Combining Texts

All the ideas for 'fragments/reports', 'Rationality' and 'Phil of Mathematics and Natural Science'

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8 ideas

2. Reason / A. Nature of Reason / 1. On Reason
You can be rational with undetected or minor inconsistencies [Harman]
     Full Idea: Rationality doesn't require consistency, because you can be rational despite undetected inconsistencies in beliefs, and it isn't always rational to respond to a discovery of inconsistency by dropping everything in favour of eliminating that inconsistency.
     From: Gilbert Harman (Rationality [1995], 1.2)
     A reaction: This strikes me as being correct, and is (I am beginning to realise) a vital contribution made to our understanding by pragmatism. European thinking has been too keen on logic as the model of good reasoning.
2. Reason / A. Nature of Reason / 6. Coherence
A coherent conceptual scheme contains best explanations of most of your beliefs [Harman]
     Full Idea: A set of unrelated beliefs seems less coherent than a tightly organized conceptual scheme that contains explanatory principles that make sense of most of your beliefs; this is why inference to the best explanation is an attractive pattern of inference.
     From: Gilbert Harman (Rationality [1995], 1.5.2)
     A reaction: I find this a very appealing proposal. The central aim of rational thought seems to me to be best explanation, and I increasingly think that most of my beliefs rest on their apparent coherence, rather than their foundations.
14. Science / C. Induction / 1. Induction
Enumerative induction is inference to the best explanation [Harman]
     Full Idea: We might think of enumerative induction as inference to the best explanation, taking the generalization to explain its instances.
     From: Gilbert Harman (Rationality [1995], 1.5.2)
     A reaction: This is a helpful connection. The best explanation of these swans being white is that all swans are white; it ceased to be the best explanation when black swans turned up. In the ultimate case, a law of nature is the explanation.
14. Science / C. Induction / 3. Limits of Induction
Induction is 'defeasible', since additional information can invalidate it [Harman]
     Full Idea: It is sometimes said that inductive reasoning is 'defeasible', meaning that considerations that support a given conclusion can be defeated by additional information.
     From: Gilbert Harman (Rationality [1995], 1.4.5)
     A reaction: True. The point is that being defeasible does not prevent such thinking from being rational. The rational part of it is to acknowledge that your conclusion is defeasible.
14. Science / C. Induction / 4. Reason in Induction
All reasoning is inductive, and deduction only concerns implication [Harman]
     Full Idea: Deductive logic is concerned with deductive implication, not deductive reasoning; all reasoning is inductive
     From: Gilbert Harman (Rationality [1995], 1.4.5)
     A reaction: This may be an attempt to stipulate how the word 'reasoning' should be used in future. It is, though, a bold and interesting claim, given the reputation of induction (since Hume) of being a totally irrational process.
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Ordinary rationality is conservative, starting from where your beliefs currently are [Harman]
     Full Idea: Ordinary rationality is generally conservative, in the sense that you start from where you are, with your present beliefs and intentions.
     From: Gilbert Harman (Rationality [1995], 1.3)
     A reaction: This stands opposed to the Cartesian or philosophers' rationality, which requires that (where possible) everything be proved from scratch. Harman seems right, that the normal onus of proof is on changing beliefs, rather proving you should retain them.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
The limit of science is isomorphism of theories, with essences a matter of indifference [Weyl]
     Full Idea: A science can determine its domain of investigation up to an isomorphic mapping. It remains quite indifferent as to the 'essence' of its objects. The idea of isomorphism demarcates the self-evident boundary of cognition.
     From: Hermann Weyl (Phil of Mathematics and Natural Science [1949], 25-7), quoted by Stewart Shapiro - Philosophy of Mathematics
     A reaction: Shapiro quotes this in support of his structuralism, but it is a striking expression of the idea that if there are such things as essences, they are beyond science. I take Weyl to be wrong. Best explanation reaches out beyond models to essences.