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All the ideas for 'Stipulation, Meaning and Apriority', 'The Foundations of Mathematics' and 'The Nature of Rationality'

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14 ideas

2. Reason / D. Definition / 13. Against Definition
How do we determine which of the sentences containing a term comprise its definition? [Horwich]
     Full Idea: How are we to determine which of the sentences containing a term comprise its definition?
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2)
     A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't?
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.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
You would cripple mathematics if you denied Excluded Middle [Hilbert]
     Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists.
     From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4
     A reaction: [p.476 in Van Heijenoort]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich]
     Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8)
     A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified.
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
Understanding needs a priori commitment [Horwich]
     Full Idea: Understanding is itself based on a priori commitment.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12)
     A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional.
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
Meaning is generated by a priori commitment to truth, not the other way around [Horwich]
     Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8)
     A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it.
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich]
     Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12)
     A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge.
If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich]
     Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9)
     A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate.
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich]
     Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11)
     A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away.
18. Thought / A. Modes of Thought / 5. Rationality / a. 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.
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.
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.