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Ideas of Keith Devlin, by Text

[American, fl. 1996, Dean of Science at St Mary's College. Senior Researcher at Stanford University.]

1997 Goodbye Descartes
Ch. 1 p.7 Sentences of apparent identical form can have different contextual meanings
     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.
Ch. 1 p.7 How do we parse 'time flies like an arrow' and 'fruit flies like an apple'?
     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.
Ch. 2 p.24 Space and time are atomic in the arrow, and divisible in the tortoise
     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?
Ch. 2 p.27 The distinction between sentences and abstract propositions is crucial in logic
     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.
Ch. 2 p.43 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors'
     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.
Ch. 2 p.48 Where a conditional is purely formal, an implication implies a link between premise and conclusion
     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.
Ch. 4 p.80 Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens
     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'.
Ch. 4 p.83 Predicate logic retains the axioms of propositional logic
     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.
Ch. 4 p.85 Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic
     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.
Ch. 5 p.111 People still say the Hopi have no time concepts, despite Whorf's later denial
     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.
Ch. 8 p.192 Montague's intensional logic incorporated the notion of meaning
     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.
Ch. 8 p.207 Situation theory is logic that takes account of context
     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').
Ch.11 p.261 Logic was merely a branch of rhetoric until the scientific 17th century
     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.