display all the ideas for this combination of texts
7 ideas
| 10206 | Modal operators are usually treated as quantifiers [Shapiro] |
| Full Idea: It is common now, and throughout the history of philosophy, to interpret modal operators as quantifiers. This is an analysis of modality in terms of ontology. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) |
| 19033 | Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter] |
| Full Idea: Deontic modality can be divided into sentence-modifying 'ought-to-be' modals, and predicate-modifying 'ought-to-do' modals. | |
| From: Barbara Vetter (Potentiality [2015], 6.9.2) | |
| A reaction: [She cites Brennan 1993] These two seem to correspond to what is 'good' (ought to be), and what is 'right' (ought to do). Since I like that distinction, I also like this one. |
| 19032 | S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter] |
| Full Idea: Wedgwood (2007:220) argues that S5 is undesirable because it excludes that necessary truths may have contingent grounds. | |
| From: Barbara Vetter (Potentiality [2015], 6.4 n5) | |
| A reaction: Cameron defends the possibility of necessity grounded in contingency, against Blackburn's denial of it. It's interesting that we choose the logic on the basis of the metaphysics. Shouldn't there be internal reasons for a logic's correctness? |
| 19036 | The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter] |
| Full Idea: Subscribers to the Barcan formula must either be committed to the existence of mere possibilia (such as possible unicorns), or deny many unactualised possibilities of existence. | |
| From: Barbara Vetter (Potentiality [2015], 7.5) | |
| A reaction: It increasingly strikes me that the implications of the Barcan formula are ridiculous. Williamson is its champion, but I'm blowed if I can see why. What could a possible unicorn be like? Without them, must we say unicorns are impossible? |
| 10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
| Full Idea: One version of the Axiom of Choice says that for every set A of nonempty sets, there is a function whose domain is A and whose value, for every a ∈ A, is a member of a. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 1) |
| 10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
| Full Idea: If the Axiom of Choice says we can choose one member from each of a set of non-empty sets and put the chosen elements together in a set, this licenses the constructor to do an infinite amount of choosing. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.3) | |
| A reaction: This is one reason why the Axiom was originally controversial, and still is for many philosophers. |
| 10207 | Anti-realists reject set theory [Shapiro] |
| Full Idea: Anti-realists reject set theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: That is, anti-realists about mathematical objects. I would have thought that one could accept an account of sets as (say) fictions, which provided interesting models of mathematics etc. |