise tomorrow (and I can even predict when and where). As Stephen J. Gould wrote:

In science, “fact” can only mean “confirmed to such a degree that it would be perverse to withhold provisional assent.” I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms.

24 Responses to “Inductive Reasoning In Science”

  1. “If nature were inscrutable and the laws and constants that we infer from it of no utility, then science should not have progressed much or at all over the last few hundred years.”

    I dub thee Novella’s Principle Of Utility.

    In the ongoing debate between scientists and nonmaterialists, post-modernists, metaphysicians, et al, I sometimes get a little frustrated with the depth and complexity of the scientific arguments for the efficacy of science, feeling it too often arcs 45 degrees over the recipients’ heads. How much clearer and precise to simply state “it works”.

    Any argument or philosophy that would unseat science as the preeminent method for reliable, practical discovery must also explain why this ‘rationally unjustified’ method nonetheless works.

  2. Miko says:

    It’s also worth pointing out that the initial argument is invalid since making presupposes that it isn’t true: by making an argument that the future need not resemble the past, you are presupposing that the words you are using have specific meanings, will continue to have those meanings in the future, will be translatable through certain media both now and in the future, and will be recognizable and comprehensible to your listener/reader at the future moment in which they are perceived. If one truly didn’t believe that there was a reason to suspect that nature would (at least to some degree) be uniform in the future, one would have no motive to use language to convey this fact, and so one that argues thus (other than as a philosophical exercise) is being deceitful.

  3. howlingmadhowie says:

    it’s rubbish, isn’t it? science works. that’s the most important thing. whatever philosophical ponderings you can create about the validity of science, the lightbulb still does turn on when i flip the switch. if it will tomorrow or not is unimportant. if the laws of science changed to that extent, we wouldn’t be here to consider it.

  4. Matthew says:

    This is an outstanding explanation. Well done.

  5. miller says:


    How much clearer and precise to simply state “it works”.

    The problem is, how do you know that it will work in the future, without first presupposing that the future will be like the past? This argument is utterly unpersuasive! But, yeah, I’m persuaded by it. :)

  6. Don’t need to know. You adjust PRN. It’s a ‘so far, so good’ proposition.

  7. howlingmadhowie says:

    you could argue that science is about discerning laws from past events. the application of the law to predict the future is engineering :)

  8. MadScientist says:

    Hahaha; this is even more amateur than Thomas Aquinas.

    1. This statement is vague and almost meaningless, but let’s interpret the “future resembling the past” as “repetition of known experiments will continue to produce results consistent with past experiments”
    1.a. This is already wrong; it does not quantify what must change and by how much. Today we see a tree and tomorrow it’s a smoldering stump; obviously the past observation was no indication of what the future observation would be in this case. However, if I push a silly person off a cliff’s edge I expect them to fall today, I would expect another silly person to fall when I push them off a cliff’s edge the next day and so on. At any rate, ‘1.a’ is immediately obvious as being bogus and you really have to be extremely generous (and wrong) to accept such a ridiculous claim.

    2. What is the basis for this ridiculous claim? It’s obviously ass-backwards unless we limit ourselves to the alleged arguments and accept the bogus claim in 1.a as true. If we look at the real world, much of it looks the same as yesterday; in fact many things change so slowly that we don’t immediately notice. As far as (1) goes, repeated experiments still produce consistent results.

    3. This is incorrect and requires one to accept that (2) and (1.a) are absolutely true. The claim that ‘deduction cannot establish a principle…’ is nothing but a silly word game; a banana cannot sing the Star Spangled Banner either, but what has this got to do with the basic claim that we cannot make any predictions whatsoever about the future?

    4. Even more nonsense. Since this nonsense presupposes all the previous nonsense, why waste time explaining.

    5. Since the ‘principle of uniformity of nature’ was not adequately defined to begin with, this is an absolutely lame statement. The insinuation that the validity of inductive reasoning is dependent on a false premise put forth by the debater is laughable.

