15 ideas
| 6211 | Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes] |
| Full Idea: The passion of laughter is nothing else but sudden glory arising from some sudden conception of some eminency in ourselves, by comparison with the infirmity of others, or with our own formerly. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.IX.13) | |
| A reaction: Laughter tends to involve something unusual. We don't just burst out with a glory of vanity whenever we meet some inferiority in another person. |
| 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. |
| 15990 | Every individual thing which exists has an essence, which is its internal constitution [Locke] |
| Full Idea: I take essences to be in everything that internal constitution or frame for the modification of substance, which God in his wisdom gives to every particular creature, when he gives it a being; and such essences I grant there are in all things that exist. | |
| From: John Locke (Letters to Edward Stillingfleet [1695], Letter 1), quoted by Simon Blackburn - Quasi-Realism no Fictionalism | |
| A reaction: This is the clearest statement I have found of Locke's commitment to essences, for all his doubts about whether we can know such things. Alexander says (ch.13) Locke was reacting against scholastic essence, as pertaining to species. |
| 15994 | If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke] |
| Full Idea: What reaches to knowledge, I think may be called certainty; and what comes short of certainty, I think cannot be knowledge. | |
| From: John Locke (Letters to Edward Stillingfleet [1695], Letter 2), quoted by Simon Blackburn - Quasi-Realism no Fictionalism | |
| A reaction: I much prefer that fallibilist approach offered by the pragmatists. Knowledge is well-supported belief which seems (and is agreed) to be true, but there is a small shadow of doubt hanging over all of it. |
| 6213 | A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes] |
| Full Idea: The will is not voluntary: for a man can no more say he will will, than he will will will, and so make an infinite repetition of the word 'will', which is absurd and insignificant. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.XII.5) | |
| A reaction: A nice simple point, allied to Nietzsche's notion that thoughts are uncontrollable (Idea 2291). Even Aquinas, who is quite a fan of free will, spotted the problem (Idea 1854). Personally I agree with Hobbes. Free will is a shibboleth. |
| 6208 | Conceptions and apparitions are just motion in some internal substance of the head [Hobbes] |
| Full Idea: Conceptions and apparitions are nothing really, but motion in some internal substance of the head. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.VII.1) | |
| A reaction: Note that he carefully covers both thought in concepts and thought in images, and also that he is not saying that thought is the substance, but that it is a 'motion'. This strikes me as an excellent word, and I think Hobbes is right. |
| 6209 | There is no absolute good, for even the goodness of God is goodness to us [Hobbes] |
| Full Idea: There is no such thing as absolute goodness, considered without relation: for even the goodness which we apprehend in God Almighty, is his goodness to us. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.VII.3) | |
| A reaction: Plato's view of goodness is much more absolute than that of religion, as he proposes the Good as the eternal underpinning of nature. I agree with Hobbes that if God is the source of goodness, that will prevent goodness from being truly absolute. |
| 6210 | Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes] |
| Full Idea: For an utmost end, in which the ancient philosophers have placed felicity, there is no such thing in this world, nor way to it: for while we live, we have desires, and desire presupposeth a further end. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.VII.6) | |
| A reaction: Kant's definition of happiness (Idea 1452) seems to be the underlying idea, and hence with the same implication (of impossibility). However, an alcoholic locked in a brewery would seem to have all that Hobbes requires for happiness. |
| 6212 | Lust involves pleasure, and also the sense of power in pleasing others [Hobbes] |
| Full Idea: Lust consists of two appetites together, to please, and to be pleased, and the delight men take in delighting is not sensual, but a pleasure or joy of the mind consisting in the imagination of the power they have so much to please. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.IX) | |
| A reaction: Hobbes would rather burst a blood-vessel than admit any altruism. If you take pleasure in pleasing someone else, why can't that simply be because of the other person's pleasure, with which we sympathise, rather than relishing our own 'power'? |