5 ideas
| 15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
| Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed. | |
| From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication | |
| A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians. |
| 15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
| Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time. | |
| From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities. |
| 14617 | Predicates can't apply to what doesn't exist [Stalnaker] |
| Full Idea: Nothing can be predicated of something which does not exist. | |
| From: Robert C. Stalnaker (Merely Possible Propositions [2010], p.28) | |
| A reaction: [He says he is 'agreeing with Plantinga' on this] This seems very puzzling, as you can obviously say that dragons do not exist, but they breathe fire. Why can't you attach predicates to hypothetical objects? |
| 14616 | A 'Russellian proposition' is an ordered sequence of individual, properties and relations [Stalnaker] |
| Full Idea: A 'Russellian proposition' is an ordered sequence containing the individual, along with properties and relations. | |
| From: Robert C. Stalnaker (Merely Possible Propositions [2010], p.22) | |
| A reaction: Since Russell took properties and relations to be features of reality, this made the whole proposition a feature of reality. This is utterly different from what I understand by the word 'proposition', which is a feature of thought, not of the world. |
| 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'). |