9 ideas
| 9148 | I think of variables as objects rather than as signs [Fine,K] |
| Full Idea: It is natural nowadays to think of variables as a certain kind of sign, but I wish to think of them as a certain kind of object. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §2) | |
| A reaction: Fine has a theory based on 'arbitrary objects', which is a rather charming idea. The cell of a spreadsheet is a kind of object, I suppose. A variable might be analogous to a point in space, where objects can locate themselves. |
| 16025 | If things change they become different - but then no one thing undergoes the change! [Gallois] |
| Full Idea: If things really change, there can't literally be one thing before and after the change. However, if there isn't one thing before and after the change, then no thing has really undergone any change. | |
| From: André Gallois (Identity over Time [2011], Intro) | |
| A reaction: [He cites Copi for this way of expressing the problem of identity through change] There is an obvious simple ambiguity about 'change' in ordinary English. A change of property isn't a change of object. Painting a red ball blue isn't swapping it. |
| 16026 | 4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois] |
| Full Idea: We have four versions of Four-Dimensionalism: the relativistic view that time is space-like; a persisting thing is identical with its history (so objects are events); past and future are equally real; or (Lewis) things extend in time, with temporal parts. | |
| From: André Gallois (Identity over Time [2011], §2.5) | |
| A reaction: Broad proposed the second one. I prefer 3-D: at any given time a thing is wholly present. At another time it is wholly present despite having changed. It is ridiculous to think that small changes destroy identity. We acquire identity by dying?? |
| 16027 | If two things are equal, each side involves a necessity, so the equality is necessary [Gallois] |
| Full Idea: The necessity of identity: a=b; □(a=a); so something necessarily = a; so something necessarily must equal b; so □(a=b). [A summary of the argument of Marcus and Kripke] | |
| From: André Gallois (Identity over Time [2011], §3) | |
| A reaction: [Lowe 1982 offered a response] The conclusion seems reasonable. If two things are mistakenly thought to be different, but turn out to be one thing, that one thing could not possibly be two things. In no world is one thing two things! |
| 9152 | If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K] |
| Full Idea: In traditional abstraction, the colour green merely has the intrinsic property of being green, other properties of things being abstracted away. But why should that be regarded as a type? It must be because the property is common to the instances. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §5) | |
| A reaction: A nice question which shows that the much-derided single act of abstraction is not sufficient to arrive at a concept, so that abstraction is a more complex matter (perhaps even a rational one) than simple empiricists believe. |
| 9149 | To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K] |
| Full Idea: In abstracting from the elements of a doubleton to obtain 2, we do not wish to abstract away from all features of the objects. We wish to take account of the fact that the two objects are distinct; this alone should be preserved under abstraction. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3) | |
| A reaction: This is Fine's strategy for meeting Frege's objection to abstraction, summarised in Idea 9146. It seems to use the common sense idea that abstraction is not all-or-nothing. Abstraction has degrees (and levels). |
| 9150 | We should define abstraction in general, with number abstraction taken as a special case [Fine,K] |
| Full Idea: Number abstraction can be taken to be a special case of abstraction in general, which can then be defined without recourse to the concept of number. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3) | |
| A reaction: At last, a mathematical logician recognising that they don't have a monopoly on abstraction. It is perfectly obvious that abstractions of simple daily concepts must be chronologically and logically prior to number abstraction. Number of what? |
| 9146 | After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K] |
| Full Idea: In Cantor's abstractionist account there can only be two numbers, 0 and 1. For abs(Socrates) = abs(Plato), since their numbers are the same. So the number of {Socrates,Plato} is {abs(Soc),abs(Plato)}, which is the same number as {Socrates}! | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §1) | |
| A reaction: Fine tries to answer this objection, which arises from §45 of Frege's Grundlagen. Fine summarises that "indistinguishability without identity appears to be impossible". Maybe we should drop talk of numbers in terms of sets. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |