11 ideas
| 24069 | Much metaphysical debate concerns what is fundamental, rather than what exists [Koslicki] |
| Full Idea: Some of the most important debates in metaphysics or ontology do not concern existential questions, but focus on questions of fundamentality. | |
| From: Kathrin Koslicki (Form, Matter and Substance [2018], 5 Intro) | |
| A reaction: In modern times we have added the structure of existence to the mere ontological catalogue, and this idea makes another important addition to our concept of metaphysics. She gives disagreement over tropes as an example. |
| 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. |
| 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. |
| 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. |
| 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? |
| 24065 | Structured wholes are united by the teamwork needed for their capacities [Koslicki] |
| Full Idea: A structured whole derives its unity from the way in which its parts interact with other parts to allow both the whole and its parts to manifest those of their capacities which require 'team work' among the parts. | |
| From: Kathrin Koslicki (Form, Matter and Substance [2018], Intro) | |
| A reaction: This is a culminating thesis of her book. She defends it at length. It looks like a nice theory for things which are lucky enough to have capacities involving teamwork. Does this mean a pebble can't be unified? She wants a dynamic view. |
| 24066 | The form explains kind, structure, unity and activity [Koslicki] |
| Full Idea: Hylomorphists tend to agree that the form (rather than matter) explains 1) kind membership, 2) structure, 3) unity, 4) characteristic activities. | |
| From: Kathrin Koslicki (Form, Matter and Substance [2018], 3.2.1) | |
| A reaction: [compressed; she explains each of them] Personally I would add continuity through change (statue/clay). Glad to see that kind membership is not part of the form. And what about explaining observed properties? Does form=essence? |
| 24067 | Hylomorphic compounds need an individual form for transworld identity [Koslicki] |
| Full Idea: It is difficult to see how forms could serve as cross-world identity principles for hylomorphic compounds, unless these forms are particular or individual entities. | |
| From: Kathrin Koslicki (Form, Matter and Substance [2018], 3.4.3) | |
| A reaction: This is a key part of her objection to treating the form as universal or generic. I agree with her view. |
| 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). |