    6. Stretch this nonsense to over 800 pages and you can earn a place next to Thomas Aquinas in the Hall of Stupid.

    The arguments are specious and absurd to begin with and thus establish nothing. Science doesn’t even come into the picture. There aren’t even any funny misdirections like “Nothing is better than a big juicy steak. Breadcrumbs are better than nothing. Therefore breadcrumbs are better than a big juicy steak.”

  9. AL says:

    I’ve never been a fan of the Popperian argument that falsification is deductive. To me, falsification is inductive as well. If you make an experimental observation that contradicts the prediction of a theory, you cannot immediately deduce that the theory is false. You must still ask yourself if you perhaps made an observational, experimental or measurement error. Only after you repeatedly and consistently observe a series of observations that contradict a theory, then you can (tentatively, because it may still be discovered later your observations were biased) conclude the theory has been falsified. This is still induction through and through.

    That said, this argument about science presupposing the uniformity of nature is somewhat peculiar. To me, science is about describing the universe. Certainly, the more interesting descriptions are the ones that we can make predictions from, in other words, the ones for which some kind of uniformity from past to future holds. But if it turns out our universe were entirely capricious and whimsical, lacking any uniformity, then we could still have one descriptive albeit uninteresting and entirely useless scientific law: “the universe is capricious and whimsical.” This law would be entirely of no utility to us,* unlike using gravitational laws to launch ships into space, etc., but it would still be a law in the sense of a generalization grounded by the empirical evidence.

    *This of course assumes that intelligent observers can exist in a universe that was entirely whimsical and capricious, which I would argue can not be the case, since brain function requires, among many many other things, your sodium channels to behave regularly and not whimsically.

  10. Rob says:

    OK. Tell your friend to take a gun, stick it in his mouth and pull the trigger. I bet he will not take you up on it. Why? every other time this happened it was not pretty. But how does he know that THIS TIME he wont get a ice cream sundae in his mouth?

  11. MadScientist says:

    @Rob: yeah, I usually put that sort of thing to self-proclaimed philosophers, except that I never tell them to use a gun. The funny thing is they never do follow through because they understand as much as anyone else that things will not change so drastically overnight simply because they publicly deny consistency. On the other hand, if someone were deluded enough to try it on, I’d have an interesting time explaining things to a judge and jury. I could still get in trouble for prodding a delusional person into doing something stupid. People are sometimes deluded that badly though. Only a few years ago there was news from the Philippines that some small sect attacked some military troops in the belief that some amulet they were wearing made them impervious to bullets. Unfortunately some troops died because they really didn’t want to shoot people they deemed to be outgunned; the sect members of course didn’t fare so well when the military fought back. Another case that comes to mind is the Chinese Boxer Rebellion. Then of course you have the whacko cults by people such as David Koresh and Applegate – those particular whack-jobs may no longer be a threat, but you can safely bet there are others.

  12. Max says:

    I often hear how scientists are thrilled when new observations challenge the prevailing theory, because it means they made a new discovery.
    But you know who’s not thrilled? Decisionmakers who have already based decisions and policies on the prevailing theory, women who developed breast cancer or heart disease after being placed on hormone replacement therapy, and anyone else with a stake in the prevailing theory.

    For example, take safety standards. Last time I checked, there was no evidence that the powerful magnetic fields used in MRI damage tissues, but common sense says that extreme doses of anything are unhealthy. I’m sure that X-rays were deemed safe when first invented. What’s the chance that science is wrong about MRI, and common sense is right? Can you put a number on it?

    Given that every scientific theory is a work in progress, at what point is there enough confidence to base major decisions on it? When even the most reductionist discipline of Physics has no clue what 95% of the universe is made of, what hope is there for the study of complex systems like climate, economy, and the human body and mind?

  13. Well, that’s it. Science is done. No point in going on with it.

  14. AL says:

    “Given that every scientific theory is a work in progress, at what point is there enough confidence to base major decisions on it?”

    This is something everybody has to deal with everyday, whether they are scientists or not. Everybody has to make decisions in the face of imperfect information. Science is still the best way to make inferences from imperfect information, and I challenge any dissenter to propose a better method. Good luck with that.

