Philosophical devices: proofs, probabilities, possibilities, and sets
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2012
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIX, 192 S. Ill., graph. Darst. 22 cm |
| ISBN: | 0199651728 9780199651726 0199651736 9780199651733 |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
LISTOFBOXES PREFAEE
INTRODUETION
PART I
SETSAND NUMBERS
I NAIVE SETS AND RUSSELL S PARADOX 1.1 SETS
1,2 MEMBERSHIP AND THE AXIOM OFEXTENSIONALITY
1,3 UNIONS, INTERSECTIONS, AND THE EMPTY SET 1,4 SUBSETS
1.5 MEMBERS VERSUS SUBSETS
1. 6 POWER SETS
1,7 THE AXIOM OF COMPREHENSION
1.8 RUSSELL S SET
1,9 RUSSELL S PARADOX
1,10 BARBERS AND SETS
1.11 ALTERNATIVES TO NAIVE SET THEORY
FURTHER READING
EXERCISES
2 INFINITE SETS
2.1 SOME INFINITE SETS
2.2 DIFFERENT KINDS OFNUMBERS
CONTENTS
XIII
XV
XVII
3
3
4
5 6
6
8
9
10
11
12
13
15
15
17
17
18
VII
IMAGE 2
2.3 TWO SENSES OF MORE 20
2.4 DENUMERABILITY 22
2.5 MORE DENUMERABLE SETS 24
2.6 THE NON-DENUMERABILITY OF THE REAL NUMBERS 25
2.7 THE ABUNDANCE OF THE REAL NUMBERS 27
FURTHER READING 28
EXERCISES 28
3 ORDERS OFINFINITY 30
J.L SOME HARDER STUFF 3 0
3.2 THE NUMERICAL SIZE OF SETS 30
3.3 THE REALS AND THE POWER SET OF THE NATURAL NUMBERS 32
3.4 THE CONTINUUM HYPOTHESIS 35
3.5 AN INFINITY OFINFINITIES 36
3.6 THE GENERALIZED CONTINUUM HYPOTHESIS 38
FURTHER READING 40
EXERCISES 40
PART 11
ANALYTICITY, APRIORICITY, AND NECESSITY
4 KINDS OFTRUTHS
4.1 THREE DISTINCTIONS AMONG TRUTHS
4.2 ANALYTIC AND SYNTHETIC
4.3 APRIORI AND APOSTERIORI
4.4 SYNTHETIC A PRIORIS
4.5 HOW IS SYNTHETIC APRIORI KNOWLEDGE POSSIBLE?
4.6 PURE AND APPLIED GEOMETRY
FURTHER READING
EXERCISES
5 POSSIBLE WORLDS
5.1 NECESSITYAND CONTINGENCY
5.2 APOSTERIORI NECESSITIES
VIII
45
45
45
46
47
49
50
56
56
58
58
59
CONTENTS
IMAGE 3
5.3 APRIORI CONTINGENCIES 60
5.4 POSSIBILITY AND NECESSITY 61
5.5 POSSIBLE WORLDS 62
5.6 NECESSITY AND POSSIBILITY IN TERMS OFWORLDS 63
5.7 CONSTRAINTS ON POSSIBLE WORLDS 64
5.8 ESSENTIAL PROPERTIES 66
5.9 THE NATURE OFNECESSITY 67
5.10 DIFFERENT KINDS OFPOSSIBILITY 68
FURTHER READING 70
EXERCISES 70
6 NAMING AND NECESSITY 72
6.1 TWO READINGS OFSTATEMENTS OFNECESSITY 72
6.2 SCOPE DISTINCTIONS 73
6.3 JULIUS AND THE INVENTOR OF THE ZIP 74
64 RIGID DESIGNATORS 75
6.5 THE CAUSAL THEORY OFREFERENCE 76
6.6 RIGIDITY AND THE CAUSAL THEORY 77
6.7 OE DICTO AND OE RE 78
6.8 NECESSARY AND APRIORI AGAIN 80
6.9 A LIMIT TO SCEPTICISM ABOUT APOSTERIORI NECESSITY 81
FURTHER READING 85
EXERCISES 85
PART 111
THE NATURE AND USES OF PROBABILITY
7 KINDS OFPROBABILITY
7.1 PROBABILITIES OFPROPOSITIONS
7.2 KOLMOGOROV S AXIOMS
7.3 SOME CONSEQUENCES
7.4 JOINT PROBABILITIES
7.5 SUBJECTIVE AND OBJECTIVE PROBABILITIES
CONTENTS IX
IMAGE 4
X
7.6 SUBJECTIVE PROBABILITY 95
N ACTION, UTILITY, AND SUBJECTIVE PROB ABILITY 96
7.8 DUTCH BOOKS 98
7.9 OBJECTIVE PROBABILITY 99
FURTHER READING 102
EXERCISES 102
8 CONSTRAINTS ON CREDENCE 104
8.1 THE PRINCIPAL PRINCIPLE 104
8.2 CONDITIONAL PROB ABILITY 106
8.3 UPDATING DEGREES OFBELIEF-CONDITIONALIZATION 107
8.4 BAYES THEOREM 109
8.5 CONDITIONAL PROBABILITIES AND CONDITIONAL STATEMENTS 110
8.6 MATERIAL CONDITIONALS III
8.7 INDICATIVE AND SUBJUNCTIVE CONDITIONALS 114
8.8 RATIONAL AND METAPHYSICAL CHANGES 115
FURTHER READING 117
EXERCISES 117
9 CORRELATIONS AND CAUSES 119
9.1 PROBABILISTIC INDEPENDENCE 119
9.2 PROBABILISTIC DEPENDENCE 120
9.3 CORRELATION 121
9.4 CAUSATION AND CORRE1ATION 122
9.5 SCREENING OFF 123
9.6 SPURIOUS CORRE1ATIONS 124
9.7 RANDOMIZED EXPERIMENTS 125
9.8 SURVEY RESEARCH 127
9.9 SIMPSON S PARADOX 129
FURTHER READING 131
EXERCISES 131
CONTENTS
IMAGE 5
PART IV
LOGICS AND THEORIES
