popper-logic-scientific-discovery

More documents

Recommendations

Info

appendix *vii 389 and ‘ ’.) The use of these symbols can be explained by the following rules: (1) ‘C(a) C(b)’ and thus its equivalent ‘p(b) p(a)’ may be used to state that the content of a is greater than that of b—at least in the sense of the fine structure of content. We shall thus assume that C(a) C(b) entails C(a) C(b), and that this in turn entails C(a) � C(b), that is to say, the falsity of C(a) C(b) always entails C(a) C(b). (4) Corresponding rules will hold for p(a) p(b), etc. The problem now arises of determining the cases in which we may say that C(a) C(b) holds even though we have C(a) = C(b). A number of cases are fairly clear; for example, unilateral entailment of b by a. More generally, I suggest the following rule: If for all sufficiently large finite universes (that is, for all universes with more than N members, for some sufficiently large N), we have C(a) >C(b), and thus, in accordance with rule (3), C(a) C(b), we retain C(a) C(b) for an infinite universe even if, for an infinite universe, we obtain C(a) = C(b). This rule seems to cover most cases of interest, although perhaps not all. 15 The problem of a1 = ‘All planets move in circles’ and a2 = ‘All planets move in ellipses’ is clearly covered by our rule, and so is even the case of comparing a1 and a3 = ‘All planets move in ellipses with an eccentricity other than zero’; for p(a3)>p(a1) will hold in all sufficiently large finite universes (of possible observations, say) in the simple sense that there are more possibilities compatible with a3 than with a1. * 15 Related problems are discussed in considerable detail in John Kemeny’s very stimulating paper ‘A Logical Measure Function’, Journal of Symb. Logic 18, 1953, pp. 289 ff. Kemeny’s model language is the second of three to which I allude on p. xxiv of my Preface, 1958. It is, in my opinion, by far the most interesting of the three. Yet as he shows on p. 294, his language is such that infinitistic theorems—such as the principle that every number has a successor—must not be demonstrable in it. It thus cannot contain the usual system of arithmetic.
390 new appendices The fine-structure of content and of probability here discussed not only affects the limits, 0 and 1, of the probability interval, but it affects in principle all probabilities between 0 and 1. For let a 1 and a 2 be universal laws with p(a 2) = 0 and p(a 1) p(a 2), as before; let b be not entailed by either a 1 or a 2 or their negations; and let 0 < p(b) = r
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 28:
ACKNOWLEDGMENTS, 1960 and 1968 I wi
Page 32 and 33:
1 A SURVEY OF SOME FUNDAMENTAL PROB
Page 34 and 35:
a survey of some fundamental proble
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
trivial; for metaphysics has usuall
Page 44 and 45:
Page 46 and 47:
non-contradictory, a possible world
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
2 ON THE PROBLEM OF A THEORY OF SCI
Page 58 and 59:
on the problem of a theory of scien
Page 60 and 61:
Page 62 and 63:
Page 64:
Part II Some Structural Components
Page 67 and 68:
38 some structural components of a
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
5 THE PROBLEM OF THE EMPIRICAL BASI
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
10 CORROBORATION, OR HOW A THEORY S
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
Page 313 and 314:
284 appendices it is connected with
Page 315 and 316:
APPENDIX ii The General Calculus of
Page 317 and 318:
288 appendices —we obtain from (2
Page 319 and 320:
APPENDIX iii Derivation of the Firs
Page 321 and 322:
292 appendices (6,1) αF″(σ´ m.
Page 323 and 324:
294 appendices after effect) in the
Page 325 and 326:
296 appendices (b) An analogous met
Page 327 and 328:
298 appendices position), then we a
Page 329 and 330:
300 appendices incoherent photons.
Page 331 and 332:
302 appendices interposition of a f
Page 333 and 334:
304 appendices wave-packets (obtain
Page 335 and 336:
306 appendices slit. This angle φ
Page 337 and 338:
308 appendices latter, if we use hi
Page 339 and 340:
310 new appendices The first two of
Page 341 and 342:
APPENDIX *i Two Notes on Induction
Page 343 and 344:
314 new appendices statements’;*
Page 345 and 346:
316 new appendices be the source fr
Page 347 and 348:
318 new appendices with the help of
Page 349 and 350:
320 new appendices logical interpre
Page 351 and 352:
322 new appendices It is desirable
Page 353 and 354:
324 new appendices operations—con
Page 355 and 356:
326 new appendices (3) It will be a
Page 357 and 358:
328 new appendices (7) The derivati
Page 359 and 360:
330 new appendices There are three
Page 361 and 362:
332 new appendices that is to say,
