Combining Texts

All the ideas for 'fragments/reports', 'The Basing Relation' and 'Set Theory and the Continuum Hypothesis'

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8 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales]
     Full Idea: Thales was the first thinker in the west to believe that the arché (the basis of things) was intelligible.
     From: comment on Thales (fragments/reports [c.585 BCE]) by David Roochnik - The Tragedy of Reason p.138
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
     Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
     From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
     A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius]
     Full Idea: Necessity is the strongest of things, for it rules everything.
     From: report of Thales (fragments/reports [c.585 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.2.9
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta]
     Full Idea: We must distinguish between something's being a 'reason for which' a creature believes something, and its being a 'reason why' a creature believes something. ...We must also distinguish a 'reason for which' from a 'reason to' believe something.
     From: Ram Neta (The Basing Relation [2011], Intro)
     A reaction: He doesn't spell the distinctions out clearly. I take it that 'for which' is my personal justification, 'why' is the dodgy prejudices that cause my belief. and 'to' is some actual good reasons, of which I may be unaware.
The basing relation of a reason to a belief should both support and explain the belief [Neta]
     Full Idea: A reason has a 'basing relation' with a belief if it (i) rationally supports holding the belief, and (ii) explains why the belief is held.
     From: Ram Neta (The Basing Relation [2011], Intro)
     A reaction: Presumably a false reason would fit this account. Why not talk of 'grounding', or is that word now reserved for metaphysics? If I hypnotise you into a belief, would my hypnotic power be the basing reason? Fits (ii), but not (i).
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle]
     Full Idea: Thales says water is the first principle (which is why he declared the earth is on water); perhaps he concluded this from seeing that all food is moist.
     From: report of Thales (fragments/reports [c.585 BCE], A12) by Aristotle - Metaphysics 983b12
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle]
     Full Idea: Thales seems, from what is recorded of him, to have supposed that the soul is something productive of movement, if he really said that the magnet has soul because it produces movement in iron.
     From: report of Thales (fragments/reports [c.585 BCE]) by Aristotle - De Anima 405a20
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius]
     Full Idea: When asked whether a man who did wrong could escape the notice of the gods, Thales is said to have replied: 'No, not even if he thinks wrong.'
     From: report of Thales (fragments/reports [c.585 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.Th.9