18 ideas
| 19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
| Full Idea: The devil is evil but nonetheless wise; he was a wise angel, and through no loss of knowledge, but, rather, through some sort of affective restructuring tried and failed to take over the throne. | |
| From: Dennis Whitcomb (Wisdom [2011], 'Argument') | |
| A reaction: ['affective restructuring' indeed! philosophers- don't you love 'em?] To fail at something you try to do suggests a flaw in the wisdom. And the new regime the devil wished to introduce doesn't look like a wise regime. Not convinced. |
| 1765 | Diogenes said avoidance of philosophy is the lack of a desire to live properly [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: When a man said that he was not suited to philosophy, Diogenes said to him, 'Why then do you live, if you have no desire to live properly.' | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: Meaning philosophy is already more practice than theory. |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| Full Idea: Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1) | |
| A reaction: This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results. |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| Full Idea: Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9) | |
| A reaction: As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful. |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| Full Idea: In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1) | |
| A reaction: This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns. |
| 6303 | Sets are positions in patterns [Resnik] |
| Full Idea: On my view, sets are positions in certain patterns. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5) | |
| A reaction: I have always found the ontology of a 'set' puzzling, because they seem to depend on prior reasons why something is a member of a given set, which cannot always be random. It is hard to explain sets without mentioning properties. |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| Full Idea: An objection is that structuralism fails to explain why certain mathematical patterns are unified wholes while others are not; for instance, some think that an ontological account of mathematics must explain why a triangle is not a 'random' set of points. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.4) | |
| A reaction: This is an indication that we are not just saying that we recognise patterns in nature, but that we also 'see' various underlying characteristics of the patterns. The obvious suggestion is that we see meta-patterns. |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| Full Idea: If we take mathematics at its word, there are too many mathematical objects for it to be plausible that they are all mental or physical objects. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: No one, of course, has ever claimed that they are, but this is a good starting point for assessing the ontology of mathematics. We are going to need 'rules', which can deduce the multitudinous mathematical objects from a small ontology. |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| Full Idea: I argue that mathematical knowledge has its roots in pattern recognition and representation, and that manipulating representations of patterns provides the connection between the mathematical proof and mathematical truth. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: The suggestion that patterns are at the basis of the ontology of mathematics is the most illuminating thought I have encountered in the area. It immediately opens up the possibility of maths being an entirely empirical subject. |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| Full Idea: Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3) | |
| A reaction: This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component? |
| 1762 | When someone denied motion, Diogenes got up and walked away [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes replied to one who asserted that there was no such thing as motion by getting up and walking away. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 7813 | Cynicism was open to anyone, and needed neither education nor sophistication [Diogenes of Sin., by Grayling] |
| Full Idea: An advantage of Cynicism was that it was open to anyone who could grasp its simple teachings. Understanding it required neither education nor sophistication. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: This was the source of the well-known opposition of Diogenes to Plato's Academy, and it makes him a key predecessor of the teachings of Jesus. Personally I think the really good life is difficult, and it needs education and careful rational thought. |
| 1763 | Diogenes said a plucked chicken fits Plato's definition of man [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Plato defined man as a two-footed featherless animal, so Diogenes plucked a cock and brought it into the school, and said, 'This is Plato's man'. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: You have to be very serious about your philosophy to enact your counterexamples, rather than just suggest them. Which university will actually reconstruct the Trolley Problem? |
| 5071 | The Cynics rejected what is conventional as irrational, and aimed to live by nature [Taylor,R on Diogenes of Sin.] |
| Full Idea: The Cynics were convinced of the purely conventional foundation of Athenian values, which meant they had no rational foundation at all. They therefore rejected them in favour of what is correct and worthwhile by nature. | |
| From: comment on Diogenes (Sin) (reports [c.360 BCE]) by Richard Taylor - Virtue Ethics: an Introduction Ch.8 | |
| A reaction: This shows how the Cynics are key players in the progress of the nomos-physis debate, which keeps resurfacing as relativism vs absolutism, cognitivism vs non-cognitivism, and even romanticism vs classicism. The trouble is, convention is natural! |
| 7812 | For peace of mind, you need self-government, indifference and independence [Diogenes of Sin.] |
| Full Idea: There are three essential conditions for peace of mind: autarchy, apathy and freedom. Autarchy is self-government and self-sufficiency; apathy is indifference to what the world can do to you; the freedom is from dependence and possessions. | |
| From: Diogenes (Sin) (reports [c.360 BCE]), quoted by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: Quite good advice, but I don't see 'peace of mind' as the highest human ideal. The basic suggestion here is live alone and do nothing. Certainly don't get married, or have children, or try to achieve anything. |
| 1764 | Diogenes said he was a citizen of the world [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said he was a citizen of no country, but of the world. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 5968 | Diogenes masturbated in public, wishing he could get rid of hunger so easily [Diogenes of Sin., by Plutarch] |
| Full Idea: Chrysippus praises Diogenes for saying to bystanders as he masturbated in public, "Would that I could thus rub the hunger too out of my belly". | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Plutarch - 70: Stoic Self-contradictions 1044b | |
| A reaction: So it is not quite true that people only need corn and water. Diogenes' remark doesn't explain why he did it in public. Was it to defy local convention (as befits a citizen of the world), or was it to teach? |
| 1766 | Diogenes said that the most excellent thing among men was freedom of speech [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said that the most excellent thing among men was freedom of speech. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |