# Deduction vs Induction — are they equally valid?

I've been reading on deduction vs induction as two primary modes of reasoning. Can't exactly remember where but I have also seen deduction being described as backward and induction as forward thinking. I understand that the former starts with an assumption and then seeks out ways to confirm or disconfirm it using observations and evidence whereas the latter starts with observations and evidence to abstract out resulting theories.

I was just wondering if one method has been generally considered more valid or at least preferred, in academic or other credible communities, than the other. Excuse my bias but, in my humble opinion, induction appears as more scientific and valid while deduction appears like not much more than confirming existing biases.

Or is it an apple vs orange comparison of two concepts that are differently applicable depending on the context?

Deduction is a useful way of working out the consequences of an idea in some contexts. This is useful for science since it allows you to do stuff like working out whether two theories are consistent with one another, or to work out the consequences of a theory so it can be experimentally tested.

Induction is supposed to be a method that does the following. (1) It starts with experimental data or observations. (2) From those observations it somehow gets a theory. (3) Further observations somehow show the theory is true or probably true.

Induction, as described above, is impossible. It is not a method that can be followed. As such, nobody has ever followed it. Nor will anyone ever follow it.

The problems start with the first step. What are you supposed to observe and why? What experiments are you supposed to do and why? How are you supposed to construct an experiment without knowing what to look for?

The second problem is that no number of observations is equivalent in any sense to a theory. It's not even equivalent to an explanation of a single event never mind an explanation of how the whole world works. Your experimental equipment records some events that happen during the experiment and not others. The unobserved events in general contribute to the outcome so that if you get them wrong you mess up the experiment. For example, you may observe the distribution of electrons reflected from an object in an electron microscope, but you don't observe the electrons while they are at the object you're trying to look at, nor while they are in flight. You guess that the electrons are not doing anything unintended and you learn about faults by seeing that the results look wrong if you do stuff wrong. The third step is also impossible for the same reason, and also because a theory refers to events that nobody could ever observe, e.g. - nobody was around 70 million years ago to observe an actual dinosaur.

Karl Popper solved the problem of induction: that is, the problem that induction is impossible and so can't be a method used by scientists. Science actually works by noticing a problem with a current explanation, guessing solutions to that problem, criticising the solution until only one is left and it has no known criticisms and then moving on to a new problem. See "The Fabric of Reality" chapters 3 and 7 by David Deutsch, "The Beginning of Infinity" by Deutsch, Chapters 1 and 2 and "Realism and the Aim of Science" chapter I by Popper and "Objective Knowledge" Chapter 1 by Popper.

So the distinction between induction and deduction is that deduction is sometimes useful and induction is nonsense.

• "Pure" induction is usually distinguished from the hypothetico-deductive model of science where one dreams up various hypothetical models of how the world might work, deduces their experimental consequences, and compares with empirical reality. This is compatible with Bayesian hypothesis testing, where instead of trying to absolutely falsify any theory one updates the subjective probabilities one assigns to different theories based on the results of empirical tests (usually considered a type of inductive reasoning though not 'pure' induction of the kind you describe) – Hypnosifl Feb 6 at 19:46
• See people.loyno.edu/~folse/HypDeduc.html and people.loyno.edu/%7Efolse/HypDeduc5.html (from the philosophy of science course site at people.loyno.edu/%7Efolse/Phil236f02.html ) for more on the difference between the hypothetico-deductive model vs. the purely inductivist model, and see the "criticisms" section of people.loyno.edu/%7Efolse/Popper.html along with my comment at philosophy.stackexchange.com/a/76670/10780 for problems with Popper's falsificationism as a model for how science works (in my comment I argue for a Bayesian/hypothetico-deductive model) – Hypnosifl Feb 6 at 19:50
• There are many criticisms of Bayesian epistemology by critical rationalists, such as curi.us/1417-bayes-and-induction and youtube.com/watch?v=wfzSE4Hoxbc There are no answers to any of these criticisms. – alanf Feb 7 at 22:17
• Your criticism of Popper was answered by Popper youtube.com/watch?v=TYO54PggzXA The criticisms section of the website you linked states some criticisms of Popper, including the criticism by Putnam. The authors state that Popper stonewalled these criticisms, but provides no examples, despite the fact that Popper explicitly replied to Putnam in Volume 2 of "The Philosophy of Karl Popper" edited by Schilpp and in other places. This is bad scholarship and bad philosophy. – alanf Feb 7 at 22:27
• I took a look at that youtube video and the sections of Popper's book "The Logic of Scientific Discovery" that it references, but from the book (especially chapter 4 which the video draws our attention to), Popper doesn't seem to be addressing the objection that falsifying evidence can a matter of degree of confidence (as is confirming evidence, which he doesn't think exists at all), instead he is talking about an idea called "conventionalism" which takes a more nihilistic position that whether evidence favors a theory is purely a matter of the conventions we adopt, – Hypnosifl Feb 8 at 23:00

