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I'm reading the "On Induction" by Bertrand Russell at the moment. The argument itself makes sense to me. However, I can't formulate a set of premises for an assignment I have to complete. Is it simply what he states in the passage?

(a) The greater the number of cases in which a thing the sort A has been found associated with a thing the sort B, the more probable it is (if no cases of failure of association are known) that A is always associated with B;

(b) Under the same circumstances, a sufficient number of cases of the association of A with B will make it nearly certain that A is always associated with B, and will make this general law approach certainty without limit.

Or is there something else I'm missing here? Any help would be appreciated.

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I'm not sure what your assignment is asking for. One of Russell's hallmark habits of mind is that he sifted through bodies of work then pointed out hidden premises then went on to reduce the number of premises to bare minimum. If your assignment is asking students to use Russell's methods to analyse Russell's work, I am indeed surprised; this is a great idea.

Premise 1. We cannot draw inferences from experience to what is not experienced unless we know general principles of some kind by means of which such inferences can be drawn.

A sure way to demonstratively prove all cases is to examine each and every case. To prove all ships in your squadron are mission capable, every and each ship must be thoroughly inspected. When it is impossible to demonstratively prove every and each case, general principles of some sort must be known in order to draw inferences from particular to general.

Premise 2. If P implies Q, then the probability of P is less than the probability of Q because whenever P happens Q happens, whereas when Q happens P may or may not happen.

Premise 3. Failed cases cannot disprove a probability statement. An improbable event can nevertheless happen; that an improbable event happened does not invalidate the statement that this event is an improbable event.

Suppose a man, as of January 1, 2000, had seen a great number of swans, all of which are white, and he speculated that all swans are white. Even if all the swans he saw after he made that statement turned out to be black, his later experience cannot invalidate the statement he made on January 1, 2000 because counter examples cannot invalidate a probability statement.

Premise 4. A principle cannot be used to prove itself. Using examined cases to prove unexamined cases relies on the inductive principle itself, thus inductive principle cannot be proved by enumerating examined cases.

No. 1 says the inductive principle is need in order to make inferences from particulars to general.

No. 2 says the probability of the general law is less likely than the particular case.

No. 3 says the inductive principle cannot be disproved by experience.

No. 4 says the inductive principle cannot be proved by experience.

  • if a zero-probability event occurs, then your probabilities were wrong. compare non-occurance of an event with probability 1. – user20153 Sep 18 '17 at 18:30
  • I changed zero-probability to improbable to avoid an uninteresting controversy. – George Chen Sep 19 '17 at 15:52

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