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. |
| 19079 | For idealists reality is like a collection of beliefs, so truths and truthmakers are not distinct [Young,JO] |
| Full Idea: Idealists do not believe that there is an ontological distinction between beliefs and what makes beliefs true. From their perspective, reality is something like a collection of beliefs. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §2.1) | |
| A reaction: This doesn't seem to me to wholly reject truthmakers, since beliefs can still be truthmakers for one another. This is something like Davidson's view, that only beliefs can justify other beliefs. |
| 19076 | Coherence theories differ over the coherence relation, and over the set of proposition with which to cohere [Young,JO] |
| Full Idea: Coherence theories of truth differ on their accounts of the coherence relation, and on their accounts of the set (or sets) of propositions with which true propositions occur (the 'specified set'). | |
| From: James O. Young (The Coherence Theory of Truth [2013], §1) | |
| A reaction: Coherence is clearly more than consistency or mutual entailment, and I like to invoke explanation. The set has to be large, or the theory is absurd (as two absurdities can 'cohere'). So very large, or very very large, or maximally large? |
| 19077 | Two propositions could be consistent with your set, but inconsistent with one another [Young,JO] |
| Full Idea: It is unsatisfactory for the coherence relation to be consistency, because two propositions could be consistent with a 'specified set', and yet be inconsistent with each other. That would imply they are both true, which is impossible. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §1) | |
| A reaction: I'm not convinced by this. You first accept P because it is consistent with the set; then Q turns up, which is consistent with everything in the set except P. So you have to choose between them, and might eject P. Your set was too small. |
| 19078 | Coherence with actual beliefs, or our best beliefs, or ultimate ideal beliefs? [Young,JO] |
| Full Idea: One extreme for the specified set is the largest consistent set of propositions currently believed by actual people. A moderate position makes it the limit of people's enquiries. The other extreme is what would be believed by an omniscient being. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §1) | |
| A reaction: One not considered is the set of propositions believed by each individual person. Thoroughgoing relativists might well embrace that one. Peirce and Putnam liked the moderate one. I'm taken with the last one, since truth is an ideal, not a phenomenon. |
| 19084 | Coherent truth is not with an arbitrary set of beliefs, but with a set which people actually do believe [Young,JO] |
| Full Idea: It must be remembered that coherentists do not believe that the truth of a proposition consists in coherence with an arbitrarily chosen set of propositions; the coherence is with a set of beliefs, or a set of propositions held to be true. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §3.1) | |
| A reaction: This is a very good response to critics who cite bizarre sets of beliefs which happen to have internal coherence. You have to ask why they are not actually believed, and the answer must be that the coherence is not extensive enough. |
| 19083 | How do you identify the best coherence set; and aren't there truths which don't cohere? [Young,JO] |
| Full Idea: The two main objections to the coherence theory of truth are that there is no way to identify the 'specified set' of propositions without contradiction, ...and that some propositions are true which cohere with no set of beliefs. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §3.1/2) | |
| A reaction: The point of the first is that you need a prior knowledge of truth to say which of two sets is the better one. The second one is thinking of long-lost tiny details from the past, which seem to be true without evidence. A huge set might beat the first one. |
| 19075 | Deflationary theories reject analysis of truth in terms of truth-conditions [Young,JO] |
| Full Idea: Unlike deflationary theories, the coherence and correspondence theories both hold that truth is a property of propositions that can be analyzed in terms of the sorts of truth-conditions propositions have, and the relation propositions stand in to them. | |
| From: James O. Young (The Coherence Theory of Truth [2013], Intro) | |
| A reaction: This is presumably because deflationary theories reject the external relations of a proposition as a feature of its truth. This evidently leaves them in need of a theory of meaning, which may be fairly minimal. Horwich would be an example. |
| 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? |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 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. |
| 19074 | Are truth-condtions other propositions (coherence) or features of the world (correspondence)? [Young,JO] |
| Full Idea: For the coherence theory of truth, the truth conditions of propositions consist in other propositions. The correspondence theory, in contrast, states that the truth conditions of propositions are ... objective features of the world. | |
| From: James O. Young (The Coherence Theory of Truth [2013], Intro) | |
| A reaction: It is obviously rather important for your truth-conditions theory of meaning that you are clear about your theory of truth. A correspondence theory is evidently taken for granted, even in possible worlds versions. |
| 19082 | Coherence truth suggests truth-condtions are assertion-conditions, which need knowledge of justification [Young,JO] |
| Full Idea: Coherence theorists can argue that the truth conditions of a proposition are those under which speakers tend to assert it, ...and that speakers can only make a practice of asserting a proposition under conditions they can recognise as justifying it. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §2.2) | |
| A reaction: [compressed] This sounds rather verificationist, and hence wrong, since if you then asserted anything for which you didn't know the justification, that would remove its truth, and thus make it meaningless. |
| 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. |