Philosophy of Science, Logic, and Mathematics in the Twentieth Century

By Stuart G. Shanker | Go to book overview

NOTES
1
[4.45]. The original title was Logisch-Philosophisce Abhandlung. The title Tractatus Logico-Philosophicus was suggested by G.E. Moore. For a composition and publication history, see [4.48], 1-33, 255ff. For the history and circumstances of its composition, see [4.22] chs 7-8 and [4.23], chs 5-8.
2
Numbers in parentheses marked T are Tractatus section numbers.
3
Wittgenstein's usage differs from Russell's. For Russell, G.E. Moore's having recorded with Thelonius Monk is a negative fact. For Wittgenstein it is not a fact of any kind and the relevant negative fact is that Moore did not record with Thelonius.
4
I use 'world' for what [T2.06] calls 'reality'; Wittgenstein's worlds include only positive facts.
5
Wittgenstein wrote a version of the truth table in 1912 on the back of a paper Russell presented to the Cambridge moral sciences club [4.22], 160. Quine says truth tables were used to set out truth functions independently of the Tractatus in papers by Łukasiewicz, and Post in 1920-1, and that Peirce described a non-tabular version of essentially the same method in 1885 [4.26], 14.
6
For example since N (3) has the same truth conditions as (2), we had best pick another once we have got (3). For a complete discussion for the case of two elementary propositions see [4.1], 133ff.
7
See [4.38], 480ff.
8
For details, see [4.1], 135ff.
9
[4.24], 297.
10
Cp. [4.1], 133-4.
11
[4.2], 312. We need the next steps because merely to select p as a value of is not to construct it by joint denial.
12
[4.47], section 94.
13
For a discussion of this problem for the case of quantified propositions, see [4.19].
14
A model according to von Wright; a diagram according to Malcolm. [4.21], 8, 57.
15
Cp. [4.46], 7, 27.
16
Cp. [4.37], [4.38].
17
[4.47], Section 94.
18
[4.25], 321. Anachronistically speaking, to judge 'one thing' is to believe something definite enough to determine the truth conditions of the belief. Wittgenstein's quotation of some of this in connection with picturing at [4.47], section 518, makes it plausible (without proving) that he knew the passage when he wrote TS. For another version of the argument see [4.3], 6ff.
19
[4.28], 28-33, [4.30], 528-33, [4.35], 193ff.
20
[4.6], 144.
21
[4.31], ch. XII, [4.34], 43, [4.36], part II, chs i-iii.
22
[4.12], 56-78. For a concise statement of Frege's version of the problem, see [4.14], 117ff. See also [4.1].
23
[4.14, 127].
24
For example, if there is no such person as Odysseus, the name 'Odysseus' lacks

-187-

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Philosophy of Science, Logic, and Mathematics in the Twentieth Century
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • General Editors' Preface vii
  • Acknowledgements xiii
  • Chronology xv
  • Introduction 1
  • Notes 8
  • Chapter 1 - Philosophy of Logic 9
  • Bibliography 39
  • Chapter 2 - Philosophy of Mathematics in the Twentieth Century 50
  • Chapter 3 - Frege 124
  • Bibliography 153
  • Chapter 4 - Wittgenstein's Tractatus 157
  • Notes 187
  • Chapter 5 - Logical Positivism 193
  • Bibliography 210
  • Chapter 6 - The Philosophy of Physics 214
  • Bibliography 233
  • Chapter 7 - The Philosophy of Science Today 235
  • Chapter 8 - Chance, Cause and Conduct: Probability Theory and the Explanation of Human Action 266
  • Chapter 9 - Cybernetics 292
  • Bibliography 313
  • Chapter 10 - Descartes' Legacy: the Mechanist/Vitalist Debates 315
  • Notes 366
  • Glossary 376
  • Index 444
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