Combining Texts

All the ideas for 'works', 'Set Theory and the Continuum Hypothesis' and 'The Nature of Rationality'

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8 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
I do not care if my trivial beliefs are false, and I have no interest in many truths [Nozick]
     Full Idea: I find that I do not mind at all the thought that I have some false beliefs (of US state capitals), and there are many truths I do not care to know at all (total grains of sand on the beach).
     From: Robert Nozick (The Nature of Rationality [1993], p.67)
     A reaction: A useful corrective to anyone who blindly asserts that truth is the supreme human value. I would still be annoyed if someone taught me lies about these two types of truth.
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Maybe James was depicting the value of truth, and not its nature [Nozick]
     Full Idea: We might see William James's pragmatic view that truth is what works as depicting the value of truth, and not its nature.
     From: Robert Nozick (The Nature of Rationality [1993], p.68)
     A reaction: James didn't think that he was doing this. He firmly says that this IS truth, not just the advantages of truth. Another view is that pragmatists are giving a test for truth.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
     Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
     From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
     A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Rationality is normally said to concern either giving reasons, or reliability [Nozick]
     Full Idea: The two themes permeating the philosophical literature are that rationality is a matter of reasons, or that rationality is a matter of reliability.
     From: Robert Nozick (The Nature of Rationality [1993], p.64)
     A reaction: Since a clock can be reliable, I would have thought it concerns reasons. Or an unthinking person could reliably recite truths from memory. There is also the instrumental view of rationality.
In the instrumental view of rationality it only concerns means, and not ends [Nozick]
     Full Idea: On the instrumental conception of rationality, it consists in the effective and efficient achievement of goals, ends, and desires. About the goals themselves it has little to say.
     From: Robert Nozick (The Nature of Rationality [1993], p.64)
     A reaction: [He quotes Russell 1954 p.viii as expressing this view] A long way from Greek logos, which obviously concerns the rational selection of right ends (for which, presumably, reasons can be given). In practice our ends may never be rational, of course.
Is it rational to believe a truth which leads to permanent misery? [Nozick]
     Full Idea: If a mother is presented with convincing evidence that her son has committed a grave crime, but were she to believe it that would make her life thereafter miserable, is it rational for her to believe her son is guilty?
     From: Robert Nozick (The Nature of Rationality [1993], p.69)
     A reaction: I assume there is a conflict of rationalities, because there are conflicting ends. Presumably most mothers love the truth, but most of us also aim for happy lives. It is perfectly rational to avoid discovering a horrible family truth.
Rationality needs some self-consciousness, to also evaluate how we acquired our reasons [Nozick]
     Full Idea: Rationality involves some degree of self-consciousness. Not only reasons are evaluated, but also the processes by which information arrives, is stored, and recalled.
     From: Robert Nozick (The Nature of Rationality [1993], p.74)
     A reaction: I defend the idea that animals have a degree of rationality, because they can make sensible judgements, but I cannot deny this idea. Rationality comes in degrees, and second-level thought is a huge leap forward in degree.