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17807
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To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
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Full Idea:
In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
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From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
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A reaction:
This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
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17806
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It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
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Full Idea:
According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
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From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
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A reaction:
I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
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8842
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The best argument for immediate justification is not the Regress Argument, but considering examples [Pryor]
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Full Idea:
The best argument for immediate justification is not the Regress Argument, but from considering examples, such as I have a headache, I am raising my arm, I am imagining my grandmother, or seeing how dominoes could fill a chessboard.
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From:
James Pryor (There is immediate Justification [2005], §3)
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A reaction:
Most of his examples depend on the fact that they cannot be challenged by anyone else, because they are within his own mind. The dominoes require complex thought. The first two could be erroneous if he was dreaming.
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8843
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Impure coherentists accept that perceptions can justify, unlike pure coherentists [Pryor]
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Full Idea:
Pure coherentists claim that a belief can only be justified by its relations to other beliefs; impure coherentists are willing to give some non-beliefs, such as perceptual experiences, a justifying role.
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From:
James Pryor (There is immediate Justification [2005], §4)
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A reaction:
I think I would vote for the pure version. The distinction that is needed, I think, is between justification and evidence. You have to surmise causal links and explanations before you can see an experience as evidence, and then justification.
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8846
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Reasons for beliefs can be cited to others, unlike a raw headache experience [Pryor]
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Full Idea:
If you have reasons for your belief, they should be considerations you could in principle cite, or give, to someone who doubted or challenged the belief. You can't give some else a non-propositional state like a headache.
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From:
James Pryor (There is immediate Justification [2005], §6)
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A reaction:
On the whole I agree, but if someone asked you to justify your claim that there is a beautiful sunset over the harbour, you could just say 'Look!'. Headaches are too private. The person must still see that the sunset is red, and not the window.
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2171
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The 'will' doesn't exist; there is just conclusion, then action [Homer, by Williams,B]
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Full Idea:
Homer left out another mental action lying between coming to a conclusion and acting on it; and he did well, since there is no such action, and the idea is the invention of bad philosophy.
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From:
report of Homer (The Iliad [c.850 BCE]) by Bernard Williams - Shame and Necessity II - p.37
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A reaction:
This is a characteristically empiricist view, which is found in Hobbes. The 'will' seems to have a useful role in folk psychology. We can at least say that coming to a conclusion that I should act, and then actually acting, are not the same thing.
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21819
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Plato says the Good produces the Intellectual-Principle, which in turn produces the Soul [Homer, by Plotinus]
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Full Idea:
In Plato the order of generation is from the Good, the Intellectual-Principle; from the Intellectual-Principle, the Soul.
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From:
report of Homer (The Iliad [c.850 BCE], 509b) by Plotinus - The Enneads 5.1.08
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A reaction:
The doctrine of Plotinus merely echoes Plato, in that case, except that the One replaces the Form of the Good. Does this mean that what is first in Plotinus is less morally significant, and more concerned with reason and being?
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