9 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. |
| 3643 | The concept of mind excludes body, and vice versa [Descartes] |
| Full Idea: The concept of body includes nothing at all which belongs to the mind, and the concept of mind includes nothing at all which belongs to the body. | |
| From: René Descartes (Reply to Fourth Objections [1641], 225) | |
| A reaction: A headache? Hunger? The mistake, I think, is to regard the mind as entirely conscious, thus creating a sharp boundary between two aspects of our lives. As shown by blindsight, I take many of my central mental operations to be pre- or non-conscious. |
| 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. |
| 21236 | Instead of gravitational force, we now have a pervasive gravitational field [Farmelo] |
| Full Idea: Physics replaced the notion that bodies exert gravitational force on each other by the more effective picture that the bodies in the universe give rise to a pervasive gravitational field which exerts a force on each particle. | |
| From: Graham Farmelo (The Strangest Man [2009], 08) | |
| A reaction: This still uses the word 'force'. I sometimes get the impression that gravity is the curvature of space, but gravity needs more. Which direction along the curvature are particles attracted? The bottom line is the power of the bodies. |
| 21235 | The Schrödinger waves are just the maths of transforming energy values to positions [Farmelo] |
| Full Idea: Dirac showed that the Schrödinger waves were simply the mathematical quantities involved in transforming the description of a quantum based on its energy values to one based on possible values of its position. | |
| From: Graham Farmelo (The Strangest Man [2009], 08) | |
| A reaction: Does this eliminate actual physical 'waves' from the theory? |
| 21234 | Experiments show that fundamental particles of one type are identical [Farmelo] |
| Full Idea: It is an established experimental fact ...that every single fundamental particle in the universe is the same and identical to all other particles of the same type. | |
| From: Graham Farmelo (The Strangest Man [2009], 07) | |
| A reaction: A loud groan is heard from the tomb of Leibniz. I'm unclear how experiments can establish this. If electrons have internal structure (which is not ruled out) then uniformity is highly unlikely. |