12 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. |
| 6375 | The taste of chocolate is a 'finer-grained' sensation than the taste of sweetness [Polger] |
| Full Idea: The taste of chocolate is presumably a 'finer-grained' sensation than the taste of sweetness. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.1.4) | |
| A reaction: An interesting distinction when it comes to what they are like, and whether two very different brains can realise them. Sweetness might be the same for most creatures, but the tast of chocolate subtly different. |
| 6381 | The mind and the self are one, and the mind-self is a biological phenomenon [Polger] |
| Full Idea: We should return to the old idea that the mind and the self are one and combine it with the new idea that the mind-self is a biological phenomenon. | |
| From: Thomas W. Polger (Natural Minds [2004], §8.3) | |
| A reaction: This doesn't make allowance for the fact that some parts of my mind seem like irritating visitors, and other parts seem like the home-owner. Personally I take the self to be the brain's central controller, or the centre (forum) of brain integration. |
| 6378 | Teleological functions explain why a trait exists; causal-role functions say what it does [Polger] |
| Full Idea: Teleological functions help explain why a trait has come to exist; causal-role functions tell what a trait does or is apt to do. | |
| From: Thomas W. Polger (Natural Minds [2004], §5.4) | |
| A reaction: The teleological view has the merit of nesting nicely with the theory of evolution, and with Aristotelian virtue ethics (which I like). Causal-role functionalism focuses better on what is actually happening inside the head. |
| 6380 | Identity theory says consciousness is an abstraction: a state, event, process or property [Polger] |
| Full Idea: Identity theories locate consciousness at a certain order of abstraction, typically among neurophysiological states, events, processes, or properties. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.7.6) | |
| A reaction: I increasingly think that processes are the answer. My new analogy for the mind is a waterfall: its physical ontology is simple, it only exists because there is a sustained process, and it is far too complex to predict individual droplet outcomes. |
| 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? |
| 6379 | A mummified heart has the teleological function of circulating blood [Polger] |
| Full Idea: A preserved heart in a jar of formaldehyde has the teleological function of circulating blood. | |
| From: Thomas W. Polger (Natural Minds [2004], §5.4) | |
| A reaction: A nice illustration. |
| 6377 | Teleological notions of function say what a thing is supposed to do [Polger] |
| Full Idea: Teleological notions of function specify not just what a thing happens to do, but what it is supposed to do. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.5.3) | |
| A reaction: This is the basis of a distinct theory of the mind. It seems to be akin to the 'dispositions' of behaviourism, so that the mind becomes once more a theoretical and abstract entity, rather than a thing of occurrent events and processes. |