58 ideas
| 6602 | Philosophy is like a statue which is worshipped but never advances [Bacon] |
| 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] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| 16639 | Only individual bodies exist [Bacon] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 16625 | In hylomorphism all the explanation of actions is in the form, and the matter doesn't do anything [Bacon] |
| 16033 | There are only individual bodies containing law-based powers, and the Forms are these laws [Bacon] |
| 16724 | The senses deceive, but also show their own errors [Bacon] |
| 12121 | We don't assume there is no land, because we can only see sea [Bacon] |
| 3648 | Empiricists are collecting ants; rationalists are spinning spiders; and bees do both [Bacon] |
| 12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
| 6603 | Nature is revealed when we put it under pressure rather than observe it [Bacon] |
| 21950 | Science must clear away the idols of the mind if they are ever going to find the truth [Bacon] |
| 12127 | Many different theories will fit the observed facts [Bacon] |
| 12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
| 8122 | True works of art transmit completely new feelings [Tolstoy] |
| 8121 | Art is when one man uses external signs to hand on his feelings to another man [Tolstoy] |
| 8124 | The highest feelings of mankind can only be transmitted by art [Tolstoy] |
| 8123 | The purpose of art is to help mankind to evolve better, more socially beneficial feelings [Tolstoy] |
| 22710 | People estimate art according to their moral values [Tolstoy] |
| 8125 | The upper classes put beauty first, and thus freed themselves from morality [Tolstoy] |
| 8064 | We separate the concept of beauty from goodness, unlike the ancients [Tolstoy] |
| 12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
| 16624 | Stripped and passive matter is just a human invention [Bacon] |
| 12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |
| 7399 | Even without religion, there are many guides to morality [Bacon] |