Induction
from 350 BCE Named by Aristotle; the problem with it named by Hume in 1739
Reasoning from many particular cases to a general claim, which is how nearly everything is learned and which nothing has ever justified.
- Active
- from 350 BCE
- Where
- Athens, later Edinburgh
- Status
- In use
- Tradition
- Forms of inference
What it is
Induction moves from observed cases to a claim covering cases not yet observed. Every swan seen has been white, so swans are white. The bridge has held every day this year, so it will hold tomorrow.
Unlike deduction it genuinely adds something: the conclusion says more than the premises do. That is exactly why it is useful and exactly why it cannot be guaranteed. Every inductive argument can have true premises and a false conclusion without any error having been made along the way.
How it works
Gather cases. Check that they vary in the respects that might matter and not only in ways that do not. Generalise, and hold the generalisation loosely enough to give it up.
The quality of an induction depends almost entirely on the second step. A thousand observations all made in the same place at the same time of year are worth less than fifty made across different conditions, because the thousand have not tested the thing the generalisation is exposed to.
The form of the inference
- Case 1 has property P
- Case 2 has property P
- Cases 3 through n have property P
- The cases vary in the respects that could matter
- Therefore all cases of this kind probably have property P
The argument
Proposition This dam will supply the house through the dry season.
- The dam has been measured at the end of every dry season for eleven years.
- In each of those years it finished the season above the intake pipe.
- Those eleven years included the two driest on the district record and one year of failed autumn rain.
- So the dam has held through the range of conditions the district actually produces.
Therefore The dam will probably hold through this dry season too.
Note the third step, which is doing the real work. Eleven wet years would have supported the same conclusion far more weakly, and the argument would have looked identical.
What it is good for
Every empirical claim there is. Science, medicine, agriculture, insurance and ordinary practical life all rest on it, and no substitute has ever been found. It is also the only method here that improves with more evidence rather than with more care.
Where it fails
It has no justification, and this is not a gap waiting to be filled. Hume's argument is that any defence of induction must either be deductive, which it cannot be since the conclusion outruns the premises, or itself inductive, which assumes the very thing in question. Three centuries of attempts have not dislodged this.
In practice it fails through unrepresentative samples. Eleven years of records taken during a wet decade will confidently predict a dam that empties in the twelfth, and nothing in the form of the argument shows the trouble.
Common misconceptions
That a large sample makes an induction safe. Size helps only if the sample varies across the dimension that matters; ten thousand cases from one narrow band of conditions establish very little.
Also that Hume's problem is a sceptical parlour trick. He was not recommending that anyone stop using induction — he thought we could not stop — only that we should be clear that habit, not reason, is what carries us.
Where it came from
Aristotle names it and treats it as a way of arriving at the first principles that deduction then works from. It becomes the central problem of philosophy in 1739 when Hume asks what entitles us to it.
What became of it
Reformulated rather than solved. Probability theory, Bayesian confirmation and statistical inference all give it a precise shape without answering the original question.
Lasting influence
The problem of induction shaped everything after it: Kant wrote the Critique in response to it, Popper built falsificationism to avoid it, and the whole apparatus of modern statistics is an attempt to work within it.
Why it still matters
Every empirical claim you will read today depends on it, including all the ones that turn out to be wrong.
Put another way
Walking on a floor you have never been under.
Texts
David Hume, An Enquiry Concerning Human Understanding
Section IV states the problem in about ten pages and has never been answered. Shorter and clearer than the Treatise version.
Where to start
Read Hume's Enquiry, section IV, before reading anything written about it. The argument is simple and the commentary is not.
The surprising bit
The most-used form of reasoning in existence is the one nobody has been able to justify, and knowing this changes nothing about how anyone proceeds.
In their own words
All inferences from experience suppose that the future will resemble the past
Who held it
John Stuart Mill
Connections
- Set against
- Deduction
- Influenced
- Abduction, Probabilistic inference
- Parallel to
- Mathematical induction
The verdict
Indispensable and unjustifiable at the same time. The honest position is to use it and to say so.