Combining Philosophers

All the ideas for Archimedes, L. Jonathan Cohen and Alcmaeon

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
Alcmaeon was the first to say the brain is central to thinking [Alcmaeon, by Staden, von]
     Full Idea: Alcmaeon apparently was the first Greek to assign central cognitive and biological functions to the brain.
     From: report of Alcmaeon (fragments/reports [c.490 BCE]) by Heinrich von Staden - Alcmaeon
     A reaction: The name of Alcmaeon should be remembered with honour. This was 200 years before Aristotle, who still hadn't worked it out. I presume Alcmaeon inferred the truth from head injuries, which is overwhelming evidence, if you notice it.
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Natural laws result from eliminative induction, where enumerative induction gives generalisations [Cohen,LJ, by Psillos]
     Full Idea: Cohen contends that statements that express laws of nature are the products of eliminative induction, where accidentally true generalisations are the products of enumerative induction.
     From: report of L. Jonathan Cohen (The Problem of Natural Laws [1980], p.222) by Stathis Psillos - Causation and Explanation §7.1
     A reaction: The idea is that enumerative induction only offers the support of positive instances, where eliminative induction involves attempts to falsify a range of hypotheses. This still bases laws on observed regularities, rather than essences or mechanisms.
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle]
     Full Idea: Alcmaeon says that the soul is immortal because it resembles immortal things and that this affection belongs to it because it is always in movement, like divine things, such the moon, the sun, the stars and the whole heaven.
     From: report of Alcmaeon (fragments/reports [c.490 BCE], DK 24) by Aristotle - De Anima 405a30
     A reaction: Hm. Fish and rivers seem to be continually moving too. Presumably we are like gods, but then Greek gods seem awfully like humans. I don't know the history of belief in immortality; an interesting topic.