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. |
| 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. |
| 7306 | If the only property of a name was its reference, we couldn't explain bearerless names [Miller,A] |
| Full Idea: If having a reference were the only semantic property in terms of which we could explain the functioning of names, we would be in trouble with respect to names that simply have no bearer. | |
| From: Alexander Miller (Philosophy of Language [1998], 2.1.1) | |
| A reaction: (Miller is discussing Frege) 'Odysseus' is given as an example. Instead of switching to a bundle of descriptions, we could say that we just imagine an object which is stamped with the name. Names always try to refer. |
| 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? |
| 7322 | Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A] |
| Full Idea: We should distinguish 'constitutive scepticism' (about the existence of certain sorts of facts) from the traditional 'epistemological scepticism' (which concedes that the sort of fact in question exists, but questions our right to claim knowledge of it). | |
| From: Alexander Miller (Philosophy of Language [1998], 4.7) | |
| A reaction: I would be inclined to call the first type 'ontological scepticism'. Miller is discussing Quine's scepticism about meaning. Atheists fall into the first group, and agnostics into the second. An important, and nicely simple, distinction. |
| 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. |
| 7325 | Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A] |
| Full Idea: Dispositional facts are facts about what we will do, not about what we ought to do, and as such cannot capture the normativity of meaning. | |
| From: Alexander Miller (Philosophy of Language [1998], 6.2) | |
| A reaction: Miller is discussing language, but this raises a nice question for all behaviourist accounts of mental events. Perhaps there is a disposition to behave in a guilty way if you do something you think you shouldn't do. (Er, isn't 'guilt' a mental event?) |
| 7324 | Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A] |
| Full Idea: Grice wants to explain linguistic meaning in terms of the content of propositional attitudes, Dummett has championed the view that propositional attitudes must be explained by linguistic meaning, while Davidson says they must be explained together. | |
| From: Alexander Miller (Philosophy of Language [1998], 6.1) | |
| A reaction: A useful map. My intuition says propositional attitudes come first, for evolutionary reasons. We are animals first, and speakers second. Thought precedes language. A highly social animal flourishes if it can communicate. |
| 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. |
| 7323 | If truth is deflationary, sentence truth-conditions just need good declarative syntax [Miller,A] |
| Full Idea: On a deflationary concept of truth, for a sentence to possess truth-conditions it is sufficient that it be disciplined by norms of correct usage, and that it possess the syntax distinctive of declarative sentences. | |
| From: Alexander Miller (Philosophy of Language [1998], 5.3) | |
| A reaction: Idea 6337 gives the basic deflationary claim. He mentions Boghossian as source of this point. So much the worse for the deflationary concept of truth, say I. What are the truth-conditions of "Truth rotates"? |
| 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. |
| 7315 | 'Jones is a married bachelor' does not have the logical form of a contradiction [Miller,A] |
| Full Idea: The syntactic notion of contradiction (p and not-p) is well understood, but is no help in explaining analyticity, since "Jones is a married bachelor" is not of that syntactic form. | |
| From: Alexander Miller (Philosophy of Language [1998], 4.2) | |
| A reaction: This point is based on Quine. This means we cannot define analytic sentences as those whose denial is a contradiction, even though that seems to be true of them. Both the Kantian and the modern logical versions of analyticity are in trouble. |
| 7328 | The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A] |
| Full Idea: Properly construed, the principle of charity is a holistic constraint applying, not to individual beliefs, but rather to systems of belief: we must interpret a speaker so that most of the beliefs in his system are, by our lights, true. | |
| From: Alexander Miller (Philosophy of Language [1998], 8.7) | |
| A reaction: This is a lot more plausible than applying the principle to individual sentences, particularly if you are in the company of habitual ironists or constitutional liars. |
| 7329 | Maybe we should interpret speakers as intelligible, rather than speaking truth [Miller,A] |
| Full Idea: A more sophisticated version of the principle of charity holds that we interpret speakers not as necessarily having beliefs that are true by our own lights, but as having beliefs that are intelligible by our own lights. | |
| From: Alexander Miller (Philosophy of Language [1998], 8.7) | |
| A reaction: Consider Idea 4161 in the light of this. Presumably this means that we treat them as having a coherent set of beliefs, even if they seem to us to fail to correspond to reality. I prefer the stronger version that there has to be some proper truth in there. |
| 7333 | The Frege-Geach problem is that I can discuss the wrongness of murder without disapproval [Miller,A] |
| Full Idea: The main problem faced by non-cognitivism is known as the Frege-Geach problem: if I say "If murder is wrong, then getting your brother to murder people is wrong", that is an unasserted context, and I don't necessarily express disapproval of murder. | |
| From: Alexander Miller (Philosophy of Language [1998], 9.2) | |
| A reaction: The emotivist or non-cognitivist might mount a defence by saying there is some second-order or deep-buried emotion involved. Could a robot without feelings even understand what humans meant when they said "It is morally wrong"? |
| 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. |