Induction

 

1   The problem of Induction

An argument has premises and a conclusion. The premises are meant to support the conclusion.  We evaluate arguments by asking two questions.  (1)  Are the premises true?   (2)  What support do the premises lend to the conclusion?
 

1.1  Deductive arguments

Logicians are interested solely in the question of support (the second question) not the question concerning the truth of premises.  In a deductively valid argument the support which the premises lend to the conclusion is complete.  That is, it is logically impossible for the premises to be true and the conclusion false.

Example: All university students are clever, because all university students are insane and all insane people are clever.

The conclusion of the argument is stated first: all university students are clever.  The premises which are meant to support this come after:  all university students are insane and all insane people are clever).  The argument is not particularly good, because the premises are almost certainly false.  The argument is not sound.  Still, the truth of the premises would guarantee the truth of the conclusion, and that is all that is required for the argument to be deductively valid. The essential feature of a deductive argument is that the information in the conclusion never really goes beyond the information which is packed into the premises, taken as a whole.
 

1.2  Inductive arguments

Often we give reasons for our beliefs about the world, but the reasons we have do not always yield deductively valid arguments.    In an inductive argument the premises do not deductively entail the conclusion.  At best they support the conclusion.  There are a wide variety of inductive arguments, but one kind which is very important (and which have tended to dominate the debate) is that of arguments in which the premises tell us about the past, and the conclusion tells us about the future.  For example:

Examples:    The sun has risen every day in the past. Therefore,  the sun will rise tomorrow.

                     Bread has always nourished me in the past.  Therefore,  bread will nourish me again tomorrow.

In both cases we daily rely on the premises supporting the conclusion.  But in both cases the premises do not support the conclusion deductively.  It is logically possible for the premises to be true and the conclusion false.
 

2  Our reliance on induction

What is clear is that all of our expectations and beliefs about the future, and about those things we have not directly experienced, must be based on some kind of inductive argument, either directly (past-to-future) or via some general principles (e.g. Newton's laws of motion) which are supported inductively (particular-to-general).  All of our knowledge, if we have any at all, about what has not yet been directly experienced, is based on induction.  So we face a dilemma:  either induction can be justified or we have no knowledge about what is not directly experienced. The second horn of this dilemma would be disastrous for empiricism.  Most of what we think we know is knowledge about what we are not currently experiencing.  If genuine knowledge is confined to particular experienced facts of the present moment then our knowledge would be very thin indeed: certainly nothing to write home (or a study guide) about.
 

3   Can induction be justified?

David Hume, the famous Scottish sceptic, raised the problem of the justification of induction over two hundred years ago.  What follows is derived from Hume's argument against the possibility of a justification of induction.

 What would a justification of induction have to show?  Would it have to show that inductive arguments always lead from true premises to true conclusions?  No: that would be far too stringent.  Strong inductive arguments don't purport to lead from truths to truths without exception.  They purport to lead from truths to highly probably propositions, and highly probable propositions may be false.  Still, highly probable propositions must have a high probability of being true.  If Tom keeps offering us what he tells us are highly probable propositions, and those propositions keep on turning out to be false, then we would not take Tom's original claim very seriously.  A method which is meant to yield highly probable propositions ought to be right most of the time (though not necessarily all of the time).  So a justification of induction should yield the conclusion that inductively strong arguments give us truths most of the time.

 Now we can present a dilemma.  There are only two sorts of argument: deductive and inductive.  So any argument for induction would have to be either deductive or inductive.   We will present each horn of the dilemma in turn.
 

3.1 A deductive justification of induction?

What we know are particular facts about the present, and whatever we still remember about the past.  We know that inductively valid arguments have been pretty good in the past, yielding truths from truths, most of the time (in the past).  However, deductively valid arguments contain no more information in the conclusion than in the premises.  So any deductively valid argument with premises known  to be true must not contain any information about the future. In order to justify induction we have to show that inductively strong arguments yield truths from truths most of the time.   But most of the time entails most of the time in the future, and all we have is evidence about how well inductive arguments have done in the past.  So any argument which tried to establish the future reliability of inductive arguments on the basis of their past performance must be deductively invalid.  And so any argument for the reliability of induction which is deductively valid must have at least one premise which contains information about the future, and hence it contains at least one premise that could only be known to be true on the basis of induction itself.  The argument would only be of use if we could know the premisies to be true, but  we need induction to undergird our confidence in the truth of the premises.

Any argument, with premises known to be true, for the future reliability of induction would have to have the following form, or else something like it:
 

 Inductive arguments have been reliable in the past;
therefore:
 Inductive arguments will continue to be reliable in the future.
And this argument is clearly not deductively valid.  Since the truth of the conclusion of an inductive argument is not guaranteed by the truth of the premises, for all we know in the future inductive arguments might well start leading us consistently into falsehood.
 
 

3.2.  An inductive justification of induction?

Still, one might argue that such a justification of induction, by appeal to induction's reliability in the  past, is not completely unsound.  It is, after all inductively sound.   The argument is inductively sound, but, of course, to justify induction by appeal to induction is to commit a fallacy with which you should by now be familiar: begging the question.  We are trying to justify induction and yet to do so we are having to rely on induction.

        What is wrong with begging the question in this way?  Consider an analogy.  Suppose that Tom believes a certain religious system, a system expounded in detail in some holy book.  Tom tells us we ought to subscribe to this religious system as well.  We ask him to give us some argument for so believing the doctrines expounded in the book.  Tom replies: "The book can be relied on to yield truths".  We ask him how he knows this.  He replies:  "Look here, it says on page seventeen of the book that this very book contains only truths."  Tom may win some converts by this argument, but it has to be admitted that the argument is extraordinarily weak.  We want some independent reason for accepting the contents of the book.  The fact that the book assures us it is true is not an independent reason.  It presupposes the very conclusion for which we want an argument.
 

4    Summary of the dilemma:

Any justification of induction would have to be either (i) deductive or (ii) inductive.  But (i), any argument with known premises and with the conclusion that induction will work in the future will be deductively invalid.  This is because the premises must contain information only about the past, whereas the conclusion must contain information about the future.  And (ii), any inductive argument will beg the question at issue: it relies on the reliability of induction in order to establish the reliability of induction.

Exercise:   I have presented an argument to show that induction is not justifiable:  Is deduction any better off?  Can you construct an argument against the justifiability of deduction which would parallel the above argument against the justifiability of induction?  If so, what, if anything, does this show?