14 ideas
13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
Full Idea: Frege (1893) considered a definite description to be a genuine singular term (as we do), so that a sentence like 'The present King of France is bald' would have the same logical form as 'Harry Truman is bald'. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by M Fitting/R Mendelsohn - First-Order Modal Logic | |
A reaction: The difficulty is what the term refers to, and they embrace a degree of Meinongianism - that is that non-existent objects can still have properties attributed to them, and so can be allowed some sort of 'existence'. |
9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
Full Idea: The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual. | |
From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17 | |
A reaction: In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it. |
18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
Full Idea: If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
A reaction: This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics. |
18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
Full Idea: It cannot be demanded that everything be proved, because that is impossible; but we can require that all propositions used without proof be expressly declared as such, so that we can see distinctly what the whole structure rests upon. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.2), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 'What' |
10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
Full Idea: Frege opts for his famous definition of numbers in terms of extensions of the concept 'equal to the concept F', but he then (in 'Grundgesetze') needs a theory of extensions or classes, which he provided by means of Basic Law V. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' §1 |
9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
Full Idea: Cantor pointed out explicitly to Frege that it is a mistake to take the notion of a set (i.e. of that which has a cardinal number) to simply mean the extension of a concept. ...Frege's later assumption of this was an act of recklessness. | |
From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by William W. Tait - Frege versus Cantor and Dedekind III | |
A reaction: ['recklessness' is on p.61] Tait has no sympathy with the image of Frege as an intellectual martyr. Frege had insufficient respect for a great genius. Cantor, crucially, understood infinity much better than Frege. |
18165 | My Basic Law V is a law of pure logic [Frege] |
Full Idea: I hold that my Basic Law V is a law of pure logic. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.4), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
A reaction: This is, of course, the notorious law which fell foul of Russell's Paradox. It is said to be pure logic, even though it refers to things that are F and things that are G. |
15391 | A substance is, roughly, a basic being or subject at the foundation of reality [Robb] |
Full Idea: A substance is a basic being, something at reality's foundation. What exactly this means is a matter of some controversy. Some philosophers think of substance as an ultimate subject, something that has properties but isn't a property. | |
From: David Robb (Substance [2009], 'Intro') | |
A reaction: This seems to capture the place of 'substance' in contemporary metaphysics. I think of 'substance' as a placeholder for some threatened account, even in Aristotle. |
15392 | If an object survives the loss of a part, complex objects can have autonomy over their parts [Robb] |
Full Idea: Sometimes a whole can survive a loss of parts: the chair would still exist if it lost one of its legs. This seems to give complex objects a sort of autonomy over their parts. | |
From: David Robb (Substance [2009], 'Ident') | |
A reaction: There is then a puzzle as to how much loss of parts the whole can survive, and why. The loss of a major part could be devastating, so why do all wholes not exhibit this relation to all their parts? I demand rules, now! |
2602 | What experience could prove 'If a=c and b=c then a=b'? [Descartes] |
Full Idea: Please tell me what the corporeal motion is that is capable of forming some common notion to the effect that 'things which are equal to a third thing are equal to each other'. | |
From: René Descartes (Comments on a Certain Broadsheet [1644], p.366) |
2600 | The mind's innate ideas are part of its capacity for thought [Descartes] |
Full Idea: I have never written or taken the view that the mind requires innate ideas which are something distinct from its own faculty of thinking. | |
From: René Descartes (Comments on a Certain Broadsheet [1644], p.365) |
2601 | Qualia must be innate, because physical motions do not contain them [Descartes] |
Full Idea: The ideas of pains, colours, sounds etc. must be all the more innate if, on the occasion of certain corporeal motions, our mind is to be capable of representing them to itself, for there is no similarity between these ideas and the corporeal motions. | |
From: René Descartes (Comments on a Certain Broadsheet [1644], p.365) | |
A reaction: Simple and brilliant! We know perfectly well that there is no redness zooming through the air from a tomato (or the air would be pink!). Redness occurs when the light arrives, so we add the redness, so it is innate. |
9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
Full Idea: In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5 | |
A reaction: As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts. |
13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
Full Idea: Frege took the study of concepts and their extensions to be within logic. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Stewart Shapiro - Foundations without Foundationalism 7.1 | |
A reaction: This is part of the plan to make logic a universal language (see Idea 13664). I disagree with this, and with the general logicist view of the position of logic. The logical approach thins concepts out. See Deleuze/Guattari's horror at this. |