73 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
5728 | The concept of truth was originated by the senses [Lucretius] |
19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
19121 | We can reduce properties to true formulas [Halbach/Leigh] |
19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
5702 | The senses are much the best way to distinguish true from false [Lucretius] |
5729 | If the senses are deceptive, reason, which rests on them, is even worse [Lucretius] |
5697 | The only possible standard for settling doubts is the foundation of the senses [Lucretius] |
5727 | Most supposed delusions of the senses are really misinterpretations by the mind [Lucretius] |
5714 | Even simple facts are hard to believe at first hearing [Lucretius] |
5718 | The mind is in the middle of the breast, because there we experience fear and joy [Lucretius] |
5717 | The mind is a part of a man, just like a hand or an eye [Lucretius] |
21387 | The separate elements and capacities of a mind cannot be distinguished [Lucretius] |
5709 | The actions of the mind are not determinate and passive, because atoms can swerve [Lucretius] |
5695 | Only bodies can touch one another [Lucretius] |
5711 | The earth is and always has been an insentient being [Lucretius] |
5712 | Particles may have sensation, but eggs turning into chicks suggests otherwise [Lucretius] |
5719 | The mind moves limbs, wakes the body up, changes facial expressions, which involve touch [Lucretius] |
5724 | Lions, foxes and deer have distinct characters because their minds share in their bodies [Lucretius] |
5713 | You needn't be made of laughing particles to laugh, so why not sensation from senseless seeds? [Lucretius] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
6611 | One man's meat is another man's poison [Lucretius] |
5730 | Our bodies weren't created to be used; on the contrary, their creation makes a use possible [Lucretius] |
5726 | The dead are no different from those who were never born [Lucretius] |
5705 | Nature only wants two things: freedom from pain, and pleasure [Lucretius] |
5716 | Nature runs the universe by herself without the aid of gods [Lucretius] |
5704 | There can be no centre in infinity [Lucretius] |
5703 | The universe must be limitless, since there could be nothing outside to limit it [Lucretius] |
5693 | Everything is created and fed by nature from atoms, and they return to atoms in death [Lucretius] |
5701 | If an object is infinitely subdivisible, it will be the same as the whole universe [Lucretius] |
5708 | In downward motion, atoms occasionally swerve slightly for no reason [Lucretius] |
17004 | Nothing can break the binding laws of eternity [Lucretius] |
5696 | If there were no space there could be no movement, or even creation [Lucretius] |
5706 | Atoms move themselves [Lucretius] |
5700 | It is quicker to break things up than to assemble them [Lucretius] |
5698 | We can only sense time by means of movement, or its absence [Lucretius] |
5715 | This earth is very unlikely to be the only one created [Lucretius] |
5694 | Nothing can be created by divine power out of nothing [Lucretius] |
5699 | If matter wasn't everlasting, everything would have disappeared by now [Lucretius] |
5707 | The universe can't have been created by gods, because it is too imperfect [Lucretius] |
5710 | Gods are tranquil and aloof, and have no need of or interest in us [Lucretius] |
5731 | Why does Jupiter never hurl lightning from a blue sky? [Lucretius] |
5722 | For a separated spirit to remain sentient it would need sense organs attached to it [Lucretius] |
5725 | An immortal mind couldn't work harmoniously with a mortal body [Lucretius] |
5720 | Spirit is mortal [Lucretius] |
5721 | The mind is very small smooth particles, which evaporate at death [Lucretius] |
5723 | If spirit is immortal and enters us at birth, why don't we remember a previous existence? [Lucretius] |