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Directory:Jon Awbrey/Papers/Information = Comprehension × Extension (view source)
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We come next to consider inductions. In inferences of this kind we proceed as if upon the principle that as is a sample of a class so is the whole class. The word ''class'' in this connection means nothing more than what is denoted by one term, — or in other words the sphere of a term. Whatever characters belong to the whole sphere of a term constitute the content of that term. Hence the principle of induction is that whatever can be predicated of a specimen of the sphere of a term is part of the content of that term. And what is a specimen? It is something taken from a class or the sphere of a term, at random — that is, not upon any further principle, not selected from a part of that sphere; in other words it is something taken from the sphere of a term and not taken as belonging to a narrower sphere. Hence the principle of induction is that whatever can be predicated of something taken as belonging to the sphere of a term is part of the content of that term. But this principle is not axiomatic by any means. Why then do we adopt it? (Peirce 1866, Lowell Lecture 7, CE 1, 462–463).
<p>We come next to consider inductions. In inferences of this kind we proceed as if upon the principle that as is a sample of a class so is the whole class. The word ''class'' in this connection means nothing more than what is denoted by one term, — or in other words the sphere of a term. Whatever characters belong to the whole sphere of a term constitute the content of that term. Hence the principle of induction is that whatever can be predicated of a specimen of the sphere of a term is part of the content of that term. And what is a specimen? It is something taken from a class or the sphere of a term, at random — that is, not upon any further principle, not selected from a part of that sphere; in other words it is something taken from the sphere of a term and not taken as belonging to a narrower sphere. Hence the principle of induction is that whatever can be predicated of something taken as belonging to the sphere of a term is part of the content of that term. But this principle is not axiomatic by any means. Why then do we adopt it?</p>
<p>(Peirce 1866, Lowell Lecture 7, CE 1, 462–463).</p>
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