23 ideas
| 9944 | We understand some statements about all sets [Putnam] |
| Full Idea: We seem to understand some statements about all sets (e.g. 'for every set x and every set y, there is a set z which is the union of x and y'). | |
| From: Hilary Putnam (Mathematics without Foundations [1967], p.308) | |
| A reaction: His example is the Axiom of Choice. Presumably this is why the collection of all sets must be referred to as a 'class', since we can talk about it, but cannot define it. |
| 9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
| Full Idea: I do not believe mathematics either has or needs 'foundations'. | |
| From: Hilary Putnam (Mathematics without Foundations [1967]) | |
| A reaction: Agreed that mathematics can function well without foundations (given that the enterprise got started with no thought for such things), the ontology of the subject still strikes me as a major question, though maybe not for mathematicians. |
| 9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
| Full Idea: I believe that under certain circumstances revisions in the axioms of arithmetic, or even of the propositional calculus (e.g. the adoption of a modular logic as a way out of the difficulties in quantum mechanics), is fully conceivable. | |
| From: Hilary Putnam (Mathematics without Foundations [1967], p.303) | |
| A reaction: One can change the axioms of a system without necessarily changing the system (by swapping an axiom and a theorem). Especially if platonism is true, since the eternal objects reside calmly above our attempts to axiomatise them! |
| 9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
| Full Idea: Mathematics might be 'empirical' in the sense that one is allowed to try to put alternatives into the field. | |
| From: Hilary Putnam (Mathematics without Foundations [1967], p.303) | |
| A reaction: He admits that change is highly unlikely. It take hardcore Millian arithmetic to be only changeable if pebbles start behaving very differently with regard to their quantities, which appears to be almost inconceivable. |
| 9941 | Science requires more than consistency of mathematics [Putnam] |
| Full Idea: Science demands much more of a mathematical theory than that it should merely be consistent, as the example of the various alternative systems of geometry dramatizes. | |
| From: Hilary Putnam (Mathematics without Foundations [1967]) | |
| A reaction: Well said. I don't agree with Putnam's Indispensability claims, but if an apparent system of numbers or lines has no application to the world then I don't consider it to be mathematics. It is a new game, like chess. |
| 9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
| Full Idea: Surely the mere fact that we may never know whether the continuum hypothesis is true or false is by itself just no reason to think that it doesn't have a truth value! | |
| From: Hilary Putnam (Mathematics without Foundations [1967]) | |
| A reaction: This is Putnam in 1967. Things changed later. Personally I am with the younger man all they way, but I reserve the right to totally change my mind. |
| 3847 | Man is nothing else but the sum of his actions [Sartre] |
| Full Idea: Man is nothing else but the sum of his actions. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.41) | |
| A reaction: This might be plausible if unperformed actions are included. For some people, their whole life story consists of what they failed to do. |
| 3846 | Man IS freedom [Sartre] |
| Full Idea: There is no determinism - man is free, man IS freedom. …Man is condemned to be free. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.34) |
| 3843 | There is no human nature [Sartre] |
| Full Idea: There is no human nature. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.28) | |
| A reaction: Everything which can be individuated has a nature, say I, wearing my Aristotelian lapel badge. Does he think the same of cats? Does he think the mind is a blank page? |
| 20762 | There are no values to justify us, and no excuses [Sartre] |
| Full Idea: There are no values or commands to turn to which legitimize our conduct. …We are alone with no excuses. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.296), quoted by Kevin Aho - Existentialism: an introduction 6 'Bad' | |
| A reaction: If there are no values or duties, why might you ever need excuses? |
| 3852 | If values depend on us, freedom is the foundation of all values [Sartre] |
| Full Idea: Once a man has seen that values depend upon himself, he can only will one thing, and that is freedom as the foundation of all values. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.51) | |
| A reaction: I don't think so. Is freedom the foundation of all arithmetic, because I am untrammelled when doing addition? Values are ridiculous if they don't reflect facts. |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'. | |
| From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro | |
| A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it. |
| 20764 | In becoming what we want to be we create what we think man ought to be [Sartre] |
