13 ideas
8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
17535 | Dispositionality has its own distinctive type of modality [Mumford/Anjum] |
Full Idea: We contend that dispositionality involves a non-alethic, sui generis, irreducible modality. | |
From: S.Mumford/R.Lill Anjum (Dispositional Modality [2011], 1) | |
A reaction: This is a lovely bold proposal, and seems to be supported by Werner Heisenberg, in Idea 17534. |
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) |