9 ideas
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. |
10414 | Abstract objects are constituted by encoded collections of properties [Zalta, by Swoyer] |
Full Idea: In Zalta's view abstract objects are correlated with collections of properties. ..They encode, as well as exemplify, properties; indeed, an abstract object (such as a Euclidean triangle) is constituted by the properties it encodes. | |
From: report of Edward N. Zalta (Abstract Objects:intro to Axiomatic Metaphysics [1983]) by Chris Swoyer - Properties 6.3 | |
A reaction: If we are going to explain abstract objects with properties, then properties had better not be abstract objects. Zalta has a promising idea if we start from a nominalist and naturalistic view of properties (built from physical powers). 'Encode'? |
10415 | Properties make round squares and round triangles distinct, unlike exemplification [Zalta, by Swoyer] |
Full Idea: On Zalta's view, properties with the same encoding extensions are identical, but may be distinct with the same exemplification extension. So the properties of being a round square and a round triangle are distinct, but with the same exemplification. | |
From: report of Edward N. Zalta (Abstract Objects:intro to Axiomatic Metaphysics [1983]) by Chris Swoyer - Properties | |
A reaction: (For Zalta's view, see Idea 10414) I'm not sure about 'encoding' (cf. Hodes's use of the word), but the idea that an abstract object is just a bunch of possible properties (assuming properties have prior availability) seems promising. |
8969 | We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne] |
Full Idea: Geach argued that the notion of absolute identity should be abandoned. ..We can only grasp the meaning of a count noun when we associate it with a criterion of identity, expressed by a particular relative identity sortal. | |
From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by John Hawthorne - Identity | |
A reaction: In other words, identity needs categorisation. Hawthorne concludes that Geach is wrong. Geach clearly has much common usage on his side. 'What's that?' usually invites a categorisation. Sameness of objects seems to need a 'respect'. |
16075 | Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach] |
Full Idea: Geach's denial of absolute identity has drastic implications for logic, semantics and set theory. He must deny the axiom of extensionality in set theory, for example. | |
From: comment on Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6 | |
A reaction: I'm beginning to think we have two entirely different concepts here - the logicians' and mathematicians' notion of when two things are identical, and the ordinary language concept of two things being 'the same'. 'We like the same music'. |
12152 | Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach] |
Full Idea: Identity is relative. When one says 'x is identical with y' this is an incomplete expression. It is short for 'x is the same A as y', where 'A' represents some count noun understood from the context of utterance. | |
From: Peter Geach (Reference and Generality (3rd ed) [1980], p.39), quoted by John Perry - The Same F I | |
A reaction: Perry notes that Geach's view is in conscious opposition to Frege, who had a pure notion of identity. We say 'they are the same insofar as they are animals', but not 'they are the same animal'. Perfect identity involves all possible A's. |
16073 | Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman] |
Full Idea: Geach rejects the standard formulation of Leibniz's Law as incomplete, since it includes a non-relativized identity predicate. | |
From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6 | |
A reaction: Not many people accept Geach's premiss that identity is a relative matter. I agree with Wiggins on this, that identity is an absolute (and possibly indefinable). The problem with the Law is what you mean by a 'property'. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |