| 17438 | Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki] |
| Full Idea: For Frege, the distinction between what we count and what we do not count is drawn by our concepts. ...We can describe the very same external phenomena either as the leaves of a tree or its foliage. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 3 | |
| A reaction: Hm. We can't obey 'count the foliage', but we all know that foliage is countable stuff, where water isn't. Nature has a say here - it isn't just a matter of our concepts. |
| 17427 | Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki] |
| Full Idea: Frege's proposal can be isolation as discreteness, i.e. absence of overlap, between the objects counted; and isolation as drawing of conceptual boundaries. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 1 |
| 17437 | Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki] |
| Full Idea: Non-arbitrary division concerns the internal structure of the things falling under a concept. Its point is to ensure that we cannot go on dividing these units arbitrarily and still expect to find more things of the same kind. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.3 | |
| A reaction: Counting something red is given as an example. This seems to define mass-terms, or stuff. |
| 17426 | A concept creating a unit must isolate and unify what falls under it [Frege] |
| Full Idea: Only a concept which isolates what falls under it in a definite manner, and which does not permit any arbitrary division of it into parts, can be a unit relative to finite Number. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54), quoted by Kathrin Koslicki - Isolation and Non-arbitrary Division 1 | |
| A reaction: This is the key modern proposal for the basis of counting, by trying to get at the sort of concept which will turn something into a 'unit'. The concept must isolate and unify. Why should just one concept do that each time? |
| 17428 | Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki] |
| Full Idea: Roughly, Frege's picture of counting is this. When we count something, we determine what number belongs to a given concept. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1 | |
| A reaction: If the concept were 'herd of sheep' that would need a context before there could be a fixed number. You can count until you get bored, like counting stars to get to sleep. 'Count off 20 sheep' has the number before the counting starts. |
| 12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry] |
| Full Idea: If we list the words 'bull', 'bull' and 'cow', it is often said that there are three 'word tokens' but only two 'word types', but Geach says there are not two kinds of object to be counted, but two different ways of counting the same object. | |
| From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by John Perry - The Same F II | |
| A reaction: Insofar as the notion that a 'word type' is an 'object', my sympathies are entirely with Geach, to my surprise. Geach's point is that 'bull' and 'bull' are the same meaning, but different actual words. Identity is relative to a concept. |
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| Full Idea: If we count the concept 'coin in this box', we could regard coin as the 'unit', while taking 'in this box' to limit the scope. Counting coins in two boxes would be not a difference in unit (kind of object), but in scope. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') | |
| A reaction: This is a very nice alternative to the Fregean view of counting, depending totally on the concept, and rests more on a natural concept of object. I prefer Ayers. Compare 'count coins till I tell you to stop'. |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| Full Idea: If we accepted that counting objects always presupposes some sortal, it is surely clear that the class of objects to be counted could be designated by two sortals rather than one. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
| A reaction: His nice example is an object which is both 'a single piece of wool' and a 'sweater', which had better not be counted twice. Wiggins struggles to argue that there is always one 'substance sortal' which predominates. |
| 17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
| Full Idea: My thesis C says that to specify something or other under which a and b coincide is to specify a concept f which qualifies for this purpose only if it yields a principle of counting for fs. ...I submit that C is false, though a near miss. | |
| From: David Wiggins (Sameness and Substance [1980], 1.1) |
| 17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
| Full Idea: My principle C seems unnecessary ...since it is one thing to see how many fs there are...but another to have a perfectly general method. ...One could answer whether this f-compliant is the same as that one, but there are too many ways to articulate it. | |
| From: David Wiggins (Sameness and Substance [1980], 2.8) | |
| A reaction: His famous example is trying to count the Pope's crown, which is made of crowns. A clearer example might be a rectangular figure divided up into various overlapping rectangles. Individuation is easy, but counting is contextual. |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| Full Idea: The invitation to number the instances of some non-sortal concept is intelligible only if it is relativised to a sortal. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: I take this to be an essentially Fregean idea, as when we count the boots when we have decided whether they fall under the concept 'boot' or the concept 'pair'. I also take this to be the traditional question 'what units are you using'? |
| 17434 | We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki] |
| Full Idea: The reason we have a hard time counting the branches and the waves is because our concepts 'branches on the tree' and 'waves on the ocean' do not determine sufficiently precise boundaries: the concepts do not draw a clear invisible line around each thing. | |
| From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2) | |
| A reaction: This is the 'isolation' referred to in Frege. |