Combining Texts

Ideas for 'Thinking About Mathematics', 'Five Milestones of Empiricism' and 'Letters to Samuel Clarke'

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5 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
The principle of sufficient reason is needed if we are to proceed from maths to physics [Leibniz]
     Full Idea: In order to proceed from mathematics to physics the principle of sufficient reason is necessary, that nothing happens without there being a reason why it should be thus rather than otherwise.
     From: Gottfried Leibniz (Letters to Samuel Clarke [1716], §2)
There is always a reason why things are thus rather than otherwise [Leibniz]
     Full Idea: Nothing happens without a sufficient reason why it should be thus rather than otherwise.
     From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 3.2)
No reason could limit the quantity of matter, so there is no limit [Leibniz]
     Full Idea: There is no possible reason which could limit the quantity of matter; therefore there cannot in fact be any such limitation.
     From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 4.21)
2. Reason / D. Definition / 7. Contextual Definition
Contextual definition shifted the emphasis from words to whole sentences [Quine]
     Full Idea: Contextual definition precipitated a revolution in semantics. The primary vehicle of meaning is seen no longer as the word, but as the sentence.
     From: Willard Quine (Five Milestones of Empiricism [1975], p.69)
     A reaction: I think the idea is that the term is now supported entirely by its surrounding language, and not by its denotation of something in the world.
Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine]
     Full Idea: If Bentham found some term convenient but ontologically embarrassing, contextual definition enabled him in some cases to continue to enjoy the services of the term while disclaiming its denotation.
     From: Willard Quine (Five Milestones of Empiricism [1975], p.68)
     A reaction: In Quine's terms this would be to withdraw the term from the periphery of the theory, where it has to meet the world, and make it part of the inner connections of the theory. He suggests that Bentham invented this technique.