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Ideas for 'Parmenides', 'Ideas' and 'Frege philosophy of mathematics'

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5 ideas

2. Reason / A. Nature of Reason / 1. On Reason
When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato]
     Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect.
     From: Plato (Parmenides [c.364 BCE], 135e)
2. Reason / B. Laws of Thought / 5. Opposites
Opposites are as unlike as possible [Plato]
     Full Idea: Opposites are as unlike as possible.
     From: Plato (Parmenides [c.364 BCE], 159a)
2. Reason / C. Styles of Reason / 1. Dialectic
Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato]
     Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic.
     From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71
     A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light.
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
     Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11)
     A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems
2. Reason / E. Argument / 3. Analogy
Babylonian thinking used analogy, rather than deduction or induction [Watson]
     Full Idea: In Babylon thought seems to have worked mainly by analogy, rather than by the deductive or inductive processes we use in the modern world.
     From: Peter Watson (Ideas [2005], Ch.04)
     A reaction: Analogy seems to be closely related to induction, if it is comparing instances of something. Given their developments in maths and astronomy, they can't have been complete strangers to the 'modern' way of thought.