60 ideas
| 1695 | Without extensive examination firm statements are hard, but studying the difficulties is profitable [Aristotle] |
| 1697 | The contrary of good is bad, but the contrary of bad is either good or another evil [Aristotle] |
| 1698 | Both sides of contraries need not exist (as health without sickness, white without black) [Aristotle] |
| 11034 | The differentiae of genera which are different are themselves different in kind [Aristotle] |
| 18367 | A true existence statement has its truth caused by the existence of the thing [Aristotle] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
| 11033 | Predications of predicates are predications of their subjects [Aristotle] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 11044 | One is prior to two, because its existence is implied by two [Aristotle] |
| 11042 | Parts of a line join at a point, so it is continuous [Aristotle] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 11041 | Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 11286 | Primary being must be more than mere indeterminate ultimate subject of predication [Politis on Aristotle] |
| 1700 | There are six kinds of change: generation, destruction, increase, diminution, alteration, change of place [Aristotle] |
| 1699 | A thing is prior to another if it implies its existence [Aristotle] |
| 18366 | Of interdependent things, the prior one causes the other's existence [Aristotle] |
| 3311 | The categories (substance, quality, quantity, relation, action, passion, place, time) peter out inconsequentially [Benardete,JA on Aristotle] |
| 11035 | There are ten basic categories for thinking about things [Aristotle] |
| 13121 | Substance,Quantity,Quality,Relation,Place,Time,Being-in-a-position,Having,Doing,Being affected [Aristotle, by Westerhoff] |
| 16116 | Aristotle derived categories as answers to basic questions about nature, size, quality, location etc. [Aristotle, by Gill,ML] |
| 21345 | Aristotle said relations are not substances, so (if they exist) they must be accidents [Aristotle, by Heil] |
| 16155 | Aristotle promoted the importance of properties and objects (rather than general and particular) [Aristotle, by Frede,M] |
| 11032 | Some things said 'of' a subject are not 'in' the subject [Aristotle] |
| 11038 | We call them secondary 'substances' because they reveal the primary substances [Aristotle] |
| 16739 | Four species of quality: states, capacities, affects, and forms [Aristotle, by Pasnau] |
| 11037 | Colour must be in an individual body, or it is not embodied [Aristotle] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 16154 | Aristotle gave up his earlier notion of individuals, because it relied on universals [Aristotle, by Frede,M] |
| 12351 | Genus and species are substances, because only they reveal the primary substance [Aristotle, by Wedin] |
| 1694 | Substances have no opposites, and don't come in degrees (including if the substance is a man) [Aristotle] |
| 16091 | Is primary substance just an ultimate subject, or some aspect of a complex body? [Aristotle, by Gill,ML] |
| 11280 | Primary being is 'that which lies under', or 'particular substance' [Aristotle, by Politis] |
| 11040 | A single substance can receive contrary properties [Aristotle] |
| 16140 | Secondary substances do have subjects, so they are not ultimate in the ontology [Aristotle, by Frede,M] |
| 10965 | In earlier Aristotle the substances were particulars, not kinds [Aristotle, by Lawson-Tancred] |
| 11036 | A 'primary' substance is in each subject, with species or genera as 'secondary' substances [Aristotle] |
| 8287 | Earlier Aristotle had objects as primary substances, but later he switched to substantial form [Aristotle, by Lowe] |
| 12350 | Things are called 'substances' because they are subjects for everything else [Aristotle] |
| 11039 | A primary substance reveals a 'this', which is an individual unit [Aristotle] |
| 12361 | Primary substances are ontological in 'Categories', and explanatory in 'Metaphysics' [Aristotle, by Wedin] |
| 3315 | Aristotle denigrates the category of relation, but for modern absolutists self-relation is basic [Benardete,JA on Aristotle] |
| 12349 | Only what can be said of many things is a predicable [Aristotle, by Wedin] |
| 11837 | Some predicates signify qualification of a substance, others the substance itself [Aristotle] |
| 11043 | It is not possible for fire to be cold or snow black [Aristotle] |
| 1696 | Change goes from possession to loss (as in baldness), but not the other way round [Aristotle] |