21 ideas
| 22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
| Full Idea: The circularity in a definition where the property being defined is used in the definition is now known as 'impredicativity'. ...Some cases ('the tallest man in the room') are unproblematic, as they pick him out, and don't conjure him into existence. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Impred') | |
| A reaction: [part summary] |
| 22301 | The Identity Theory says a proposition is true if it coincides with what makes it true [Potter] |
| Full Idea: The Identity Theory of truth says a proposition is true just in case it coincides with what makes it true. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 23 'Abs') | |
| A reaction: The obvious question is how 'there are trees in the wood' can somehow 'coincide with' or 'be identical to' the situation outside my window. The theory is sort of right, but we will never define the relationship, which is no better than 'corresponds'. |
| 22324 | It has been unfortunate that externalism about truth is equated with correspondence [Potter] |
| Full Idea: There has been an unfortunate tendency in the secondary literature to equate externalism about truth with the correspondence theory. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 65 'Truth') | |
| A reaction: Quite helpful to distinguish internalist from externalist theories of truth. It is certainly the case that robust externalist views of truth have unfortunately been discredited merely because the correspondence account is inadequate. |
| 22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
| Full Idea: Natural deduction systems generally depend on conditional proof, but for Frege everything is asserted unconditionally. The modern turnstile |- is allowed to have antecedents, and hence to represent inference rather than Frege's judgement sign |---. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 03 'Axioms') | |
| A reaction: [compressed] Shockingly, Frege's approach seems more psychological than the modern approach. I would say that the whole point of logic is that it has to be conditional, because the truth of the antecedents is irrelevant. |
| 22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |
| Full Idea: Deductivism is a good account of large parts of mathematics, but stumbles where mathematics is directly applicable to the world. It fails to explain how we detach the antecedent so as to arrive at unconditional conclusions. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Deduc') | |
| A reaction: I suppose the reply would be that we have designed deductive structures which fit our understanding of reality - so it is all deductive, but selected pragmatically. |
| 22295 | Modern logical truths are true under all interpretations of the non-logical words [Potter] |
| Full Idea: In the modern definition, a 'logical truth' is true under every interpretation of the non-logical words it contains. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 19 'Frege's') | |
| A reaction: What if the non-logical words are nonsense, or are used inconsistently ('good'), or ambiguously ('bank'), or vaguely ('bald'), or with unsure reference ('the greatest philosopher' becomes 'Bentham')? What qualifies as an 'interpretation'? |
| 22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter] |
| Full Idea: Gödel's theorem does not refute formalism outright, because the committed formalist need not recognise the metalinguistic notion of truth to which the theorem appeals. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 45 'Log') | |
| A reaction: The theorem was prior to Tarski's account of truth. Potter says Gödel avoided explicit mention of truth because of this problem. In general Gödel showed that there are truths outside the formal system (which is all provable). |
| 22298 | Why is fictional arithmetic applicable to the real world? [Potter] |
| Full Idea: Fictionalists struggle to explain why arithmetic is applicable to the real world in a way that other stories are not. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Math') | |
| A reaction: We know why some novels are realistic and others just the opposite. If a novel aimed to 'model' the real world it would be even closer to it. Fictionalists must explain why some fictions are useful. |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| Full Idea: I. Nothing exists. a) Not-Being does not exist. b) Being does not exist as everlasting, as created, as both, as One, or as Many. II. If anything does exist, it is incomprehensible. III. If existence is comprehensible, it is incommunicable. | |
| From: report of Gorgias (fragments/reports [c.443 BCE], B03) by Diogenes Laertius - Lives of Eminent Philosophers 09 | |
| A reaction: [Also Sextus Empiricus, Against Logicians I.65-] For Part I he works through all the possible modes of being he can think of, and explains why none of them are possible. It is worth remembering that Gorgias loved rhetoric, not philosophy! |
| 22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
| Full Idea: The word 'concrete' is often used as the negative of 'abstract', with the slightly odd consequence that desires and hallucinations are thereby classified as concrete. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Numb') | |
| A reaction: There is also the even more baffling usage of 'abstract' for the most highly generalised mathematics, leaving lower levels as 'concrete'. I favour the use of 'generalised' wherever possible, rather than 'abstract'. |
| 22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |
| Full Idea: From the successor function we can deduce its ancestral, the 'greater than' relation, which is a strict total ordering of the natural numbers. (Frege did not mention this, but Dedekind worked it out, when expounding definition by recursion). | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Def') | |
| A reaction: [compressed] |
| 22281 | A material conditional cannot capture counterfactual reasoning [Potter] |
| Full Idea: What the material conditional most significantly fails to capture is counterfactual reasoning. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 04 'Sem') | |
| A reaction: The point is that counterfactuals say 'if P were the case (which it isn't), then Q'. But that means P is false, and in the material conditional everything follows from a falsehood. A reinterpretation of the conditional might embrace counterfactuals. |
| 22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter] |
| Full Idea: Knowledge might result from a reliable and an unreliable process. ...Is something knowledge if you were told it by a drunken schoolteacher? | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 66 'Rel') | |
| A reaction: Nice example. The listener must decide which process to rely on. But how do you decide that, if not by assessing the likely truth of what you are being told? It could be a bad teacher who is inspired by drink. |
| 22273 | Traditionally there are twelve categories of judgement, in groups of three [Potter] |
| Full Idea: The traditional categorisation of judgements (until at least 1800) was as universal, particular or singular; as affirmative, negative or infinite; as categorical, hypothetical or disjunctive; or as problematic, assertoric or apodictic. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 02 'Trans') | |
| A reaction: Arranging these things in neat groups of three seems to originate with the stoics. Making distinctions like this is very much the job of a philosopher, but arranging them in neat equinumerous groups is intellectual tyranny. |
| 22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter] |
| Full Idea: Frege's mirroring principle (that the structure of thoughts mirrors that of language) has the uncomfortable consequence that since the phrase 'the concept "horse"' is saturated, it cannot refer to something unsaturated, which includes concepts. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 16 'Conc') |
| 22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter] |
| Full Idea: Compositionality is best seen as saying the semantic value of a string is explained by the strings lower down its parsing tree. It is unimportant whether a string is always parsed in terms of its own substrings. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem') | |
| A reaction: That is, the analysis must explain the meaning, but the analysis can contain more than the actual ingredients of the sentence (which would be too strict). |
| 22282 | 'Direct compositonality' says the components wholly explain a sentence meaning [Potter] |
| Full Idea: Some authors urge the strong notion of 'direct compositionality', which requires that the content of a sentence be explained in terms of the contents of the component parts of that very sentence. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem') | |
| A reaction: The alternative is that meaning is fully explained by an analysis, but that may contain more than the actual components of the sentence. |
| 22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter] |
| Full Idea: The principle of compositionality is more popular among philosophers of logic than of language, because the subtle context-sensitivity or ordinary language makes providing a compositional semantics for it a daunting challenge. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Lang') | |
| A reaction: Logicians love breaking complex entities down into simple atomic parts. Linguistics tries to pin down something much more elusive. |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| Full Idea: Gorgias insists that the art of persuasion is superior to all others because it enslaves all the rest, with their own consent, not by force, and is therefore by far the best of all the arts. | |
| From: report of Gorgias (fragments/reports [c.443 BCE]) by Plato - Philebus 58a | |
| A reaction: A nice point, and it is not unreasonable to rank the arts in order of their power. To enchant, without achieving agreement, and to speak truth without persuading, are both very fine, but there is something about success that cannot be gainsaid. |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| Full Idea: Destroy the seriousness of others with laughter, and their laughter with seriousness. | |
| From: Gorgias (fragments/reports [c.443 BCE]), quoted by Aristotle - The Art of Rhetoric 1419b | |
| A reaction: This sounds like brilliant tactical advice, which should be on the wall of every barrister's chambers. This is a case of rhetoric having something to teach us which is nothing at all to do with truth. It is more like learning karate. |
| 7482 | Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson] |
| Full Idea: The idea of resurrection in Judaism seems to have first developed around 160 BCE, during the time of religious martyrdom, and as a response to it (the martyrs were surely not dying forever?). It is first mentioned in the book of Daniel. | |
| From: report of Anon (Dan) (27: Book of Daniel [c.165 BCE], Ch.7) by Peter Watson - Ideas | |
| A reaction: Idea 7473 suggests that Zoroaster beat them to it by 800 years. |