The problem of induction


Induction vs. deduction

Examples of deduction

  • All swans are white. Liddy is a swan. So Liddy is white.
  • If it rains, the race will be canceled. It is raining. So the race will be canceled.

Examples of inductive reasoning

  • All the swans that have been observed were white. Therefore, the next swan we come across will also be white.
  • 95% of the swans in Australia are black. There is a swan in Sydney Harbour in Australia. Therefore it is most likely that the swan is black.
  • Her current boyfriend is just like her old one. She was unhappy the last time and she won't be this time either.

How is induction justified?

Focus on this argument:

  1. Food from the HKU canteen has never managed to kill me.
  2. Therefore, food from the HKU canteen is not going to kill me tomorrow.

Are you justified in accepting the conclusion? Note that:

  • The argument is not deductively valid. It is possible for the premise to be true while the conclusion is false.
  • Is there a hidden assumption? "If P has always been true, then P will also be true tomorrow."
    • But how do we justify this assumption? Experience? Logic?

Hume's criticism of the justification of induction

David Hume (1711-1776)

  1. Induction cannot be justified a priori (based on pure reasoning and logic).
  2. Induction cannot be justified a posteriori (based on experience).
  3. Justification for induction is either a priori or a posteriori.
  4. Therefore, induction cannot be justified.

@When on innumerable occasions we observe certain experiences succeeding others, we naturally feel under similar circumstances in the future like events or causes will be followed by like effects... only custom or habit may validly be said to serve as the foundation for this causal idea.@

Kant "Introduction" Prolegomena to Any Future Metaphysics

@I openly confess, the suggestion of David Hume was the very thing, which many years ago first interrupted my dogmatic slumber, and gave my investigations in the field of speculative philosophy quite a new direction@

Hume Treatise, Book I, Part IV, Section VII, p. 269 in the Selby-Bigge edition

Note: Hume does not argue that we should give up induction. He thinks we are psychologically incapable of giving up induction.

@Most fortunately it happens that, since reason is incapable of dispelling these clouds, nature herself suffices to that purpose, and cures me of this philosophical melancholy and delirium, either by relaxing this bent of mind, or by some avocation and lively impression of my senses which obliterate all these chimeras. I dine, I play a game of back-gammon, I converse and I am merry with my friends; and when after three or four hours' amusement, I would return to these speculations, they appear so cold and strain'd, and ridiculous, that I cannot find in my heart to enter into them any further.@