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.
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.