Combining Philosophers

All the ideas for Paul M. Pietroski, Gerhard Gentzen and Craig Bourne

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21 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
14018 Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
14008 The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
11022 Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11065 The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
11023 The logical connectives are 'defined' by their introduction rules [Gentzen]
11213 Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13832 Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10067 Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
8. Modes of Existence / A. Relations / 1. Nature of Relations
14009 It is a necessary condition for the existence of relations that both of the relata exist [Bourne]
14010 All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne]
19. Language / B. Reference / 5. Speaker's Reference
21650 No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
14016 The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne]
14019 Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
14013 Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
14015 No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
14007 How can presentists talk of 'earlier than', and distinguish past from future? [Bourne]
14011 Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne]
14017 Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
14003 Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne]
14005 B-series objects relate to each other; A-series objects relate to the present [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
14006 Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne]