Combining Philosophers

All the ideas for Herodotus, Leopold Kronecker and Ariston

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6 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
20768 Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]
     Full Idea: He said that dialectical arguments were like spiderswebs: although they seem to indicate craftsmanlike skill, they are useless.
     From: report of Ariston (fragments/reports [c.250 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.161
     A reaction: Useful for the spider, but useless to Ariston.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12427 All of mathematics is properties of the whole numbers [Kronecker]
     Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers.
     From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5
     A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
10091 God made the integers, all the rest is the work of man [Kronecker]
     Full Idea: God made the integers, all the rest is the work of man.
     From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro
     A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
3049 The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]
     Full Idea: The chief good is to live in perfect indifference to all those things which are of an intermediate character between virtue and vice.
     From: report of Ariston (fragments/reports [c.250 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.2.1
23. Ethics / D. Deontological Ethics / 1. Deontology
3549 Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]
     Full Idea: Ariston says that rules are useless if you are virtuous, and useless if you are not.
     From: report of Ariston (fragments/reports [c.250 BCE]) by Julia Annas - The Morality of Happiness 2.4
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]
     Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born.
     From: Herodotus (The Histories [c.435 BCE], 2.123.2)