Page 363 and 364:
334 new appendices invalid, and sho
Page 365 and 366:
336 new appendices simplified syste
Page 367 and 368: 338 new appendices The following co
Page 369 and 370: 340 new appendices able to show tha
Page 371 and 372: 342 new appendices obtain p(a, c) =
Page 373 and 374: 344 new appendices The second examp
Page 375 and 376: 346 new appendices first consistenc
Page 377 and 378: 348 new appendices S′ ={0, 1, 2,
Page 379 and 380: 350 new appendices B1 is violated b
Page 381 and 382: 352 new appendices always fill the
Page 383 and 384: 354 new appendices It should be men
Page 385 and 386: APPENDIX *v Derivations in the Form
Page 387 and 388: 358 new appendices (26) (Eb) (Ea) p
Page 389 and 390: 360 new appendices (Applying B2 twi
Page 391 and 392: 362 new appendices form: it is unco
Page 393 and 394: 364 new appendices In order to prov
Page 395 and 396: 366 new appendices which is neverth
Page 397 and 398: 368 new appendices the other axioms
Page 399 and 400: 370 new appendices between rain and
Page 401 and 402: 372 new appendices in the widest po
Page 403 and 404: APPENDIX *vii Zero Probability and
Page 405 and 406: 376 new appendices favourable possi
Page 407 and 408: 378 new appendices (4) p(a) = lim p
Page 409 and 410: 380 new appendices The same point m
Page 411 and 412: 382 new appendices inferences from
Page 413 and 414: 384 new appendices the required a a
Page 415 and 416: 386 new appendices ‘universe’
Page 417: 388 new appendices All this does no
Page 421 and 422: APPENDIX *viii Content, Simplicity,
Page 423 and 424: 394 new appendices each entry repre
Page 425 and 426: 396 new appendices But formula (*)
Page 427 and 428: 398 new appendices (−) d(a 1)p(a
Page 429 and 430: 400 new appendices thus becomes som
Page 431 and 432: APPENDIX *ix Corroboration, the Wei
Page 433 and 434: 404 new appendices I will now brief
Page 435 and 436: 406 new appendices of the brevity o
Page 437 and 438: 408 new appendices who identify, ex
Page 439 and 440: 410 new appendices Kemeny.) Therefo
Page 441 and 442: 412 new appendices DEGREE OF CONFIR
Page 443 and 444: 414 new appendices (4.5) C(x 1x 2 o
Page 445 and 446: 416 new appendices strongly upon P(
Page 447 and 448: 418 new appendices (vii) If C(x) =
Page 449 and 450: 420 new appendices to be slightly a
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,
Page 457 and 458: 428 new appendices behaviour of E a
Page 459 and 460: 430 new appendices either if δ is
Page 461 and 462: 432 new appendices statistical inte
Page 463 and 464: 434 new appendices them, there is a
Page 465 and 466: 436 new appendices statements e, f,
Page 467 and 468: 438 new appendices simply deceive o
Page 469 and 470:
APPENDIX *x Universals, Disposition
Page 471 and 472:
442 new appendices One can easily s
Page 473 and 474:
444 new appendices statement such a
Page 475 and 476:
446 new appendices more abstract. T
Page 477 and 478:
448 new appendices natural laws see
Page 479 and 480:
450 new appendices indirect proof.
Page 481 and 482:
452 new appendices physical theory
Page 483 and 484:
454 new appendices is deducible fro
Page 485 and 486:
456 new appendices A little reflect
Page 487 and 488:
458 new appendices differ (if at al
Page 489 and 490:
460 new appendices the world. And a
Page 491 and 492:
462 new appendices the phenomenalis
Page 493 and 494:
APPENDIX *xi On the Use and Misuse
Page 495 and 496:
466 new appendices a gravitational
Page 497 and 498:
468 new appendices with, its co-ord
Page 499 and 500:
470 new appendices based upon his f
Page 501 and 502:
472 new appendices moving freely be
Page 503 and 504:
474 new appendices of insuperable b
Page 505 and 506:
476 new appendices Einstein.) The m
Page 507 and 508:
478 new appendices photographic pla
Page 509 and 510:
480 new appendices My impression is
Page 511 and 512:
482 new appendices letter were to b
Page 513 and 514:
484 new appendices statistical desc
Page 515 and 516:
486 new appendices
Page 517 and 518:
488 new appendices
Page 519 and 520:
490 name index Carnap, R. 7n, 13n,
Page 521 and 522:
492 name index Mises, R. 133, 135n,
Page 523 and 524:
SUBJECT INDEX Italicized page numbe
Page 525 and 526:
496 subject index Binomial formula
Page 527 and 528:
498 subject index Cosmology, its pr
Page 529 and 530:
500 subject index Empirical basis s
Page 531 and 532:
502 subject index and ad hoc hypoth
Page 533 and 534:
504 subject index 150&nt, see also
Page 535 and 536:
506 subject index Modus Ponens 71n,
Page 537 and 538:
508 subject index 319-20; indutive
Page 539 and 540:
510 subject index 142&n, 154n, 174&
Page 541 and 542:
512 subject index experiment 474-5,
show all

popper-logic-scientific-discovery

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?