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18189
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ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
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Full Idea:
We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
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From:
Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
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A reaction:
Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).
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16730
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If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
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Full Idea:
Since these atoms are the whole of the corporeal matter or substance that exists in bodies, if we conceive or notice anything else to exist in these bodies, that is not a substance but only some kind of mode of the substance.
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From:
Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
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A reaction:
If the atoms have a few qualities of their own, are they just modes? If they are genuine powers, then there can be emergent powers, which are rather more than mere 'modes'.
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16619
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We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
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Full Idea:
Nothing beyond qualities is perceived by the senses. …When we refer to the substance in which the qualities inhere, we do this through induction, by which we reason that some subject lies under the quality.
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From:
Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.1
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A reaction:
He talks of 'induction' (in an older usage), but he seems to mean abduction, since he never makes any observations of the substances being proposed.
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20723
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Only when working people are poor do they remain obedient to God [Calvin, by Weber]
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Full Idea:
Calvin made the much-quoted statement that only when the people, i.e. the mass of labourers and craftsmen, were poor did they remain obedient to God.
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From:
report of Jean Calvin (works [1549]) by Max Weber - The Protestant Ethic and the Spirit of Capitalism 5
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A reaction:
This is only one aspect of Christian influence. The alternative is John Wesley's exhortation to work diligently, live modestly, save, invest and get rich. Most people want a comfortable intermediate state, but who proclaims that?
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16593
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Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
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Full Idea:
The vulgar think atoms lack parts and are free of all magnitude, and hence nothing other than a mathematical point, but it is something solid and hard and compact, as to leave no room for division, separation and cutting. No force in nature can divide it.
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From:
Pierre Gassendi (Syntagma [1658], II.1.3.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2
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A reaction:
If you gloatingly think the atom has now been split, ask whether electrons and quarks now fit his description. Pasnau notes that though atoms are indivisible, they are not incorruptible, and could go out of existence, or be squashed.
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16729
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How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]
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Full Idea:
If the only material principles of things are atoms, having only size, shape, and weight, or motion, then why are so many additional qualities created and existing within the things: color, heat, flavor, odor, and innumerable others?
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From:
Pierre Gassendi (Syntagma [1658], II.1.5.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
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A reaction:
This is pretty much the 'hard question' about the mind-body relation. Bacon said that heat was just motion of matter. I would say that this problem is gradually being solved in my lifetime.
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