33 ideas
| 19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
| Full Idea: The devil is evil but nonetheless wise; he was a wise angel, and through no loss of knowledge, but, rather, through some sort of affective restructuring tried and failed to take over the throne. | |
| From: Dennis Whitcomb (Wisdom [2011], 'Argument') | |
| A reaction: ['affective restructuring' indeed! philosophers- don't you love 'em?] To fail at something you try to do suggests a flaw in the wisdom. And the new regime the devil wished to introduce doesn't look like a wise regime. Not convinced. |
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 15105 | F(x) walked into a bar. The barman said.. [Sommers,W] |
| Full Idea: F(x) walked into a bar. The barman said, 'Sorry, we don't cater for functions'. | |
| From: Will Sommers (talk [2019]) |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
| A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
| A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
| A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
| 12408 | Sartre to Waitress: Coffee with no cream, please... [Sommers,W] |
| Full Idea: Sartre to Waitress: Coffee with no cream, please. Waitress: Sorry, we're out of cream; would no milk do? | |
| From: Will Sommers (talk [2019]) |
| 12397 | Said Plato: 'The things that we feel... [Sommers,W] |
| Full Idea: Said Plato: 'The things that we feel/ Are not ontologically real,/ But just the excrescence/ Of numinous essence/ Our senses can never reveal.' [Basil Ransome-Davis] | |
| From: Will Sommers (talk [2019]) |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| Full Idea: The first demand of logic is of a sharp boundary. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
| A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
| 12407 | Barman to Descartes: Would you like another drink?... [Sommers,W] |
| Full Idea: Barman to Descartes: Would you like another drink? Descartes: I think not (...and promptly vanishes) | |
| From: Will Sommers (talk [2019]) |
| 12399 | There was a young student called Fred... [Sommers,W] |
| Full Idea: There was a young student called Fred,/ Who was questioned on Descartes and said:/ 'It's perfectly clear/ That I'm not really here,/ For I haven't a thought in my head.' [V.R. Ormerod] | |
| From: Will Sommers (talk [2019]) |
| 20963 | A philosopher and his wife are out for a drive... [Sommers,W] |
| Full Idea: A philosopher and his wife are out for a drive in the country. 'Oh look!' she says, 'Those sheep have been shorn.' 'Yes', says the philosopher, 'on this side'. | |
| From: Will Sommers (talk [2019]) |
| 12404 | Dear Sir, Your astonishment's odd.... [Sommers,W] |
| Full Idea: (reply to 12403) Dear Sir, Your astonishment's odd:/ I am always about in the Quad./ And that's why the tree/ Will continue to be,/ Since observed by Yours faithfully, God.' [anon] | |
| From: Will Sommers (talk [2019]) |
| 12403 | There once was a man who said: 'God... [Sommers,W] |
| Full Idea: There once was a man who said: 'God/ Must think it exceedingly odd/ If he finds that this tree/ Continues to be,/ When there's no-one about in the Quad.' [Ronald Knox] (reply in 12404) | |
| From: Will Sommers (talk [2019]) |
| 12402 | ..But if he's a student of Berkeley... [Sommers,W] |
| Full Idea: (continued from 12401) ..But if he's a student of Berkeley,/ One thing will emerge, rather starkly,/ That he ought to believe/ What his senses perceive,/ No matter how dimly or darkly. [Leslie Johnson] | |
| From: Will Sommers (talk [2019]) |
| 12409 | The philosopher Berkeley once said.. [Sommers,W] |
| Full Idea: The philosopher Berkeley once said/ In the dark to a maid in his bed:/ 'No perception, my dear,/ Means I'm not really here,/ But only a thought in your head.' [P.W.R. Foot] | |
| From: Will Sommers (talk [2019]) |
| 14694 | "My dog's got synaesthesia." How does he smell? ..... [Sommers,W] |
| Full Idea: "My dog's got synaesthesia." How does he smell? "Purple." | |
| From: Will Sommers (talk [2019]) |
| 12401 | A toper who spies in the distance... [Sommers,W] |
| Full Idea: A toper who spies in the distance,/ Striped tigers, will get some assistance/ From reading Descartes,/ Who holds that it's part/ Of his duty to doubt their existence. ... [Leslie Johnson] - (continued in 12402) | |
| From: Will Sommers (talk [2019]) |
| 12410 | There once was a man who said 'Damn!... [Sommers,W] |
| Full Idea: There once was a man who said 'Damn!/ It is borne in upon me I am/ An engine that moves/ In predestinate grooves:/ I'm not even a bus, I'm a tram.' [M.E. Hare] | |
| From: Will Sommers (talk [2019]) |
| 9392 | How do behaviourists greet each other? [Sommers,W] |
| Full Idea: How do behaviourists greet each other? Hi - you're fine, how am I? | |
| From: Will Sommers (talk [2019]) |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
| A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
| 12405 | 'If you're aristocratic,' said Nietzsche... [Sommers,W] |
| Full Idea: 'If you're aristocratic,' said Nietzsche,/ 'It's thumbs up, you're OK. Pleased to mietzsche./ If you're working-class bores,/ It's thumbs down and up yours!/ If you don't know your place, then I'll tietzsche.' [Gerry Hamill] | |
| From: Will Sommers (talk [2019]) |
| 9391 | Why do anarchists drink herbal tea? [Sommers,W] |
| Full Idea: Why do anarchists drink herbal tea? Because proper tea is theft. | |
| From: Will Sommers (talk [2019]) |
| 12400 | Cries the maid: 'You must marry me Hume!'... [Sommers,W] |
| Full Idea: Cries the maid: 'You must marry me Hume!'/ A statement that made David fume./ He said: 'In cause and effect,/ There is a defect;/ That it's mine you can only assume.' [P.W.R. Foot] | |
| From: Will Sommers (talk [2019]) |
| 16527 | Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W] |
| Full Idea: Causation - we all thought we knew it / Till Hume came along and saw through it / We notice that A / Follows B every day / And frankly that's all there is to it. | |
| From: Will Sommers (talk [2019]) |
| 17592 | The barman called 'Time!', and Augustine said..... [Sommers,W] |
| Full Idea: The barman called 'Time!'. Augustine: 'I don't know what you mean, though I did before you said that'. | |
| From: Will Sommers (talk [2019]) |
| 15208 | The past, present and future walked into a bar.... [Sommers,W] |
| Full Idea: The past, present and future walked into a bar. It was tense. | |
| From: Will Sommers (talk [2019]) |