20 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. |
| 6859 | Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson] |
| Full Idea: Certain advances in philosophical standards have been made within analytic philosophy, and there would be a serious loss of integrity involved in abandoning them in the way required to participate in current continental philosophy. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.151) | |
| A reaction: The reply might be to concede the point, but say that the precision and rigour achieved are precisely what debar analytical philosophy from thinking about the really interesting problems. One might as well switch to maths and have done with it. |
| 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. |
| 6862 | Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson] |
| Full Idea: Fuzzy logic is based on a continuum of degrees of truth, but it is committed to the idea that it is half-true that one identical twin is tall and the other twin is not, even though they are the same height. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.154) | |
| A reaction: Maybe to be shocked by a contradiction is missing the point of fuzzy logic? Half full is the same as half empty. The logic does not say the twins are different, because it is half-true that they are both tall, and half-true that they both aren't. |
| 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. |
| 6858 | Formal logic struck me as exactly the language I wanted to think in [Williamson] |
| Full Idea: As soon as I started learning formal logic, that struck me as exactly the language that I wanted to think in. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001]) | |
| A reaction: It takes all sorts… It is interesting that formal logic might be seen as having the capacity to live up to such an aspiration. I don't think the dream of an ideal formal language is dead, though it will never encompass all of reality. Poetic truth. |
| 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. |
| 18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
| Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible. | |
| From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4 | |
| A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'. |
| 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? |
| 6863 | Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson] |
| Full Idea: If one is very close to a conceptual boundary, then one's judgement will be too unreliable to constitute knowledge, and therefore one will be ignorant. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.156) | |
| A reaction: This is the epistemological rather than ontological interpretation of vagueness. It sounds very persuasive, but I am reluctant to accept that reality is full of very precise boundaries which we cannot quite discriminate. |
| 6861 | What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson] |
| Full Idea: The problem of vagueness is the problem of what logic is correct for vague concepts, and correspondingly what notions of truth and falsity are applicable to vague statements (does one need a continuum of degrees of truth, for example?). | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.153) | |
| A reaction: This certainly makes vagueness sound like one of the most interesting problems in all of philosophy, though also one of the most difficult. Williamson's solution is that we may be vague, but the world isn't. |
| 6860 | How can one discriminate yellow from red, but not the colours in between? [Williamson] |
| Full Idea: If one takes a spectrum of colours from yellow to red, it might be that given a series of colour samples along that spectrum, each sample is indiscriminable by the naked eye from the next one, though samples at either end are blatantly different. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.151) | |
| A reaction: This seems like a nice variant of the Sorites paradox (Idea 6008). One could demonstrate it with just three samples, where A and C seemed different from each other, but other comparisons didn't. |
| 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. |