11 ideas
| 2661 | Dialectic is speech cast in the form of logical argument [Cicero] |
| Full Idea: Dialectic is speech cast in the form of logical argument. | |
| From: M. Tullius Cicero (Academica [c.45 BCE], I.viii.32) |
| 2673 | There cannot be more than one truth [Cicero] |
| Full Idea: There cannot be more than one truth. | |
| From: M. Tullius Cicero (Academica [c.45 BCE], II.xlviii.147) |
| 2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
| Full Idea: It is a fundamental principle of dialectic that every statement is either true or false. So is this a true proposition or a false one: "If you say that you are lying and say it truly, you lie"? | |
| From: M. Tullius Cicero (Academica [c.45 BCE], II.xxix.95) |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 13230 | Particular essence is often captured by generality [Steiner,M] |
| Full Idea: Generality is often necessary for capturing the essence of a particular. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.36) | |
| A reaction: The most powerful features of an entity are probably those which are universal, like intelligence or physical strength in a human. Those characteristics are powerful because they compete with the same characteristic in others (perhaps?). |
| 2664 | If we have complete healthy senses, what more could the gods give us? [Cicero] |
| Full Idea: If human nature were interrogated by some god as to whether it was content with its own senses in a sound and undamaged state or demanded something better, I cannot see what more it could ask for. | |
| From: M. Tullius Cicero (Academica [c.45 BCE], II.vii.19) |
| 2665 | How can there be a memory of what is false? [Cicero] |
| Full Idea: How can there possibly be a memory of what is false? | |
| From: M. Tullius Cicero (Academica [c.45 BCE], II.vii.22) |
| 20800 | Every true presentation can have a false one of the same quality [Cicero] |
| Full Idea: [The sceptical Academics say] what is false cannot be perceived, but every true presentation is such that there can be a false presentation of the same quality. | |
| From: M. Tullius Cicero (Academica [c.45 BCE], II.40) | |
| A reaction: It was the stoics who focused the discussion on 'presentations'. This claim is purely theoretical; no one has ever experienced a false presentation of talking to a family member that was as vivid as the real thing. |
| 13229 | Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M] |
| Full Idea: Maybe to deduce a theorem as an instance of a generalization is more explanatory than to deduce it correctly. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.32) | |
| A reaction: Steiner eventually comes down against this proposal, on the grounds that some proofs are too general, and hence too far away from the thing they are meant to explain. |
| 13231 | Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M] |
| Full Idea: My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.34) | |
| A reaction: He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing. |
| 2672 | Virtues must be very detached, to avoid being motivated by pleasure [Cicero] |
| Full Idea: None of the virtues can exist unless they are disinterested, for virtue driven to duty by pleasure as a sort of pay is not virtue at all but a deceptive sham and pretence of virtue. | |
| From: M. Tullius Cicero (Academica [c.45 BCE], II.xlvi.140) |