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Ideas for 'fragments/reports', 'The Philosopher's Toolkit' and 'Philosophy of Mathematics'

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7 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

4632	'Natural' systems of deduction are based on normal rational practice, rather than on axioms [Baggini /Fosl]

4631	In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use [Baggini /Fosl]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets

9634	Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR]

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets

9613	Naïve set theory assumed that there is a set for every condition [Brown,JR]

9615	Nowadays conditions are only defined on existing sets [Brown,JR]

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets

9617	The 'iterative' view says sets start with the empty set and build up [Brown,JR]

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

9642	A flock of birds is not a set, because a set cannot go anywhere [Brown,JR]