34 ideas
12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
12756 | Substance is a force for acting and being acted upon [Leibniz] |
12121 | We don't assume there is no land, because we can only see sea [Bacon] |
12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
12127 | Many different theories will fit the observed facts [Bacon] |
12755 | Final causes can help with explanations in physics [Leibniz] |
12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
12760 | Something rather like souls (though not intelligent) could be found everywhere [Leibniz] |
12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
12759 | There are atoms of substance, but no atoms of bulk or extension [Leibniz] |
12718 | Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz] |
12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |
11854 | If there is some trace of God in things, that would explain their natural force [Leibniz] |
12758 | It is plausible to think substances contain the same immanent force seen in our free will [Leibniz] |
19408 | To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz] |