81 ideas
| 23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
| 3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
| 7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
| 7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
| 23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
| 7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
| 7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
| 14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
| 7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
| 7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
| 7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
| 7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
| 7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
| 7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
| 7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
| 7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
| 20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
| 3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
| 17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
| 556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
| 7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
| 563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
| 565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
| 557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
| 7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
| 7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
| 9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
| 13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
| 7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
| 7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
| 13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
| 13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
| 7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
| 593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
| 7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
| 7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
| 7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
| 7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
| 7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
| 7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
| 7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
| 7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
| 7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
| 7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
| 13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
| 11237 | Only universals have essence [Plato, by Politis] |
| 11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
| 7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
| 7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
| 7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
| 1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
| 3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
| 7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
| 2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
| 9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
| 94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
| 17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
| 6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
| 2912 | Plato is boring [Nietzsche on Plato] |
| 1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |