# Inductive reasoning and probability: probability of the conclusion versus probability of the supporting relation?

It is often admitted that inductive reasoning has something to do with probability.

While in a ( valid) deduction the premises necessarily imply the conclusion, in an inductive reasoning the premises make the conclusion probable.

But this is somewhat ambiguous: does probability qualify here the conclusion itself or the supporting relation between the premisses and the conclusion?

Suppose P1, P2, P3 are the premises of an inductive reasoning and C is the conclusion.

What does it mean to say that this inductive reasoning is strong.

Does it mean that

(1) Probabably ( P1&P2&P3 --> C) is true.

or that

(2) P1&P2&P3 --> (Probably C is true)?

It seems difficult to admit interpretation (2) for inserting the probability notion in the conclusion itself might turn the reasoning into a deductive one.

(1) No woman has ever been elected President of the US. (2) Therefore, probably the next President will not be a woman.

This argument is not inductive ( it seems to me) since the ( statistical) probability of the gender of the next President is defined by the actual gender of the previous Presidents. So, arguably, this reasoning is deductive ( I mean, the conclusion is analytically contained in the premise).

• "1)No woman has ever been elected President of the US. 2) Therefore, probably the next President will not be a woman." This argument takes earlier elections as the single factor the gender of the President, which is a (false) axiom, wherefore it attempts to prove a "statistical probability." – user96931 Nov 23 '19 at 19:43
• The distinction you are making is somewhat outdated. In probability logic, one can use a qualitative probability operator □, or quantify it numerically. But either way, this is applied to all statements, including those of the form P→C. Evaluation of the probability of conclusions is then done according to some rules, so even "inductive" reasoning is deductive, in this sense. – Conifold Nov 24 '19 at 2:13