Combining Texts

All the ideas for 'Philosophical Explanations', 'Elements of Intuitionism (2nd ed)' and 'The Metaphysics of Space-Time Substantivalism'

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4 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic

18832	Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett]
	Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result.
	From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3
	A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent.

11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs

3570	Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
	Full Idea: Nozick suggests that knowledge is just belief which 'tracks the truth' (hence leaving out justification).
	From: report of Robert Nozick (Philosophical Explanations [1981]) by Michael Williams - Problems of Knowledge Ch. 2

13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts

2748	A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
	Full Idea: Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth").
	From: report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1
	A reaction: This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that.

27. Natural Reality / C. Space / 4. Substantival Space

19035	General Relativity allows substantivalism about space-time - that it has independent properties [Hoefer]
	Full Idea: General Relativity describes space-time in a way that allows it to exist with determinate properties not reducible to the properties and relations of its material contents. Hence nearly all physicists and philosophers writing on GR are substantivalists.
	From: Carl Hoefer (The Metaphysics of Space-Time Substantivalism [1996], p.5), quoted by Barbara Vetter - Potentiality 7.3
	A reaction: I'm encouraged by this, as I instinctly favour substantivalism. Imagine removing all the objects from space-time, one by one. What happens as you approach the end of the task? Once they are removed, can they be replaced?