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Why
Entertaining a Hypothesis is not the Same with Accepting (Classifying) It as
True
By Dmytro
Sepetyi,
In the article
"What Do Arguments Achieve?", among other things, David Miller challenges
what he calls "the orthodox view among philosophers of science" about
acceptance of a theory in science:
“It is conceded that there is a sense in which
accepting a hypothesis amounts to no more than entertaining it; we talk of working hypotheses, and of assumptions
made for the sake of argument. It is
nonetheless objected that central sense in which a scientific hypothesis is
accepted is sturdier; it means something established, though the usual
expression is acceptance as true.
Such acceptance comes after the hypothesis has been formulated, and only after
it has been tested” (Miller 2006, 90-91)
It is not quite clear,
how Popper’s view relates to this "orthodox view". In quite a many
places Popper writes that empirical scientific hypotheses are to be tentatively
accepted as true if they have successfully passed severe examinations (attempts
of empirical falsification) up to present moment. This well conforms to "the
orthodox view", as described by Miller, except the phrase “it means
something established”.
But Miller quotes one
Popper’s statement from Conjectures and
Refutations which sounds rather differently:
"…science can be regarded as growing
system of problems, rather as a system of beliefs. And for a system of
problems, the tentative acceptance of a theory or a conjecture means hardly
more than that it is considered worthy of criticism." (quot. by: Miller
2006, 90)
It is not quite clear
whether Popper talks here about acceptance
as true or about "a sense in which accepting a hypothesis amounts to
no more than entertaining it"; and nothing in this statement tells us that
they are to be identified. But Miller adduces this statement to support his
view exactly to this effect.
David Miller proposes that
empirical scientific hypotheses are to be tentatively accepted (classified) as
true as soon as they are proposed, without any examination whatever. On
Miller’s account, examinations are needed only to expel – reclassify as false –
those theories which were earlier accepted (classified) as true. Hence, we need not distinguish 1) entertainment of
a hypothesis – i.e., considering it as a possible candidate for adoption and 2)
acceptance of a hypothesis as true. Miller supports this contention with the
argument, which I will try to analyze by small parts:
“This orthodox inductivist picture of how
science proceeds makes little sense if we regard the growth of knowledge as an
objective matter. There is no such activity as accepting as true a hypothesis
that has already been accepted.” (Miller 2006, 91)
Isn’t this merely
playing with words 'accepting' - 'accepted'? If a hypothesis "has already
been accepted" in the sense "entertained", without accepting it
as true, then accepting it as true is some extra "activity" or event.
And saying that it "makes little sense" doesn’t qualify as an
argument.
“According to the revised principle of
empiricism, a hypothesis that has been accepted into science as worthy of
discussion remains accepted unless it is rejected.” (Miller 2006, 91)
Who objects? A
hypothesis that has been accepted into science as worthy of discussion (not as
true) remains accepted (as worthy of discussion, but not as true), unless it is
rejected.
“Nothing happens to it. … There is
no objective change; the hypothesis was accepted, and remains accepted, and its
status is unaltered.” (Miller 2006, 91)
Non sequitur.
If we distinguish acceptance as worthy of discussion (entertaining) from
acceptance as true, then something may happen to it – it may be accepted as
true. The hypothesis was earlier accepted as worthy of discussion, and now it
is accepted as true, its status is altered.
“…the relation between a hypothesis and the
class of accepted statements is changed when the hypothesis is itself accepted
or rejected. It is not changed when it is established or accepted as true.”
(Miller 2006, 91)
Nothing of the sort. The
objective relations between a hypothesis and whatever statement don’t depend on
any of these things. What depends is the class of accepted statements. But
there are really two classes of "accepted statements". There is the
class of statements accepted as worthy of discussion and the class of
statements accepted as true.
As for the class of
statements accepted as worthy of
discussion, it is influenced by entertaining
a new hypothesis only in that this hypothesis is added to the class,
without whatever consequences for other members of the class. (Entertaining a
new hypothesis doesn’t force us logically neither to accept any of other
entertained statements as true nor to reject any as false.) And the class of statements accepted as worthy of discussion may be changed
by rejection of the hypothesis (previously
entertained) if, and only if, it is rejected as unworthy of further discussion. If it is rejected in the sense of
(tentative) falsification, but still considered as worthy of further
discussion, it remains in the class.
As for the class of
statements accepted as true, it is
not influenced by our entertaining a hypothesis (accepting it as worthy of
discussion). It is influenced by our accepting (classifying) a hypothesis as
true, or by our rejecting a hypothesis (classifying it as false). If a
hypothesis is accepted as true then it is added to the class of accepted
statements, and everything that contradicts is must be excluded from the class.
If a hypothesis is rejected, then its negation is added to the class of
accepted statements. If it is entertained, nothing is added and nothing excluded.
I think that decisive
argument against Miller’s "unorthodox view" is Alan Musgrave’s argument:
nothing prevents us from entertaining two (or more) alternative theories which
contradict one another; but, if we respect the central core of logics – the
rule of non-contradiction – we can’t accept (classify) them both as true. This
would mean to accept (classify) as true self-contradictory statement. (Musgrave
2007, 194)
But Miller is not deterred
even by this. In the same book, the article “Making Falsification Bite”, he proposes
to “marry” falsificationism with “paraconsistent logics” (which permits
contradictions) and states: “Whatever Musgrave may opine, it is not madness to
conjecture that each of two mutually contradictory hypotheses is true” (Miller
2006, 255).
