popper-logic-scientific-discovery

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ACKNOWLEDGMENTS, 1960 and 1968 I wish to thank Mr. David G. Nicholls for communicating to me the admirable passage, now printed on page xvii, which he discovered among the Acton Manuscripts in the Library of Cambridge University (Add. MSS 5011:266). The reprint of the book gives me the welcome opportunity to quote this passage. Summer 1959 preface, 1959 xxvii In this second English edition four short Addenda have been added to the appendices. Minor mistakes have been corrected, and I have made a few linguistic improvements. Misprints have been corrected that were brought to my notice by Imre Lakatos, David Miller, and Alan Musgrave. They also suggested many new entries in the Index of Subjects. I am very grateful to them. My greatest debt is to Paul Bernays who, shortly after this book had appeared in English, checked through my axiomatization of the probability calculus, especially the new appendix *v. I value his approval more highly than I can express in words. It does not, of course, absolve me from bearing the sole responsibility for any mistake I may have made. November 1967 K. R. P.
Page 2: The Logic of Scientific Discovery
Page 5 and 6: Logik der Forschung first published
Page 8 and 9: CONTENTS Translators’ Note xii Pr
Page 10 and 11: contents ix 7 37 Logical Ranges. No
Page 12 and 13: iii Derivation of the First Form of
Page 14 and 15: translators’ note xiii In these n
Page 16 and 17: PREFACE TO THE FIRST EDITION, 1934
Page 18 and 19: There is nothing more necessary to
Page 20 and 21: preface, 1959 xix Language analysts
Page 22 and 23: xxii preface, 1959 perception or kn
Page 24 and 25: preface, 1959 xxiii essence of phil
Page 26 and 27: preface, 1959 xxv elaborate and fam
Page 30: Part I Introduction to the Logic of
Page 33 and 34: 4 the logic of science statements (
Page 35 and 36: 6 the logic of science principle of
Page 37 and 38: 8 the logic of science us. Someone
Page 39 and 40: 10 the logic of science other state
Page 41 and 42: 12 the logic of science system of s
Page 43 and 44: 14 the logic of science by Schlick*
Page 45 and 46: 16 the logic of science that I am m
Page 47 and 48: 18 the logic of science Now in my v
Page 49 and 50: 20 the logic of science by introduc
Page 51 and 52: 22 the logic of science Here too a
Page 53 and 54: 24 the logic of science reproduced
Page 55 and 56: 26 the logic of science establish o
Page 57 and 58: 28 the logic of science The way in
Page 59 and 60: 30 the logic of science meaningful
Page 61 and 62: 32 the logic of science 11 METHODOL
Page 63 and 64: 34 the logic of science certainly t
Page 66 and 67: 3 THEORIES The empirical sciences a
Page 68 and 69: theories 39 event in question. (The
Page 70 and 71: theories 41 8 ft.). Formal logic (i
Page 72 and 73: theories 43 the following kind: ‘
Page 74 and 75: theories 45 I believe that my usage
Page 76 and 77: etween universal and singular state
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theories 49 statement. On the contr
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from contradiction (whether self-co
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theories 53 but as a statement-equa
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theories 55 deduced from them. High
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4 FALSIFIABILITY The question wheth
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falsifiability 59 instruments satis
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on the ground that the experimenter
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falsifiability 63 findings of Miche
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falsifiability 65 and ‘A catastro
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falsifiability 67 hypothesis must b
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falsifiability 69 This suggests the
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various basic statements belonging
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falsifiability 73 consistency fail
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the problem of the empirical basis
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statement with a fact is nothing el
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(There is a widespread belief that
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have, after all, allowed psychologi
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6 DEGREES OF TESTABILITY Theories m
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actually encounter and observe, and
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33 DEGREES OF FALSIFIABILITY COMPAR
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degrees of testability 101 testabil
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versa. The better testable statemen
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of degrees of falsifiability to a l
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degrees of testability 107 statemen
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degrees of testability 109 demand t
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successful in guiding our choice be
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degrees of testability 113 would im
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a simple theorem of the theory of d
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zero dimensional classes 1 one dime
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degrees of testability 119 common,
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7 SIMPLICITY There seems to be litt
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simplicity 123 for one, gives a neg
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simplicity 125 criticism. It will a
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I have already shown that theories
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particularly simple; but a law whic
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experience; a point with which I ag
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8 PROBABILITY In this chapter I sha
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y mixing water and alcohol’, illu
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probability 137 probability stateme
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of the theory in its present form.
