OBSERVATION AND THE PROBLEM OF INDUCTION[i]

Ted Everett, SUNY-Geneseo

(Creighton Club, March 1998)

                                                                             

I want to present what I think is a new approach to the problem of induction.  I will try to show that the traditional problem can be gotten around by means of a theory of general observations.  I do not have such a theory, but I have a few, naive suggestions in the direction of such a theory.  I will suggest that many of our general beliefs, which we usually take to be the conclusions of inductive inferences based on observations of particular facts, can instead be seen themselves as reports of observations of general facts.  These general beliefs are arguably no more "inferential" in nature than the particular beliefs upon which they are usually thought to be based.  If this is right, then the problem of induction can be solved - in the sense of being collapsed, in effect, into the more basic problem of perception.

Let me be as clear as I can about what I think I can establish.  My primary concern is to point out that there is a possible new line on the problem of induction in terms of general observations - a view that ought to be considered, but which is somehow missing from standard treatments.  My secondary concern, and it is far secondary, is to argue for the plausibility of the idea that there really are such general observations.  I do not want the value of this paper to hang on whether that idea is independently more plausible than other theories about observation.  I am not at all sure that it is.  What is important about the idea - and this is my main point - is that it seems to get us out of the problem of induction.  If this is right, then it might be worth some future effort to work the idea out in detail. 

 

The problem

An inductive inference is often defined as one in which the conclusion does not follow necessarily from the premises - so it is not deductively valid - but in which the premises seem to render the conclusion more likely.  This is sometimes seen as a matter of the conclusion's somehow adding to the content of the premises.  As Brian Skyrms puts it, "If an argument is inductively strong, its conclusion makes factual claims that go beyond the factual information given in the premises."[ii]  Wesley Salmon calls anything like this an "ampliative" inference.[iii]

(i), (ii) and (iii) below are simple examples of these "ampliative inferences".

 

            (i)         This raven is black.                          

That raven is black.                            

           All ravens are black.                           

 

            (ii)        Some ravens are black.                    

           All ravens are black.                           


            (iii)      All observed ravens are black.           

           All ravens are black.                           

 

Clearly, the conclusions of these little arguments do not follow necessarily from their premises, and evidently this is because the conclusions say more than the premises, in that they talk about all ravens, and not just those mentioned in the premises.  The problem of induction is often understood to be the problem of justifying inferences like these.

Why should we care at all about the problem of induction?  Why not just concede that all inductive arguments are invalid, and have done with it?  The answer is that we seem to depend on such inferences in our scientific theories, as well as in ordinary life.  That is, (a) we accept as part of our knowledge many statements that can be viewed as the conclusions of ampliative inferences, and (b) we further believe that such knowledge originates in inferences of that sort.[iv]  If no such inferences are valid, then it looks like we must give up much of what we now believe. 

For those who wish to preserve those general beliefs under challenge by the problem of induction, there are two main avenues of approach.  Direct approaches concentrate on part (b) above, trying to show how inductive inferences are approximately valid - that is, add probability to their conclusions, or in some other way tend to make them more believable.  End-run approaches concentrate on (a) above, by attempting to justify our belief in the "conclusions" without reference to the arguments that they are usually thought to require.  A successful attempt of this sort would solve the broader problem at hand, i.e. to account for non-deductive, scientific knowledge in general (which is what we are after fundamentally), even if it means giving up on induction itself as traditionally understood.  The approach that I am suggesting here is an end-run approach.


Why do we think that "inductive conclusions", such as that all ravens are black, require inductive arguments?  Because we are empiricists, in the broad sense that we believe (or would like to believe) that there are two and only two basic ingredients in human knowledge: observation and valid reasoning.  It may be that we can figure out some things, e. g. the truths of mathematics, by deductive reasoning alone.  But our knowledge of ravens is not like that; it must be based on observation as well. Unfortunately for general beliefs, it seems that all that we can observe at one time is this or that raven (or, at most, some small number of ravens) and its properties.  The general statement, that all ravens are black, is not deducible from any reasonable number of reports of such observations about particular ravens, though those are all we have to go on.  This is why we have a problem, and why it looks as if we need to find some way of justifying ampliative arguments.  But I want to deny the implicit claim that the general facts in question are themselves non-observational.  I want to suggest that we know them (when we do know them), in essentially the same way that we know particular facts.

