22 ideas
| 9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
| Full Idea: Frege expressly denies that a correct definition need capture the sense of the expression it defines: it need only get the reference right. | |
| From: report of Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.3 | |
| A reaction: This might hit up against the renate/cordate problem, of two co-extensive concepts, where the definition gets the extension right, but the intension wrong. |
| 9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
| Full Idea: Since every definition is an equation, one cannot define equality itself. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This seems a particularly nice instance of the general rule that 'you have to start somewhere'. It is a nice test case for the nature of meaning to ask 'what do you understand when you understand equality?', given that you can't define it. |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| Full Idea: Counting rests itself on a one-one correlation, namely of numerals 1 to n and the objects. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]), quoted by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: Parsons observes that counting will establish a one-one correspondence, but that doesn't make it the aim of counting, and so Frege hasn't answered Husserl properly. Which of the two is conceptually prior? How do you decide. |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| Full Idea: When Husserl says that sameness of number can be shown by one-one correlation, he forgets that this counting itself rests on a univocal one-one correlation, namely that between the numerals 1 to n and the objects of the set. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is the platonist talking. Neo-logicism is attempting to build numbers just from the one-one correlation of objects. |
| 9586 | In a number-statement, something is predicated of a concept [Frege] |
| Full Idea: In a number-statement, something is predicated of a concept. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.328) | |
| A reaction: A succinct statement of Frege's theory of numbers. By my lights that would make numbers at least second-order abstractions. |
| 9580 | Our concepts recognise existing relations, they don't change them [Frege] |
| Full Idea: The bringing of an object under a concept is merely the recognition of a relation which previously already obtained, [but in the abstractionist view] objects are essentially changed by the process, so that objects brought under a concept become similar. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege's view would have to account for occasional misapplications of concepts, like taking a dolphin to be a fish, or falsely thinking there is someone in the cellar. |
| 9589 | Numbers are not real like the sea, but (crucially) they are still objective [Frege] |
| Full Idea: The sea is something real and a number is not; but this does not prevent it from being something objective; and that is the important thing. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.337) | |
| A reaction: This seems a qualification of Frege's platonism. It is why people start talking about abstract items which 'subsist', instead of 'exist'. It shows Frege's motivation in all this, which is to secure logic and maths from the vagaries of psychology. |
| 9577 | The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
| Full Idea: The most naïve opinion of number is that it is something like a heap in which things are contained. The next most naïve view is the conception of number as the property of a heap, cleansing the objects of their particulars. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.323) | |
| A reaction: A hundred toothbrushes and a hundred sponges can be seen to contain the same number (by one-to-one mapping), without actually knowing what that number is. There is something numerical in the heap, even if the number is absent. |
| 9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
| Full Idea: If an object is just presentation, we can pay less attention to a property and it disappears. By letting one characteristic after another disappear, we obtain concepts that are increasingly more abstract. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege despises this view. Note there is scope in the despised view for degrees or levels of abstraction, defined in terms of number of properties ignored. Part of Frege's criticism is realist. He retains the object, while Husserl imagines it different. |
| 12177 | Human artefacts may have essences, in their purposes [Popper] |
| Full Idea: One might adopt the view that certain things of our own making, such as clocks, may well be said to have 'essences', viz. their 'purposes', and what makes them serve these purposes. | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3 n17) | |
| A reaction: This is from one of the arch-opponents of essentialism. Could we take him on a slippery slope into essences for evolved creatures, or their organs? His argument says admitting an essence for a clock prevents using it for another purpose. |
| 12176 | Science does not aim at ultimate explanations [Popper] |
| Full Idea: I contest the essentialist doctrine that science aims at ultimate explanations, one which cannot be further explained, and which is in no need of any further explanation. | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3) | |
| A reaction: If explanations are causal, this seems to a plea for an infinite regress of causes, which is an odd thing to espouse. Are the explanations verbal descriptions or things in the world. There can be no perfect descriptions, but there may be ultimate things. |
| 9581 | Many people have the same thought, which is the component, not the private presentation [Frege] |
| Full Idea: The same thought can be grasped by many people. The components of a thought, and even more so the things themselves, must be distinguished from the presentations which in the soul accompany the grasping of a thought. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.325) | |
| A reaction: This is the basic realisation, also found in Russell, of how so much confusion has crept into philosophy, in Berkeley, for example. Frege starts down the road which leads to the externalist view of content. |
| 9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
| Full Idea: If from a black cat and a white cat we disregard colour, then posture, then location, ..we finally derive something which is completely without restrictions on content; but what is derived from the objects does differ, although it is not easy to say how. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: This is a key objection to abstractionism for Frege - we are counting two cats, not two substrata of essential catness, or whatever. But what makes a cat countable? (Key question!) It isn't its colour, or posture or location. |
| 9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
| Full Idea: Inattention is a very strong lye which must not be too concentrated, or it dissolves everything (such as the connection between the objects), but must not be too weak, to produce sufficient change. Personally I cannot find the proper dilution. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.330) | |
| A reaction: We may sympathise with the lack of precision here (frustrating for a logician), but it is not difficult to say of a baseball defence 'just concentrate on the relations, and ignore the individuals who implement it'. You retain basic baseball skills. |
| 9588 | Number-abstraction somehow makes things identical without changing them! [Frege] |
| Full Idea: Number-abstraction simply has the wonderful and very fruitful property of making things absolutely the same as one another without altering them. Something like this is possible only in the psychological wash-tub. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.332) | |
| A reaction: Frege can be awfully sarcastic. I don't really see his difficulty. For mathematics we only need to know what is countable about an object - we don't need to know how many hairs there are on the cat, only that it has identity. |
| 9583 | Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege] |
| Full Idea: The psychological logicians are concerned with the sense of the words and with the presentations, which they do not distinguish from the sense; but the mathematicians are concerned with the matter itself, with the reference of the words. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is helpful for showing the point of his sense/reference distinction; it is part of his campaign against psychologism, by showing that there is a non-psychological component to language - the reference, where it meets the public world. |
| 9584 | Identity baffles psychologists, since A and B must be presented differently to identify them [Frege] |
| Full Idea: The relation of sameness remains puzzling to a psychological logician. They cannot say 'A is the same as B', because that requires distinguishing A from B, so that these would have to be different presentations. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This is why Frege needed the concept of reference, so that identity could be outside the mind (as in Hesperus = Phosophorus). Think about an electron; now think about a different electron. |
| 17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
| Full Idea: Explanatory significance, hence naturalness, comes in degrees: positing some kinds may be very explanatory, positing others, only a little bit explanatory, positing others still, not explanatory at all. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 4) | |
| A reaction: He mentions 'cousin' as a natural kind that is not very explanatory of anything. It interests us as humans, but not at all in other animals, it seems. ...Nice thought, though, that two squirrels might be cousins... |
| 12175 | Galilean science aimed at true essences, as the ultimate explanations [Popper] |
| Full Idea: The third of the Galilean doctrines of science is that the best, the truly scientific theories, describe the 'essences' or the 'essential natures' of things - the realities which lie behind the appearances. They are ultimate explanations. | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3) | |
| A reaction: This seems to be the seventeenth century doctrine which was undermined by Humeanism, and hence despised by Popper, but is now making a comeback, with a new account of essence and necessity. |
| 12179 | Essentialist views of science prevent further questions from being raised [Popper] |
| Full Idea: The essentialist view of Newton (due to Roger Cotes) ...prevented fruitful questions from being raised, such as, 'What is the cause of gravity?' or 'Can we deduce Newton's theory from a more general independent theory?' | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3) | |
| A reaction: This is Popper's main (and only) objection to essentialism - that it is committed to ultimate explanations, and smugly terminates science when it thinks it has found them. This does not strike me as a problem with scientific essentialism. |
| 17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |
| Full Idea: The signs are that the higher categories are not natural kinds and so the Linnaean hierarchy must be abandoned. ...This is not abandoning a hierarchy altogether, it is not abandoning a tree of life. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 6) | |
| A reaction: Devitt's underlying point is that the higher and more general kinds do not have an essence (a specific nature), which is the qualification to be a natural kind. They explain nothing. Essence is the hallmark of natural kinds. Hmmm. |
| 17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
| Full Idea: Species pluralism is the view that there are several equally good accounts of what it is to be a species. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 7) | |
| A reaction: Devitt votes for it, and cites Dupré, among many other. Given the existence of rival accounts, all making good points, it is hard to resist this view. |