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if sequences of penny tosses showed
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modified, namely, so as to demand n
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How this is to be understood will b
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54 FINITE SEQUENCES. ORDINAL SELECT
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Since every element of α has eithe
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construct other sequences, again wi
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probability 153 begin with the segm
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probability 155 called a ‘referen
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probability 157 which the correspon
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questions about the origins or ‘s
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probability 161 example of a collec
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distances of the elements from an a
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probability 165 binomial formula (3
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probability 167 segment 0,0, anothe
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segments possessing the property
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probability 171 only slightly from
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63 BERNOULLI’S THEOREM AND THE PR
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probability 175 behaviour which I h
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probability 177 conversely: if it h
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probability 179 (2) Requirement of
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of the calculus of probability. Wit
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probability 183 upon my criterion o
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probability 185 property ‘1’, a
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probability 187 the uniqueness of p
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probability 189 interpreted as ‘m
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probability 191 probability, the ph
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probability 193 as molecular collis
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probability 195 magnitude of ε cha
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probability 197 But this answer rai
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probability 199 events are, or are
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probability 201 at times may indeed
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probability 203 class of occurrence
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probability 205 express all we know
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tion I regard the practicability of
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9 SOME OBSERVATIONS ON QUANTUM THEO
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some observations on quantum theory
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affected, for example by irradiatio
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outside it. Schrödinger later show
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mechanics. On this view, the theory
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78 INDETERMINIST METAPHYSICS some o
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corroboration, or how a theory stan
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APPENDIX i Definition of the Dimens
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appendix i 285 relatively atomic st
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(1,1) N(α.β.γ) N(α) N(α.β) N(
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To the numerator of this formula we
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assume that (2) holds for all n, m
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APPENDIX iv A Method of Constructin
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appendix iv 295 αF′(1) = αF′(
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APPENDIX v Examination of an Object
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appendix v 299 (c) In a similar way
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APPENDIX vi Concerning a Non-Predic
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appendix vi 303 This assumption, ho
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APPENDIX vii Remarks Concerning an
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holds, and therefore also (6) (7) |
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NOTE TO NEW APPENDICES, 1959 EDITIO
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new appendices 311 Yet I had not on
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views were discussed, by the Circle
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appendix *i 315 statement turns out
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appendix *i 317 either lead to an i
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APPENDIX *ii A Note on Probability,
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A3 A4 B1 B2 B3 There are at least o
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(An example of an interpretation of
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APPENDIX *iii On the Heuristic Use
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‘p(2) + p(4)’ we can write, mor
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APPENDIX *iv The Formal Theory of P
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interpretation according to which a
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p(x) = p(x). Thus the derivability
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where e is evidence in favour of th
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A1 There are elements c and d in S
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appendix *iv 339 C + , similarly, t
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A3 is needed to prove that p(a, a)
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(E) There are elements a, b, and c
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Now we can define, p(a, b) = lim q(
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appendix *iv 347 if we consider tha
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The redundancy of the usual systems
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among those elements of S which are
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appendix *iv 353 (ii) An admissible
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appendix *iv 355 Although every Bor
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A3 B1 B2 C p(a, a) = p(b, b). p(ab,
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(43) p(a, (bc)((ab)c)) = 1 42 (subs
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This is the generalization of the u
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(90) p(a, c) = p(b, c) → p(ā, c)
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Then we obtain: (i) If a and b are
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whether a necessary statement is ne
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APPENDIX *vi On Objective Disorder
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appendix *vi 371 which from the ver
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and also of the older appendix *ii.
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ook (sections 80, 81, and 83) by a
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and (see page 346) (3) a = lim a n
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Although from the point of view of
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But let us now consider the view th
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favour, more probable than its nega
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sequence, so that we can attribute
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appendix *vii 387 my Postscript.) H
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appendix *vii 389 and ‘ ’.) The
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appendix *vii 391 thus to a set of
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appendix *viii 393 smaller the numb
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a planet rather than to a point of
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Our theorem has been derived by con
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appendix *viii 399 with the same nu
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ecome clear to us that a high degre
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probability > 1/2. (They even faile
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appendix *ix 405 and that the asser
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Like (5), theorem (6) expresses a f
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appendix *ix 409 here merely follow
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appendix *ix 411 corroboration or a
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and thus entails part of the conten
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appendix *ix 415 7. Why have C(x, y
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special cases. To remedy these defe
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not as much as can be formalized. B
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Thus I prefer to look upon (2) and
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appendix *ix 423 atomic statements
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than upon rational arguments; thus,
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present paper, whether the objectiv
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(5) Now let h be the statement P(a,
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appendix *ix 431 9. One may see fro
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the same likelihood—i.e.P(e, h) =
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The first problem I have in mind is
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appendix *ix 437 likelihood to zero
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appendix *ix 439 falsifiability of
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appendix *x 441 saying that a repet
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appendix *x 443 showing that one si
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appendix *x 445 to the fact that un
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appendix *x 447 (5) That theories t
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eached. But were there a natural la
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Thus natural necessity or impossibi
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p(a) = p(a, ā) = 0; and the same m
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(D) a→ N b is true if, and only i
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appendix *x 457 edly contains impli
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appendix *x 459 induction—perhaps
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appendix *x 461 situation created b
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appendix *x 463 But I think I have
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appendix *xi 465 motion. 2 It dispr
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appendix *xi 467 mechanical work wi
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appendix *xi 469 measure the moment
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appendix *xi 471 significance only
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appendix *xi 473 left. This will (a
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appendix *xi 475 electron’s posit
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seen) by Heisenberg’s imaginary e
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light’. And this assertion, we ha
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APPENDIX *xii The Experiment of Ein
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appendix *xii 483 findings is merel
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appendix *xii 485
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appendix *xii 487
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NAME INDEX The letter ‘q’ stand
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Hobbes, Th. xxiii Hossiasson, J. 26
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Thirring, H. 210q&n Tornier, E. 137
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Almost certain 171; almost follows
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confusion 249n, 408, 414n, 415, 437
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456; essential 452; implicit 51-4;
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Falsifiability, degree of see Testa
Page 532 and 533:
Independence, logical of an axiom o
Page 534 and 535:
Mathematical rules for generating s
Page 536 and 537:
physics, see also Quantum theory; R
Page 538 and 539:
discontinuity in 302-3; interpretat
Page 540 and 541:
143, 151n, 157, 160, 162, section 5
Page 542:
Truth-function 113n, 284, 315 Truth
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