10 SYNTAX AND SEMANTIES 137
10.1 VALIDITY 137
10.2 LOGIE AND METALOGIC 138
10.3 DIFFERENT KINDS OFLOGIE 139
10.4 TRUTH-FUNETIONAL CONNEETIVES 139
10.5 SYNTAX AND SEMANTICS 142
10.6 SYNTAETIC CONSEQUENEE 143
10.7 SEMANTIC CONSEQUENEE 144
FURTHER READING 148
EXERCISES 148
11 SOUNDNESS AND COMPLETENESS 149
11.1 SOUNDNESS AND COMPLETENESS 149
11.2 PROVING SOUNDNESS AND COMPLETENESS 150
11.3 REFLEETIONS ON CIREULARITY 151
11.4 PREDICATE LOGIE 153
11.5 PREDICATE SYNTAX 154
11.6 PREDIEATE SEMANTICS 156
11.7 PREDICATE LOGIC-SOUNDNESS AND COMPLETENESS 157
11.8 PREDICATE LOGIC-UNDEEIDABILITY 157
11.9 SECOND-ORDER LOGIC 159
11.10 THE INEOMPLETENESS OFSECOND-ORDER LOGIE 161
FURTHER READING 163
12 THEORIES AND GOEDEL S THEOREM 164
12.1 THEORIES 164
12.2 SYNTAX AND SEMANTIES FOR THEORIES 165
12.3 THEORETICAL COMPLETENESS 166
CONTENTS XI
IMAGE 6
12.4 COMPLETENESS FOR THEORIES VERSUS COMPLETENESS
FOR LOGICS 168
12.5 GOEDEL S THEOREM STATED 169
12.6 A SKETCH OF GOEDEL S PROOF 170
12.7 THE INESCAPABILITY OF GOEDEL S THEOREM 173
12.8 META-THEORIZING 174
FURTHER READING 177
SOLUTIONS TO EXERCISES 179
INDEX 189
|
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| author | Papineau, David 1947- |
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| bvnumber | BV040443425 |
| classification_rvk | CC 2400 |
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| discipline | Philosophie |
| edition | 1. ed. |
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| isbn | 0199651728 9780199651726 0199651736 9780199651733 |
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| physical | XIX, 192 S. Ill., graph. Darst. 22 cm |
| publishDate | 2012 |
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| publisher | Oxford Univ. Press |
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| spelling | Papineau, David 1947- Verfasser (DE-588)131460145 aut Philosophical devices proofs, probabilities, possibilities, and sets David Papineau 1. ed. Oxford Oxford Univ. Press 2012 XIX, 192 S. Ill., graph. Darst. 22 cm txt rdacontent n rdamedia nc rdacarrier Literaturangaben Philosophy, Modern Logik (DE-588)4036202-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Beweis (DE-588)4132532-1 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Logik (DE-588)4036202-4 s DE-604 V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025291214&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Papineau, David 1947- Philosophical devices proofs, probabilities, possibilities, and sets Philosophy, Modern Logik (DE-588)4036202-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4079013-7 (DE-588)4132532-1 (DE-588)4151278-9 |
| title | Philosophical devices proofs, probabilities, possibilities, and sets |
| title_auth | Philosophical devices proofs, probabilities, possibilities, and sets |
| title_exact_search | Philosophical devices proofs, probabilities, possibilities, and sets |
| title_full | Philosophical devices proofs, probabilities, possibilities, and sets David Papineau |
| title_fullStr | Philosophical devices proofs, probabilities, possibilities, and sets David Papineau |
| title_full_unstemmed | Philosophical devices proofs, probabilities, possibilities, and sets David Papineau |
| title_short | Philosophical devices |
| title_sort | philosophical devices proofs probabilities possibilities and sets |
| title_sub | proofs, probabilities, possibilities, and sets |
| topic | Philosophy, Modern Logik (DE-588)4036202-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Philosophy, Modern Logik Wahrscheinlichkeitstheorie Beweis Einführung |
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