display all the ideas for this combination of texts
14 ideas
| 9144 | Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert] |
| Full Idea: Fine says creative definitions can found mathematics. His 'procedural postulationism' says one stipulates not truths, but certain procedures for extending a domain. The procedures can be stated without invoking an abstract ontology. | |
| From: report of Kit Fine (The Limits of Abstraction [2002], 100) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 4 | |
| A reaction: (For creative definitions, see Idea 9143) This sounds close in spirit to fictionalism, but with the emphasis on the procedure (which can presumably be formalized) rather than a pure act of imaginative creation. |
| 10141 | Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K] |
| Full Idea: Many different kinds of mathematical objects (natural numbers, the reals, points, lines, figures, groups) can be regarded as forms of abstraction, with special theories having their basis in a general theory of abstraction. | |
| From: Kit Fine (The Limits of Abstraction [2002], I.4) | |
| A reaction: This result, if persuasive, would be just the sort of unified account which the whole problem of abstact ideas requires. |
| 8770 | 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach] |
| Full Idea: I call 'abstractionism' the doctrine that a concept is acquired by a process of singling out in attention some one feature given in direct experience - abstracting it - and ignoring the other features simultaneously given - abstracting from them. | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §6) | |
| A reaction: Locke seems to be the best known ancestor of this view, and Geach launches a vigorous attack against it. However, contemporary philosophers still refer to the process, and I think Geach should be crushed and this theory revived. |
| 10135 | We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K] |
| Full Idea: A principle of abstraction is 'conceptual' when the items upon which it abstracts are concepts (e.g. a one-one correspondence associated with a number), and 'objectual' if they are objects (parallel lines associated with a direction). | |
| From: Kit Fine (The Limits of Abstraction [2002], I) |
| 9142 | Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert] |
| Full Idea: Fine considers abstraction principles as instances of reconceptualization (rather than implicit definition, or using the Context Principle). This centres not on reference, but on new senses emerging from analysis of a given sense. | |
| From: report of Kit Fine (The Limits of Abstraction [2002], 035) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 2 | |
| A reaction: Fine develops an argument against this view, because (roughly) the procedure does not end in a unique result. Intuitively, the idea that abstraction is 'reconceptualization' sounds quite promising to me. |
| 10137 | Abstractionism can be regarded as an alternative to set theory [Fine,K] |
| Full Idea: The uncompromising abstractionist rejects set theory, seeing the theory of abstractions as an alternative, rather than as a supplement, to the standard theory of sets. | |
| From: Kit Fine (The Limits of Abstraction [2002], I.1) | |
| A reaction: There is also a 'compromising' version. Presumably you still have equivalence classes to categorise the objects, which are defined by their origin rather than by what they are members of... Cf. Idea 10145. |
| 10138 | An object is the abstract of a concept with respect to a relation on concepts [Fine,K] |
| Full Idea: We can see an object as being the abstract of a concept with respect to a relation on concepts. For example, we may say that 0 is the abstract of the empty concept with respect to the relation of one-one correspondence. | |
| From: Kit Fine (The Limits of Abstraction [2002], I.2) | |
| A reaction: This is Fine's attempt to give a modified account of the Fregean approach to abstraction. He says that the reference to a relation will solve the problem of identity between abstractions. |
| 8771 | 'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience [Geach] |
| Full Idea: Nowhere in the sensible world could you find anything to be suitably labelled 'or' or 'not'. So the abstractionist appeals to an 'inner sense', or hesitation for 'or', and of frustration or inhibition for 'not'. Personally I see a threat in 'or else'! | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §7) | |
| A reaction: This is a key argument of Geach's against abstractionism. As a logician he prefers to discuss connectives rather than, say, colours. I think they might be meta-abstractions, which you create internally once you have picked up the knack. |
| 8772 | We can't acquire number-concepts by extracting the number from the things being counted [Geach] |
| Full Idea: The number-concepts just cannot be got by concentrating on the number and abstracting from the kind of things being counted. | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §8) | |
| A reaction: This point is from Frege - that if you 'abstract away' everything apart from the number, you are simply left with nothing in experience. The objection might, I think, be met by viewing it as second-order abstraction, perhaps getting to a pattern first. |
| 8773 | Abstractionists can't explain counting, because it must precede experience of objects [Geach] |
| Full Idea: The way counting is learned is wholly contrary to abstractionist preconceptions, because the series of numerals has to be learned before it can be applied. | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §8) | |
| A reaction: You might learn to parrot the names of numbers, but you could hardly know what they meant if you couldn't count anything. See Idea 3907. I would have thought that individuating objects must logically and pedagogically precede counting. |
| 8774 | The numbers don't exist in nature, so they cannot have been abstracted from there into our languages [Geach] |
| Full Idea: The pattern of the numeral series that is grasped by a child exists nowhere in nature outside human languages, so the human race cannot possibly have discerned this pattern by abstracting it from some natural context. | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §8) | |
| A reaction: This is a spectacular non sequitur, which begs the question. Abstractionists precisely claim that the process of abstraction brings numerals into human language from the natural context. Structuralism is an attempt to explain the process. |
| 8778 | Blind people can use colour words like 'red' perfectly intelligently [Geach] |
| Full Idea: It is not true that men born blind can form no colour-concepts; a man born blind can use the word 'red' with a considerable measure of intelligence; he can show a practical grasp of the logic of the word. | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §10) | |
| A reaction: Weak. It is obvious that they pick up the word 'red' from the usage of sighted people, and the usage of the word doesn't guarantee a grasp of the concept, as when non-mathematicians refer to 'calculus'. Compare Idea 7377 and Idea 7866. |
| 8777 | If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted? [Geach] |
| Full Idea: Since we can use the terms 'black' and 'cat' in situations not including any black object or any cat, how could this part of the use be got by abstraction? | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §10) | |
| A reaction: [He is attacking H.H. Price] It doesn't seem a huge psychological leap to apply the word 'cat' when we remember a cat, and once it is in the mind we can play games with our abstractions. Cats are smaller than dogs. |
| 8779 | We can form two different abstract concepts that apply to a single unified experience [Geach] |
| Full Idea: It is impossible to form the concept of 'chromatic colour' by discriminative attention to a feature given in my visual experience. In seeing a red window-pane, I do not have two sensations, one of redness and one of chromatic colour. | |
| From: Peter Geach (Mental Acts: their content and their objects [1957], §10) | |
| A reaction: Again Geach begs the question, because abstractionists claim that you can focus on two different 'aspects' of the one experience, as that it is a 'window', or it is 'red', or it is not a wall, or it is not monochrome. |