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Ideas for 'Mahaprajnaparamitashastra', 'On the General Idea of Proof Theory' and 'A Subject with No Object'

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4 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 / E. Structures of Logic / 6. Relations in Logic

9926	A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen]
	Full Idea: While in general a relation is taken to be a set of ordered pairs <u, v> = {{u}, {u, v}}, and hence a set of sets of sets, in special cases a relation can be represented by a set of sets.
	From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.a)
	A reaction: [See book for their examples, which are <, symmetric, and arbitrary] The fact that a relation (or anything else) can be represented in a certain way should never ever be taken to mean that you now know what the thing IS.

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)

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes

9932	The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen]
	Full Idea: Recent commentators have de-emphasised the set paradoxes because they play no prominent part in motivating the most articulate and active opponents of set theory, such as Kronecker (constructivism) or Brouwer (intuitionism), or Weyl (predicativism).
	From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.1.b)
	A reaction: This seems to be a sad illustration of the way most analytical philosophers have to limp along behind the logicians and mathematicians, arguing furiously about problems that have largely been abandoned.