In the book 'Introduction of the theory of Statistics' by Mood,Graybill,Boes (third edition)on page 220 (Chapter 6 on Sampling) you can read: 'Inductive inference is well known to be a hazardous process.In fact,it is a theorem of logic that in inductive inference uncertainty is present.One simply cannot make absolutely certain generalization.' What theorem of logic do they refer to? Can you give me please some reference to this fundamental result ?
A theorem about inductive inference
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1I assume you mean inductive inference in [this sense](http://en.wikipedia.org/wiki/Inductive_inference); this is actually different from inductive reasoning in [logic](http://en.wikipedia.org/wiki/Inductive_reasoning), which means that results in logic should not necessarily apply directly. Since we don't all have the book, can you briefly describe what it is meant by inductive inference in your book? – 2012-01-25
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0In the book when they talk about inductive inference they mean the extension from the particular to the general,the common practice in natural and physical science.The book is an introductory one and the authors don't give a formal definition of inductive inference;they only say that on the opposite side there is deductive inference in which conclusion are conclusive when in inductive inferece the conclusion are only probable.I took a look at the book of Rudolf Carnap 'Logical foundations of Probability' hoping to find an answer but it is very long and not easy to read. – 2012-01-25
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1Instead of Carnap, first read through the second link I posted above, in particular the section "Is induction reliable?" and the references thereof. I disagree with the statement that "it is a theorem". It is more that the very definition of inductive reasoning allows for the conclusion to be false. – 2012-01-25