Combining Texts

All the ideas for 'Reply to Fourth Objections', 'works' and 'The Human Body is a sort of Machine'

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5 ideas

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

3340	Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
	Full Idea: Von Neumann defines each number as the set of all smaller numbers.
	From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280

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

3355	Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
	Full Idea: Von Neumann suggested that functions be pressed into service to replace sets.
	From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

22716	Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
	Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers.
	From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm'
	A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started.

17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism

3643	The concept of mind excludes body, and vice versa [Descartes]
	Full Idea: The concept of body includes nothing at all which belongs to the mind, and the concept of mind includes nothing at all which belongs to the body.
	From: René Descartes (Reply to Fourth Objections [1641], 225)
	A reaction: A headache? Hunger? The mistake, I think, is to regard the mind as entirely conscious, thus creating a sharp boundary between two aspects of our lives. As shown by blindsight, I take many of my central mental operations to be pre- or non-conscious.

26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes

19376	A machine is best defined by its final cause, which explains the roles of the parts [Leibniz]
	Full Idea: Any machine ...is best defined in terms of its final cause, so that in the description of the parts it is therefore apparent in what way each of them is coordinated with the others for the intended us.
	From: Gottfried Leibniz (The Human Body is a sort of Machine [1683], p.290), quoted by Richard T.W. Arthur - Leibniz 3 'Machines'
	A reaction: We would use the 'function', an inherently teleological concept, and a concept which is almost indispensable for giving an illuminating description of the world. If nature is dispositional, it points towards things. Leibniz views persons as machines.