60 ideas
14025 | The weaker version of Truthmaker: 'truth supervenes on being' [Crisp,TM] |
14023 | The Truthmaker thesis spells trouble for presentists [Crisp,TM] |
14024 | Truthmaker has problems with generalisation, non-existence claims, and property instantiations [Crisp,TM] |
15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
14021 | Worm Perdurantism has a fusion of all the parts; Stage Perdurantism has one part at a time [Crisp,TM] |
21181 | Relativity and Quantum theory give very different accounts of forces [Hesketh] |
21183 | Thermodynamics introduced work and entropy, to understand steam engine efficiency [Hesketh] |
21191 | Photons are B and W° bosons, linked by the Higgs mechanism [Hesketh] |
21199 | Spinning electric charge produces magnetism, so all fermions are magnets [Hesketh] |
21180 | Electrons are fundamental and are not made of anything; they are properties without size [Hesketh] |
21189 | Electrons may have smaller components, bound by a new force [Hesketh] |
21184 | Physics was rewritten to explain stable electron orbits [Hesketh] |
21182 | Quantum mechanics is our only theory, and is very precise, and repeatedly confirmed [Hesketh] |
21187 | Virtual particles can't be measured, and can ignore the laws of physics [Hesketh] |
21185 | Colour charge is positive or negative, and also has red, green or blue direction [Hesketh] |
21195 | In Supersymmetry the Standard Model simplifies at high energies [Hesketh] |
21194 | The Standard Model omits gravity, because there are no particles involved [Hesketh] |
21197 | Standard Model forces are one- two- and three-dimensional [Hesketh] |
21188 | Quarks and leptons have a weak charge, for the weak force [Hesketh] |
21186 | Quarks rush wildly around in protons, restrained by the gluons [Hesketh] |
21192 | Neutrinos only interact with the weak force, but decays produce them in huge numbers [Hesketh] |
21196 | To combine the forces, they must all be the same strength at some point [Hesketh] |
21190 | 'Space' in physics just means location [Hesketh] |
14020 | 'Eternalism' is the thesis that reality includes past, present and future entities [Crisp,TM] |
14026 | Presentists can talk of 'times', with no more commitment than modalists have to possible worlds [Crisp,TM] |
14022 | The only three theories are Presentism, Dynamic (A-series) Eternalism and Static (B-series) Eternalism [Crisp,TM] |
21193 | The universe is 68% dark energy, 27% dark matter, 5% regular matter [Hesketh] |
21198 | If a cosmic theory relies a great deal on fine-tuning basic values, it is probably wrong [Hesketh] |