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appendix *ix 439 falsifiability of probabilistic or statistical theories and of falsifying statistical tests has just been published as this new edition goes to the press. It is Donald A. Gillies, ‘A Falsifying Rule for Probability Statements’, B.J.P.S. 22, 1971, pp. 231–261.
APPENDIX *x Universals, Dispositions, and Natural or Physical Necessity (1) The fundamental doctrine which underlies all theories of induction is the doctrine of the primacy of repetitions. Keeping Hume’s attitude in mind, we may distinguish two variants of this doctrine. The first (which Hume criticized) may be called the doctrine of the logical primacy of repetitions. According to this doctrine, repeated instances furnish a kind of justification for the acceptance of a universal law. (The idea of repetition is linked, as a rule, with that of probability.) The second (which Hume upheld) may be called the doctrine of the temporal (and psychological) primacy of repetitions. According to this second doctrine, repetitions, even though they should fail to furnish and kind of justification for a universal law and for the expectations and beliefs which it entails, nevertheless induce and arouse these expectations and beliefs in us, as a matter of fact—however little ‘justified’ or ‘rational’ this fact (or these beliefs) may be. Both variants of this doctrine of the primacy of repetitions, the stronger doctrine of their logical primacy and the weaker doctrine of their temporal (or causal or psychological) primacy, are untenable. This may be shown with the help of two entirely different arguments. My first argument against the primacy of repetitions is the following. All the repetitions which we experience are approximate repetitions; and by
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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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Page 421 and 422: APPENDIX *viii Content, Simplicity,
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Page 425 and 426: 396 new appendices But formula (*)
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Page 431 and 432: APPENDIX *ix Corroboration, the Wei
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Page 437 and 438: 408 new appendices who identify, ex
Page 439 and 440: 410 new appendices Kemeny.) Therefo
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Page 443 and 444: 414 new appendices (4.5) C(x 1x 2 o
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Page 451 and 452: 422 new appendices length, to take
Page 453 and 454: 424 new appendices A THIRD NOTE ON
Page 455 and 456: 426 new appendices (3) P(a) = P(a,
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Page 461 and 462: 432 new appendices statistical inte
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Page 465 and 466: 436 new appendices statements e, f,
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Page 477 and 478: 448 new appendices natural laws see
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Page 481 and 482: 452 new appendices physical theory
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Page 485 and 486: 456 new appendices A little reflect
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Page 491 and 492: 462 new appendices the phenomenalis
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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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