Combining Texts

All the ideas for 'works', 'The Principles of Science' and 'On the General Idea of Proof Theory'

unexpand these ideas     |    start again     |     specify just one area for these texts

5 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13827 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
13826 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)
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8628 I hold that algebra and number are developments of logic [Jevons]
     Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination.
     From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15
     A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here.
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
     Full Idea: Philosophers are the forefathers of heretics.
     From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]
     Full Idea: I believe because it is absurd ('Credo quia absurdum est').
     From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
     A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.