19 ideas
| 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. |
| 22227 | For Sartre there is only being for-itself, or being in-itself (which is beyond experience) [Sartre, by Daigle] |
| Full Idea: The two most fundamental modes of being in Sartre's ontology are being in-itself, and being for-itself. ...The in-itself lies beyond our experience of it. | |
| From: report of Jean-Paul Sartre (Being and Nothingness [1943]) by Christine Daigle - Jean-Paul Sartre 2.2 | |
| A reaction: This appears to be Kant's ding-an-sich, paired with Heidegger's Dasein. If those are the only options, then reality is either subjective or unknown, which seems to make Sartre an idealist, but he asserted that phenomena vindicate the in-itself. |
| 20743 | Appearances do not hide the essence; appearances are the essence [Sartre] |
| Full Idea: We reject the dualism of appearance and essence. The appearance does not hide the essence, it reveals it; it is the essence. | |
| From: Jean-Paul Sartre (Being and Nothingness [1943], p.4-5), quoted by Kevin Aho - Existentialism: an introduction 2 'Phenomenology' | |
| A reaction: This idea, expressed in the language of Hegel and Husserl, strikes me as the same as the analytic phenomenalism of Mill and Ayer. Hence I take it to be wrong. |
| 6151 | Sartre says consciousness is just directedness towards external objects [Sartre, by Rowlands] |
| Full Idea: Sartre defends a view of consciousness as nothing but a directedness towards objects, insisting that these objects are transcendent with respect to that consciousness; hence Sartre is one of the first genuine externalists. | |
| From: report of Jean-Paul Sartre (Being and Nothingness [1943]) by Mark Rowlands - Externalism Ch.1 | |
| A reaction: An ancestor here is, I think, Schopenhauer (Idea 4166). The idea is attractive, as we are brought up with idea that we have a thing called 'consciousness', but if you removed its contents there would literally be nothing left. |
| 6164 | Sartre rejects mental content, and the idea that the mind has hidden inner features [Sartre, by Rowlands] |
| Full Idea: Sartre's attack on the idea that consciousness has contents is an attack on the idea that the mental possesses features that are hidden, inner and constituted or revealed by the individual's inwardly directed awareness. | |
| From: report of Jean-Paul Sartre (Being and Nothingness [1943]) by Mark Rowlands - Externalism Ch.5 | |
| A reaction: This is part of the move towards 'externalism' about the mind. The notion of 'content' implies a container. It seems slightly ridiculous, though, to try to say that the mind just 'is the world'. How is reasoning possible, and the relation of ideas? |
| 7074 | Man is a useless passion [Sartre] |
| Full Idea: Man is a useless passion. | |
| From: Jean-Paul Sartre (Being and Nothingness [1943], IV.2.III) | |
| A reaction: Memorable and neat. Since all of existence is ultimately 'useless', that part of it is not a revelation. The notion that we are essentially a 'passion' chimes nicely with David Hume's view, against the enlightenment rational view, and against Aristotle. |
| 6687 | Man is the desire to be God [Sartre] |
| Full Idea: Man fundamentally is the desire to be God. | |
| From: Jean-Paul Sartre (Being and Nothingness [1943], p.556?), quoted by Gordon Graham - Eight Theories of Ethics Ch.5 | |
| A reaction: It is better to see man (as seen all the way through the European tradition) as caught between the self-images of being an angel and being a 'quintessence of dust' (Hamlet). |
| 22228 | Sartre's freedom is not for whimsical action, but taking responsibility for our own values [Sartre, by Daigle] |
| Full Idea: Readers often confuse Sartre's notion of freedom with the freedom of acting whimsically ....but since there is no God, we must create our own values. Freedom is not merely a licence to act whimsically.; it entails responsibility. | |
| From: report of Jean-Paul Sartre (Being and Nothingness [1943]) by Christine Daigle - Jean-Paul Sartre 2.3 | |
| A reaction: The idea that we create our values comes from Nietzsche. Did Sartre want everyone to behave like an übermensch? How can you form a society from individuals who create private values, even if they (somehow) take responsibility for them? |
| 22233 | Love is the demand to be loved [Sartre] |
| Full Idea: Love is the demand to be loved. | |
| From: Jean-Paul Sartre (Being and Nothingness [1943], p.488), quoted by Christine Daigle - Jean-Paul Sartre 2.5 | |
| A reaction: Is that all love is? Hard to imagine someone loving another person without hoping that the other person will reciprocate. You need high self-esteem to 'demand' it. Low self-esteem merely hopes for it. He says the other person may feel the same. |
| 7453 | Galen's medicine followed the mean; each illness was balanced by opposite treatment [Galen, by Hacking] |
| Full Idea: Galen ran medicine on the principle of the mean; afflictions must be treated by contraries; hot diseases deserve cold medicine and moist illnesses want drying agents. (Paracelsus rebelled, treating through similarity). | |
| From: report of Galen (On Medical Experience [c.169]) by Ian Hacking - The Emergence of Probability Ch.5 | |
| A reaction: This must be inherited from Aristotle, with the aim of virtue for the body, as Aristotle wanted virtue for the psuché. In some areas Galen is probably right, that natural balance is the aim, as in bodily temperature control. |
| 20755 | Fear concerns the world, but 'anguish' comes from confronting my self [Sartre] |
| Full Idea: Anguish is distinguished from fear in that fear is fear of being in the world whereas anguish is anguish before myself. | |
| From: Jean-Paul Sartre (Being and Nothingness [1943], p.65), quoted by Kevin Aho - Existentialism: an introduction 5 'Radical' | |
| A reaction: I'm guessing that the anguish comes from the horror of the infinite choices available to me. Once you've made major life choices with full commitment (such as marriage), does that mean that existentialism becomes irrelevant? |
| 20760 | Sincerity is not authenticity, because it only commits to one particular identity [Sartre, by Aho] |
| Full Idea: Being sincere [in Sartre] has nothing to do with authenticity because, in committing ourselves to a particular identity, we strip away the possibility of transcendence by reducing ourselves to a thing. | |
| From: report of Jean-Paul Sartre (Being and Nothingness [1943]) by Kevin Aho - Existentialism: an introduction 6 'Bad' | |
| A reaction: I take this to mean that sincerity says genuinely what role you are playing (such as a waiter), but authenticity is recognition that you don't have to play that role. I think. |
| 22231 | We flee from the anguish of freedom by seeing ourselves objectively, as determined [Sartre] |
| Full Idea: We are always ready to take refuge in a belief in determinism if this freedom weighs upon us or if we need an excuse. Thus we flee from anguish by attempting to apprehend ourselves from without as an Other or a thing. | |
| From: Jean-Paul Sartre (Being and Nothingness [1943], p.82), quoted by Christine Daigle - Jean-Paul Sartre 2.4 | |
| A reaction: I would have thought we blame social pressures, or biological pressures, rather than metaphysical determinism, but it amounts to the same thing. If we are not free then probably nothing else is. |