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We mention, therefore, only a few philosophers:
Bacon objected to earlier methodology because he judged it to
have failed to obtain generalisations which showed the 'signs' of being
true. He is very clear what one of these signs is: (The New Organon
Bk.1 LXXIII) "Of all signs there is none more certain or more noble than
that taken from fruits. For fruits and works are as it were sponsors
and sureties for the truth of philosophies....Celsus ..tells us that the
experimental part of medicine was first discovered, and that afterwards
men philosophized about it, and hunted for and assigned causes; and not
by an inverse process that philosophy and the knowledge of causes led to
the discovery and development of the experimental part... Brutes by their
natural instinct have produced many discoveries, whereas men by discussion
and the conclusions of reason {he means reasoning by syllogism from premature
abstractions} have given birth to few or none...Wherefore, as in religion
we are warned to show our faith by works, so in philosophy by the same
rule the system should be judged of by its fruits, and pronounced frivolous
if it be barren, more especially if, in place of fruits of grape and olives,
it bear thorns and briers of dispute and contention".
In CVI he continues: "But in establishing axioms by this
kind of induction, we must also examine and try whether the axiom so established
be framed to the measure of those particulars only from which it is derived,
or whether it be larger and wider. And if it be larger and wider,
we must observe whether by indicating to us new particulars it confirm
that wideness and largeness as by a collateral security, that we may not
either stick fast in things already known, or loosely grasp at shadows
and abstract forms, not at things solid and realized in matter. And
when this process shall have come into use, then at last shall we see the
dawn of a solid hope".
Whewell 's methodology was explicitly hypothetico-deductivist. He was happy with hypotheses moving a long way from observations - and hence from direct testing. He therefore extolled the virtues of M11, as a way of establishing the truth-content of such hypotheses indirectly.
Mill was famously uneasy about Whewell's enthusiasm for M11, but actually only in certain circumstances - where we agree with Mill. The circumstances that concerned him were when a theory had already shown its truth content by successfully doing improbable things. He argued that in this case, a further successful novel fact prediction did not significantly increase the corroboration for the theory, since its truth was already established. If it was true, it would have these successful consequences anyway.
Popper based his methodology on falsification, for the discovery of error, and on severe testing, for corroboration. A theory is corroborated if it goes out on a limb, makes a prediction which is improbable on the basis of background knowledge - or competing theories, and the prediction is found to be correct.
Lakatos changed the unit of assessment from a single theory to
a sequence of theories - a research programme - following Duhem. The main
indicator of the success of a research programme, which makes it 'progress',
is successful prediction of novel facts. A programme which can only accommodate
the facts by ad hoc defensive manoeuvres - especially those that
make it more complex - is 'degenerating'.
Lakatos made no serious attempt, of which I am aware, to justify the
importance of novel fact prediction as an indicator of truth.
For the descriptive methodologist, the role of this method in physics
is inescapable. Current investigators give us examples from the present
and the past, involving its use, judged to be typical good practice. For
example, if the quark theory predicted that high-energy electrons would
scatter off a proton as though it contained three tiny fractionally-charged
entities inside it - and if, then, the experiment was done, and the electrons
did scatter off exactly as predicted - then this is (the physicists say)
classic evidence that the quark theory has some truth in it. No-one, they
say, would persist in the view that it was just a human fiction, in the
face of such evidence - indirect though it is.
In this attitude, the physicists are merely restating a common view.
If I say that I have been at the cinema all afternoon, and my girlfriend
does not believe me, she may ask me what time the performance started.
If I tell her it started at 2:25, and she checks in the paper, and it was
2:25, then she is more inclined to believe me. Why? Because on the first
theory, I went to the cinema; I would then tend to know the time that the
performance began. On the second theory, I did not go; I would then probably
be guessing the time, in which case the chance of guessing it correctly
is very small. The novel fact, in this case, is the event of me stating
the time for the performance to start, correctly. Since the first theory
has successfully predicted it, it contains some truth.