24 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. |
| 1765 | Diogenes said avoidance of philosophy is the lack of a desire to live properly [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: When a man said that he was not suited to philosophy, Diogenes said to him, 'Why then do you live, if you have no desire to live properly.' | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: Meaning philosophy is already more practice than theory. |
| 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? |
| 1762 | When someone denied motion, Diogenes got up and walked away [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes replied to one who asserted that there was no such thing as motion by getting up and walking away. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 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. |
| 7813 | Cynicism was open to anyone, and needed neither education nor sophistication [Diogenes of Sin., by Grayling] |
| Full Idea: An advantage of Cynicism was that it was open to anyone who could grasp its simple teachings. Understanding it required neither education nor sophistication. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: This was the source of the well-known opposition of Diogenes to Plato's Academy, and it makes him a key predecessor of the teachings of Jesus. Personally I think the really good life is difficult, and it needs education and careful rational thought. |
| 1763 | Diogenes said a plucked chicken fits Plato's definition of man [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Plato defined man as a two-footed featherless animal, so Diogenes plucked a cock and brought it into the school, and said, 'This is Plato's man'. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: You have to be very serious about your philosophy to enact your counterexamples, rather than just suggest them. Which university will actually reconstruct the Trolley Problem? |
| 5071 | The Cynics rejected what is conventional as irrational, and aimed to live by nature [Taylor,R on Diogenes of Sin.] |
| Full Idea: The Cynics were convinced of the purely conventional foundation of Athenian values, which meant they had no rational foundation at all. They therefore rejected them in favour of what is correct and worthwhile by nature. | |
| From: comment on Diogenes (Sin) (reports [c.360 BCE]) by Richard Taylor - Virtue Ethics: an Introduction Ch.8 | |
| A reaction: This shows how the Cynics are key players in the progress of the nomos-physis debate, which keeps resurfacing as relativism vs absolutism, cognitivism vs non-cognitivism, and even romanticism vs classicism. The trouble is, convention is natural! |
| 7812 | For peace of mind, you need self-government, indifference and independence [Diogenes of Sin.] |
| Full Idea: There are three essential conditions for peace of mind: autarchy, apathy and freedom. Autarchy is self-government and self-sufficiency; apathy is indifference to what the world can do to you; the freedom is from dependence and possessions. | |
| From: Diogenes (Sin) (reports [c.360 BCE]), quoted by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: Quite good advice, but I don't see 'peace of mind' as the highest human ideal. The basic suggestion here is live alone and do nothing. Certainly don't get married, or have children, or try to achieve anything. |
| 1764 | Diogenes said he was a citizen of the world [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said he was a citizen of no country, but of the world. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 5968 | Diogenes masturbated in public, wishing he could get rid of hunger so easily [Diogenes of Sin., by Plutarch] |
| Full Idea: Chrysippus praises Diogenes for saying to bystanders as he masturbated in public, "Would that I could thus rub the hunger too out of my belly". | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Plutarch - 70: Stoic Self-contradictions 1044b | |
| A reaction: So it is not quite true that people only need corn and water. Diogenes' remark doesn't explain why he did it in public. Was it to defy local convention (as befits a citizen of the world), or was it to teach? |
| 1766 | Diogenes said that the most excellent thing among men was freedom of speech [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said that the most excellent thing among men was freedom of speech. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |