5 ideas
| 18758 | Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee] |
| Full Idea: Church showed that logic has a proof procedure, but no decision procedure. If an argument is invalid, there is a model with true premises and false conclusion, but the model will typically be infinite, so there is no way to display it concretely. | |
| From: report of Alonzo Church (A Note on the entscheidungsproblem [1936]) by Vann McGee - Logical Consequence 5 |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 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. |