Inductivist and Hypothetico-Deductivist Models of Justification

The general philosophical outlook which we are calling the empiricist consensus answered the question
of authority by saying, in effect, that we are rational to believe scientific explanations because such
explanations are based on laws or theories which are justified by observational, empirical evidence.  Thus
an account of this process by which observational evidence justifies laws and theories lies at the heart
of the empiricist consensus.  From the consensus outlook this question was to be answered by providing
a "logic of justification."

     Both inductivism and hypothetico-deductivism are philosophical theories designed to account
for how such a logic justifies the laws and theories employed in scientific explanations.  Thus they can
be considered as rival philosophical responses to the question of authority, i.e., why is it rational to believe scientific explanations?  For most consensus defenders to say the justificatory relationship between evidence and
that which it supports is a "logical" relation meant in effect that it was a relation between statements.

Note: What is tacitly left out of any such an account is an appeal to such "extra-logical" features such as other beliefs of the human scientists who make such "logical inferences," or their professional subculture, or the wider circle of human culture generally with its manifold of different interests.
     Prior to this century many philosophers, particularly those with an empiricist orientation,
attempted to justify our knowledge of general laws and theories on the basis of an inductive inference
starting from observation statements known to be true  directly by observation. Such statements can be said to be  "verified" directly by experience and all justification of other statements -the laws and theories which enter into scientific explanations- is based on this empirical "foundation."
Inductivists hold that an alleged inductive inference from particular observation statements to general statements of a theory, (i.e., "laws"), is that which justifies the authority we accord scientific explanations which appeal to such laws and theories.

Inductivists hope that the truth of the general law was could be proved to follow from the presumably
unproblematic truth of the allegedly directly verifiable observation statements.  In traditional Western
theories of knowledge, such proof, which would establish the necessity of the truth of the belief, was
required to make that belief genuine "knowledge."

     However, the inductivist picture of scientific method faced two devastating difficulties:

 The first is known as "Hume's problem" or simply "the problem of induction."  Ever since David Hume's analysis of synthetic statements (which he called "judgments of matters of fact"), the hopes for such an inductivist "logic" have been generally frustrated.  Hume argued, in effect, that our belief in any "general statement" purporting to refer to all members of one class as belonging to another class, i.e. of the logical form "All A are B." derives from sensory experiences of one set of sensations temporally followed by another set of sensations (Hume called them "impressions").  However, no amount of such past evidence can ever establish the truth of a claim that these two sets of sensations are necessarily connected, for that would apply to future, as yet unobserved, sensations.  Nevertheless, on the basis of such experience, we certainly do come to believe that such regularities will persist into the future.  Hume gave the origin of this belief a psychological explanation which expressed as a "habit" of expecting one set of sensations when one has other sets of sensations which we form because of repeated experience of the two sets temporally conjoined in the past.  Thus we come to believe in "the principle of the uniformity of nature" (i.e. that nature will follw regular "laws") for psychological, rather than logical, reasons.

     Most contemporary philosophers would concede there is no way to prove a non-trivial general
empirical statement inductively from any finite set of particular observation statements.  The last
nineteenth century inductivist J.S.Mill, thought he succeeded, but while "Mill's methods" or "canons" of
inductive reasoning are useful techniques for arriving at generalizations from particulars, they fail to
establish even any probability of the truth of such generalizations, much less their necessary truth.

