17 ideas
| 23881 | All thought about values is philosophical, and thought about anything else is not philosophy [Weil] |
| Full Idea: All reflections bearing on the notion of value and on the hierarchy of values is philosophical; all efforts of thought bearing on anything other than value are, if one examines them closely, foreign to philosophy. | |
| From: Simone Weil (Reflections on Value [1941], p.30) | |
| A reaction: If nothing else proves that Weil is a platonist, this does. She, of course, has a transcendent and religious view of values, whereas I just see them as concepts which embody what is important. That said, I'm not far off agreeing with this. |
| 23885 | Philosophy aims to change the soul, not to accumulate knowledge [Weil] |
| Full Idea: Philosophy does not consist in accumulating knowledge, as science does, but in changing the whole soul. | |
| From: Simone Weil (Reflections on Value [1941], p.33) | |
| A reaction: I agree, roughly. In the sense that philosophy is a much more personal matter than any pure pursuit of knowledge, such as geology. Though a life in geology could change your soul. Not just any old change, of course…. |
| 23886 | Systems are not unique to each philosopher. The platonist tradition is old and continuous [Weil] |
| Full Idea: People believe that every philosopher has a system that contradicts all the others! But there is a tradition, genuinely philosophical, that is as old as humanity itself. …Plato is the most perfect representative of this tradition. | |
| From: Simone Weil (Reflections on Value [1941], p.33) | |
| A reaction: I see roughly two traditions. If you believe in transcendence you follow Plato, like Simone. If you are a naturalist (like me) you follow Aristotle. A third tradition might be much more sceptical. |
| 23884 | Truth is a value of thought [Weil] |
| Full Idea: Truth is a value of thought. The word 'truth' cannot have any other meaning. | |
| From: Simone Weil (Reflections on Value [1941], p.32) | |
| A reaction: This makes a nice change from truth being a mere predicate. I would call truth the criterion of success in thought, and that counts as a value, so she is right. |
| 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. |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 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. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 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. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 23882 | Ends, unlike means, cannot be defined, which is why people tend to pursue means [Weil] |
| Full Idea: Everything that can be taken as an end cannot be defined. Means, such as power and money, are easily defined, and that is why people orient themselves exclusively towards the acquisition of means. | |
| From: Simone Weil (Reflections on Value [1941], p.31) | |
| A reaction: Nice, but too neat, because so many activities can be treated either as means or as ends, and often as both. It makes sense that people pursue what is clear to them. |
| 23883 | Minds essentially and always strive towards value [Weil] |
| Full Idea: For the mind essentially and always, in whatever manner it is disposed, strives towards value. | |
| From: Simone Weil (Reflections on Value [1941], p.31) | |
| A reaction: A typically platonist thought. If you accept my view that values identify what is important, the thought is plausible. We might distinguish between what the mind pointlessly entertains, and what it 'strives' for. |