14 ideas
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934. | |
| From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8 |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning. | |
| From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3 | |
| A reaction: Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences. |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions. | |
| From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8 | |
| A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here? |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these. | |
| From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III | |
| A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives. |
| 13832 | Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking] |
| Full Idea: Gentzen thought that his natural deduction gets at the heart of logical reasoning, and used the sequent calculus only as a convenient tool for proving his chief results. | |
| From: report of Gerhard Gentzen (Investigations into Logical Deduction [1935]) by Ian Hacking - What is Logic? §05 |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic. | |
| From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5 | |
| A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make. |
| 14963 | Surely the past phases of a thing are not parts of the thing? [Broad] |
| Full Idea: It is plainly contrary to common sense to say that the phases in the history of a thing are parts of the thing. | |
| From: C.D. Broad (Examination of McTaggart's Philosophy [1933], I.349-50), quoted by Richard Cartwright - Scattered Objects n18 | |
| A reaction: Nicely expressed! To suggest that me ten years ago is a mere part of some huge me, or that you are only talking to a part of me now, is a very long way indeed from normal usage. |
| 14759 | A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad] |
| Full Idea: A thing is simply a long event, throughout the course of which there is either qualitative similarity or continuous qualitative change, together with a characteristic spatio-temporal unity. | |
| From: C.D. Broad (Scientific Thought [1923], 10 'Duration') | |
| A reaction: At least he is trying to give some sort of principle that links the stages of the event together. |
| 11842 | If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad] |
| Full Idea: We call a lightning flash or a motor accident an event, but refuse to apply this to the cliffs of Dover. ...But quantitative differences (of time) give no good grounds for calling one bit of history an event, and refusing the name to another bit. | |
| From: C.D. Broad (Scientific Thought [1923], p.54), quoted by David Wiggins - Sameness and Substance Renewed 2.3 n13 | |
| A reaction: Wiggins calls this proposal a 'terrible absurdity', but it seems to me to demand attention. There is a case to be made for a 'process' to be the fundamental category of our ontology, with stable physical objects seen in that light. |
| 7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
| Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory. | |
| From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1 | |
| A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises. |
| 8160 | The present and past exist, but the future does not [Broad, by Dummett] |
| Full Idea: Not only the present but also the past exist, but the future (so long as it is the future) does not. | |
| From: report of C.D. Broad (Scientific Thought [1923]) by Michael Dummett - Thought and Reality 1 | |
| A reaction: This is quite appealing, and seems right if you believe that every truth has a truthmaker, and that there are no truths about the future. And yet the whole misery of people dying is that they cease to exist. |
| 14609 | We could say present and past exist, but not future, so that each event adds to the total history [Broad] |
| Full Idea: One theory accepts the reality of the present and the past, but holds that the future is simply nothing at all. Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. | |
| From: C.D. Broad (Scientific Thought [1923], II) | |
| A reaction: This is now known as Broad's 'Growing Block' view of time. It is tempting to say that neither past nor future exist, but it seems undeniable that statements about the past can be wholly true, unlike those about the future. |
| 22933 | We imagine the present as a spotlight, moving across events from past to future [Broad] |
| Full Idea: We imagine presentness moving, like the spot of light from a policeman's bulls eye traversing the fronts of houses in a street. What is illuminated is present, what was illuminated is past, and what is not yet illuminated is the future. | |
| From: C.D. Broad (Scientific Thought [1923], II) | |
| A reaction: This is the 'moving spotlight' compromise theory, which retains the B-series eternal sequence of ordered events, but adds the A-series privileged present moment. Le Poidevin says Broad represents time twice over. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |