Mathematics, Science and Epistemology: Volume 2, Philosophical Papers

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Cambridge University Press, Oct 16, 1980 - Mathematics - 296 pages
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Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.
  

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Contents

Infinite regress and foundations of mathematics
3
1 Stopping infinite regress in science
4
by the logicotrivialization of mathematics
10
3 by a trivial metatheory
20
A renaissance of empiricism in the recent philosophy of mathematics?
24
the new vogue in mathematical philosophy?
25
2 Quasiempirical versus Euclidean theories
28
3 Mathematics is quasiempirical
30
Changes in the problem of inductive logic
128
inductive justification and inductive method
129
weak inductive justification degree of confirmation
131
3 The weak and strong atheoretical theses
138
confirmation theory without theories
142
c The conflation of the weak and the strong atheoretical theses
145
d The interconnection between the weak and strong atheoretical theses
147
e A Carnapian logic of discovery
149

4 Potential falsifiers in mathematics
35
5 Periods of stagnation in the growth of quasiempirical theories
41
Cauchy and the continuum the significance of nonstandard analysis for the history and philosophy of mathematics
43
2 Cauchy and the problem of uniform convergence
45
3 A new solution
47
4 What caused the downfall of Leibnizs theory?
53
5 Was Cauchy a forerunner of Robinson?
55
6 Metaphysical versus technical
58
7 Appraisal of mathematical theories
59
What does a mathematical proof prove?
61
The method of analysissynthesis
70
b Analysissynthesis and heuristic
72
c The Cartesian Circuit and its breakdown
75
c1 The Circuit is neither empiricist nor intellectualist The source of knowledge is the Circuit as a whole
77
c2 Induction and deduction in the Circuit
79
c3 The continuity between Pappus and Descartes
83
c4The Cartesian Circuit in mathematics
88
how failed attempts at refutations may be heuristic starting points of research programmes
93
b An analysissynthesis in physics which does not explain what it set out to explain
97
c Pappusian analysessyntheses in Greek geometry
99
d False awareness about analysissynthesis
101
The problem of appraising scientific theories three approaches
107
b Demarcationism
108
c Elitism
111
2 Elitism and allied philosophical positions
112
b Elitists for authoritarianism and historicism
116
c Elitists for pragmatism
117
Necessity Kneale and Popper
121
2 The epistemologicalmethodological level
124
3 The continuity of logical and natural necessity
126
4 Probability evidential support rational belief and betting quotients
151
a Are degrees of evidential support probabilities?
152
b Are degrees of rational belief degrees of evidential support or are they rational betting quotients?
157
c Are rational betting quotients probabilities?
159
5 The collapse of the weak atheoretical thesis
160
b The abdication of the inductive judge
165
method
170
b Acceptability
173
c Acceptability
181
7 Theoretical support for predictions versus testevidential support for theories
192
Appendix On Poppers three notes on degree of corroboration
193
On Popperian historiography
201
Appendix on ultrafalsificationism
208
Anomalies versus crucial experiments a rejoinder to Professor Grunbaum
211
2 The impossibility of Grunbaumian crucial experiments and the possibility of appraising scientific growth without them
216
3 On practical advice
218
4 The characteristic of science is not rational belief but rational replacement of propositions
220
Understanding Toulmin
224
1 Three schools of thought on the normative problem of appraising scientific theories
225
2 Toulmin and the Wittgensteinian thoughtpolice
228
3 Toulmins Darwinian synthesis of Hegel and Wittgenstein
235
4 Conclusion
241
A letter to the Director of the London School of Economics
247
The teaching of the history of science
254
The social responsibility of science
256
References
259
Lakatos bibliography
274
Indexes
277
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About the author (1980)

Lakatos was professor of logic at the London School of Economics.

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