The distinction that I want to employ between general and particular statements, facts, etc. needs a more definite characterization.  There are two syntactic types of statements that one usually finds listed as the premises in inductive arguments.  Some are singular claims of the form "this A is B" or "the C A is B", such as "this raven is black" or "the twelfth observed raven is black".  Others are universal statements of the form "All C A's are B's", such as "all of the ravens in such-and-such a sample are black", or "all observed ravens are black".  It appears that none of the statements usually used as inductive premises have the simple form "all A's are B's".  Now, this is certainly a contingent, language-dependent feature of ordinary observation reports.  One could always, for example, introduce a term like "obsraves" to denote the class of ravens that have been observed, and then produce the simple universal statement "all obsraves are black".  One could also artificially produce a statement like "all ravens are unobserved or black."  But given the way that we normally speak, it appears that the usual inductive premises about A's are effectively particular, in the sense that none of them affirms anything straightforwardly about the entire class of A's, but only about various members, or about a certain subclass.

I will call any contingent statement that is effectively particular in normal language in the way that I have described, or is in some other way appropriately similar to "this raven is black", a p-statement.  I will call any contingent statement that takes the form of a simple universal affirmative sentence, or is in some other way appropriately similar to "all ravens are black", a u-statement.  In what follows, I will call the facts (if they exist) to which p-statements and u-statements correspond p-facts and u-facts.  I will call the objects (if any) to which the subject terms of those statements refer p-objects and u-objects.  And I will call observations (if they occur) of p-facts and u-facts p-observations and u-observations, respectively.  I hope that these definitions are not offensively imprecise.  My point is just to focus on the kinds of statements that are involved in alleged inductive inferences, as distinct from the epistemic roles that those statements are supposed to play.

Now I can summarize my understanding of the problem of induction as a set of five mutually inconsistent sentences:

 

(1)  Our knowledge has the form of a set of observation-reports, closed under valid inference.

(2)  Observation-reports are all p-statements.

(3)  All valid inferences are deductive.

(4)  It is impossible to deduce a u-statement from any set of p-statements.

(5)  We have knowledge of the truth of some u-statements.

 


A diagnosis of the problem

Any reasonable approach to the problem of induction must falsify at least one of these five statements.  To reject (5) would be to embrace skepticism with respect to the whole class of "inductive conclusions".  This is a possible view, but not what we should call a solution to the problem.

Statement (4) is hard to deny.  I cannot prove that it is true, for the obvious reason that the classes of u- and p-statements are only vaguely defined.  But it is demonstrably true for the standard cases that I have in mind - for example, no proposition of the form (x)(Ax ® Bx) can be deduced from any set of propositions of the forms (Aa & Ba) and (x)((Ax & Cx) ® Bx).

In most more traditional presentations of the problem (such as Salmon's), it is simply presupposed that something like statement (3) must be rejected if the problem is to admit of a solution.  There have been many attempts to prove that one or another non-deductive inference pattern is valid (or "correct", or "strong", or something else, if it is assumed that "valid" means the same thing as "deductively valid").  None of these efforts has gained wide acceptance.

(1) is a concise statement of the central claim of empiricism.  While it is certainly subject to various technical objections, I doubt that more than a few contemporary philosophers of science would wish to deny it wholesale, or in spirit.  Even those who take themselves to be non- or anti-empiricists (for example, Richard Boyd) base their rejection of empiricism on some other claim that they consider essential to it.  This does not entail that (1) is true, of course.  My point is rather that induction is only a problem for empiricists in the first place.

Statement (2) is plainly the weakest statement of the five.  I admit that it would appear in isolation to be true, but it also seems to be rather superficial, and contingent in a way that the other statements in the group do not.  I believe that whatever truth (2) has is a matter more of philosophical convention than of anything important in the structure of the world.  The view, that only p-facts may be observed, is not an essential claim of empiricism itself.  It stems, rather, from a certain traditional theory of observation, which in turn depends on certain semantic and metaphysical assumptions.  This theory has ridden along with empiricism since Locke largely unchallenged, although the positive reasons for accepting it have had more to do with convenience and simplicity than with any real hold of their own on our intuitions.  It is, in fact, a theory of observation that most present-day philosophers cheerfully deny when it causes problems in other contexts.  

 

A coherent solution


Deny statement (2) above.  Assert in its place that ordinary u-statements like "all ravens are black" are sometimes acceptable reports of observation, or are deductive consequences of more general u-statements that are reports of observation.  I admit that this may sound strange, given the way that we ordinarily speak about our observations.  But ordinary usage is hardly decisive in epistemology; dialectical considerations are important, too.  And the view that I am suggesting would provide a very straightforward solution to the problem of induction - no induction at all, i.e. no "ampliative" inferences, just observation and deductive reasoning.  If this idea works, it should be worth some effort to make it plausible.

It may not be altogether clear that the proposed solution survives even elementary tests against common sense.  For example, does it not imply that scientific research is unnecessary?  If u-facts were observable, could one not just look out the window to gain instant general knowledge about birds, trees, gravity, and everything else?  The answer is no, my view does not have to be fleshed out so radically.  The u-statements in question, the ones that I am saying should be counted as reports of observations, should be thought of as tentative, defeasible reports, of weak or partial u-observations, the mere reportability of which is no guarantee of their truth.

After all, hardly anyone these days believes that absolute certainty attaches to any statements at all, p-statements included.  On my view, observational knowledge should still be seen as highly incomplete, and its relation to theoretical knowledge as problematic in various ways.  What I am trying to do here is to detach the real problem of how to turn observational, prima facie knowledge into justified beliefs, from the artificial problem of how to bridge an essentially syntactic gap between particular and universal statements.

 The new view is also not intended to get around the possibility that one is just a brain in a vat, hence that reports of observations are unreliable in general.  We are left, that is, with the problem of perception.  But the problem of induction is supposed to be a separate, further problem about a certain set of claims to knowledge, taking other claims for granted.  If it can be shown, as I am trying to show, that the first kind of claim is not relevantly more problematic than the second, then the problem of induction ought to be considered solved.


My solution could be seen as filling in a certain gap in the existing, hypothetico-deductive approach to confirmation and induction.  This approach, championed in different versions by Carl Hempel and Karl Popper, is widely held to be both attractive and unworkable.  In this approach, as in mine, there is no such thing as induction per se.  What happens instead (freely translated) is that typical u-statements are initially written down in one's mental notebook only in pencil - that is, as hypotheses, not to be believed (because there is not any good initial reason to believe them), but just to be considered.  Once they are on the list, they can be tested by deducing predictive p-statements from them, and then observing whether or not the predictions turn out to be true.  In Hempel's version, an hypothesis will become more believable if it is confirmed by true predictions.  In Popper's, the hypothesis is made more acceptable by its surviving attempts to find predictions that turn out to be false.  Now, these procedures (one or both) strike many philosophers as a better description of scientific reasoning than mere enumerative (as it were, blind) induction.  It does seem correct to say that u-statements acquire greater and greater credibility as they pass successfully through more comprehensive and more rigorous tests.  But, as Salmon and others have pointed out, neither version of the hypothetico-deductive approach provides a real solution to the problem of induction, because each fails to show how testing can justify one's belief in the hypothesis.

