30 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
18789 | Intuitionist logic looks best as natural deduction [Mares] |
18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
18782 | The connectives are studied either through model theory or through proof theory [Mares] |
10816 | We can use mereology to simulate quantification over relations [Lewis] |
18783 | Many-valued logics lack a natural deduction system [Mares] |
18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
10808 | Mathematics is generalisations about singleton functions [Lewis] |
10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |