Fri 6 Jun, 2008 10:51 am
The thesis to be presented here is that every inductive argument is a form of question begging. It is commonly recognised that inductive inference is invalid i.e. the conclusion of an inductive argument may be false even when the premises are true. However, it is also commonly thought that the premises of an inductive argument can provision a good reason, partial justification, or support for its conclusion. In this view, an inductive argument is not to be evaluated for its validity, as deductive arguments are, but for its cogency. I disagree.
First, consider the following inductive argument, where the symbol |< represents inductive entailment.
[indent]1. a is y, b is y, c is y, d is y |< every x is y[/indent]
Second, note that a universal statement is equivalent to the list of its infinitely many singular instances.
[indent]2. every x is y =||= a is y, b is y, c is y, d is y, ...[/indent]
Third, observe that from a list of infinitely many singular instances we can deduce any arbitrary list of its members.
[indent]3. a is y, b is y, c is y, d is y, ... |= a is y, b is y, c is y, d is y[/indent]
Fourth, according to the transitivity of deductive inference, it follows from the arguments presented on lines 2 and 3 that 4 is true.
[indent]4. every x is y |= a is y, b is y, c is y, d is y[/indent]
Fifth, note that the above argument is a reversal of the premises and conclusion presented by the inductive argument in line 1 and is also valid. Moreover, that if any of the singluar instances in the conclusion is false then the premise is also false, in accordance with the principle that falsity is retransmitted from the conclusion to the premises of a valid argument.
[indent]5. a is y, b is y, c is y, d is y |= a is y, b is y, c is y, d is y[/indent]
Finally, since the conclusion of the inductive argument presented by line 1 is true only if the premises are true, and false otherwise, it follows that the premises can only provide a good reason to think that the conclusion is true if they provide some good reason to think that they, themselves, are not false. In other words, the premises in the deductive argument presented in line 5 must provide a good reason to think that their conclusion is true. However, this argument, though valid, begs the question by assuming precisely that which it is intended to give us a good reason to accept.
In conclusion: to the extent that an inductive inference is cogent it also begs the question, and with regard to the content of the conclusion to which it does not beg the question it is simply invalid. That is, inductive arguments have the remarkable quality of being both invalid and question begging, a feat which I would have scarcely thought possible.
Interesting thesis... I always enjoyed inductive logic and reasoning. You are able to put a definitive spin on an analogical subject. You have a good perspective.