| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| Full Idea: Classes may be regarded as logical fictions, manufactured out of defining characteristics. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II n1) | |
| A reaction: I agree with this. The idea that in addition to the members there is a further object, the set containing them, is absurd. Sets are a tool for thinking about the world. |
| 9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
| Full Idea: Armstrong has difficulty explaining how laws entail regularities. There is no real modality in the basic components of the world, but he wants to support counterfactuals. His official position is a kind of fictionalism. | |
| From: comment on David M. Armstrong (A World of States of Affairs [1997], 49-51) by Alexander Bird - Nature's Metaphysics 4.4.4 | |
| A reaction: Armstrong seems to be up against the basic problems that laws won't explain anything if they are merely regularities (assuming they are not decrees of a supernatural force). |
| 8909 | Abstractions may well be verbal fictions, in which we ignore some features of an object [Lewis] |
| Full Idea: The inevitable hypothesis is that abstractions are verbal fictions. We say we are speaking about abstractions when we are speaking abstractly about the original thing. We are ignoring some features, not introducing a new thing lacking those features. | |
| From: David Lewis (On the Plurality of Worlds [1986], 1.7) | |
| A reaction: Thus Lewis ends up pretty close to Locke and the traditional view. This makes abstraction not a feat of platonic perception, in which magical non-material objects are spotted, but a feat of counterfactual imagination. |
| 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. |
| 8864 | We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo] |
| Full Idea: It is not that the contents of sentences are inexpressible without quantifying over events, worlds, etc. (they aren't). But the logical relations become much more tractable if we represent them quantificationally. | |
| From: Stephen Yablo (Apriority and Existence [2000], §13) | |
| A reaction: Yablo is explaining why we find ourselves committed to abstract objects. It is essentially, as I am beginning to suspect, a conspiracy of logicians. What on earth is 'the empty set' when it is at home? What's it made of? |
| 19494 | Fictionalism allows that simulated beliefs may be tracking real facts [Yablo] |
| Full Idea: The fictionalist offers the option that your simulated beliefs and assertions may be tracking a realm of genuine facts, or a realm of what you take to be facts. | |
| From: Stephen Yablo (Go Figure: a Path through Fictionalism [2001], 13) | |
| A reaction: This means that fictionalism does not have to be an error theory. That is, we aren't mistakenly believing something that we actually made up. Instead we are sensibly believing something we know to be not literally true. Love it. |
| 19489 | For me, fictions are internally true, without a significant internal or external truth-value [Yablo] |
| Full Idea: A 'myth' or fiction for me is a true internal statement (a statement endorsed by the rules) whose external truth value is as may be, the point being that that truth value is from an internal standpoint quite irrelevant. | |
| From: Stephen Yablo (Does Ontology Rest on a Mistake? [1998], IX) | |
| A reaction: This contrasts with Carnap, for whom talk of 'ghosts' is false in an internal thing-framework. Yablo seems here to say a statement can be true while having no truth value. Presumably he is relaxing the internal rules. |
| 19490 | Make-believe can help us to reason about facts and scientific procedures [Yablo] |
| Full Idea: Make-believe games can make it easier to reason about facts, to systematize them, to visualize them, to spot connections with other facts, and to evaluate potential lines of research. | |
| From: Stephen Yablo (Does Ontology Rest on a Mistake? [1998], XI) | |
| A reaction: This is the key pragmatic defence of the fictionalist view of abstract objects. Fictions are devices to help us think better. I think a lot of ontology turns out that way. |
| 19491 | 'The clouds are angry' can only mean '...if one were attributing emotions to clouds' [Yablo] |
| Full Idea: It is an open question whether the clouds that we call 'angry' are literally F, for any F other than 'such that it would be natural and proper to regard them as angry if one were going to attribute emotions to clouds'. | |
| From: Stephen Yablo (Does Ontology Rest on a Mistake? [1998], XII) | |
| A reaction: His point is that it is TRUE, in those circumstances, that the clouds are angry. Thus fictions are a valid and useful part of ordinary sensible course, giving real information. I like it. |
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| Full Idea: Fictionalism takes an epistemology of the concrete to be more promising than concrete-and-abstract, but fictionalism requires an epistemology of the actual and possible, secured without the benefits of model theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.2) | |
| A reaction: The idea that possibilities (logical, natural and metaphysical) should be understood as features of the concrete world has always struck me as appealing, so I have (unlike Shapiro) no intuitive problems with this proposal. |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| Full Idea: One result of the structuralist perspective is a healthy blurring of the distinction between mathematical and ordinary objects. ..'According to the structuralist, physical configurations often instantiate mathematical patterns'. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.4) | |
| A reaction: [The quotation is from Penelope Maddy 1988 p.28] This is probably the main reason why I found structuralism interesting, and began to investigate it. |
| 12445 | If fictional objects really don't exist, then they aren't abstract objects [Azzouni] |
| Full Idea: It's robustly part of common sense that fictional objects don't exist in any sense at all, and this means they aren't abstracta either. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.3) | |
| A reaction: Nice. It is so easy to have some philosopher dilute and equivocate over the word 'object' until you find yourself committed to all sorts of daft things as somehow having objectual existence. We can discuss things which don't exist in any way at all. |