Combining Texts

All the ideas for 'The Ages of the World', 'Les quaestiones de anima (lectures on the soul)' and 'Paradoxes of the Infinite'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

4 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9987	An aggregate in which order does not matter I call a 'set' [Bolzano]
	Full Idea: An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'.
	From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX
	A reaction: The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

10856	A truly infinite quantity does not need to be a variable [Bolzano]
	Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable.
	From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10
	A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity.

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

16618	Intellectual and moral states, and even the soul itself, depend on prime matter for their existence [Blasius, by Pasnau]
	Full Idea: Blasius argued that prime matter is the subject of all our intellectual and moral states. This implies that such states cannot exist apart from the body, which seems to imply further that the soul itself cannot exist apart from the body.
	From: report of Blasius of Parma (Les quaestiones de anima (lectures on the soul) [1385], I.8 p.65) by Robert Pasnau - Metaphysical Themes 1274-1671 06.3
	A reaction: It seems that, under pressure, Blasius recanted this view in lectures given eleven years later.

23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character

20957	We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]
	Full Idea: Nobody has chosen their character; and yet this does not stop anybody attributing the action which follows from his character to themself as a free action.
	From: Friedrich Schelling (The Ages of the World [1810], I.93)
	A reaction: This pinpoints a very nice ambivalence about our attitudes to our own characters. We all have some pride and shame about who we are, without having chosed who we are. At least when we are young. But we make the bed we lie in.