34 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 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. |
| 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) |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 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) |