113 ideas
20186 | Unlike knowledge, wisdom cannot be misused [Zagzebski] |
19694 | Wisdom is the property of a person, not of their cognitive state [Zagzebski, by Whitcomb] |
20221 | Precision is only one of the virtues of a good definition [Zagzebski] |
20220 | Objection by counterexample is weak, because it only reveals inaccuracies in one theory [Zagzebski] |
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] |
458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
20188 | Modern epistemology is too atomistic, and neglects understanding [Zagzebski] |
20223 | Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski] |
20217 | Truth is valuable, but someone knowing the truth is more valuable [Zagzebski] |
20191 | Some beliefs are fairly voluntary, and others are not at all so [Zagzebski] |
20222 | Knowledge either aims at a quantity of truths, or a quality of understanding of truths [Zagzebski] |
20225 | For internalists Gettier situations are where internally it is fine, but there is an external mishap [Zagzebski] |
20226 | Gettier problems are always possible if justification and truth are not closely linked [Zagzebski] |
20228 | We avoid the Gettier problem if the support for the belief entails its truth [Zagzebski] |
20227 | Gettier cases arise when good luck cancels out bad luck [Zagzebski] |
20194 | Intellectual virtues are forms of moral virtue [Zagzebski] |
20210 | A reliable process is no use without the virtues to make use of them [Zagzebski] |
20206 | Intellectual and moral prejudice are the same vice (and there are other examples) [Zagzebski] |
20208 | We can name at least thirteen intellectual vices [Zagzebski] |
20215 | A justified belief emulates the understanding and beliefs of an intellectually virtuous person [Zagzebski] |
20187 | Epistemic perfection for reliabilism is a truth-producing machine [Zagzebski] |
462 | One vision is produced by both eyes [Empedocles] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
20218 | The self is known as much by its knowledge as by its action [Zagzebski] |
22765 | Wisdom and thought are shared by all things [Empedocles] |
1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
20205 | The feeling accompanying curiosity is neither pleasant nor painful [Zagzebski] |
20202 | Motives involve desires, but also how the desires connect to our aims [Zagzebski] |
20216 | Modern moral theory concerns settling conflicts, rather than human fulfilment [Zagzebski] |
552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
20193 | Moral luck means our praise and blame may exceed our control or awareness [Zagzebski] |
20199 | Nowadays we doubt the Greek view that the flourishing of individuals and communities are linked [Zagzebski] |
20196 | Virtue theory is hopeless if there is no core of agreed universal virtues [Zagzebski] |
20200 | A virtue must always have a corresponding vice [Zagzebski] |
20201 | Eight marks distingush skills from virtues [Zagzebski, by PG] |
20203 | Virtues are deep acquired excellences of persons, which successfully attain desire ends [Zagzebski] |
20207 | Every moral virtue requires a degree of intelligence [Zagzebski] |
20214 | Virtue theory can have lots of rules, as long as they are grounded in virtues and in facts [Zagzebski] |
20213 | We need phronesis to coordinate our virtues [Zagzebski] |
20209 | For the virtue of honesty you must be careful with the truth, and not just speak truly [Zagzebski] |
20197 | The courage of an evil person is still a quality worth having [Zagzebski] |
589 | 'Nature' is just a word invented by people [Empedocles] |
21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
459 | All change is unity through love or division through hate [Empedocles] |
13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
461 | God is a pure, solitary, and eternal sphere [Empedocles] |
466 | God is pure mind permeating the universe [Empedocles] |
1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
1522 | It is wretched not to want to think clearly about the gods [Empedocles] |