11 ideas
| 7910 | Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha] |
| Full Idea: As though your turban or your clothes were on fire, so with a sense of urgency should you apply your intellect to the comprehension of the truths. | |
| From: Ashvaghosha (Saundaranandakavya [c.50], XVI) | |
| A reaction: The best philosophers need no such urging. I retain a romantic view that we should be 'natural' in these things. See Plato's views in Idea 2153 and 1638. However, maybe I should be confronted with this quotation every morning when I awake. |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 6900 | A prior understanding of beauty is needed to assert that the Form of the Beautiful is beautiful [Westaway] |
| Full Idea: If it were asserted that the Form of the Beautiful was itself beautiful, such a statement would require a prior understanding of the concept of beauty, so would immediately lead to an infinite regress, so the Forms can't be self-predicating. | |
| From: Luke Westaway (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: This is a nice clear statement of the mess that Plato gets himself into if he wants the Forms to be self-predicating. Clearly the Form of the Beautiful can't be beautiful, but must be that which gives other things their beauty. |
| 6956 | At what point does an object become 'whole'? [Westaway] |
| Full Idea: At what point does an object become 'whole'? | |
| From: Luke Westaway (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: This nice question strikes me as the central one in mereology. It is tempting to reply that the matter is entirely conventional, but there seems an obvious fact about something missing if one piece is absent from a jigsaw, or a cube is chipped. |
| 7335 | The Chinese Room should be able to ask itself questions in Mandarin [Westaway] |
| Full Idea: If the Chinese Room is functionally equivalent to a Mandarin speaker, it ought to be able to ask itself questions in Mandarin (and it can't). | |
| From: Luke Westaway (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: Searle might triumphantly say that this proves there is no understanding in the room, but the objection won't go away, because the room is presumably functionally equivalent to a speaker, and not just a mere translator (who might use mechanical tricks). |
| 7909 | The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha] |
| Full Idea: The Eightfold Path has three steps concerning morality - right speech, right bodily action, and right livelihood; three of wisdom - right views, right intentions, and right effort; and two of tranquillity - right mindfulness and right concentration. | |
| From: Ashvaghosha (Saundaranandakavya [c.50], XVI) | |
| A reaction: Most of this translates quite comfortably into the aspirations of western philosophy. For example, 'right effort' sounds like Kant's claim that only a good will is truly good (Idea 3710). The Buddhist division is interesting for action theory. |
| 7908 | At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha] |
| Full Idea: When an accomplished saint comes to the end, he does not go anywhere down in the earth or up in the sky, nor into any of the directions of space, but because his defilements have become extinct he simply ceases to be disturbed. | |
| From: Ashvaghosha (Saundaranandakavya [c.50], XVI) | |
| A reaction: To 'cease to be disturbed' is the most attractive account of heaven I have encountered. It all sounds a bit dull though. I wonder, as usual, how they know all this stuff. |