15 ideas
| 8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
| Full Idea: Chihara's programme is to replace talk of sets with talk of open sentences. Instead of speaking of the set of all cats, we talk about the open sentence 'x is a cat'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: As Shapiro points out, this is following up Russell's view that sets should be replaced with talk of properties. Chihara is expressing it more linguistically. I'm in favour of any attempt to get rid of sets. |
| 10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
| Full Idea: Chihara's system is a version of type theory. Translate thus: replace variables of sets of type n with level n variables over open sentences, replace membership/predication with satisfaction, and high quantifiers with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 |
| 8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
| Full Idea: Chihara's system is similar to simple type theory; he replaces each type with variables over open sentences, replaces membership (or predication) with satisfaction, and replaces quantifiers over level 1+ variables with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: This is interesting for showing that type theory may not be dead. The revival of supposedly dead theories is the bread-and-butter of modern philosophy. |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| Full Idea: Chihara has proposal a modal primitive, a 'constructability quantifier'. Syntactically it behaves like an ordinary quantifier: Φ is a formula, and x a variable. Then (Cx)Φ is a formula, read as 'it is possible to construct an x such that Φ'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: We only think natural numbers are infinite because we see no barrier to continuing to count, i.e. to construct new numbers. We accept reals when we know how to construct them. Etc. Sounds promising to me (though not to Shapiro). |
| 13083 | The essence is the necessary properties, and the concept includes what is contingent [Leibniz] |
| Full Idea: Of the essence of a particular thing is what pertains to it necessarily and perpetually; of the concept of an individual thing on the other hand is what pertains to it contingently or per accidens. | |
| From: Gottfried Leibniz (Human Freedom and Divine choice [1690], Grua 383), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 3.3.1 | |
| A reaction: This arbitrates on the apparent conflict between his remarks in Idea 13077 and Idea 10382. There seems to be a distinction between the 'concept' of a thing, and the 'complete concept', the latter including the contingent properties. |
| 2705 | How can intuitionists distinguish universal convictions from local cultural ones? [Hare] |
| Full Idea: There are convictions which are common to most societies; but there are others which are not, and no way is given by intuitionists of telling which are the authoritative data. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.454) | |
| A reaction: It seems unfair on intuitionists to say they haven't given a way to evaluate such things, given that they have offered intuition. The issue is what exactly they mean by 'intuition'. |
| 2712 | You can't use intuitions to decide which intuitions you should cultivate [Hare] |
| Full Idea: If it comes to deciding what intuitions and dispositions to cultivate, we cannot rely on the intuitions themselves, as intuitionists do. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.461) | |
| A reaction: Makes intuitionists sound a bit dim. Surely Hume identifies dispositions (such as benevolence) which should be cultivated, because they self-evidently improve social life? |
| 2706 | Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare] |
| Full Idea: Emotivists concluded too hastily that because naturalism and intuitionism are false, you cannot reason about moral questions, because they assumed that the only questions you can reason about are factual ones. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.455) | |
| A reaction: Personally I have a naturalistic view of ethics (based on successful functioning, as indicated by Aristotle), so not my prob. Why can't we reason about expressive emotions? We reason about art. |
| 2708 | An 'ought' statement implies universal application [Hare] |
| Full Idea: In any 'ought' statement there is implicit a principle which says that the statement applies to all precisely similar situations. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.456) | |
| A reaction: No two situations can ever be 'precisely' similar. Indeed, 'precisely similar' may be an oxymoron (at least for situations). Kantians presumably like this idea. |
| 2704 | If morality is just a natural or intuitive description, that leads to relativism [Hare] |
| Full Idea: Non-descriptivists (e.g. prescriptivists) reject descriptivism in its naturalist or intuitionist form, because they are both destined to collapse into relativism. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.453) | |
| A reaction: I'm not clear from this why prescriptism would not also turn out to be relativist, if it includes evaluations along with facts. |
| 2703 | Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare] |
| Full Idea: Ethical descriptivism is the view that ethical sentence-meaning is wholly determined by truth-conditions. …Prescriptivists think there is a further element of meaning, which expresses prescriptions or evaluations or attitudes which we assent to. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.452) | |
| A reaction: Not sure I understand either of these. If all meaning consists of truth-conditions, that will apply to ethics. If meaning includes evaluations, that will apply to non-ethics. |
| 2707 | If there can be contradictory prescriptions, then reasoning must be involved [Hare] |
| Full Idea: Prescriptivists claim that there are rules of reasoning which govern non-descriptive as well as descriptive speech acts. The standard example is possible logical inconsistency between contradictory prescriptions. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.455) | |
| A reaction: The example doesn't seem very good. Inconsistency can appear in any area of thought, but that isn't enough to infer full 'rules of reasoning'. I could desire two incompatible crazy things. |
| 2709 | Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare] |
| Full Idea: Universal prescriptivists hold that 'ought'-judgements are prescriptive like plain imperatives, but differ from them in being universalisable. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.457) | |
| A reaction: Sounds a bit tautological. Which comes first, the normativity or the universalisability? |
| 2711 | Prescriptivism implies a commitment, but descriptivism doesn't [Hare] |
| Full Idea: Prescriptivists hold that moral judgements commit the speaker to motivations and actions, but non-moral facts by themselves do not do this. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.459) | |
| A reaction: Surely hunger motivates to action? I suppose the key word is 'commit'. But lazy people are allowed to make moral judgements. |
| 2710 | Moral judgements must invoke some sort of principle [Hare] |
| Full Idea: To make moral judgements is implicitly to invoke some principle, however specific. | |
| From: Richard M. Hare (Universal Prescriptivism [1991], p.458) |