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experience; a point with which I agree. He believes that he must therefore choose the ‘simplest’ theory. But since the conventionalist does not treat his theories as falsifiable systems but rather as conventional stipulations, he obviously means by ‘simplicity’ something different from degree of falsifiability. The conventionalist concept of simplicity turns out to be indeed partly aesthetic and partly practical. Thus the following comment by Schlick (cf. section 42) applies to the conventionalist concept of simplicity, but not to mine: ‘It is certain that one can only define the concept of simplicity by a convention which must always be arbitrary.’ 1 It is curious that conventionalists themselves have overlooked the conventional character of their own fundamental concept—that of simplicity. That they must have overlooked it is clear, for otherwise they would have noticed that their appeal to simplicity could never save them from arbitrariness, once they had chosen the way of arbitrary convention. From my point of view, a system must be described as complex in the highest degree if, in accordance with conventionalist practice, one holds fast to it as a system established forever which one is determined to rescue, whenever it is in danger, by the introduction of auxiliary hypotheses. For the degree of falsifiability of a system thus protected is equal to zero. Thus we are led back, by our concept of simplicity, to the methodo<strong>logic</strong>al rules of section 20; and especially also to that rule or principle which restrains us from indulgence in ad hoc hypotheses and auxiliary hypotheses: to the principle of parsimony in the use of hypotheses. Addendum, 1972 In this chapter I have tried to show how far degrees of simplicity can be identified with degrees of testability. Nothing depends on the word ‘simplicity’: I never quarrel about words, and I did not seek to reveal the essence of simplicity. What I attempted was merely this: Some great scientists and philosophers have made assertions about simplicity and its value for science. I suggested that some of these 1 Schlick, ibid., p. 148. simplicity 131
132 some structural components of a theory of experience assertions can be better understood if we assume that when speaking about simplicity they sometimes had testability in mind. This elucidates even some of Poincaré’s examples, though it clashes with his views. Today I should stress two further points: (1) We can compare theories with respect to testability only if at least some of the problems they are supposed to solve coincide. (2) Ad hoc hypotheses cannot be compared in this way.
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The Logic of Scientific Discovery
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Logik der Forschung first published
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CONTENTS Translators’ Note xii Pr
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contents ix 7 37 Logical Ranges. No
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iii Derivation of the First Form of
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translators’ note xiii In these n
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PREFACE TO THE FIRST EDITION, 1934
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There is nothing more necessary to
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preface, 1959 xix Language analysts
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xxii preface, 1959 perception or kn
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preface, 1959 xxiii essence of phil
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preface, 1959 xxv elaborate and fam
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ACKNOWLEDGMENTS, 1960 and 1968 I wi
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1 A SURVEY OF SOME FUNDAMENTAL PROB
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a survey of some fundamental proble
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trivial; for metaphysics has usuall
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non-contradictory, a possible world
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2 ON THE PROBLEM OF A THEORY OF SCI
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on the problem of a theory of scien
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Part II Some Structural Components
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38 some structural components of a
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5 THE PROBLEM OF THE EMPIRICAL BASI
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10 CORROBORATION, OR HOW A THEORY S
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284 appendices it is connected with
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APPENDIX ii The General Calculus of
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288 appendices —we obtain from (2
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APPENDIX iii Derivation of the Firs
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292 appendices (6,1) αF″(σ´ m.
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294 appendices after effect) in the
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296 appendices (b) An analogous met
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298 appendices position), then we a
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300 appendices incoherent photons.
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302 appendices interposition of a f
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304 appendices wave-packets (obtain
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306 appendices slit. This angle φ
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308 appendices latter, if we use hi
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310 new appendices The first two of
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APPENDIX *i Two Notes on Induction
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314 new appendices statements’;*
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316 new appendices be the source fr
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318 new appendices with the help of
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320 new appendices logical interpre
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322 new appendices It is desirable
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324 new appendices operations—con
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326 new appendices (3) It will be a
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328 new appendices (7) The derivati
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330 new appendices There are three
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332 new appendices that is to say,
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334 new appendices invalid, and sho
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336 new appendices simplified syste
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338 new appendices The following co
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340 new appendices able to show tha
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342 new appendices obtain p(a, c) =
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344 new appendices The second examp
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346 new appendices first consistenc
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348 new appendices S′ ={0, 1, 2,
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350 new appendices B1 is violated b
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352 new appendices always fill the
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354 new appendices It should be men
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APPENDIX *v Derivations in the Form
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358 new appendices (26) (Eb) (Ea) p
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360 new appendices (Applying B2 twi
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362 new appendices form: it is unco
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364 new appendices In order to prov
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366 new appendices which is neverth
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368 new appendices the other axioms
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370 new appendices between rain and
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372 new appendices in the widest po
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APPENDIX *vii Zero Probability and
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376 new appendices favourable possi
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378 new appendices (4) p(a) = lim p
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380 new appendices The same point m
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382 new appendices inferences from
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384 new appendices the required a a
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386 new appendices ‘universe’
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388 new appendices All this does no
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390 new appendices The fine-structu
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APPENDIX *viii Content, Simplicity,
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394 new appendices each entry repre
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396 new appendices But formula (*)
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398 new appendices (−) d(a 1)p(a
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400 new appendices thus becomes som
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APPENDIX *ix Corroboration, the Wei
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404 new appendices I will now brief
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406 new appendices of the brevity o
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408 new appendices who identify, ex
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410 new appendices Kemeny.) Therefo
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412 new appendices DEGREE OF CONFIR
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414 new appendices (4.5) C(x 1x 2 o
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416 new appendices strongly upon P(
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418 new appendices (vii) If C(x) =
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420 new appendices to be slightly a
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422 new appendices length, to take
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424 new appendices A THIRD NOTE ON
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426 new appendices (3) P(a) = P(a,
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428 new appendices behaviour of E a
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430 new appendices either if δ is
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432 new appendices statistical inte
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434 new appendices them, there is a
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436 new appendices statements e, f,
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438 new appendices simply deceive o
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APPENDIX *x Universals, Disposition
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442 new appendices One can easily s
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444 new appendices statement such a
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446 new appendices more abstract. T
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448 new appendices natural laws see
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450 new appendices indirect proof.
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452 new appendices physical theory
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454 new appendices is deducible fro
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456 new appendices A little reflect
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458 new appendices differ (if at al
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460 new appendices the world. And a
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462 new appendices the phenomenalis
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APPENDIX *xi On the Use and Misuse
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466 new appendices a gravitational
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468 new appendices with, its co-ord
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470 new appendices based upon his f
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472 new appendices moving freely be
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474 new appendices of insuperable b
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476 new appendices Einstein.) The m
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478 new appendices photographic pla
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480 new appendices My impression is
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482 new appendices letter were to b
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484 new appendices statistical desc
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486 new appendices
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488 new appendices
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490 name index Carnap, R. 7n, 13n,
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492 name index Mises, R. 133, 135n,
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SUBJECT INDEX Italicized page numbe
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496 subject index Binomial formula
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498 subject index Cosmology, its pr
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500 subject index Empirical basis s
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502 subject index and ad hoc hypoth
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504 subject index 150&nt, see also
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506 subject index Modus Ponens 71n,
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508 subject index 319-20; indutive
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510 subject index 142&n, 154n, 174&
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512 subject index experiment 474-5,
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