23 ideas
| 14255 | We understand things through their dependency relations [Fine,K] |
| Full Idea: We understand a defined object (what it is) through the objects on which it depends. | |
| From: Kit Fine (Ontological Dependence [1995], II) | |
| A reaction: This places dependency relations right at the heart of our understanding of the world, and hence shifts traditional metaphysics away from existence and identity. The notion of explanation is missing from Fine's account. |
| 14250 | Metaphysics deals with the existence of things and with the nature of things [Fine,K] |
| Full Idea: Metaphysics has two main areas of concern: one is with the nature of things, with what they are; and the other is with the existence of things, with whether they are. | |
| From: Kit Fine (Ontological Dependence [1995], I) | |
| A reaction: This paper is part of a movement which has shifted metaphysics to a third target - how things relate to one another. The possibility that this third aim should be the main one seems quite plausible to me. |
| 14259 | Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K] |
| Full Idea: In Wooster as the witless bachelor and Jeeves as the crafty manservant, and one valet to the other, we will have the counterpart, within the framework of real definition, to the simultaneous definition of two terms. | |
| From: Kit Fine (Ontological Dependence [1995], III) | |
| A reaction: This is wonderful grist to the mill of scientific essentialism, which endeavours to produce an understanding through explanation of the complex interactions of nature. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 14253 | An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K] |
| Full Idea: It seems wrong to identify the 'being' of an object, its being what it is, with its existence. In one respect existence is too weak; for there is more to an object than mere existence; also too strong, for an object's nature need not include existence. | |
| From: Kit Fine (Ontological Dependence [1995], I) | |
| A reaction: The word 'being' has been shockingly woolly, from Parmenides to Heidegger, but if you identify it with a thing's 'nature' that strikes me as much clearer (even if a little misty). |
| 14261 | There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K] |
| Full Idea: An object 'weakly' depends upon another if it is ineliminably involved in one of its definitions; and it 'strongly' depends upon the other if it is ineliminably involved in all of its definitions. | |
| From: Kit Fine (Ontological Dependence [1995], III) | |
| A reaction: It is important to remember that a definition can be very long, and not just what might go into a dictionary. |
| 14251 | A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K] |
| Full Idea: A natural account of dependence in terms of modality and existence is that one thing x will depend on another thing y just in case it is necessary that y exists if x exists (or in the symbolism of modal logic, □(Ex→Ey). | |
| From: Kit Fine (Ontological Dependence [1995], I) | |
| A reaction: He is going to criticise this view (which he traces back to Aristotle and Husserl). It immediately seems possible that there might be counterexamples. x might depend on y, but not necessarily depend on y. Necessities may not produce dependence. |
| 14257 | An object depends on another if the second cannot be eliminated from the first's definition [Fine,K] |
| Full Idea: The objects upon which a given object depends, according to the present account, are those which must figure in any of the logically equivalent definitions of the object. They will, in a sense, be ineliminable. | |
| From: Kit Fine (Ontological Dependence [1995], II) | |
| A reaction: This is Fine's main proposal for the dependency relationship, with a context of Aristotelian essences understood as definitions. Sounds pretty good to me. |
| 14254 | Dependency is the real counterpart of one term defining another [Fine,K] |
| Full Idea: The notion of one object depending upon another is the real counterpart to the nominal notion of one term being definable in terms of another. | |
| From: Kit Fine (Ontological Dependence [1995], II) | |
| A reaction: This begins to fill out the Aristotelian picture very nicely, since definitions are right at the centre of the nature of things (though a much more transitional part of the story than Fine seems to think). |
| 14252 | We should understand identity in terms of the propositions it renders true [Fine,K] |
| Full Idea: We should understand the identity or being of an object in terms of the propositions rendered true by its identity rather than the other way round. | |
| From: Kit Fine (Ontological Dependence [1995], I) | |
| A reaction: Behind this is an essentialist view of identity, rather than one connected with necessary properties. |
| 14256 | How do we distinguish basic from derived esssences? [Fine,K] |
| Full Idea: How and where are we to draw the line between what is basic to the essence and what is derived? | |
| From: Kit Fine (Ontological Dependence [1995], II) | |
| A reaction: He calls the basic essence 'constitutive' and the rest the 'consequential' essence. This question is obviously very challenging for the essentialist. See Idea 22. |
| 14258 | Maybe some things have essential relationships as well as essential properties [Fine,K] |
| Full Idea: It is natural to suppose, in the case of such objects as Wooster and Jeeves, that in addition to possessing constitutive essential properties they will also enter into constitutive essential relationships. | |
| From: Kit Fine (Ontological Dependence [1995], III) | |
| A reaction: I like this. If we are going to have scientific essences as structures of intrinsic powers, then the relationships between the parts of the essence must also be essential. That is the whole point - that the powers dictate the relationships. |
| 23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
| Full Idea: Individuals and objects have a real essence, or constitution of nature, from which all their qualities flow: but this essence our faculties do not comprehend. They are therefore incapable of definition. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: Aha - he's one of us! I prefer the phrase 'essential nature' of an object, which is understood, I think, by everyone. I especially like the last bit, directed at those who mistakenly think that Aristotle identified the essence with the definition. |
| 14260 | An object only essentially has a property if that property follows from every definition of the object [Fine,K] |
| Full Idea: We can say that an object essentially has a certain property if its having that property follows from every definition of the object, while an object will definitively have a given property if its having that property follows from some definition of it. | |
| From: Kit Fine (Ontological Dependence [1995], III) | |
| A reaction: Presumably that will be every accurate definition. This nicely allows for the fact that at least nominal definitions may not be unique, and there is even room for real definitions not to be fully determinate (thus, how far should they extend?). |
| 11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
| Full Idea: Reid pointed out how easily conceivable mathematical and geometric impossibilities are. | |
| From: report of Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], IV.III) by George Molnar - Powers 11.3 | |
| A reaction: The defence would be that you have to really really conceive them, and the only way the impossible can be conceived is by blurring it at the crucial point, or by claiming to conceive more than you actually can |
| 23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
| Full Idea: An individual is expressed by a proper name, or by a general word joined to distinguishing circumstances; if unknown, it may be pointed out to the senses; when beyond the reach of the senses it may be picked out by an imperfect but true description. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: [compressed] If Putnam, Kripke and Donnellan had read this paragraph they could have save themselves a lot of work! I take reference to be the activity of speakers and writers, and these are the main tools of the trade. |
| 23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |
| Full Idea: The meaning of a word (such as 'felony') is the thing conceived; and that meaning is the conception affixed to it by those who best understand the language. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: He means legal experts. This is precisely that same as Putnam's account of the meaning of 'elm tree'. His discussion here of reference is the earliest I have encountered, and it is good common sense (for which Reid is famous). |