30 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. |
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| Full Idea: Anaximander was the first to produce a philosophical book (later conventionally titled 'On Nature'), if not the first to produce a book at all. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by István Bodnár - Anaximander | |
| A reaction: Wow! Presumably there were Egyptian 'books', but this still sounds like a stupendous claim to fame. |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| Full Idea: Something which is established in the centre and has equality in relation to the extremes has no more reason to move up than it has down or to the sides (so the earth is stationary) | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A26) by Aristotle - On the Heavens 295b11 |
| 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? |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| Full Idea: Anaximander discovers the contradictory character of our world: it perishes from its own qualities. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Friedrich Nietzsche - Unpublished Notebooks 1872-74 19 [239] | |
| A reaction: A lovely gloss on Anaximander, though I am not sure that I understand what Nietzsche means. |
| 14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
| Full Idea: Some deep essentialists resist the need to explain the structure under de re modal properties, taking them as primitive. One version (which we can call 'substance theory') takes them to fall under a sortal concept, with no further explanation. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: A very helpful identification of what Wiggins stands for, and why I disagree with him. The whole point of essences is to provide a notion that fits in with sciences, which means they must have an explanatory role, which needs structures. |
| 14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
| Full Idea: If the substance essentialist holds that the sort an object belongs to determines its de re modal properties (rather than the other way round), then he needs to give an (ontological, not conceptual) explanation of what determines an object's sort. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: See Idea 14193 for 'substance essentialism'. I find it quite incredible that anyone could think that a thing's sort could determine its properties, rather than the other way round. Even if sortals are conventional, they are not arbitrary. |
| 14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
| Full Idea: The explanation of material constitution given by substance essentialism is that there are multiple objects. A person is essentially human-shaped (falling under the human sort), while their hunk of tissue is accidentally human-shaped (as tissue). | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: At this point sortal essentialism begins to look crazy. Persons are dubious examples (with sneaky dualism involved). A bronze statue is essentially harder to dent than a clay one, because of its bronze. If you remake it of clay, it isn't the same statue. |
| 14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
| Full Idea: Absolutely unrestricted qualitative composition would imply that objects with incompatible properties and objects such as winged pigs or golden mountains were actual. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §5) | |
| A reaction: Note that this is 'qualitative' composition, and not composition of parts. The objection seems to rule out unrestricted qualitative composition, since you could hardly combine squareness with roundness. |
| 14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
| Full Idea: Essentialism says that objects have their properties essentially. 'Deep' essentialists take the (nontrivial) essential properties of an object to determine its nature. 'Shallow' essentialists substitute context-dependent truths for the independent ones. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: If the deep essence determines a things nature, we should not need to say 'nontrivial'. This is my bete noire, the confusion of essential properties with necessary ones, where necessary properties (or predicates, at least) can indeed be trivial. |
| 14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
| Full Idea: The deep essentialist holds that most objects have essential properties such that there are many ways they could not be, or many changes through which they could not persist. Objects' modal profiles characterize their natures. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: This is the view I like, especially the last bit. If your modal profile doesn't determine your nature, then what does? Think of how you sum up a person at a funeral. Your modal profile is determined by dispositions and powers. |
| 14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
| Full Idea: Two objections to deep essentialism are that it falters when faced with a skeptical objection concerning arbitrariness, and the need for a reductive account of de re modality. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: An immediate response to the second objection might be to say that modal facts about things are not reducible. The charge of arbitrariness (i.e. total arbitrariness, not just a bit of uncertainty) is the main thing a theory of essences must deal with. |
| 14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
| Full Idea: I reject the view that an object's de re modal properties determine its relations to possibilia. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §3) | |
| A reaction: You'll have to read Paul to see why, but I flat disagree with her on this. The whole point of accepting such properties is to determine the modal profile of the thing, and hence see how it can fit into and behave in the world. |
| 14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
| Full Idea: A 'modal realist' believes that there are many concrete worlds, while the 'actualist' believes in only one concrete world, the actual world. The 'ersatzist' is an actualist who takes nonactual possible worlds and their contents to be abstracta. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: My view is something like that modal realism is wrong, and actualism is right, and possible worlds (if they really are that useful) are convenient abstract fictions, constructed (if we have any sense) out of the real possibilities in the actual world. |
| 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. |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| Full Idea: The essential nature, whatever it is, of the non-limited is everlasting and ageless. | |
| From: Anaximander (fragments/reports [c.570 BCE], B2), quoted by (who?) - where? |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| Full Idea: Those thinkers are in error who postulate ...a single matter, for this cannot exist without some 'perceptible contrariety': this Boundless, which they identify with the 'original real', must be either light or heavy, either hot or cold. | |
| From: comment on Anaximander (fragments/reports [c.570 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 329a10 | |
| A reaction: A dubious objection, I would say. If there has to be a contrasting cold thing to any hot thing, what happens when the cold thing is removed? |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| Full Idea: The non-limited is the original material of existing things; their source is also that to which they return after destruction, according to necessity; they give justice and make reparation to each other for injustice, according to the arrangement of Time. | |
| From: Anaximander (fragments/reports [c.570 BCE], B1), quoted by Simplicius - On Aristotle's 'Physics' 24.13- | |
| A reaction: Simplicius is quoting Theophrastus |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| Full Idea: Anaximander said that the first principle and element of existing things was the boundless; it was he who originally introduced this name for the first principle. | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A09) by Simplicius - On Aristotle's 'Physics' 9.24.14- | |
| A reaction: Simplicius is quoting Theophrastus |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |
| Full Idea: The parts of all things are susceptible to change, but the whole is unchangeable. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.An.2 |