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All the ideas for 'Mahaprajnaparamitashastra', 'On the General Idea of Proof Theory' and 'Against the Mathematicians'

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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)
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
20795 Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus]
     Full Idea: Dogmatists say something can be its own criterion. The straight is the standard of itself, and a set of scales establishes the equality of other things and of itself, and light seems to reveal not just other things but also itself.
     From: Sextus Empiricus (Against the Mathematicians [c.180], 442)
     A reaction: Each of these may be a bit dubious, but deserves careful discussion.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
20794 How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus]
     Full Idea: The dogmatists ask how the sceptic can show there is no criterion. If without a criterion, he is untrustworthy; with a criterion he is turned upside down. He says there is no criterion, but accepts a criterion to establish this.
     From: Sextus Empiricus (Against the Mathematicians [c.180], 440)
     A reaction: This is also the classic difficulty for foundationalist views of knowledge. Is the foundation justified, or not?
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').