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7485
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For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson]
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Full Idea:
For Pythagoreans, one, 1, is not a true number but the 'essence' of number, out of which the number system emerges.
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From:
report of Pythagoras (reports [c.530 BCE], Ch.8) by Peter Watson - Ideas Ch.8
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A reaction:
I think this is right! Counting and numbers only arise once the concept of individuality and identity have arisen. Counting to one is no more than observing the law of identity. 'Two' is the big adventure.
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22110
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Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
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Full Idea:
According to Aquinas, what demonstration provides is not so much knowledge as conceived by foundationalists as depth of understanding and explanatory insight.
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From:
Kretzmann/Stump (Aquinas, Thomas [2005]), quoted by Kretzmann/Stump - Aquinas, Thomas 11
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A reaction:
It was noticeable that Aristotle didn't make clear what demonstration aims to achieve, and he didn't employ it elsewhere in his writings. We aim for understanding, not for well grounded propositions. Understanding needs implications and mechanisms.
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9381
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If some inferences are needed to fix meaning, but we don't know which, they are all relevant [Fodor/Lepore, by Boghossian]
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Full Idea:
The Master Argument for linguistic holism is: Some of an expression's inferences are relevant to fixing its meaning; there is no way to distinguish the inferences that are constitutive (from Quine); so all inferences are relevant to fixing meaning.
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From:
report of J Fodor / E Lepore (Holism: a Shopper's Guide [1993], §III) by Paul Boghossian - Analyticity Reconsidered
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A reaction:
This would only be if you thought that the pattern of inferences is what fixes the meanings, but how can you derive inferences before you have meanings? The underlying language of thought generates the inferences? Meanings are involved!
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3053
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Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius]
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Full Idea:
Pythagoras taught that virtue is harmony, and health, and universal good, and God.
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From:
report of Pythagoras (reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.1.19
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A reaction:
I like the link with health, because I consider that a bridge over the supposed fact-value gap. Very Pythagorean to think that virtue is harmony. Plato liked that thought.
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5244
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For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle]
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Full Idea:
Some even think that what is just is simple reciprocity, as the Pythagoreans maintained, because they defined justice simply as having done to one what one has done to another.
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From:
report of Pythagoras (reports [c.530 BCE], 28) by Aristotle - Nicomachean Ethics 1132b22
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A reaction:
One wonders what Pythagoreans made of slavery. Aristotle argues that officials, for example, have superior rights. The Pythagorean idea makes fairness the central aspect of justice, and that must at least be partly right.
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