16 ideas
| 7914 | To try to be wise all on one's own is folly [Rochefoucauld] |
| Full Idea: To try to be wise all on one's own is sheer folly. | |
| From: La Rochefoucauld (Maxims [1663], 231) | |
| A reaction: I agree strongly with this. There are counter-examples, of whom Spinoza may be the greatest, and Nietzsche thought that philosophy was essentially a solitary business, but most of us are not Spinoza or Nietzsche. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics. | |
| From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2 | |
| A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases. |
| 7118 | La Rochefoucauld's idea of disguised self-love implies an unconscious mind [Rochefoucauld, by Sartre] |
| Full Idea: La Rochefoucauld is one of the first to have made use of the unconscious without naming it: for him, amour-propre conceals itself in the most diverse disguises. | |
| From: report of La Rochefoucauld (Maxims [1663]) by Jean-Paul Sartre - Transcendence of the Ego I (C) | |
| A reaction: It seems odd that no one before that ever thought that someone might have hidden motives of which even they themselves were unaware. How about Iago, or Macbeth, or Hamlet? It is a profound change in our view of human nature. |
| 7912 | Judging by effects, love looks more like hatred than friendship [Rochefoucauld] |
| Full Idea: If love be judged by its most visible effects it looks more like hatred than friendship. | |
| From: La Rochefoucauld (Maxims [1663], 072) | |
| A reaction: Presumably he is thinking of pursuit, possession and jealousy. The remark is plausible if you add the word 'sometimes' to it, but as a universal generalisation it is ridiculous, the product of a society where they competed to exceed in cynicism. |
| 7915 | Supreme cleverness is knowledge of the real value of things [Rochefoucauld] |
| Full Idea: Supreme cleverness is knowledge of the real value of things. | |
| From: La Rochefoucauld (Maxims [1663], 244) | |
| A reaction: Good. Right at the heart of wisdom is some kind of grasp of right values. It is so complex and subtle that it seems like pure intuition, but I am sure that reason is involved. 'Intelligent' people tend to be better at it. Some justifications can be given. |
| 7917 | Realising our future misery is a kind of happiness [Rochefoucauld] |
| Full Idea: To realise how much misery we have to face is in itself a kind of happiness. | |
| From: La Rochefoucauld (Maxims [1663], 570) | |
| A reaction: Probably true. Knowing that you have got hold of the truth is a sort of happiness in any area, no matter how grim the truth. However, a happy life could easily be poisoned by brooding on the future. Should the happily married brood on future solitude? |
| 7913 | Virtue doesn't go far without the support of vanity [Rochefoucauld] |
| Full Idea: Virtue would not go far without vanity to bear it company. | |
| From: La Rochefoucauld (Maxims [1663], 200) | |
| A reaction: Rochefoucauld's cynicism gets a bit tedious, but lovers of virtue must face up to this possibility when they consider what motivates them. At the heart of Aristotle there is a missing question, of what is so good about right-functioning and virtue. |
| 7916 | True friendship is even rarer than true love [Rochefoucauld] |
| Full Idea: Rare though true love may be, true friendship is rarer still. | |
| From: La Rochefoucauld (Maxims [1663], 473) | |
| A reaction: This seems to be true. Our culture doesn't encourage friendship as a high ideal. Are women better at friendship than men? Which culture, past or present, led to the greatest flourishing of friendship? Epicurus's Garden? |
| 9299 | We are bored by people to whom we ourselves are boring [Rochefoucauld] |
| Full Idea: Almost always we are bored by people to whom we ourselves are boring. | |
| From: La Rochefoucauld (Maxims [1663], 555) | |
| A reaction: An obvious exception would be a celebrity being bored with their fans. Their very excess of interest is precisely what is boring. If two people communicate well, it is unlikely that either of them will ever be bored. |