Combining Philosophers

All the ideas for Saunders MacLane, Richard T.W. Arthur and Margaret Cavendish

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4 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

18189	ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
	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.
	From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
	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).

10. Modality / B. Possibility / 1. Possibility

19378	Early modern possibility is what occurs sometime; for Leibniz, it is what is not contradictory [Arthur,R]
	Full Idea: For Descartes, Hobbes and Spinoza, if a state of things is possible, it must occur at some time, whether past, present or future. For Leibniz possibility makes no reference to time; an individual is possible if its concept contains no contradiction.
	From: Richard T.W. Arthur (Leibniz [2014], 4 'Contingent')
	A reaction: It has always struck me as fallacious to say that anything that is possible must at some time occur. If '6' is possible on the die, what will constrain it to eventually come up when thrown? Mere non-contradiction doesn't imply possibility either.

17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism

19380	Occasionalism contradicts the Eucharist, which needs genuine changes of substance [Arthur,R]
	Full Idea: The Jesuits rejected occasionalism ... because it is incompatible with the Catholic interpretation of the Eucharist, which there is genuine change of substance of the bread into the substance of Christ (transubstantiation).
	From: Richard T.W. Arthur (Leibniz [2014], 5 'Substance')
	A reaction: Not sure I understand this, but I take it that the Eucharist needs a real relation across the substance-spirit boundary, and not just a co-ordination.

17. Mind and Body / E. Mind as Physical / 1. Physical Mind

23221	The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish]
	Full Idea: Sensitive and rational matter …makes not only the Brain, but all Thoughts, Conceptions, Imaginations, Fancy, Understanding, Memory, Remembrance, and whatsoever motions are in the Head or Brain.
	From: Margaret Cavendish (Philosophical Letters [1664], p.185), quoted by Matthew Cobb - The Idea of the Brain 2
	A reaction: Judging by the date of this, and that she is a Cavendish, the influence of Hobbes must be strong, which was brave in 1664. A very strong statement of reductive physicalism, making sure that nothing is left out.