17 ideas
| 21855 | Only in the 1780s did it become acceptable to read Spinoza [Lord] |
| Full Idea: It was not until the 1780s that it became acceptable to read the works of Spinoza, and even then it was not without a frisson of danger. | |
| From: Beth Lord (Spinoza's Ethics [2010], Intro 'Who?') | |
| A reaction: Hence we hear of Wordsworth and Coleridge reading him with excitement. So did Kant read him? |
| 4424 | A warlike philosopher challenges problems to single combat [Nietzsche] |
| Full Idea: A warlike philosopher challenges problems to single combat. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Wise §7) | |
| A reaction: And what do pacifist philosophers do? It is a moot point whether philosophy is even possible without a streak of aggression. Otherwise you circle the problem, but don't confront it. |
| 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. |
| 21866 | Hobbes and Spinoza use 'conatus' to denote all endeavour for advantage in nature [Lord] |
| Full Idea: 'Conatus' [translated as 'striving' by Curley] is used by early modern philosophers, including Thomas Hobbes (a major influence of Spinoza), to express the notion of a thing's endeavour for what is advantageous to it. It drives all things in nature. | |
| From: Beth Lord (Spinoza's Ethics [2010], p.88) | |
| A reaction: I think it is important to connect conatus to Nietzsche's talk of a plurality of 'drives', which are an expression of the universal will to power (which is seen even in the interactions of chemistry). Conatus is also in Leibniz. |
| 2886 | The distinction between egoistic and non-egoistic acts is absurd [Nietzsche] |
| Full Idea: There are neither egoistic nor unegoistic actions: both concepts are psychologically nonsense. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], 4.5) | |
| A reaction: Not quite true, but I like this observation. The idea that you could divide everyone's actions into these two groups is certainly nonsense. But some people are more altruistic than others! |
| 4426 | A bad result distorts one's judgement about the virtue of what one has done [Nietzsche] |
| Full Idea: I should prefer to exclude the bad result, the consequences, from the question of value as a matter of principle. Faced with a bad result, one loses all too easily the right perspective for what one has done. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Clever §1) | |
| A reaction: If the perspective is easily lost, we should make more effort, not ignore consequences. The question is whether you could have foreseen or controlled the consequences. |
| 4425 | The overcoming of pity I count among the noble virtues [Nietzsche] |
| Full Idea: The overcoming of pity I count among the noble virtues. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Wise §4) | |
| A reaction: Hm. I can just about see that there might be more important things than compassion for suffering, but I can't see any human activity that makes it worthwhile to trample on pity. |
| 20132 | To become what you are you must have no self-awareness [Nietzsche] |
| Full Idea: To become what one is, one must not have the faintest notion of what one is. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], II.9), quoted by Brian Leiter - Nietzsche On Morality 3 'fatalism' | |
| A reaction: [Don't understand 'II.9'] Enigmatic but striking. As I understand it, Nietzsche thought that knowing what you are is virtually impossible, though he spent a lifetime studying himself. Would you recognise someone who had become what they are? |
| 20144 | Eternal recurrence is the highest attainable affirmation [Nietzsche] |
| Full Idea: Eternal recurrence is the highest formula of affirmation that is at all attainable. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], III.Z-1?), quoted by Brian Leiter - Nietzsche On Morality | |
| A reaction: Did Nietzsche have in mind an even higher formulation that was unattainable? The aim of eternal recurrence is to offer the highest possible ideal that remains rooted in the nature of ordinary life. It is a cut-down version of the Form of the Good. |
| 2889 | One repays a teacher badly if one remains only a pupil [Nietzsche] |
| Full Idea: One repays a teacher badly if one remains only a pupil. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Fore) |
| 2887 | I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche] |
| Full Idea: I have absolutely no knowledge of atheism as an outcome of reasoning, still less an event: with me it is obvious by instinct. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], 3.1) |