28 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. |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
From: Ian Rumfitt ("Yes" and "No" [2000]) | |
A reaction: This is the standard view which Rumfitt sets out to challenge. |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
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. |
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. |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
8388 | Causation is either direct realism, Humean reduction, non-Humean reduction or theoretical realism [Tooley] |
Full Idea: The main approaches to causation I shall refer to as direct realism, Humean reductionism, non-Humean reductionism, and indirect or theoretical realism. | |
From: Michael Tooley (Causation and Supervenience [2003], 2) | |
A reaction: The first simply observes causation (Anscombe), the second reduces it to regularity (Hume), the third reduces it to other natural features (Fair, Salmon, Dowe), the fourth takes an instrumental approach (Armstrong, Tooley). I favour the third approach. |
8389 | Causation distinctions: reductionism/realism; Humean/non-Humean states; observable/non-observable [Tooley] |
Full Idea: The three main distinctions concerning causation are between reductionism and realism; between Humean and non-Humean states of affairs; and between states that are immediately observable and those that are not. | |
From: Michael Tooley (Causation and Supervenience [2003], 2) | |
A reaction: I favour reductionism over realism, because I like the question 'If x is real, what is it made of?' I favour non-Humean states of affairs, because I think constant conjunction is very superficial. I presume the existence of non-observable components. |
8393 | We can only reduce the direction of causation to the direction of time if we are realist about the latter [Tooley] |
Full Idea: A reductionist can hold that the direction of causation is to be defined in terms of the direction of time; but this response is only available if one is prepared to adopt a realist view of the direction of time. | |
From: Michael Tooley (Causation and Supervenience [2003], 4.2.1.2) | |
A reaction: A nice illustration of the problems that arise if we try to be reductionist about everything. Personally I prefer my realism to be about time rather than about causation. Time, I would say, makes causation possible, not the other way around. |
8390 | Causation is directly observable in pressure on one's body, and in willed action [Tooley] |
Full Idea: The arguments in favour of causation being observable appeal especially to the impression of pressure upon one's body, and to one's introspective awareness of willing, together with the perception of the event which one willed. | |
From: Michael Tooley (Causation and Supervenience [2003], 3) | |
A reaction: [He cites Evan Fagels] Anscombe also cites words which have causality built into their meaning. This would approach would give priority to mental causation, and would need to demonstrate that similar things happen out in the world. |
8392 | Probabilist laws are compatible with effects always or never happening [Tooley] |
Full Idea: If laws of causation are probabilistic then the law does not entail any restrictions upon the proportion of events that follow a cause: ...it can have absolutely any value from zero to one. | |
From: Michael Tooley (Causation and Supervenience [2003], 4.1.3) | |
A reaction: This objection applies to an account of laws of nature, and also to definitions of causes as events which increase probabilities. One needn't be fully committed to natural necessity, but it must form some part of the account. |
8399 | The actual cause may not be the most efficacious one [Tooley] |
Full Idea: A given type of state may be causally efficacious, but not as efficacious as an alternative states, so it is not true that even a direct cause need raise the probability of its effect. | |
From: Michael Tooley (Causation and Supervenience [2003], 6.2.4) | |
A reaction: My intuition is that explaining causation in terms of probabilities entirely misses the point, which mainly concerns explaining the sense of necessitation in a cause. This idea give me a good reason for my intuition. |
8391 | In counterfactual worlds there are laws with no instances, so laws aren't supervenient on actuality [Tooley] |
Full Idea: If a counterfactual holds in a possible world, that is presumably because a law holds in that world, which means there could be basic causal laws that lack all instances. But then causal laws cannot be totally supervenient on the history of the universe. | |
From: Michael Tooley (Causation and Supervenience [2003], 4.1.2) | |
A reaction: A nice argument, which sounds like trouble for Lewis. One could deny that the laws have to hold in the counterfactual worlds, but then we wouldn't be able to conceive them. |
8394 | Explaining causation in terms of laws can't explain the direction of causation [Tooley] |
Full Idea: The most serious objection to any account of causation in terms of nomological relations alone is that it can't provide any account of the direction of causation. | |
From: Michael Tooley (Causation and Supervenience [2003], 5.1) | |
A reaction: Cf. Idea 8393. I am not convinced that there could be an 'account' of the direction of causation, so I am inclined to take it as given. If we take 'powers' (active properties) as basic, they would have a direction built into them. |
8398 | Causation is a concept of a relation the same in all worlds, so it can't be a physical process [Tooley] |
Full Idea: Against the view that causation is a particular physical process, might it not be argued that the concept of causation is the concept of a relation that possesses a certain intrinsic nature, so that causation must be the same in all possible worlds? | |
From: Michael Tooley (Causation and Supervenience [2003], 5.4) | |
A reaction: This makes the Humean assumption that laws of nature might be wildly different. I think it is perfectly possible that physical processes are the only way that causation could occur. Alternatively, the generic definition of 'cause' is just very vague. |