Combining Texts

All the ideas for 'Contextualist Solutions to Scepticism', 'Mathematics without Numbers' and 'Summa Contra Gentiles'

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8 ideas

1. Philosophy / A. Wisdom / 2. Wise People
22115 Wise people should contemplate and discuss the truth, and fight against falsehood [Aquinas]
     Full Idea: The role of the wise person is to meditate on the truth, especially the truth regarding the first principle, and to discuss it with others, but also to fight against the falsity that is its contrary.
     From: Thomas Aquinas (Summa Contra Gentiles [1268], I.1.6), quoted by Kretzmann/Stump - Aquinas, Thomas 14
     A reaction: So nice to hear someone (from no matter how long ago) saying that wisdom is concerned with truth. If you lose your grip on truth (which many thinkers seem to have done) you must also abandon wisdom. Then fools rule.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8698 Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
     Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
     A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?
9557 Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
     Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3
     A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world).
10263 Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
     Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
     From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
     A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
19508 Contextualism needs a semantics for knowledge sentences that are partly indexical [Schiffer,S]
     Full Idea: Contextualist semantics must capture the 'indexical' nature of knowledge claims, the fact that different utterances of a knowledge sentence with no apparent indexical terms can express different propositions.
     From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.325), quoted by Keith DeRose - The Case for Contextualism 1.5
     A reaction: Schiffer tries to show that this is too difficult, and DeRose defends contextualism against the charge.
19509 The indexical aspect of contextual knowledge might be hidden, or it might be in what 'know' means [Schiffer,S]
     Full Idea: One might have a 'hidden-indexical' theory of knowledge sentences: they contain constituents that are not the semantic values of any terms; ...or 'to know' itself might be indexical, as in 'I know[easy] I have hands' or 'I know[tough] I have hands'.
     From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.326-7), quoted by Keith DeRose - The Case for Contextualism 1.5
     A reaction: [very compressed] Given the choice, I would have thought it was in 'know', since to say 'either you know p or you don't' sounds silly to me.
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
20700 Without God's influence every operation would stop, so God causes everything [Aquinas]
     Full Idea: If God's divine influence stopped, every operation would stop. Every operation, therefore, of everything is traced back to him as cause.
     From: Thomas Aquinas (Summa Contra Gentiles [1268], III.67), quoted by Brian Davies - Introduction to the Philosophy of Religion 3 'Freedom'
     A reaction: If the systematic interraction of mind and body counts as an 'operation', then this seems to imply Occasionalism.
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
15202 Eternity coexists with passing time, as the centre of a circle coexists with its circumference [Aquinas]
     Full Idea: The centre of a circle is directly opposite any designated point on the circumference. In this way, whatever is in any part of time coexists with what is eternal as being present to it even though past or future with respect to another part of time.
     From: Thomas Aquinas (Summa Contra Gentiles [1268], I.66), quoted by Robin Le Poidevin - Past, Present and Future of Debate about Tense 2 c
     A reaction: A nice example of a really cool analogy which almost gets you to accept something which is actually completely incomprehensible.