14 ideas
13917 | Metaphysics aims to identify categories of being, and show their interdependency [Lowe] |
Full Idea: The central task of metaphysics is to chart the possibilities of existence by identifying the categories of being and the relations of ontological dependency in which beings of different categories stand to one another. | |
From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], Intro) | |
A reaction: I am beginning to think that he is right about the second one, and that dependency and grounding relations are the name of the game. I don't have Lowe's confidence that philosophers can parcel up reality in neat and true ways. |
13919 | Philosophy aims not at the 'analysis of concepts', but at understanding the essences of things [Lowe] |
Full Idea: The central task of philosophy is the cultivation of insights into natures or essences, and not the 'analysis of concepts', with which it is apt to be confused. | |
From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 1) | |
A reaction: This immediately strikes me as a false dichotomy. I like the idea of trying to understand the true natures of things, but how are we going to do it in our armchairs? |
9915 | V = L just says all sets are constructible [Putnam] |
Full Idea: V = L just says all sets are constructible. L is the class of all constructible sets, and V is the universe of all sets. | |
From: Hilary Putnam (Models and Reality [1977], p.425) |
13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
Full Idea: Putnam claims that the Löwenheim-Skolem theorems indicate that there is no 'fact of the matter' whether all sets are constructible. | |
From: report of Hilary Putnam (Models and Reality [1977]) by Stewart Shapiro - Foundations without Foundationalism | |
A reaction: [He refers to the 4th and 5th pages of Putnam's article] Shapiro offers (p.109) a critique of Putnam's proposal. |
9913 | The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam] |
Full Idea: The Löwenheim-Skolem Theorem says that a satisfiable first-order theory (in a countable language) has a countable model. ..I argue that this is not a logical antinomy, but close to one in philosophy of language. | |
From: Hilary Putnam (Models and Reality [1977], p.421) | |
A reaction: See the rest of this paper for where he takes us on this. |
9914 | It is unfashionable, but most mathematical intuitions come from nature [Putnam] |
Full Idea: Experience with nature is undoubtedly the source of our most basic 'mathematical intuitions', even if it is unfashionable to say so. | |
From: Hilary Putnam (Models and Reality [1977], p.424) | |
A reaction: Correct. I find it quite bewildering how Frege has managed to so discredit all empirical and psychological approaches to mathematics that it has become a heresy to say such things. |
10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
13918 | Holes, shadows and spots of light can coincide without being identical [Lowe] |
Full Idea: Holes are things of such a kind that they can coincide without being identical - as are, for example, shadows and spots of light. | |
From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 1) | |
A reaction: His point is that they thereby fail one of the standard tests for being an 'object'. |
13921 | All things must have an essence (a 'what it is'), or we would be unable to think about them [Lowe] |
Full Idea: Things must have an essence, in the sense of 'what it is to be the individual of that kind', or it would make no sense to say we can talk or think comprehendingly about things at all. If we don't know what it is, how can we think about it? | |
From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
A reaction: Lowe presents this as a sort of Master Argument for essences. I think he is working with the wrong notion of essence. All he means is that things must have identities to be objects of thought. Why equate identity with essence, and waste a good concept? |
13922 | Knowing an essence is just knowing what the thing is, not knowing some further thing [Lowe] |
Full Idea: To know something's essence is not to be acquainted with some further thing of a special kind, but simply to understand what exactly that thing is. | |
From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
A reaction: I think he is wrong about this, or at least is working with an unhelpful notion of essence. Identity is one thing, and essence is another. I take essences to be certain selected features of things, which explain their nature. |
13920 | Each thing has to be of a general kind, because it belongs to some category [Lowe] |
Full Idea: Any individual thing must be a thing of some general kind - because, at the very least, it must belong to some ontological category. | |
From: E.J. Lowe (Two Notions of Being: Entity and Essence [2008], 2) | |
A reaction: Where does the law that 'everything must have a category' come from? I'm baffled by remarks of this kind. Where do we get the categories from? From observing the individuals. So which has priority? Not the categories. Is God a kind? |