Combining Philosophers

All the ideas for Buddhaghosa, Michael Hallett and Mark Jago

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

6 ideas

4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
15382 Paraconsistent reasoning can just mean responding sensibly to inconsistencies [Jago]
     Full Idea: A practical application of paraconsistent reasoning is in large databases. It does not mean that contradictions could be true, but only that we sometimes need to draw sensible conclusions from inconsistent data. 'Dialethists' believe some contradictions.
     From: Mark Jago (Paraconsistent Logic [2010])
     A reaction: Interesting as a more cautious and sensible attitude to the scandal of paraconsistency.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17833 The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
     Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical.
     From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213)
17834 Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
     Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets.
     From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215)
     A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets).
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17837 Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
     Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory.
     From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17836 The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
     Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself.
     From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217)
25. Social Practice / F. Life Issues / 1. Causing Death
7907 Human killing is worse if the victim is virtuous [Buddhaghosa]
     Full Idea: In the case of humans killing is the more blameworthy the more virtuous the victim is.
     From: Buddhaghosa (Papancasudani [c.400], 9.7-10)
     A reaction: This sentiment has almost become a taboo in western society, and yet it is present all the time. The greatest outcry is about murders of really good citizens. Occasionally the murder of a villain causes little regret.