12 ideas
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
Full Idea: How are we to determine which of the sentences containing a term comprise its definition? | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2) | |
A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't? |
8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified. |
9342 | Understanding needs a priori commitment [Horwich] |
Full Idea: Understanding is itself based on a priori commitment. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional. |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it. |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge. |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9) | |
A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate. |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11) | |
A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away. |
22474 | Unlike aesthetic evaluation, moral evaluation needs a concept of responsibility [Foot] |
Full Idea: Moral, as opposed to aesthetic, evaluation does require some distinction between actions for which we are responsible and those for which we are not responsible. | |
From: Philippa Foot (Nietzsche's Immoralism [1991], p.154) | |
A reaction: It is hard to disagree with this, but difficult to give a precise account of responsibility, probably because it is not an all-or-nothing matter. If we accept responsibility for our controlled actions, why not for our considered aesthetic judgements? |
22472 | The practice of justice may well need a recognition of human equality [Foot] |
Full Idea: I wonder whether the practice of justice may not absolutely require a certain recognition of equality between human beings, not a pretence of the equality of talents, but something deeper. | |
From: Philippa Foot (Nietzsche's Immoralism [1991], p.152) | |
A reaction: {My 'something deeper' is expressed by Foot in a quotation from Gertrude Stein]. This may well be the most fundamental division which runs across a society - between those who accept and those reject human equality. |