Combining Texts

All the ideas for 'fragments/reports', 'Against the Mathematicians' and 'Introduction to 'Hippias Minor''

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5 ideas

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
A mathematical object exists if there is no contradiction in its definition [Waterfield]
     Full Idea: A mathematical object exists provided there is no contradiction implied in its definition.
     From: Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4
     A reaction: A rather bizarre criterion for existence. Not one, for example, that you would consider applying to the existence of physical objects! But then Poincaré is the father of 'conventionalism', rather than being a platonist.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus]
     Full Idea: Dogmatists say something can be its own criterion. The straight is the standard of itself, and a set of scales establishes the equality of other things and of itself, and light seems to reveal not just other things but also itself.
     From: Sextus Empiricus (Against the Mathematicians [c.180], 442)
     A reaction: Each of these may be a bit dubious, but deserves careful discussion.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus]
     Full Idea: The dogmatists ask how the sceptic can show there is no criterion. If without a criterion, he is untrustworthy; with a criterion he is turned upside down. He says there is no criterion, but accepts a criterion to establish this.
     From: Sextus Empiricus (Against the Mathematicians [c.180], 440)
     A reaction: This is also the classic difficulty for foundationalist views of knowledge. Is the foundation justified, or not?
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.