At least if you use the sharp philsophical meaning attached to deduction and induction, then deduction is more valid than induction.

One major reason is that deduction can't go wrong, while induction can always go wrong. No matter how many white swans you've observed, the next one could always be a black one. On the other hand, if you start from 'all swans are white' and you find one black swan, you can deductively reason that your first statement is false.

You can also see that the deductive sciences, logic and mathematics, are such that we are most certain of them, while the inductive sciences are less certain and often involve theories later being proven wrong.

As to your analogy: Induction is the method by which we reason from instances to a general (as in: involving infinitely many instances) law. (You can also go from laws to a more general law).

Deduction is the method to show what (deductively) follows from what.

• i wouldn't discredit the white swan induction as completely invalid. it is valid to induce that "most swans are white" and it is a valid and useful observation even though there may be exceptions ... which prove the rule. however, some (propaganda camps) often use an exception to discredit an inductive position even though it is clearly formatted as to not be 100% predictive but representative rather of a trend based on probability. discriminative judgement may not be applicable in law perhaps but it can be very useful in investments, insurance etc – amphibient Mar 16 '17 at 22:39
• @amphibient - please, note that valid is a "technical" term in formal logic. A valid argument is an argument such that "it impossible for the premises to be true and the conclusion nevertheless to be false". If so, the "inductive generaliztion" from many white swans to the general law : "All swans are white" is not valid. – Mauro ALLEGRANZA Mar 17 '17 at 10:59
• Thus, to say "more valid than" makes little sense. The issue is with "scientific methodology"; in this context, what method: inductive vs deductive (based on hypothesis, prediction and verification) is the "most effective" ? (difficult to say : the "right" method.) – Mauro ALLEGRANZA Mar 17 '17 at 11:04
• induction is central to mathematics. without it we would have no natural numbers, for example. – user20153 Mar 17 '17 at 16:16
• induction in mathematics is different from induction applied to the real world (as does science). – Lukas Mar 20 '17 at 11:04

The 'most canonical/celebrated' exposition on this problem is probably a paper by Susan Haack:

It is often taken for granted by writers who propose — and, for that matter, by writers who oppose — 'justifications' of induction, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.

Hume presented us with a dilemma: we cannot justify induction deductively, because to do so would be to show that whenever the premisses of an inductive argument are true, the conclusion must be true too — which would be too strong; and we cannot justify induction inductively, either, because such a 'justification' would be circular. I propose another dilemma: we cannot justify deduction inductively, because to do so would be, at best, to show that usually, when the premisses of a deductive argument are true, the conclusion is true too — which would be too weak; and we cannot justify deduction deductively, either, because such a justification would be circular.

Haack, S. (1976). The justification of deduction. Mind, 85(337), 112-119.

A slightly less orthodox approach could be to take the notion of 'justification' to be well-founded, and consisting exactly of 'inductions' and 'deductions', so that attempts to 'justify' those would be simply non-sensical/misguided.