| Full Idea: In creating the man that we want to be, there is not a single one of our acts which does not at the same time create an image of man as we think he ought to be. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.293), quoted by Kevin Aho - Existentialism: an introduction 7 'Anything' | |
| A reaction: I recall this being one of my earliest thoughts about morality - that in everything we do we are all role models for the people around us. For me, that leads to virtue theory. |
| 3848 | Cowards are responsible for their cowardice [Sartre] |
| Full Idea: The existentialist, when he portrays a coward, shows him as responsible for his cowardice. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.42) |
| 20763 | When my personal freedom becomes involved, I must want freedom for everyone else [Sartre] |
| Full Idea: Freedom as the definition of man does not depend on others, but as soon as there is involvement, I am obliged to want others to have freedom at the same time that I want my own freedom. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.306), quoted by Kevin Aho - Existentialism: an introduction 7 'Anything' | |
| A reaction: Appears to be a highly Kantian sense of rational duty, and a rather odd constraint on someone whose only value is freedom. Sartre is aware that he needs an existential politics, but he's not there yet. 'Involvement' is an interesting addition to Kant. |
| 22229 | Existentialists says that cowards and heroes make themselves [Sartre] |
| Full Idea: What the existentialist says is that the coward makes himself cowardly, that the hero makes himself heroic. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.35), quoted by Christine Daigle - Jean-Paul Sartre 2.3 | |
| A reaction: A nice statement of the existential plasticity of the self, in opposition to the much stronger concept of human nature in Aristotle (who nevertheless believes you can acquire virtues and vices). |
| 3842 | Existence before essence (or begin with the subjective) [Sartre] |
| Full Idea: Existentialism says that existence comes before essence - or, if you will, that we must begin from the subjective. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.26) |
| 6868 | 'Existence precedes essence' means we have no pre-existing self, but create it through existence [Sartre, by Le Poidevin] |
| Full Idea: I take 'existence precedes essence' to mean that we do not have a pre-existing self, which organises our behaviour, but rather that we create our self as we go along, through our existence and activities. | |
| From: report of Jean-Paul Sartre (Existentialism and Humanism [1945]) by Robin Le Poidevin - Interview with Baggini and Stangroom p.222 | |
| A reaction: The direct opponent of this is Aristotle, who builds his ethics on a fairly fixed human nature, but even he agrees that we mould our moral characters through our activities, in a circular way. There are not, though, infinite possibilities in mankind. |
| 3844 | Existentialism says man is whatever he makes of himself [Sartre] |
| Full Idea: Man is nothing else but that which he makes of himself. This is the first principle of existentialism. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.28) |
| 20754 | It is dishonest to offer passions as an excuse [Sartre] |
| Full Idea: Every man who takes refuge behind the excuse of his passions is a dishonest man. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.305), quoted by Kevin Aho - Existentialism: an introduction 5 'Core' | |
| A reaction: To say 'my passion was so strong that I was too weak to resist it' doesn't sound prima facie dishonest. Sartre's idea is more of an exhortation than a fact, and sounds rather old fashioned and puritan. Do my reasons constitutes excuses? |
| 6571 | When a man must choose between his mother and the Resistance, no theory can help [Sartre, by Fogelin] |
| Full Idea: When a young man must choose between his bereft mother and the French Resistance, Sartre says no moral theory is capable of resolving the dilemma; the man must act on his own, and in the process define his moral character. | |
| From: report of Jean-Paul Sartre (Existentialism and Humanism [1945], p.35-9) by Robert Fogelin - Walking the Tightrope of Reason Ch.2 | |
| A reaction: Fogelin agrees, but rejects Sartre's claim that all morality is like this. I agree with Fogelin. However, what I like is the idea of 'defining one's moral character' by choices, but that is because it endorses the views of Aristotle (e.g. Idea 4394). |
| 3851 | If I do not choose, that is still a choice [Sartre] |
| Full Idea: If I do not choose, that is still a choice. | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.48) |
| 3845 | Without God there is no intelligibility or value [Sartre] |
| Full Idea: For the atheist existentialist there disappears with God all possibility of finding values in an intelligible heaven. (Dostoevsky wrote "If God did not exist, everything would be permitted"). | |
| From: Jean-Paul Sartre (Existentialism and Humanism [1945], p.33) |