5 ideas
10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
Full Idea: Very few things in set theory remain valid in intuitionist mathematics. | |
From: Paul Bernays (On Platonism in Mathematics [1934]) |
10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought. | |
From: Paul Bernays (On Platonism in Mathematics [1934], p.261) | |
A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist. |
10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction. | |
From: Paul Bernays (On Platonism in Mathematics [1934], p.268) | |
A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic. |
6493 | We are not conscious of pure liquidity, but of the liquidity of water [Firth] |
Full Idea: We are not conscious of liquidity, coldness, and solidity, but of the liquidity of water, the coldness of ice, and the solidity of rocks. | |
From: Roderick Firth (Sense Data and the Percept Theory [1949]), quoted by Howard Robinson - Perception 1.7 | |
A reaction: A nice point, but it might not be entirely true in a blindfold test, where one might only report properties like 'sticky' or 'warm', without having any clear concept of the substance being experienced. Firth is proposing the 'percept theory'. |
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'). |