12 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? |
| 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. |
| 4894 | I say Mary does not have new knowledge, but knows an old fact in a new way [Perry on Jackson] |
| Full Idea: I say Mary knows an old fact in a new way, but I do not find a new bit of knowledge and a new fact. | |
| From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.3 | |
| A reaction: This seems roughly the right way to attack Jackson's 'knowledge argument', by asking exactly what he means by 'knowledge'. It is hard to see how 'qualia' can be both the means of acquiring knowledge, and the thing itself. |
| 4895 | Is it unfair that physicalist knowledge can be written down, but dualist knowledge can't be [Perry on Jackson] |
| Full Idea: Jackson seems to imply that it isn't fair that all physicalist knowledge can be written down, but not all dualist knowledge can be. | |
| From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.5 | |
| A reaction: This pinpoints a problem for the 'Mary' example - that Mary's new sight of colour is claimed as 'knowledge', and yet the whole point is that it cannot be expressed in propositions (which seems to leave it as 'procedural' or 'acquaintance' knowledge). |
| 4886 | Mary knows all the physical facts of seeing red, but experiencing it is new knowledge [Jackson] |
| Full Idea: Mary knows all the physical facts. ..It seems, however, that Mary does not know all there is to know. For when she is let out of the black and white room .. she will learn what it is like to see something red. | |
| From: Frank Jackson (What Mary Didn't Know [1986], §1.4) | |
| A reaction: Jackson is begging the question. A new physical event occurs when the red wavelength stimulates Mary's visual cortex for the first time. For an empiricist raw experience creates knowledge, so it can't BE knowledge. Does Mary acquire a new concept? |
| 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. |