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<p>I might also show that no induction or hypothesis is completely true except such as we call cognitions ''a priori''.  For the chance against it is infinite.  Hence, the question what is the 'probability' of an induction or hypothesis is senseless and the true question is how much truth does an induction contain.  For the same reasons by how much truth should not be meant what proportion of inferences therefrom are true but simply of how much value are certain premisses in giving us truth by induction or hypothesis.</p>

<p>I might also show that no induction or hypothesis is completely true except such as we call cognitions ''a priori''.  For the chance against it is infinite.  Hence, the question what is the 'probability' of an induction or hypothesis is senseless and the true question is how much truth does an induction contain.  For the same reasons by how much truth should not be meant what proportion of inferences therefrom are true but simply of how much value are certain premisses in giving us truth by induction or hypothesis.</p>

<p>We must distinguish therefore the truth which an inductive or hypothetic conclusion may have by accident from that which it must have from the nature of the facts explained.  The former cannot properly be estimated.  The latter can.  For to consider first induction;  if the same conclusion result inductively as the least truthful explanation possible of two different sets of facts, it is plain that a certain amount of truth it is obliged to have on account of each instance, that is on account of the extension of the subject of the fact.  And each instance determines a certain amount of truth independently of the others.  So that the number of different kinds of instances measures the least amount of truth the induction can have.  In the same way with hypothesis the number of different properties explained measures the least possible truth of the hypothesis. (Peirce 1865, CE 1, 293–294).</p>

<p>We must distinguish therefore the truth which an inductive or hypothetic conclusion may have by accident from that which it must have from the nature of the facts explained.  The former cannot properly be estimated.  The latter can.  For to consider first induction;  if the same conclusion result inductively as the least truthful explanation possible of two different sets of facts, it is plain that a certain amount of truth it is obliged to have on account of each instance, that is on account of the extension of the subject of the fact.  And each instance determines a certain amount of truth independently of the others.  So that the number of different kinds of instances measures the least amount of truth the induction can have.  In the same way with hypothesis the number of different properties explained measures the least possible truth of the hypothesis.</p>

 

<p>(Peirce 1865, CE 1, 293&ndash;294).</p>

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