21 ideas
| 8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
| Full Idea: Until the rise of what we call the scientific method in the seventeenth century, logic was regarded largely as one aspect of rhetoric - a study of how one person't argument could convince another. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch.11) | |
| A reaction: This may well give the main reason why the Greeks invented logic in the first place. Aristotle wrote a book on rhetoric, and that was where the money was. Leibniz is clearly a key figure in the change of attitude. |
| 8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
| Full Idea: Most people find it hard to find any conclusion that fits the following premises: 'No councillors are bankers', and 'All bankers are athletes'. There is a valid conclusion ('Some athletes are not councillors') but it takes quite an effort to find it. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 2) | |
| A reaction: A nice illustration of the fact that syllogistic logic is by no means automatic and straightforward. There is a mechanical procedure, but a lot of intuition and common sense is also needed. |
| 8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
| Full Idea: Where Aristotle had 19 different inference rules (his valid syllogisms), modern propositional logic carries out deductions using just one rule of inference: modus ponens. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 4) | |
| A reaction: At first glance it sounds as if Aristotle's guidelines might be more useful than the modern one, since he tells you something definite and what implies what, where modus ponens just seems to define the word 'implies'. |
| 8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
| Full Idea: Since predicate logic merely extends propositional logic, all the axioms of propositional logic are axioms of predicate logic. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 4) | |
| A reaction: See Idea 7798 for the axioms. |
| 8091 | Situation theory is logic that takes account of context [Devlin] |
| Full Idea: In many respects, situation theory is an extension of classical logic that takes account of context. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 8) | |
| A reaction: John Barwise is cited as the parent of this movement. Many examples show that logical form is very hard to pin down, because word-meaning depends on context (e.g. 'several crumbs' differs from 'several mountains'). |
| 8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
| Full Idea: The period from 1900 to about 1960 could be described as the golden age of 'pure' logic, and 1950 to 1985 the golden age of 'applied' logic (e.g. applied to everyday reasoning, and to theories of language). | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 4) | |
| A reaction: Why do we always find that we have just missed the Golden Age? However this supports the uneasy feeling that the golden age for all advances in human knowledge is just coming to an end. Biology, including the brain, is the last frontier. |
| 8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
| Full Idea: Montague's intensional logic was the first really successful attempt to develop a mathematical framework that incorporates the notion of meaning. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 8) | |
| A reaction: Previous logics, led by Tarski, had flourished by sharply dividing meaning from syntax, and concentrating on the latter. |
| 8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
| Full Idea: Implication involves some form of link or causality between the antecedent and the consequent of an if-then; normally it says that the conclusion is a consequence of the premise (where conditionals are just defined by 'true' and 'false'). | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 2) | |
| A reaction: This distinction is a key one when discussing 'If-then' sentences. Some are merely formal conditionals, but others make real claims about where you can get to from where you are. |
| 8072 | Sentences of apparent identical form can have different contextual meanings [Devlin] |
| Full Idea: "Safety goggles must be worn in the building" is clear enough, but "dogs must always be carried on the escalator" doesn't require us to head off in search of a dog. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 1) | |
| A reaction: A nice illustration of how the requirements of logical form will often take us beyond the strict and literal meaning of a sentence, into context, tone, allusion and subjective aspects. |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| Full Idea: The arrow paradox starts with the assumption that space and time are atomic; the tortoise starts with the opposite assumption that space and time are infinitely divisible. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 2) | |
| A reaction: Aquinas similarly covers all options (the cosmos has a beginning, or no beginning). The nature of movement in a space which involves quantum leaps remains metaphysically puzzling. Where is a particle at half of the Planck time? |
| 8439 | Maybe each event has only one possible causal history [Bennett] |
| Full Idea: Perhaps it is impossible that an event should have had a causal history different from the one that it actually had. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.220) | |
| A reaction: [He cites van Inwagen for this] The idea is analagous to baptismal accounts of reference. Individuate an event by its history. It might depend (as Davidson implies) on how you describe the event. |
| 8440 | Maybe an event's time of occurrence is essential to it [Bennett] |
| Full Idea: It has been argued that an event's time of occurrence is essential to it. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.221) | |
| A reaction: [He cites Lawrence Lombard] This sound initially implausible, particularly if a rival event happened, say, .1 of a second later than the actual event. It might depend on one's view about determinism. Interesting. |
| 8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
| Full Idea: The Hopi time myth does not appear to have been stopped for a moment by the fact that Whorf himself subsequently wrote that the Hopi language does indeed have words for past, present, and future | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 5) | |
| A reaction: Arguments for relativism based on the Hopi seem now to be thoroughly discredited. Sensible people never believed them in the first place. |
| 8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
| Full Idea: How do people identify subject and verb in the sentences "time flies like an arrow" and "fruit flies like an apple"? | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 1) | |
| A reaction: A nice illustration of the fact that even if we have an innate syntax mechanism, it won't work without some semantics, and some experience of the environmental context of utterances. |
| 8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |
| Full Idea: The distinction between sentences and the abstract propositions that they express is one of the key ideas of logic. A logical argument consists of propositions, assembled together in a systematic fashion. | |
| From: Keith Devlin (Goodbye Descartes [1997], Ch. 2) | |
| A reaction: He may claim that arguments consist of abstract propositions, but they always get expressed in sentences. However, the whole idea of logical form implies the existence of propositions - there is something which a messy sentence 'really' says. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 8441 | Delaying a fire doesn't cause it, but hastening it might [Bennett] |
| Full Idea: Although you cannot cause a fire by delaying something's burning, you can cause a fire by hastening something's burning. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.223) | |
| A reaction: A very nice observation which brings out all sorts of problems about identifying causes. Bennett is criticising the counterfactual account. It is part of the problem of pre-emption, where causes are queueing up to produce a given effect. |
| 8436 | Either cause and effect are subsumed under a conditional because of properties, or it is counterfactual [Bennett] |
| Full Idea: We must choose between subsumption and counterfactual analyses of causal statements. The former means that cause and effect have some properties that enables them to be subsumed under a conditional. The latter is just 'if no-c then no-e'. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.217) | |
| A reaction: I have an immediate preference for the former account, which seems to potentially connect it with physics and features of the world which make one thing lead to another. The counterfactual account seems very thin, and is more like mere semantics. |
| 8435 | Causes are between events ('the explosion') or between facts/states of affairs ('a bomb dropped') [Bennett] |
| Full Idea: Theories of causation are split between event and fact/state of affairs theories. The first have the form 'the explosion caused the fire' (perfect nominals) and the second have the form 'the fire started because a bomb dropped' (sentential clauses). | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987]) | |
| A reaction: Surely events must have priority? The form which uses facts is drifting off into explanation, and is much more likely to involve subjective human elements and interpretations. Events are closer to the physics, and the mechanics of what happens. |
| 8437 | The full counterfactual story asserts a series of events, because counterfactuals are not transitive [Bennett] |
| Full Idea: The refinement of a simple counterfactual analysis is to say that cause and effect depend on a series of events. This must be asserted because counterfactual conditionals are well known not to be transitive. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987]) | |
| A reaction: This fills out the theory, but offers another target for critics. If the glue that binds the series is not in the counterfactuals, is it just in the mind of the speaker? How do you decide what's in the series? Cf. deciding offside in football (soccer!). |
| 8438 | A counterfactual about an event implies something about the event's essence [Bennett] |
| Full Idea: Any counterfactual about a particular event implies or presupposes something about the event's essence. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.219) | |
| A reaction: This is where the counterfactual theory suddenly becomes more interesting, instead of just being a rather bare account of the logical structure of causation. (Bennett offers some discussion of possible essential implications). |