Combining Texts

All the ideas for 'Content Preservation', 'Reply to Hellman' and 'Mathematics, Science and Language'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

18119	Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
	Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language.
	From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1
	A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking!

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

18118	Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
	Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals.
	From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1
	A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses.

12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence

9379	A sentence is obvious if it is true, and any speaker of the language will instantly agree to it [Quine]
	Full Idea: A sentence is obvious if (a) it is true and (b) any speaker of the language is prepared, for any reason or none, to assent to it without hesitation, unless put off by being asked so obvious a question.
	From: Willard Quine (Reply to Hellman [1975], p.206), quoted by Paul Boghossian - Analyticity Reconsidered §III
	A reaction: This comes from someone who is keen to deny a priori knowledge, but what are we to make of the expostulations "It's obvious, you idiot!", and "Now I see it, it's obvious!", and "It seemed obvious, but I was wrong!"?

13. Knowledge Criteria / C. External Justification / 1. External Justification

9382	Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge]
	Full Idea: I call 'entitlement' (as opposed to justification) the epistemic rights or warrants that need not be understood by or even be accessible to the subject.
	From: Tyler Burge (Content Preservation [1993]), quoted by Paul Boghossian - Analyticity Reconsidered §III
	A reaction: I espouse a coherentism that has both internal and external components, and is mediated socially. In Burge's sense, animals will sometimes have 'entitlement'. I prefer, though, not to call this 'knowledge'. 'Entitled true belief' is good.