5 ideas
| 18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
| Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result. | |
| From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3 | |
| A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent. |
| 9089 | Knowledge is a quality existing subjectively in the soul [William of Ockham] |
| Full Idea: Knowledge is a certain quality which exists in the soul as its subject ('existens subiective in anima'). | |
| From: William of Ockham (Expositio super viii libros [1340], Prologue) | |
| A reaction: One might say here that knowledge is a property, and so it might not be susceptible to further analysis. It invites the question of how you could know by introspection that you have got it, which would be an extreme internalist view. |
| 9091 | Sometimes 'knowledge' just concerns the conclusion, sometimes the whole demonstration [William of Ockham] |
| Full Idea: Sometimes 'knowledge' means evident cognition of the conclusion alone, sometimes of the demonstration as a whole. | |
| From: William of Ockham (Expositio super viii libros [1340], Prologue) | |
| A reaction: 'Demonstration' will be something like Greek 'logos' - full understanding, ability to explain and give reasons. William is certainly right about normal usage. I know the answer in a quiz, without any requirement for justifications. |
| 9090 | Knowledge is certain cognition of something that is true [William of Ockham] |
| Full Idea: Knowledge is certain cognition of something that is true. | |
| From: William of Ockham (Expositio super viii libros [1340], Prologue) | |
| A reaction: This view has problems. William is not facing up to the sceptical questions which can shake any degree of certainty, and also that someone who lacked self-confidence might know many things while always feeling uncertain about them. 'Cognition' must go! |
| 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'). |