# How does induction relate to falsifiability?

I was thinking about the question How can I know that I am not immortal? and started wondering about the relation between induction and falsifiability.

Regarding the cited question, one thinks: well, so far every one of the 100 billion human beings that ever existed died (supposedly, since we didn't verify every and each one, but let's assume). Hence, there is a high probability that I am also mortal.

But if one would choose a scientific hypothesis based on the criteria of falsifiability, the one to choose would be "I am immortal", since it's falsifiable.

I know we can add deductive reasoning from other sources of knowledge (like our knowledge of biological mechanisms), but for the sake of argument, let's stick with inductive.

So, my question is: in cases like that, how does induction relate to falsifiability, and when does one trump the other?

• Why would falsifiability urge someone to choose "I am immortal" over "I am mortal" as a falsifiable hypothesis? As I understand the question you want to stage a situation where induction and falsifiability lead to contrary hypotheses, but that simply isn't the case here. Also a scientific hypothesis usually does quantify universally ("Every x is mortal…"), not over a single case. – DBK Oct 29 '12 at 20:24
• Also note that while induction is a mode of inference, falsifiability is not. In this sense induction yields a (probable) conclusion, while falsifiability does not. (Falsification, not falsifiability, is a mode of inference, namely modus tollens.) – DBK Oct 29 '12 at 20:31
• @DBK I understand that falsifiability (not falsification) and induction play different roles. But as one tries to use those different tools for knowledge, there seems to be a point where they differ. Regarding the "I am immortal" hypothesis, it is easily falsifiable, since one simply has to die to prove it wrong. On the other hand, "I am mortal" is not falsifiable (or not easily), since one would have to check forever to see if death never came. That does not strictly contradict the induction, my question is regarding the overall relation between the two approachs. – Koeng Oct 30 '12 at 14:15
• The question is not so much which hypothesis you initially choose but which one you ultimately adopt. Supposing we start at a blank slate "I am immortal" is indeed a better hypothesis, but after looking at history it is conclusively falsified in a glance. Popper's position was that "induction" is a simple hypothetic deduction followed by confirmation in disguise: that data should be categorized in terms of "mortality" is hypothetical rather than inductive, but this step is so habitual, deduction of consequences so obvious, and confirmation so straightforward that we overlook their presence. – Conifold Aug 9 '16 at 20:25
• @DBK: "I am immortal" can be falsified easily, using a knife or a bullet. "I am mortal" cannot really be falsified - even if someone was a million years old, they could still be mortal. – gnasher729 Aug 10 '16 at 21:45

how does induction relate to falsifiability, and when does one trump the other?

Inductive Reasoning is the traditional tool of the Empiricism epistemology. Falsifiability or testability is Popper's criterion for demarcating scientific knowledge from everything else.

Perhaps a better formed version of your question would be:

How does classical Empiricism relate to Critical Rationalism and when does one trump the other?

So in your original question, the latter relates to the former most famously in the writings of Popper, first in The Logic of Scientific Discovery, then in Conjectures and Refutations.

Popper suggests his own Epistemology, titled Critical Rationalism, according to which the advancement of our knowledge goes as follows: Using creativity, you come up with a hypothesis (hypothesis here means a falsifiable statement or theory), then, you try to refute it by aiming to find counter examples of deduced statements from said hypothesis. As long as no successful such refutations has been made, your hypothesis remains a Tentative Knowledge. The other kind of knowledge Popper acknowledges of is not scientific. i.e., for Popper, all scientific knowledge is tentative in that it can never be ultimately justified. The only thing we can do is endlessly minimize our error towards an accurate description of reality.

This works, according to Popper, because if "If A then B" then given "Not B" we get "Not A". Now A is the hypothesis at question, and B is a conclusion deduced from A; If we are convinced that the conclusion is false, then by modus tollens, the hypothesis is refuted.

In this sense, every failed serious attempt to refute a hypothesis is a further corroboration of it.

The methodology suggested by the classical Empiricist epistemology, employing induction alone, is to say that if "If A then B" then given "B" we get corroboration of A. Popper attacks this by reminding us that this is not logically valid. "B" could also be explained by infinite other theories other then A. The only logical way around this is to say that A could not be true if "Not B" is true.

According to induction alone, Newtonian physics is true just as anything else is, including the Theory of Relativity. This is Popper's point: Only refutations progress our knowledge, and his canonical example is that of moving from Newton to Einstein. The newer theory replaced the old one (in terms of scientific explanation) only because it stood the tests in which the older one has failed.

It seems clear that in that case the induction should trump the non-falsifiability of the statement of "I am mortal", since it's a no-brainer ... But that no-brainer is based on intuition, not on a well defined reason.

Now this is exactly the point of Critical Rationalism. Popper is troubled by the fact that while such Inductive reasoning may seem to go hand in hand with common sense, it is entirely lacking any logical base. Exemplified in this here case by the following:

1. Your theory at hand suggests that "if men are mortal then they sometime die."
2. Your only evidence to provide here is that all the time men do die.
3. Hence, popper would note that all you have is an "If A [is true] then B [is true]" formed statement and then you have provided that indeed B is true.
4. His argument would be to stress the fact that from this point onward (as I have described above) A is true is by no logical means deducible. We all know that from "If A then B", we only get that "If not B then not A" (which is exactly the logical basis of his doctrine), but definitely not "If B then A".
5. As in, what you have provided, using Induction alone, does not leave you with the logical possibility to claim your "A" ("men are mortal").

when should one trump the other regarding induction vs falsifiability?

the answer in this context is Critical Rationalism always trumps over Induction.

• +1. But I still am not clear about the "I am immortal" hypothesis. Induction would lead me to think I am mortal, but "I am mortal" is not a falsifiable hypothesis, only "I am immortal" is... – Koeng Sep 6 '13 at 18:44
• @Koeng "I am mortal" is, as much as I can tell, not falsifiable per the Popperian criterion, because no set of potentially falsifying observation statements cold be provided for it. Hence, I believe, Popper would have considered it non-scientific. Indeed, why not choose the hypothesis "I am immortal" which according to this is scientific? Upon it's refutation it could somewhat be said that you are mortal after all :) – Geezer Sep 6 '13 at 19:46
• I'm not sure I can observe the refutation of "I am immortal" hypothesis. ;-) – Jon Ericson Sep 6 '13 at 22:45
• @SkepticalEmpiricist I understand, but that was the point of my question. It seems clear that in that case the induction should trump the non-falsifiability of the statement of "I am mortal", since it's a no-brainer. No scientist while investigating a question like this would ignore induction and say "damn, we have to suppose immortality, since mortality is not falsifiable". But that no-brainer is based on intuition, not on a well defined reason. So my question remains, when should one trump the other regarding induction vs falsifiability? – Koeng Sep 7 '13 at 6:13
• Ok @Koeng, I added part dealing directly with your issue, I think. Hope this helps. – Geezer Sep 7 '13 at 6:57

how does induction relate to falsifiability, and when does one trump the other?

Why Karl Popper wanted to say that the criteria of falsifiability is better than induction?

Popper wanted to say that induction is not justifiable. That a theory has been corroborated in the past "says nothing whatever about future performance." Popper wanted to say that it is possible to avoid assuming that the future will, or probably will, be like the past, and this is why he has claimed to have solved the problem of induction. We do not have to make the assumption, he tells us, if we proceed by formulating conjectures and attempting to falsify them. He says that, as a basis for action, we should prefer "the best-tested theory." This can only mean the theory that has survived refutation in the past; but why, since Popper says that past corroboration has nothing to do with future performance, is it rational to prefer this?

Without the inductive assumption, the fact that a theory was refuted yesterday is quite irrelevant to its truth-status today. So demising the inductive assumption makes nonsense of Popper's own theory of the growth of scientific knowledge. The more often a conjecture passes efforts to falsify it, Popper maintained, the greater becomes its "corroboration", although corroboration is also uncertain and can never be quantified by degree of probability. "Corroboration" is a form of induction, and Popper has simply sneaked induction in through a back door by giving it a new name.

Every falsification of a conjecture is simultaneously a confirmation of an opposite conjecture, and every conforming instance of a conjecture is a falsification of an opposite conjecture. If Popper bet on a certain horse to win a race, and the horse won, you would not expect him to shout, "Great! My horse failed to lose!" Astronomers look for signs of water on Mars. They do not think they are making efforts to falsify the conjecture that Mars never had water. For Popper, what Carnap called a "degree of confirmation", a logical relation between a conjecture and all relevant evidence, is a useless concept. Instead, the more tests for falsification a theory passes, the more it gains in "corroboration”. It's not so much that Popper disagreed with inductivists as that he restated their views in a bizarre and cumbersome terminology. Why scratch your left ear with your right hand?

• Nice answer. But in this case, "I am mortal" is still a non falsifiable hypothesis. The one that have been falsified over and over, gaining corroboration, is "every human being is mortal", from which I can deduce "I am mortal". Does that mean that "I am mortal" cannon be a direct scientific hypothesis (according to falsifiability only), but has to be indirectly deduced? – Koeng Feb 12 '13 at 14:22
• I didn't understand. Falsified over and over is not "every human being is mortal", but "every human being is immortal". In other words, confirmed over and over is "every human is mortal". – Annotations Feb 12 '13 at 15:20
• My bad, you're right. Consider what I said changing "falsified over and over" for "passing the test of falsification over and over". – Koeng Feb 12 '13 at 22:48
• The statement "all swans are white" and "no observation will ever show the existence of a non-white swan" are essentially equivalent from a practical perspective, but from a philosophical perspective they are certainly distinct. More importantly, the latter admits the possibility that there may exist swans which, even though they aren't white, can either make themselves appear white or conceal their existence altogether; the former does not. The practical differences between the statements are often insufficient to justify using the more verbose form in many contexts, but... – supercat Feb 6 '15 at 22:10
• ...when one is trying to use a scientific theory as the basis of an argument, such distinctions can matter. – supercat Feb 6 '15 at 22:12

Induction is a process that allegedly allows you to get theories from experimental evidence and then show they are true or probable or something like that. As Karl Popper pointed out, induction is impossible. Theories do not follow in any sense from experimental evidence since multiple different theories can be compatible with the same evidence, e.g. - Newtonian mechanics and general relativity were both consistent with a lot of experimental data gathered before the nineteenth century. There are other problems such as how do you know what information you should gather if you don't have a theory to point you in the right direction. More generally, it is not possible to justify any idea: to show it is true or probably true. Any argument has premises and rules of inference and you either have to justify those, which gets you into an infinite regress or assert that they are true without argument, in which case it is impossible to settle disputes about the stuff you assert and you could make mistakes. For example, people can and do make mistakes while doing experiments so if you assert that the experimental data are always right you will fail to notice lots of problems.

Popper provided an alternative: critical rationalism. Knowledge is created by noticing some problem with your current knowledge, guessing variations on that knowledge that might solve the problem and then criticising the variants until only one is left. All of the criticisms are also guesses about problems your ideas could have. Rationality consists in always holding your ideas open to criticism so you can try to eliminate mistakes, not in purporting to justify ideas, which is impossible. Falsification is where you criticise an idea using experimental evidence. All such criticism is conjecture and a conjecture about an experimental criticism of an idea might be refuted. A few years ago, some physicists at CERN thought they might have detected a neutrino moving faster than light, which would have been a problem for relativity, but this conjecture was refuted.

For more details, see "Logic of Scientific Discovery" and "Realism and the Aim of Science" by Karl Popper. Other books with good explanations of some of these issues include "The Fabric of Reality" and "The Beginning of Infinity" by David Deutsch.

Neither trumps the other, in fact, falsifiability is only relevant as a specific approach to induction.

Popper was dissatisfied that various other supposedly empirical theories failed to converge over time, and yet continued to elaborate themselves. Forcing risk via demanding attempted expansion as a critical criterion instead of respecting a steady state of simple continual consistency is meant to force out theories that won't converge. Continually seeing what you expect is not a good enough basis for a theory, because of confirmation biases, which ultimately make simple induction unconvincing.

Deploying falsifiability as the basis for induction is often called 'statistical inference' -- the 'statistical' reference is to Bayesian statistics, which vaguely apply even in the absence of the use of statistical methods.

If something is genuinely falsifiable, there must be a nonzero chance that it is false -- it makes a definite claim that may not be true.

Then by Bayesian reasoning, if the claim is not falsified by a few direct attacks, you can divide out the odds of its falsehood from the odds of the system from which it derives being nonsense. Requiring future statements to assume it is true theoretically increases the overall reliability of the system to which it is adjoined, if only by a tiny degree. The first few men you see die each reduce the odds that any other similarly-constructed man will be immortal, but after that, repeating it hundreds of times won't help much, the products of odds quite close to 1 stay quite close to 1.

Of course, this only applies if you think the interpretation of the theory as a whole is clear enough to have given chance of being false. Kuhn would discount that entirely -- no paradigm is so water-tight that you can actually use Bayesian statistics on it.

On the other hand, the odds of a given sub-theory being better than another, when they presume the same overall theory, might be close enough to matter. The basis they have in common puts bounds on the space of distributions to some degree. So Popperism is a good tool for what Kuhn calls normal science.

Who is the "I" that is being referred to in your question that is or is not immortal? Eastern religions say that what most consider the I - the physical mind or ego, dies with the body, but there is an inner consciousness which does not die. Who is the real "I"? Ramana Maharshi said that this is the one question we should only ask ourselves - Who am I? Enlightenment is knowing your real I, and not the I of the ego. When you know the real I, you are immortal. Joseph Campbell gave the illustration of the light bulb, the light bulb may burn out, but the electricity that gave the light to the bulb, does not. Vivekananda said that it was this sense of the real I in us that gives us the feeling that we will never die.

"Their relation"

Induction and falsifiability are two of the kinds of justification that discriminates which belief is "true".

"When does one trump the other?"

Firstly, this depends on the type of knowledge. For knowledge that's merely socially justified belief or mere sincere belief (e.g. most of religious beliefs), induction always trumps falsifiability because such kind of knowledge is immune to falsifiability. This also covers beliefs that are not falsifiable ("I am mortal").

Secondly, this depends on how practical it is to carry the tests. For knowledge that's of justified true belief kind, induction normally can provide the working concept, falsifiability the way of formulating the concepts in such a way for it to be testable, at least in principle.

So which trumps which depends on practicality of carrying out the tests, among other things. In the case of "I am immortal", testing is foolhardy so induction trumps falsifiability as a justification. But only because it is not advisable to do so.

Let's just say that your example is completely, completely wrong.

Out of the "100 billion humans", about 7 billion have not died. And there is no good evidence really that all the people who were born lets say 150 years ago or earlier are all dead, because for various reasons such people would be hiding their age and their birth date.