     For this reason the defense of inductivism today has abandoned the traditional "quest for  certainty" and embraced "probability" as the grounds for accepting explanations based on laws inductively justified by appeal to observational evidence.
Contemporary research in inductive logic no longer searches for rules by which a general conclusion could be proved to be necessarily true based on particular observation statements.  Instead it rests content with an examination of the probability of the truth of a conclusion, i.e., of a "law" or theory, given a certain set of premises, i.e., a body of statementsexpressing the observational evidence.  Such a "logic of inductive probability" of the truth of a conclusion based on a body of evidence is quite distinct from the mathematical theory of probability
which allows one to deduce the likelihood of the occurrence of a particular event given a range of
possible events.  However, much recent technical research in this direction makes use of the
mathematical theory of probability to calculate, given a fixed range of "background knowledge" regarding
a finite set of possible events, how the probability of a hypothesis is increased or decreased by occurrence
or non-occurrence of a new piece of evidence.  Because this approach makes significant technical use
of a theorem of probability known as "Bayes's rule," contemporary inductivist views are known as
"Bayesian" views.   In particular when the scientist is employed a calculating statistical generalizations
from individual cases, the theory of probability can illuminate the nature of the justificatory relationship
between observation and theory.  While this certainly represents an active option in contemporary
philosophy of science, for many in the field, post Kuhnian developments have turned attention away
from the narrow idea that there is such a "logic of justification" and thus made this issue much less
crucial to contemporary images of science than it was to holders of the consensus.
     A second area of difficulty for inductivism lies in the distinction between observational evidence and the theories it is used to support. The inductivist program depends crucially on a sharp distinction between "observation" and "theory": the observations are the evidence for the theory, the truth of the general statements of laws and theories is alleged to follow inductively from the truth of observation statements.The problem lies in the fact that with this approach we are supposed to start the scientific method with a direct verification of observation statements, and then, after observations are made, we infer the theoretical laws. However, without any prior theoretical belief, there is no particular observational question to ask; without some sort of conceptual "framework", there is no language to report the observation in.  Any real observational state of affairs can be described in a potentially infinite number of different ways.  Without any theoretical belief there is no guidance as to which of these manifold observations to make.  So how can science begin with observation statements?

     For these reasons, many defenders of the empiricist consensus  rejected inductivism  in favor
of a hypothetico-deductive or "H-D" model of justification of laws and theories.  According to this
analysis, the process of justification of theories starts with a conjecture about the world, the hypothesis,
and then science proceeds to deduce observable consequences of the hypothesis given a certain precise
specification of the "initial conditions."  Experiments are then contrived to bring about such conditions
and precise observations are performed to determine if the deductions from the hypothesis given these conditions are in fact observed to occur. If so, we speak of the hypothesis as "confirmed," if not, it is "refuted."

     Hypothetico-deductivism has two epistemological characteristics in common with inductivism:
both are empiricistic and both are foundationalistic, both of which are positions essential to the
empiricist consensus.  H-Dism is empiricistic because, even though scientists begin with a deduction
from theoretical hypotheses which are not claimed to have been induced from empirical observations,
the authority which a hypothesis commands once it becomes "accepted" as a "law," it commands only
because of its justification by empirical confirmation.  Thus though explanation and prediction flow
"downwards" deductively from hypothesis to observation statements, "authority" ("justification") flows
upwards from empirical observations to the hypotheses they confirm.  Because authority thus flows
upwards from observation to law, an H-D advocate is correctly considered a kind of empiricist, though
not of the classical inductivist sort.

     Furthermore, like inductivism, H-Dism holds that general, theoretical knowledge is knowledge
because it is erected upon a "foundation," the "given" truth of which is taken as more or less
unproblematically established by observation.  This foundation is thought to consist of a finite array of
"observation statements" each containing only observational terms and each "verified" directly by
observation.  Precisely what it is which is "directly observed" and thus serves to "verify" an observation
statement is not determined by H-Dism, and those who defend this model of justification can, and do,
differ dramatically about what they hold such "verifiers" to be.  Nevertheless, whatever these verifiers,
these basic "observation statements," might be, they serve as the "foundation" on which the structure of
empirical knowledge is erected.

     For both these reasons, H-Dism is just as much committed as is inductivism to the crucial
observational vs. theoretical distinction between different kinds of statements.  However H-Dism avoids
both the problems considered above which haunted inductivism:  a) There is no need to develop an
inductivist logic from which one infers from initial observations to theories.  This is so because
according to H-Dism the theory comes first, before the observations. However, it starts out as nothing
more than a hypothetical conjecture which awaits confirmation by observation. It comes to be an
accepted theory (and hence enter the ranks of "knowledge") only after some period of more or less
extensive confirmation.  b) Since the scientific method starts with a hypothesis, that hypothesis directs
the scientist to which observational data to gather and provides a language in which to express it.

     The H-D switch from proof to confirmation entails an abandonment of the historical goal of certainty and a pragmatic orientation which inquires into the degree of rational justification of a scientific theory.  Thus H-D advocates are "falibilists" who admit that any theory, no matter how well confirmed is potentially open to falsification in the light of new tests, and hence was not knowledge.
However, H-Dists recognized that by and large once a hypothesis has passed a period of being tested and
comes to be an accepted theory, the testing work of science leaves that hypothesis and advances to a
concern with new ones.  The general picture of scientific knowledge which one got from this accorded
well with the pyramidal construction of explanation from an apex of a few high level theoretical
principles to manifold observation statements at the base.  Growth in scientific knowledge was seen as
cumulative extending the base of the pyramid with more and more empirical evidence, and its height
by more and more all embracing general theoretical principles.
     On the H-D view, the scientist no longer appears to be a "prover of theories from the undirected accumulation of data" but now appears as a "tester of hypotheses by controlled observation".  Thus science does not start with accumulating data randomly; it starts with a hypothesis which directs what data to acquire and provides a language to express it in.  Though the DN model of explanation does not require it, most advocates of hypothetico-deductive model of justification assumed the DN model of explanation.
The validity of the argument which explains a phenomenon only assures us that the explanandum
follows from the explanans, but is the explanans "true"? If scientific explanations are to be considered
as giving us knowledge, don't we have to know their premises are true?  Would a successful prediction
from a false hypothesis count as scientific knowledge?

     Consider the three kinds of statements in the D-N model of a scientific explanation: the initial
conditions statements can be (presumably) "verified" by direct observation.  So let us take their truth
as unproblematic (at least most H-D advocates tended to do this).  Thus our model of explanation
simplifies to Hypothesis => Explanandum.  Let us also assume the statements describing the
explanandum can be verified directly by observation.

     What then can we know about the truth of the hypothesis?  It can't be verified directly by
observation because it includes what aspire to be candidates for general laws ("law-like" statements). By
definition a law is a general statement, and if it is not a purely empirical law, it will have in it
theoretical terms which do not refer to anything directly observable.  Can we infer from the truth of
the explanandum, which we observe, the truth of the hypothesis?  No, to do so is a logical fallacy known
as "affirming the consequent."  From the falsity of the explanandum (i.e. observation reveals that the
prediction was not true), we can validly infer the falsity of the hypothesis, but from the truth of the
explanandum we cannot infer the truth of the hypothesis.

In other words, even though we may validly deduce a statement describing observable phenomena from a hypothesis, i.e., predict a specific phenomenon, and observation reveals that the phenomenon does occur as predicted, we still cannot conclude from this fact that the hypothesis is necessarily true. Other hypotheses, incompatible with the original one, may also equally well predict the same phenomenon exactly as it is observed to occur. In fact it is possible to prove logically that there are an infinite number of logically possible hypotheses from which that very same observed phenomenon could have been equally validly deduced.  We express this perhaps surprising conclusion by saying that the empirical evidence "underdetermines" theory choice.
     Thus though observation can refute a hypothesis, it can never verify (i.e., prove to be true) any
hypothesis.  Consequently, like modern day inductivists, the H-D theorist also must reject the traditional
goal of certainty as the criterion of knowledge, and with this move the scientific method no longer
becomes a tool for "verification" or "proof." Instead H-D theorists must now speak in terms of
"confirmation" (or perhaps "corroboration," defined as the absence of refutation).  The question that
philosophers of science now address changes from "How do we prove the truth of this theory with the
data we've got?" to "On the basis of what empirical evidence do we conclude that it is most rational to
accept some one particular hypothesis out of all those hypotheses which have been proposed and tested
by H-D methodology?"

     Notice that insofar as the "testing of hypotheses" now becomes the central epistemic task of
science, the distinction between observational and theoretical terms remains crucial.  Since it is the
"observations" which pass judgment on the "hypothesis" the degree of credibility, or "acceptance," which
any hypothesis achieves, it will achieve only if the observational evidence is "independent" of the
hypothesis on which it is used to pass judgment. To the extent that we can show that the observational
evidence is "laden" by theoretical beliefs in a way which cannot be eliminated, we undermine the
"objectivity" of the test and thus the justification of the hypothesis.  Had we accepted a different theory
to begin with, we would have gathered different observational evidence (which that that theory led us
to obtain), which may well have led to the confirmation of that theory.

     Another crucial move in embracing H-Dism involves the question of where hypotheses come
from in the first place.  In order to avoid the problems of inductivism, H-Dism is anxious to stay away
from questions like this, because it does not want to make the hypothesis appear to be "induced" from
prior data.  H-Dism effectively moves to "table the question" as far as philosophy of science is
concerned.  Thus H-D theorists argued that it doesn't matter where the hypothesis comes from because
what makes it scientific is not its origin, where it comes from, but the fact that it has been subjected
to rigorous repeated testing - and passed (or wasn't refuted)- which turns a mere hypothesis into a
scientific theory fit for the title of "knowledge."  Therefore, the philosophical explication of scientific
knowledge does not need to ask where the hypothesis "comes from." Of course scholars interested in
history or the psychology of science might investigate such matters, but whatever they might find there
has no bearing on the philosopher's goal of showing that science provides knowledge, i.e. why science's authority is justified.

     Another way to put this is as follows: Inductivism holds that theory, to speak loosely, comes
from empirical data, but this gives rise to the problem that if there is at first no theory, one has no idea
what data to gather.  So H-Dism holds that theory, in the form of a conjectured hypothesis, precedes,
and therefore directs, the accumulation of data, which in turn then confers confirmation on the
hypothesis, turning it from a speculative conjecture into an accepted "law" or "theory."  However, if one
asks "Where does the hypothesis come from?" the H-Dist can answer that such a question is for the
"context of discovery" and is a totally separate issue from the question of the "logic" of confirmation
with which the "context of justification" is concerned.  As philosophers concerned with answering the
question of authority we need only address issues in the context of justification, for only justification
makes conjectures into scientific knowledge.  The origin of those conjectures, the concern of the
"context of discovery" is no doubt an intriguing area for psychological, historical, and sociological
analysis, but it is irrelevant to our philosophical concerns.  (Unfortunately the tendency of just this sort
of research has been to undermine the whole idea that there is an "logic" of justification at all.)

     Consequently, in embracing H-Dism, the empiricist consensus erected a very powerful distinction
between what was called the "context of justification" and the "context of discovery."  The "context of
justification" was concerned with the testing of hypotheses (taken merely as "given") by the methodology
of deducing observational tests and their confirmation (or refutation) by observation which are properly
philosophical (epistemological) matters.  The "context of discovery" refers to questions concerning the
origin of hypotheses by the efforts of "creative imagination" and the psychology of scientific genius,
matters which are appropriate subjects for historical and psychological research.

     Under this distinction, history of science has little or nothing to do with philosophy of science.
The philosopher may of course point to various episodes in the history of science to show that the
methodology he has prescribed is exemplified by great theoretical achievements.  But if historical records
and methodological prescriptions do not agree, the philosopher can always take refuge in the claim that
his business is normative; he prescribes the methodology that scientists ought to follow, but of course
real historical scientists are only human and therefore do not always do what they ought to do. The
philosopher is concerned with erecting a model of an "ideal" science, which real science may more or
less perfectly embody.

     H-Dism can be, and was, attacked on several different fronts.  First, there were problems
"internal" to the empiricist consensus that raised questions about the degree of acceptance that should
be accorded any general claim on the basis of any body of observational evidence.  Hempel and
Goodman formulated a variety of paradoxes in the H-Dist attempt to avoid the pitfalls of inductivism.
There are still, however, those philosophers who hold out hope for theories of confirmation and a good
bit of research still pursues this goal.

     Secondly, H-Dism, and all empiricistic foundationalism, can be attacked externally at its
foundation with respect to its rather naive acceptance of the incorrigibility of allegedly given
observational data.  The recognition that observation is essentially "theory-laden" did much to undermine
H-Dism's claim that the acceptability of a hypothesis is solely a function of the empirical evidence.

     Finally, H-Dism's absolute separation between the context of discovery and the context of
justification can (and, according to many, did) lead to a reconstruction of science that bears little
resemblance to the historical record left by real science and allows no philosophical understanding of
the process by which hypotheses are generated prior to their being tested.

     At present we will consider only the the first area internal difficulties raised by the goal of
developing a logic of confirmation.  The adoption of the hypothetico-deductive model of justification
involves the frank abandonment of the goal of "proving" or "verifying" hypothetical laws by induction
from particular instances.  Instead the HD theorist advocates justifying the acceptance of scientific
hypotheses on the basis of a high degree of confirmation by the observation statements which are
themselves held to be "directly verified" by observation of the world.  Much criticism from outside the
empiricist consensus was aimed at this alleged incorrigible foundation of directly verified observation
statements.  But inside the consensus it was the problem of confirmation of the hypotheses built upon
this foundation which tended to bedevil HD advocates.

     While the move away from "proof" in favor of the much weaker notion of "confirmation" seems
a reasonable strategy for empiricists in the face of the intractable problem of induction raised first by
Hume, it turns out that the ghost of that old problem comes back to haunt HDism.  Out of the
torturous and seemingly arcane debate over these problems two famous "paradoxes of confirmation" can
be distilled: the paradox of the ravens, first discovered by Hempel himself, and the "grue paradox" (or
"new riddle of induction") formulated by Nelson Goodman.  The "Paradoxes of the Gruesome Ravens"
is the jocular name for these difficulties, for reasons which shall emerge.

     Clearly the HD theorist has the burden of explicating what sort of evidence is alleged to
"confirm" a hypothesis.  For empiricists the evidence must of course be empirical, something that can
be observed.  However, all that is observed, as reported in observation statements, are particular
instances.  The basic idea was the obvious one that a hypothetical law, which is of course universal (and
so, because of the problem of induction, cannot be proved by inductive inference from observation), is
"confirmed" by each "positive instance," i.e., each instance in which what the hypothesis says is
universally so, is found by observation to be so; this is known a the "Nicod criterion" for confirmation.
Thus, the stock example of a lawlike universal statement, "All ravens are black." is confirmed by each
instance of a black raven which is observed.  In other words, it seems that we have the perfectly
reasonable and expected claim that our rational justification for accepting as a law the universal
statement that all ravens are black, is based on the evidence of observed black ravens.  But astonishingly,
this seemingly modest claim leads to absurd consequences.

