89 ideas
| 22353 | One view says objectivity is making a successful claim which captures the facts [Reiss/Sprenger] |
| 22356 | An absolute scientific picture of reality must not involve sense experience, which is perspectival [Reiss/Sprenger] |
| 22359 | Topic and application involve values, but can evidence and theory choice avoid them? [Reiss/Sprenger] |
| 22360 | The Value-Free Ideal in science avoids contextual values, but embraces epistemic values [Reiss/Sprenger] |
| 22362 | Value-free science needs impartial evaluation, theories asserting facts, and right motivation [Reiss/Sprenger] |
| 22364 | Thermometers depend on the substance used, and none of them are perfect [Reiss/Sprenger] |
| 501 | Reason is a more powerful persuader than gold [Democritus (attr)] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 22357 | The 'experimenter's regress' says success needs reliability, which is only tested by success [Reiss/Sprenger] |
| 22365 | The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 514 | Beauty is merely animal without intelligence [Democritus (attr)] |
| 525 | Behave well when alone, and feel shame in you own eyes [Democritus (attr)] |
| 502 | Good breeding in men means having a good character [Democritus (attr)] |
| 507 | Virtuous love consists of decorous desire for the beautiful [Democritus (attr)] |
| 521 | We should only choose pleasures which are concerned with the beautiful [Democritus (attr)] |
| 505 | Good and true are the same for everyone, but pleasures differ [Democritus (attr)] |
| 508 | Only accept beneficial pleasures [Democritus (attr)] |
| 520 | The great pleasures come from the contemplation of noble works [Democritus (attr)] |
| 522 | Moderation brings more pleasures, and so increases pleasure [Democritus (attr)] |
| 506 | Immoderate desire is the mark of a child, not an adult [Democritus (attr)] |
| 523 | It is as brave to master pleasure as to overcome the enemy [Democritus (attr)] |
| 503 | Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)] |
| 518 | A bad life is just a drawn-out death [Democritus (attr)] |
| 497 | Be virtuous from duty, not from fear [Democritus (attr)] |
| 499 | Repentance of shameful deeds is salvation [Democritus (attr)] |
| 524 | Virtue comes more from practice than from nature [Democritus (attr)] |
| 519 | One must avoid even speaking of evil deeds [Democritus (attr)] |
| 500 | The wrongdoer is more unfortunate than the person wronged [Democritus (attr)] |
| 1539 | The endless desire for money is a crueller slavery than poverty [Democritus (attr)] |
| 526 | Small appetite makes poverty equal to wealth [Democritus (attr)] |
| 511 | It is better to have one intelligent friend than many unintelligent [Democritus (attr)] |
| 498 | It is a great thing, when one is in adversity, to think of duty [Democritus (attr)] |
| 1541 | It is better to be poor in a democracy than be rich without freedom [Democritus (attr)] |