Combining Texts

All the ideas for 'Positivism and Realism', 'Two Chief World Systems' and 'On the General Idea of Proof Theory'

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4 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
The empiricist says that metaphysics is meaningless, rather than false [Schlick]
     Full Idea: The empiricist does not say to the metaphysician 'what you say is false', but 'what you say asserts nothing at all!' He does not contradict him, but says 'I don't understand you'.
     From: Moritz Schlick (Positivism and Realism [1934], p.107), quoted by Jonathan Schaffer - On What Grounds What 1.1
     A reaction: I take metaphysics to be meaningful, but at such a high level of abstraction that it is easy to drift into vague nonsense, and incredibly hard to assess what is meant, and whether it is correct. The truths of metaphysics are not recursive.
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
     Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments.
     From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2)
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
     Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things.
     From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1)
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
Galileo mathematised movement, and revealed its invariable component - acceleration [Galileo, by Meillassoux]
     Full Idea: Galileo conceives of movement in mathematical terms. ...In doing so, he uncovered, beyond the variations of position and speed, the mathematical invariant of movement - that is to say, acceleration.
     From: report of Galileo Galilei (Two Chief World Systems [1632]) by Quentin Meillassoux - After Finitude; the necessity of contingency 5
     A reaction: That is a very nice advert for the mathematical physics which replaced the Aristotelian substantial forms. ...And yet, is acceleration some deep fact about nature, or a concept which is only needed if you insist on being mathematical?