     Such a paradox arises because the HD advocate also wants to be able to claim that if he is
justified in accepting a law as confirmed, then everything that can be validly deduced from that law is
equally justified.  In other words, any evidence that confirms a hypothesis confirms any other hypothesis
which can be validly deduced from the original one.  Now the problem resulting from these two claims,
known as the "raven paradox," can be seen when we consider that the universal statement "All non-black
things are non-ravens" is logically equivalent to the hypothesis that "All ravens are black." in the formal
sense that each can be validly deduced from the other. [This is so because of the logical principle known
as "contraposition" in traditional logic or as "transposition" in symbolic logic.]  Now a positive instance
of the hypothesis that "All non-black things are non-ravens," would be anything that is neither black
nor a raven, for example a white piece of chalk.  One may very well agree that a white piece of chalk
is evidence which confirms the (rather silly) hypothesis that "All non-black things are non-ravens."  But
since that hypothesis is logically equivalent to the hypothesis that "All ravens are black," whatever
confirms the one, confirms the other.  Thus that same white piece of chalk also is evidence which
confirms the hypothesis that "All ravens are black."  While it would surely be rational to regard the
ornithologist's observation of black ravens as evidence for claiming that all ravens are black, it seems
preposterous to regard observation of a white piece of chalk as evidence for a hypothesis about birds!
Yet the HDist seems to be in the bind of having to agree that the justificatory work of such "indoor
ornithologists" is on a logical par with the evidence presented by the observation of birds in the bush!
Hence, the paradox.

     The "grue paradox" makes things even worse for the HDist.  Typically the scientist will not be
considering a single hypothesis but will be looking for which hypothesis is "best confirmed" by the
available evidence.  The grue paradox shows us, that if we bar induction as a means of justification, for
every hypothesis that is confirmed by some body of evidence, there are an infinite number of alternative
hypotheses inconsistent with the first which are all equally well confirmed by that same evidence.  Thus,
based on the empirical evidence alone, it would seem that there is no justification for regarding the
evidence as ever confirming one hypothesis more than another one!  Yet of course scientists frequently
make judgments that the evidence confirms one hypothesis more favorably than another; hence the
second paradox

     Here's how the paradox was presented by Goodman.  Take as our example this time the
hypothesis that "All emeralds are green."  Clearly this hypothesis is confirmed by observations of green
emeralds, i.e. its "positive instances."  Now consider a rival hypothesis: "All emeralds are grue." Here
"grue" is a new predicate which is defined as the property of being green before the year 2000 and blue
afterwards. Thus this second hypothesis that all emeralds are grue will be confirmed by any observation
of a green emerald before the year 2000, since "grue" means by definition being green before 2000.
Of course, since all observational evidence available is before the year 2000, all the evidence we have
confirms the grue hypothesis exactly as much as it confirms the green hypothesis.  Of course picking
the year 2000 is absurdly arbitrary; we could have picked any date.  So, in effect, there are an infinite
number of alternative hypotheses (each of which would have the emeralds changing color at a different
date) which are all equally well confirmed by the observed positive instances of green emeralds.  Since
our justification for accepting a hypothesis as confirmed is the empirical evidence, it follows
paradoxically that we have no rational justification for picking one hypothesis (based on the predicate
"green") as better confirmed than an infinite host of alternatives (making use of "absurd" predicates like

     Obviously, this does not reflect what really is the case in science.  The hypothesis that all
emeralds are green is in fact considered highly confirmed and accepted by all mineralogists, whereas no
one believes "All emeralds are grue."  Why do we consider "green" as "reasonable" but "grue" as utterly
"absurd"?  The reason seems obvious: no one has ever observed gems changing color on an arbitrary date
in the past, so no one has any grounds for expecting any gem to change from green to blue in the year
2000.  But to say this is just to say that we expect the future will resemble the past (the principle of
the uniformity of nature), which is of course the heart of Hume's problem of induction.  No doubt
science proceeds on this assumption of the uniformity of nature, but our task is to justify it.  Yet the
only way to justify it is to reason from the evidence which we have accumulated from the past, and that
of course is to assume the very point which is at issue, namely the reliability of inductive inference from
the past to the future.  We must conclude that the confirmationist has not escaped the problem of
induction, and so Goodman calls his "grue paradox" the "new riddle of induction."

     It would certainly be an overstatement to say that logical paradoxes such as these were
responsible for the dissolution of the empiricist consensus, but they tended to proliferate and attempts
to deal with them tended to produce yet more problems.  Thus philosophers' confidence that this was
a profitable line of research waned and made the situation ripe for an alternative approach to answering
the question of authority.