11 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. |
| 23896 | We see our character as a restricting limit, but also as an unshakable support [Weil] |
| Full Idea: Our character appears to us as a limit by which we do not want to be imprisoned, …but also as a support that we want to believe is unshakable. | |
| From: Simone Weil (On the Concept of Character [1941], p.100) | |
| A reaction: A nice perception. It is fairly easy to criticise, or even laugh at, one's own actions, but extremely hard to criticise our own character. Maybe we all wish we were more determined in our projects, but not much else. |
| 23894 | The concept of character is at the centre of morality [Weil] |
| Full Idea: We cannot pose a moral problem without putting the concept of character at its centre. | |
| From: Simone Weil (On the Concept of Character [1941], p.98) | |
| A reaction: The question for Aristotle (which I derive from Philippa Foot) is whether moral goodness simply is good character, or whether it is the actions (or even the consequences). Weil is close to modern virtue theory here. |
| 23893 | We don't see character in a single moment, but only over a period of time [Weil] |
| Full Idea: Character is constant over a period of time; the way a person is at a single moment does not at all reflect the character of this person. We do, however, concede that character changes. | |
| From: Simone Weil (On the Concept of Character [1941], p.98) | |
| A reaction: I do think, though, that there are moments in behaviour which are hugely revealing of character, even in a single remark. But I agree that most single moments do not show much. |
| 23895 | We modify our character by placing ourselves in situations, or by attending to what seems trivial [Weil] |
| Full Idea: We can modify our character, by putting ourselves in circumstances that will act on us from the outside, …or by the orientation of our attention in the moments that appear most insignificant or indifferent in our lives. | |
| From: Simone Weil (On the Concept of Character [1941], p.99) | |
| A reaction: I've never seen anyone address this question (apart from Aristotle's emphasis on training habits). Choosing your source for current affairs information strikes me as very important. What you read, what you watch, who you spend time with… |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |