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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19261
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Understanding is seeing coherent relationships in the relevant information [Kvanvig]
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Full Idea:
What is distinctive about understanding (after truth is satisfied) is the internal seeing or appreciating of explanatory and other coherence-inducing relationships in a body of information that is crucial for understanding.
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From:
Jonathan Kvanvig (The Value of Knowledge and the Pursuit of Understanding [2003], 198), quoted by Anand Vaidya - Understanding and Essence 'Distinction'
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A reaction:
For me this ticks exactly the right boxes. Coherent explanations are what we want. The hardest part is the ensure their truth. Kvanvig claims this is internal, so we can understand even if, Gettier-style, our external connections are lucky.
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9145
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We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]
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Full Idea:
We call 'cardinal number' the general concept which, by means of our active faculty of thought, arises when we make abstraction from an aggregate of its various elements, and of their order. From this double abstraction the number is an image in our mind.
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From:
George Cantor (Beitrage [1915], §1), quoted by Kit Fine - Cantorian Abstraction: Recon. and Defence Intro
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A reaction:
[compressed] This is the great Cantor, creator of set theory, endorsing the traditional abstractionism which Frege and his followers so despise. Fine offers a defence of it. The Frege view is platonist, because it refuses to connect numbers to the world.
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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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