On the view I am suggesting, however, an account can be given of why both confirmation and non-falsification tend to add epistemic weight to an hypothesis.  If we suppose that the u-statement in question makes it into one's epistemic notebook initially as the tentative report of an imperfect observation, then perhaps what are usually considered to be separate observations of confirming or non-falsifying instances can be seen instead as extensions and clarifications of the same observation.  It would be just a matter of making sure that one's initial observation is a good one - in the same way that someone who thought he had seen an individual black raven might go and catch the bird, and study it carefully, in order to add ink to his initial pencilled-in report.

Here is a second, quick objection.  It may seem that my view entails the absurd claim that all objects, from ravens to electrons, are equally observable.  But this is not so.  As long as there are some observationally acquired u-statements available, from which appropriate theoretical hypotheses can be deduced, then there is no special problem about unobservable objects.  In order to make the suggested solution work, it is really only necessary that there be one sufficiently general u-statement, the truth of which can be affirmed provisionally through observation:  "Nature is more uniform than it is diverse", or perhaps, "inductive inferences are ordinarily reliable."  Once one had such a universal principle listed, more specific u-statements could be deduced from it and jotted down, at least as likelihoods. 

So we might get something roughly like this:

 

(1) Nature is mostly uniform, induction is generally reliable, etc. (observation)

(2) Therefore, if all observed ravens are black, then probably all ravens are black. (deduction)

(3) All observed ravens are black. (observation)

(4) Therefore, probably all ravens are black. (deduction)

 


Kant and others have tried to show that some such principle is knowable a priori, but there have been no successful attempts to justify one by reason alone.  Yet if other u-statements in general could be justified observationally, why not a statement like this?

The principle of uniformity would not have to be observed in an immediate way, either.  One could start with a few more ordinary observations, to the effect that all ravens are black, all hounds have teeth, and so on.  One could then submit some of these basic statements to various sorts of testing.  If successful, the whole resulting situation could be said to be contained in a u-observation of this fact: the hypothetico-deductive method usually works.  Thereafter, one could with greater and greater confidence deduce unobserved hypotheses from the initially-weakly-observed general principle, and then through usually-successful testing add credence to both.  This kind of "bootstrap" process requires only that there be enough observational input at some level for the whole thing to get started. 

Ultimately, no belief should be seen as either purely observational or purely inferential.  All are functions of a total process that takes in observational information at various levels, framing hypotheses from the observations, testing, making more observations, and so on.  The normal psychological content of an ordinary observation was never very much like a sentence in the first place.  One has an experience, and that experience may bring some proposition to mind.  We may express the experience with the proposition, but the experience itself is something else.  If one's observational life is such a flow of basically inarticulate experience, rather than a set of sentences getting fed in through our senses, then nothing necessarily prevents our expressing some of those experiences in the form of generalities.

 

 

 


NOTES



1.  This paper is part of a larger project on observation and induction.  I want to thank Ellery Eells, Carlo Filice, David Levy, Jee-Loo Liu, Alan Sidelle, and Robert Stalnaker for comments on various drafts.

2.  In Choice and Chance (Wadsworth, Belmont CA, 1986), p. 8.

3.  In The Foundations of Scientific Inference (U. Pittsburgh, 1986), p. 8 ff.

4.  This is controversial.  There are plenty of people who want to believe in some kind of inductive inference, but who also  believe that these little forms of essentially enumerative argument are entirely worthless.  We don't know that the sun will rise tomorrow, just because we have this series of past risings of the sun.  There has got to be something else involved, that distinguishes the "law-like regularities" from the merely coincidental ones.  Bertrand Russell, when he talks about this problem in The Problems of Philosophy (New York, Galaxy 1959, pp. 60-69) mentions the inductive chicken, who concludes from the fact that the farmer has always fed him in the past, that the farmer will keep on feeding him forever.  Of course, one day the farmer rings his neck.  In a typical aside, Russell notes that the chicken might have been better off if he'd had a more nuanced epistemology.  I doubt this, since the chicken could hardly have escaped the farmer, even if he'd known his intentions.