8 ideas
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception. | |
From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3 |
17064 | 1: Coherence is a symmetrical relation between two propositions [Thagard, by Smart] |
Full Idea: 1: Coherence and incoherence are symmetrical between pairs of propositions. | |
From: report of Paul Thagard (Explanatory Coherence [1989], 1) by J.J.C. Smart - Explanation - Opening Address p.04 |
17065 | 2: An explanation must wholly cohere internally, and with the new fact [Thagard, by Smart] |
Full Idea: 2: If a set of propositions explains a further proposition, then each proposition in the set coheres with that proposition, and propositions in the set cohere pairwise with one another. | |
From: report of Paul Thagard (Explanatory Coherence [1989], 2) by J.J.C. Smart - Explanation - Opening Address p.04 |
17066 | 3: If an analogous pair explain another analogous pair, then they all cohere [Thagard, by Smart] |
Full Idea: 3: If two analogous propositions separately explain different ones of a further pair of analogous propositions, then the first pair cohere with one another, and so do the second (explananda) pair. | |
From: report of Paul Thagard (Explanatory Coherence [1989], 3) by J.J.C. Smart - Explanation - Opening Address p.04 |
17067 | 4: For coherence, observation reports have a degree of intrinsic acceptability [Thagard, by Smart] |
Full Idea: 4: Observation reports (for coherence) have a degree of acceptability on their own. | |
From: report of Paul Thagard (Explanatory Coherence [1989], 4) by J.J.C. Smart - Explanation - Opening Address p.04 | |
A reaction: Thagard makes this an axiom, but Smart rejects that and says there is no reason why observation reports should not also be accepted because of their coherence (with our views about our senses etc.). I agree with Smart. |
17068 | 5: Contradictory propositions incohere [Thagard, by Smart] |
Full Idea: 5: Contradictory propositions incohere. | |
From: report of Paul Thagard (Explanatory Coherence [1989], 5) by J.J.C. Smart - Explanation - Opening Address p.04 | |
A reaction: This has to be a minimal axiom for coherence, but coherence is always taken to be more than mere logical consistency. Mutual relevance is the first step. At least there must be no category mistakes. |
17069 | 6: A proposition's acceptability depends on its coherence with a system [Thagard, by Smart] |
Full Idea: 6: Acceptability of a proposition in a system depends on its coherence with the propositions in that system. | |
From: report of Paul Thagard (Explanatory Coherence [1989], 6) by J.J.C. Smart - Explanation - Opening Address p.04 | |
A reaction: Thagard tried to build an AI system for coherent explanations, but I would say he has no chance with these six axioms, because they never grasp the nettle of what 'coherence' means. You first need rules for how things relate. What things are comparable? |
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'). |