10 ideas
| 8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
| Full Idea: The result of joining Hume's Principle to second-order logic is a consistent system which is a foundation for arithmetic, in the sense that all the fundamental laws of arithmetic are derivable within it as theorems. This seems a vindication of logicism. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: The controversial part seems to be second-order logic, which Quine (for example) vigorously challenged. The contention against most attempts to improve Frege's logicism is that they thereby cease to be properly logical. |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| Full Idea: The Julius Caesar problem is the problem of supplying a criterion of application for 'number', and thereby setting it up as the concept of a genuine sort of object. (Why is Julius Caesar not a number?) | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 3) | |
| A reaction: One response would be to deny that numbers are objects. Another would be to derive numbers from their application in counting objects, rather than the other way round. I suspect that the problem only real bothers platonists. Serves them right. |
| 8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
| Full Idea: It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 8) | |
| A reaction: It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading. |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| Full Idea: Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2) | |
| A reaction: Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting. |
| 8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
| Full Idea: An example of a first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines; a higher-order example (which refers to first-order predicates) defines 'equinumeral' in terms of one-to-one correlation (Hume's Principle). | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: [compressed] This is the way modern logicians now treat abstraction, but abstraction principles include the elusive concept of 'equivalence' of entities, which may be no more than that the same adjective ('parallel') can be applied to them. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 23683 | Moral norms are objective, connected to facts about human goods [Foot, by Hacker-Wright] |
| Full Idea: In her early work she defends the objectivity of moral norms, demonstrating their essential connection to facts about what is good for human beings. | |
| From: report of Philippa Foot (Moral Beliefs [1959]) by John Hacker-Wright - Philippa Foot's Moral Thought Intro | |
| A reaction: I don't think she ever gave up this idea, which strikes me as thoroughly Aristotelian. The issue is how to understand what is good for us. |
| 23684 | Morality gives everyone reasons to act, irrespective of their desires [Foot, by Hacker-Wright] |
| Full Idea: In her early work she also defends moral rationalism, which is the idea that morality gives reasons for action to everyone, even those who lack the desire to do what is right. | |
| From: report of Philippa Foot (Moral Beliefs [1959]) by John Hacker-Wright - Philippa Foot's Moral Thought Intro | |
| A reaction: Evidently a rejection of the Humean view that only a desire can motivate action, including moral action. There is an ongoing debate about whether reasons can cause anything, or motivate anything. I think the contents of reasons pull us towards action. |
| 23690 | We all have reason to cultivate the virtues, even when we lack the desire [Foot, by Hacker-Wright] |
| Full Idea: Foot advocates the view that anyone has reason to cultivate the virtues, even if they lack the desire to do so at a given moment. | |
| From: report of Philippa Foot (Moral Beliefs [1959], Pt II) by John Hacker-Wright - Philippa Foot's Moral Thought 2 'Concepts' | |
| A reaction: The view which she soon abandoned, but then returned to later. It specifically repudiates the view of Hume, that only desires can motivate. I'm unsure, because the concept of 'reason' strikes me as too imprecise. She sees self-interest as a reason. |
| 22379 | The meaning of 'good' and other evaluations must include the object to which they attach [Foot] |
| Full Idea: There is no describing the evaluative meaning of 'good', evaluation, commending, or anything of the sort, without fixing the object to which they are supposed to be attached. | |
| From: Philippa Foot (Moral Beliefs [1959], p.112) | |
| A reaction: I go further, and say that a specification of the feature(s) of the object that produce the value must also be available (if requested). 'That's a good car, but I've no idea why' makes no sense. 'Apparently that's a good car', if other people know why. |