23 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'). |
| 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. |
| 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. |
| 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. |
| 4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
| Full Idea: A thought can be split up in many ways, so that now one thing, now another, appears as subject or predicate | |
| From: Gottlob Frege (On Concept and Object [1892], p.199) | |
| A reaction: Thus 'the mouse is in the box', and 'the box contains the mouse'. A simple point, but important when we are trying to distinguish thought from language. |
| 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? |
| 9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
| Full Idea: For Frege, the extension of the concept F is an object, as revealed by the fact that we use a name to refer to it. ..We must distinguish the concept, the object that falls under it, and the extension of the concept, which is the set containing the object. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This I take to be the key distinction needed if one is to grasp Frege's account of what a number is. When we say that Frege is a platonist about numbers, it is because he is committed to the notion that the extension is an object. |
| 18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
| Full Idea: Frege's theory treats existence as a property, not of things we call existent, but of concepts instantiated by those things. 'Biden exists' says our Biden-concept has instances. That is certainly not how it feels! We speak of the thing, not of concepts. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Stephen Yablo - Aboutness 01.4 | |
| A reaction: Yablo's point is that you must ask what the sentence is 'about', and then the truth will refer to those things. Frege gets into a tangle because he thinks remarks using concepts are about the concepts. |
| 10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
| Full Idea: Expositors of Frege's views have disagreed over whether abstract qualities are to be reckoned among his objects. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Bob Hale - Abstract Objects Ch.2.II | |
| A reaction: [he cites Dummett 1973:70-80, and Wright 1983:25-8] There seems to be a danger here of a collision between Fregean verbal approaches to ontological commitment and the traditional views about universals. No wonder they can't decide. |
| 10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
| Full Idea: Frege's notion of an object plays two roles in his semantics. Objects are the referents of proper names, and they are equally what predicates are true and false of. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.4 | |
| A reaction: Frege is the source of a desperate desire to turn everything into an object (see Idea 8858!), and he has the irritating authority of the man who invented quantificational logic. Nothing but trouble, that man. |
| 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. |
| 9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
| Full Idea: Frege equated the concepts under which an object falls with its properties. | |
| From: report of Gottlob Frege (On Concept and Object [1892], p.201) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
| A reaction: I take this to be false, as objects can fall under far more concepts than they have properties. I don't even think 'being a pencil' is a property of pencils, never mind 'being my favourite pencil', or 'not being Alexander the Great'. |
| 4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
| Full Idea: As I understand it, a concept is the meaning of a grammatical predicate. | |
| From: Gottlob Frege (On Concept and Object [1892], p.193) | |
| A reaction: All the ills of twentieth century philosophy reside here, because it makes a concept an entirely linguistic thing, so that animals can't have concepts, and language is cut off from reality, leading to relativism, pragmatism, and other nonsense. |
| 9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
| Full Idea: Frege felt that meanings are public property, and identified concepts (and hence 'intensions' or meanings) with abstract entities rather than mental entities. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by Hilary Putnam - Meaning and Reference p.150 | |
| A reaction: This is the germ of Wittgenstein's private language argument. I am inclined to feel that Frege approached language strictly as a logician, and didn't really care that he got himself into implausible platonist ontological commitments. |
| 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. |
| 4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |
| Full Idea: For all the multiplicity of languages, mankind has a common stock of thoughts. | |
| From: Gottlob Frege (On Concept and Object [1892], p.196n) | |
| A reaction: Given the acknowledgement here that two very different sentences in different languages can express the same thought, he should recognise that at least some aspects of a thought are non-linguistic. |
| 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. |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |