Combining Texts

All the ideas for '67: Platonic Questions', 'Syntagma' and 'On Platonism in Mathematics'

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8 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304	Very few things in set theory remain valid in intuitionist mathematics [Bernays]
	Full Idea: Very few things in set theory remain valid in intuitionist mathematics.
	From: Paul Bernays (On Platonism in Mathematics [1934])

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10303	Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
	Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought.
	From: Paul Bernays (On Platonism in Mathematics [1934], p.261)
	A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

10306	Mathematical abstraction just goes in a different direction from logic [Bernays]
	Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction.
	From: Paul Bernays (On Platonism in Mathematics [1934], p.268)
	A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic.

8. Modes of Existence / B. Properties / 8. Properties as Modes

16730	If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
	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.
	From: Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
	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'.

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

16619	We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
	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.
	From: Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.1
	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.

15. Nature of Minds / A. Nature of Mind / 2. Psuche

5960	When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch]
	Full Idea: The soul, when it has partaken of intelligence and reason and concord, is not merely a work but also a part of god and has come to be not by his agency but both from him as source and out of his substance.
	From: Plutarch (67: Platonic Questions [c.85], II.1001)
	A reaction: A most intriguing shift of view from earlier concepts of the psuché. How did this come about? This man is a pagan. The history is in the evolution of Platonism. See 'The Middle Platonists' by John Dillon. Davidson is also very impressed by reason.

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism

16593	Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
	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.
	From: Pierre Gassendi (Syntagma [1658], II.1.3.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2
	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.

16729	How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]
	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?
	From: Pierre Gassendi (Syntagma [1658], II.1.5.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4
	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.