## The Cambridge Companion to CarnapRudolf Carnap (1891-1970) is increasingly regarded as one of the most important philosophers of the twentieth century. He was one of the leading figures of the logical empiricist movement associated with the Vienna Circle and a central figure in the analytic tradition more generally. He made major contributions to philosophy of science and philosophy of logic, and, perhaps most importantly, to our understanding of the nature of philosophy as a discipline. In this volume a team of contributors explores the major themes of his philosophy and discusses his relationship with the Vienna Circle and with philosophers such as Frege, Husserl, Russell, and Quine. New readers will find this the most convenient and accessible guide to Carnap currently available. Advanced students and specialists will find a conspectus of recent developments in the interpretation of Carnap. |

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### Contents

empirical knowledge on the other Thus the constitution of | 61 |

3 Carnap and Frege | 65 |

their intensions as secondlevel properties and their extensions as | 70 |

lecture course Conceptual Notation Reck and Awodey 2004 72 | 73 |

objects and thus without logical content Freges logicism is a | 77 |

4 Carnap and Husserl | 81 |

of numerous psychologists and psychologistic logicians who sought | 84 |

psychological origin of the basic concepts of arithmetic unity | 91 |

debate22 Carnap thinks there is no welldefined question here what | 220 |

outcome is not entirely clear but it is a fact | 240 |

of scientific theories the content of which is then supplied | 247 |

11 Carnap on the rational | 248 |

epistemic interpretation for the basic concepts of an empirical | 252 |

thetheoreticalstatementstothestatus ofgenuinely syntheticclaims about the world | 254 |

v a quinean problem and its solution | 258 |

viii empiricism and reconstruction | 265 |

65 163 whereas in Husserl transcendental subjectivity pertains | 95 |

III3 Structure | 97 |

proposition expressed by it A proposition is neither a linguistic | 101 |

scientific philosophy namely as the universal a priori fundamental science | 103 |

about mentalistic semantics ever needed18 Quinean holism and the | 105 |

5 Carnap Russell and the | 106 |

scientific theories These more traditional philosophical positions | 108 |

clearer and more unified account of how these results are | 125 |

v | 127 |

6 The Aufbau and the rejection | 129 |

If aputative proposition fails to satisfythis verifiability principle andis not | 131 |

reduced to the experiences of all subjects 63 and a | 134 |

iii the languages of realism and idealism | 142 |

this is something no selfrespecting idealist and certainly no | 147 |

pretense to get to the bottom of things and held | 155 |

on the remarkable fact that it was the antiWittgensteinian camp | 157 |

formal mode distinction that the explication of scientific | 161 |

of potential knowledge claims by their evidence independently of | 175 |

8 Carnap and modern logic | 176 |

ii towards general axiomatics | 182 |

axiomatic development of theories in physics Second from early | 186 |

Such an extension of the completeness theorem is however impossible | 193 |

research during the 1920s and early 1930s one that ties | 199 |

logical | 200 |

57 Carnap envisions that colloquial statements of arithmetic will | 209 |

inadmissible then it would be selfdefeating to adopt it as | 211 |

syntactic description and investigation of calculi including those | 213 |

the relation of simultaneity is Minkowskian rather than Newtonian | 269 |

12 Carnap on probability and | 273 |

ii probability | 274 |

credited and by others in an aleatory fashion to a | 275 |

a basic set of axioms There are several equivalent versions | 276 |

II3 Later views | 278 |

primary interest to Carnap and the one to which he | 279 |

III1 The rule of succession | 280 |

the same paradoxes as the Principle of Indifference applied to | 281 |

taking on one of t possible types c1c | 282 |

IV2 The combination postulate | 283 |

v the continuum of inductive methods | 284 |

PXn+1 ei n1nt | 285 |

vii conﬁrmation of universal generalizations | 287 |

none of the observations to date are of the first | 288 |

VII3 HintikkaNiiniluoto systems | 289 |

red ball is initially 35 but the probability of selecting | 291 |

process The Schilpp volume gives a good sense of the | 292 |

having the same transition counts n | 293 |

13 Carnapian pragmatism | 295 |

scientific philosophy is intended to foster scientific progress it has | 303 |

iii carnap and american pragmatism | 307 |

first point Dewey stresses that a principled distinction between the | 311 |

valuations that influence human action will also be liberated when | 312 |

14 Quines challenge to Carnap | 316 |

not been fully investigated in recent decades is that from | 317 |

ignore them In so far as the task he adopts | 334 |

### Common terms and phrases

analysis analytic analytic/synthetic distinction arithmetic Aufbau Awodey axiomatic axioms basic C(TC calculus Carnap claims cognition concepts consequence constitutional system construction defined definition descriptive discussion distinction empirical empiricism empiricist epistemic epistemological example experience explication expressed fact factual first-order logic formal Frege Friedman G¨odel geometry guage higher-order logic Hilbert Husserl ical idea idealism implies intensional interpretation intuition Kant’s knowledge language of science later linguistic framework logic and mathematics logical empiricism Logical Syntax logical truth logicians meaning meta-language meta-logical metaphysical neo-Kantian Neurath notion objects observation phenomenology philosophy philosophy of mathematics physical postulate pragmatism precisely predicates Principia Mathematica Principle of Tolerance priori problem propositions protocol purely question Quine Quine’s R(TC rational reconstruction Raum realism rejection relation Rudolf Carnap Russell Russell’s Schlick scientific semantic sense sentences space statements structure syntactic syntax language Tarski theoretical tion traditional transcendental transcendental idealism true Vienna Circle vocabulary Wittgenstein’s