  15. Max says:

    Well, that’s it. Devil’s Advocate answered my question. No point in going on with it. Turn the population into guinea pigs.

  16. “When even the most reductionist discipline of Physics has no clue what 95% of the universe is made of, what hope is there for the study of complex systems like climate, economy, and the human body and mind?”

    Max, when you declare that the sciences of meteorology, economics, and biology are pointless because current science doesn’t know everything, expect ridicule.

  17. Max – there will always be uncertainty in medicine. And no data can prove a risk of zero for anything. However, statistics can be used to analayse data and conclude, for example, that there is a probability of X that the risk of a particular negative outcome is smaller than Y. There is a very high probability that any risk from MRI scan is very small.

    Also, in medicine we do not deal so much with absolute risk but with relative risk or risk vs benefit.

    So to answer your question directly, there is no magic threshold of confidence, but for many question we can say that we have sufficient confidence on which to base policy. Other question are currently unknown or controversial, and there is everything in between.

  18. Max says:

    Dr. Novella,

    If you know about black swans, then you know my concern. When scientists or economists estimate risks, how can they take into account the possibility of the unexpected? Before black swans were discovered, what was the probability that all swans are white? Even now, what is the probability that there are no green mammals other than the acouchi? Induction says the probability is high. My intuition says it’s low. How much money would you bet on it?

    “The Week” magazine had a contest for readers to come up with a headline about a new study that discovered something really obvious.
    The winner: “New study finds that most new studies are overturned by future studies.”

  19. Richard Smith says:

    @Max (#18): That degree of uncertainty about probabilities can quickly lead to remaining indoors to avoid what the statisticians claim is the extreme unlikelihood of a bus running you over on your front porch. Then again, what odds do they give of a meteor’s direct impact on your home?

    When it comes to personal intuition versus induction, intuition tends to come a distant second. Two words: Monty Hall.

  20. Max says:

    How often do buses run over people on their front porch, and how often does the accepted scientific view later turn out to be wrong?

    Two more words: Extraterrestrial intelligence. Intuition says it’s probable, induction says it’s improbable. What would you bet your money on?

  21. Richard Smith says:

    Regarding the possibility of extraterrestrial intelligence, this probably requires upping the ante to three words: I don’t know. The current statistical sample size is fairly limited. “All indians walk in single file – at least the one I saw did.”

    As for the infrequency of domestic bus fatalities, how confident are you about that?

  22. tmac57 says:

    Max-“When even the most reductionist discipline of Physics has no clue what 95% of the universe is made of, what hope is there for the study of complex systems like climate, economy, and the human body and mind?”
    I can imagine at the time of the invention of the abacus that someone might have wondered ” Yeah, that’s all well and good, but what if I wanted to do billions of calculations a second? That will never happen!” Science marches on my friend.

  23. Andres says:

    Sounds like the argument this fellow put forth was heavily influenced by David Hume and his ‘problem of induction’.
    This type of argument is by no means a way of the religious to try to overthrow the validity of science, since Hume himself was the originator of it.

    I do like Poppers response to it. You may want to look at Emmanuel Kant’s response to the problem of induction as well.

    Great stuff.
    Unfortunate when people get so pissed off as soon as someone challenges the notion that ‘science is the begetter of all truth’ (something many skeptics like Shermer like to say).

    I’m glad Dr. Novella embraced the challenge and answered it rather than ridiculed this guy and called him a ‘psuedo-philosopher’ like Aquinas.

  24. MS says:

    Critical rationalism / falsification solves the problem of induction so even though Hume’s argument is valid, the _logical_validity_ of science does not need to rest on induction at all.

    The notion that falsification has inductive elements has been talked about many times before and is brought up in this thread. But that post shows a lack of understanding about this issue that unfortunately to many have. Not a single attack against Popper’s approach or against critical rationalism has ever survived. In fact, all these attacks were anticipated and adequately dealt with by Popper in the 1930’s. This and more is detailed well in David Miller’s two must read books on Critical Rationalism. (Find his website for articles online). Induction and the philosophers that support it are to put it bluntly just ignorant, intellectually dishonest or living in denial.