Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'On the General Idea of Proof Theory' and 'Two letters on mind'

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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 / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
16635 Incorporeal substances are powers or forces [Descartes, by Pasnau]
     Full Idea: In one of his last letters Descartes describes incorporeal substances as 'powers or forces'.
     From: report of René Descartes (Two letters on mind [1649], Feb 1649) by Robert Pasnau - Metaphysical Themes 1274-1671 08.4
     A reaction: Only a glimmer, but I really like this idea. (Ellis flirts with it somewhere). Minds are deeply and intrinsically active things. Try ceasing to think for five minutes. Apparently 12th century Cistercian authors were keen on the idea.
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
16684 Impenetrability only belongs to the essence of extension [Descartes]
     Full Idea: It is demonstrated that impenetrability belongs to the essence of extension and not to the essence of any other thing.
     From: René Descartes (Two letters on mind [1649], More, Apr 1649), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.5
     A reaction: I'm not sure that I understand how pure extension can be impenetrable.