30 ideas
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| Full Idea: Truth in a model is interesting because it provides a transparent and mathematically tractable model - in the 'ordinary' rather than formal sense of the term 'model' - of the less tractable notion of truth. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This is an important warning to those who wish to build their entire account of truth on Tarski's rigorously formal account of the term. Personally I think we should start by deciding whether 'true' can refer to the mental state of a dog. I say it can. |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| Full Idea: There is an enormous difference between the truth of sentences in the interpreted language of set theory and truth in some model for the disinterpreted skeleton of that language. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.132) | |
| A reaction: This is a warning to me, because I thought truth and semantics only entered theories at the stage of 'interpretation'. I must go back and get the hang of 'skeletal' truth, which sounds rather charming. [He refers to set theory, not to logic.] |
| 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. |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature. |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) |
| 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. |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages. |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| Full Idea: I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic? |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| Full Idea: Arithmetic should be able to face boldly the dreadful chance that in the actual world there are only finitely many objects. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.148) | |
| A reaction: This seems to be a basic requirement for any account of arithmetic, but it was famously a difficulty for early logicism, evaded by making the existence of an infinity of objects into an axiom of the system. |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| Full Idea: The mathematical object-theorist says a number is an object that represents a cardinality quantifier, with the representation relation as the entire essence of the nature of such objects as cardinal numbers like 4. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: [compressed] This a classic case of a theory beginning to look dubious once you spell it our precisely. The obvious thought is to make do with the numerical quantifiers, and dispense with the objects. Do other quantifiers need objects to support them? |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| Full Idea: The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142) | |
| A reaction: Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers? |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| Full Idea: Talk about mirror images is a sort of fictional discourse. Statements 'about' such fictions are not made true or false by our whims; rather they 'encode' facts about the things reflected in mirrors. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.146) | |
| A reaction: Hodes's proposal for how we should view abstract objects (c.f. Frege and Dummett on 'the equator'). The facts involved are concrete, but Hodes is offering 'encoding fictionalism' as a linguistic account of such abstractions. He applies it to numbers. |
| 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) |
| 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). |
| 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) |
| 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) |