After that statement Miller
explains that “what is said shouldn’t be understood as a retreat from the
falsificationist insistence…, that contradictions are intolerable… On the
contrary, … we must never abandon our fight to resolve contradictions, since a
contradiction always indicates the presence of an error. But it would be a
folly to pretend that a state of knowledge free of contradiction is any less
utopian than a state of society free of wretchedness and oppression…” (Miller
2006, 256)
I think that this is a confusion. True, the state of knowledge free of contradictions is hardly
attainable: there are, and will always be, contradictions in our knowledge of which we aren’t aware at present
moment. And there is nothing mad in accepting as true two statements (or
theories) which contradict one another if
we aren’t aware of the contradiction. But if we are aware that a statement
(theory) X contradicts a statement (theory) Y; if we see the contradiction, we
can’t accept (classify) both X and Y as true. Such an acceptance would be
exactly “a retreat from the falsificationist insistence, that contradictions
are intolerable”. It would be exactly denial that “a contradiction always
indicates the presence of an error”.
If “a contradiction
always indicates the presence of an error” then contradiction between X and Y
indicates that either X or Y or both are mistaken, i.e. that it is impossible for
them both to be true. To admit the contrary, – that contradiction between X and
Y does not indicate that either X or
Y or both are mistaken (≡ not true); that despite the fact that X
contradicts Y they may both be true, – is to admit that a contradiction does not “always indicates the presence
of an error”. You can’t have it both ways.
******
Nevertheless, I admit
that in a sense Miller may be partly right. In a sense, scientific hypotheses
can often be reasonably accepted
(classified) as true from the very start, before making any new tests purported to test them. There
is a simple reason for this. In a sense (objective world-3 sense) scientific
hypotheses are often well tested before
they are invented. Scientific hypotheses don’t appear out of nothing without
any purpose. They are invented for solving some problems which are, to a great
extent, results of testings of their predecessors. New-invented scientific
hypothesis is already tested by such tests. It may be well reasonable to accept
(classify) as true a scientific hypothesis before
making new tests, if it is able to better account for results of those
tests which were already made on its predecessors, if it solves some problems
which its predecessors are unable to solve. Principally,
our judgment that a theory successfully solves an explanatory problem for which
it was designed is itself an initial testing which may be sufficient to
tentatively accept the theory as true if we know no other theory which solves
the problem just as well.
PS. In a later lecture (2010), Miller reverts to the idea that, given that “what we know at any moment … is inconsistent”, “here was a place where paraconsistent logic might be of some service” (where the paraconsistent logic proposed is Browerian logic. However, now Miller makes his suggestion much more modest and less objectionable, by admitting that “the paraconsistent logic proposed cannot be a logic of truth”. Instead, Miller suggests that “it may serve as a logic of what we regard as falsified”.
If I rightly understand Miller, the point is as follows. For a falsifiable (scientific empirical, on Popper’s demarcation criterion) hypothesis B, we may attribute the value “f” if we consider it as falsified, and the value C (candidate for the truth) otherwise. As for the negation of B, we should attribute to it the value C in both cases. So, for every falsifiable but unfalsified hypothesis, both the hypothesis and its negation have the value C.
Now it may well be that some paraconsistent logic (Browerian or not) can successfully model such a class C. However, two points should be made.
First, it would be a crude misdescriprion to describe the class C as the class of hypotheses that are classified as true (which was Miller’s initial point, for defense of which the idea of marrying CR with a paraconsistent logic was invoked in (Miller 2006)). It would surely be an absurd proposition that we should classify as true not only all scientific hypotheses which have successfully passed all the tests so far but their negations as well. So, Musgrave’s objection retains its strength.
(By the way, “paraconsistency” that is not about truth boils down to the point that is rather uninteresting and perfectly consistent with the “uniconsistent” logic of truth – that statements can be classified, in a lot of different ways, in accordance with some formally definable rules so that some classes can contain a statement and its negation.)
Second, Miller gives no idea as to how and for what purposes a paraconsistent model of what we regard as falsified can be serviceable. He admits that his best candidate (the Browerian logic) “is tricky to work with” and involves an operation for which “there is no easy natural-language reading”. There is no indication that, insofar as understanding of the development of knowledge is concerned, we can achieve by using a paraconsistent logic anything that cannot be easier achieved without it, in the way of informal reasoning controlled by the logic of consistency-and-truth. So far, it seems more likely than not that a paraconsistent modeling in this field will turn out a modeling for the modeling’s sake.
Literature
Miller,
D. 2006. Out of Error. Further Essays on
Critical Rationalism. Ashgate.
Miller, D. 2010. “Falsification.” Slides for a lecture given at the workshop Truth, Falsity, and Negation, Technical University of Dresden, April 2010. // The University of Warwick / Social Sciences / Department of Philosophy / David Miller [http://www2.warwick.ac.uk/fac/soc/philosophy/people/associates/miller/dresden.pdf]
Musgrave, A. 2007. Critical
Rationalism. In E.Suárez-Iñiguez, ed., The
Power of Argumentation (Poznań Studies in the Philosophy of the
Sciences and the Humanities, vol.93).
Popper. K, 2008. “What
is Dialectic”. In K.Popper, Conjectures
and Refutations.