18 ideas
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| Full Idea: The tendency to attack forms of expression rather than attempting to appreciate what is actually being said is one of the more unfortunate habits that analytic philosophy inherited from Frege. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], IV) | |
| A reaction: The key to this, I say, is to acknowledge the existence of propositions (in brains). For example, this belief will make teachers more sympathetic to pupils who are struggling to express an idea, and verbal nit-picking becomes totally irrelevant. |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| Full Idea: The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets). | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], IX) | |
| A reaction: This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely! |
| 9406 | A class is natural when everybody can spot further members of it [Quinton] |
| Full Idea: To say that a class is natural is to say that when some of its members are shown to people they pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: He concedes a number of problems with his view, but I admire his attempt to at least begin to distinguish the natural (real!) classes from the ersatz ones. A mention of causal powers would greatly improve his story. |
| 9984 | We can have a series with identical members [Tait] |
| Full Idea: Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)? | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], VII) | |
| A reaction: The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature? |
| 15730 | Extreme nominalists say all classification is arbitrary convention [Quinton] |
| Full Idea: Pure, extreme nominalism sees all classification as the product of arbitrary convention. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I'm not sure what the word 'arbitrary' is doing there. Nominalists are not daft, and if they can classify any way they like, they are not likely to choose an 'arbitrary' system. Pragmatism tells the right story here. |
| 15728 | The naturalness of a class depends as much on the observers as on the objects [Quinton] |
| Full Idea: The naturalness of a class depends as essentially on the nature of the observers who classify as it does on the nature of the objects that they classify. ...It depends on our perceptual apparatus, and on our relatively mutable needs and interests. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: This seems to translate 'natural' as 'natural for us', which is not much use to scientists, who spend quite a lot of effort combating folk wisdom. Do desirable sports cars constitute a natural class? |
| 9407 | Properties imply natural classes which can be picked out by everybody [Quinton] |
| Full Idea: To say there are properties is to say there are natural classes, classes introduction to some of whose members enables people to pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: Aristotle would like this approach, but it doesn't find many friends among modern logician/philosophers. We should go on to ask why people agree on these things. Causal powers will then come into it. |
| 15729 | Uninstantiated properties must be defined using the instantiated ones [Quinton] |
| Full Idea: Properties that have no concrete instances must be defined in terms of those that have. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I wonder what the dodo used to smell like? |
| 8520 | An individual is a union of a group of qualities and a position [Quinton, by Campbell,K] |
| Full Idea: Quinton proposes that an individual is a union of a group of qualities and a position. | |
| From: report of Anthony Quinton (The Nature of Things [1973], Pt I) by Keith Campbell - The Metaphysic of Abstract Particulars §5 | |
| A reaction: This seems the obvious defence of a bundle account of objects against the charge that indiscernibles would have to be identical. It introduces, however, 'positions' into the ontology, but maybe that price must be paid. Materialism needs space. |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| Full Idea: If the sense of a proposition about the abstract domain is given in terms of the corresponding proposition about the (relatively) concrete domain, ..and the truth of the former is founded upon the truth of the latter, then this is 'logical abstraction'. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: The 'relatively' in parentheses allows us to apply his idea to levels of abstraction, and not just to the simple jump up from the concrete. I think Tait's proposal is excellent, rather than purloining 'abstraction' for an internal concept within logic. |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| Full Idea: Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: [compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set. |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
| Full Idea: A different reading of abstraction is that it concerns, not the individuating properties of the elements relative to one another, but rather the individuating properties of the set itself, for example the concept of what is its extension. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], VIII) | |
| A reaction: If the set was 'objects in the room next door', we would not be able to abstract from the objects, but we might get to the idea of things being contain in things, or the concept of an object, or a room. Wrong. That's because they are objects... Hm. |
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| Full Idea: Why should abstraction from two equipollent sets lead to the same set of 'pure units'? | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996]) | |
| A reaction: [Tait is criticising Cantor] This expresses rather better than Frege or Dummett the central problem with the abstractionist view of how numbers are derived from matching groups of objects. |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| Full Idea: If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features. |
| 13554 | True greatness is never allowing events to disturb you [Seneca] |
| Full Idea: There is no more reliable proof of greatness than to be in a state where nothing can happen to make you disturbed. | |
| From: Seneca the Younger (On Anger (Book 3) [c.60], §06) | |
| A reaction: He specifically opposes Aristotle's view that there are times when anger is appropriate, and failure to be very angry indeed is a failure of character. |
| 13556 | Every night I critically review how I have behaved during the day [Seneca] |
| Full Idea: When the lamp has been removed from my sight, and my wife, no stranger now to my habit, has fallen silent, I examine the whole of my day and retrace my actions and words; I hide nothing from myself. | |
| From: Seneca the Younger (On Anger (Book 3) [c.60], §36) |
| 13553 | Anger is a vice which afflicts good men as well as bad [Seneca] |
| Full Idea: Other vile passions affect only the worst sort of men, but anger creeps up even on enlightened me who are otherwise sane. | |
| From: Seneca the Younger (On Anger (Book 3) [c.60], §04) | |
| A reaction: A very interesting observation for anyone who is trying to analyse the key issues in virtue theory. |
| 13552 | Anger is an extreme vice, threatening sanity, and gripping whole states [Seneca] |
| Full Idea: Other vices drive the mind on, anger hurls it headlong; ..other vices revolt from good sense, this one from sanity; ...other vices seize individuals, this is the one passion that sometimes takes hold of an entire state. | |
| From: Seneca the Younger (On Anger (Book 3) [c.60], §01) | |
| A reaction: He particularly dislikes anger because it is the vice that leads to violence. |