162 ideas
13786 | Wisdom is called 'beautiful', because it performs fine works [Plato] |
13780 | Good people are no different from wise ones [Plato] |
16281 | Honesty requires philosophical theories we can commit to with our ordinary commonsense [Lewis] |
16288 | Analysis reduces primitives and makes understanding explicit (without adding new knowledge) [Lewis] |
13778 | A dialectician is someone who knows how to ask and to answer questions [Plato] |
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
9651 | Verisimilitude might be explained as being close to the possible world where the truth is exact [Lewis] |
13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
18114 | There is no single agreed structure for set theory [Bostock] |
18107 | A 'proper class' cannot be a member of anything [Bostock] |
18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
13777 | A name is a sort of tool [Plato] |
13790 | A name-giver might misname something, then force other names to conform to it [Plato] |
13791 | Things must be known before they are named, so it can't be the names that give us knowledge [Plato] |
13789 | Anyone who knows a thing's name also knows the thing [Plato] |
18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
15731 | Quantification sometimes commits to 'sets', but sometimes just to pluralities (or 'classes') [Lewis] |
18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
18097 | The Peano Axioms describe a unique structure [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
18140 | The best version of conceptualism is predicativism [Bostock] |
18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
10470 | There are only two kinds: sets, and possibilia (actual and possible particulars) [Lewis, by Oliver] |
2063 | How can beauty have identity if it changes? [Plato] |
9650 | Supervenience concerns whether things could differ, so it is a modal notion [Lewis] |
8909 | Abstractions may well be verbal fictions, in which we ignore some features of an object [Lewis] |
9057 | Vagueness is semantic indecision: we haven't settled quite what our words are meant to express [Lewis] |
9671 | Whether or not France is hexagonal depends on your standards of precision [Lewis] |
13775 | We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato] |
15751 | Surely 'slept in by Washington' is a property of some bed? [Lewis] |
15735 | Properties don't have degree; they are determinate, and things have varying relations to them [Lewis] |
9656 | The 'abundant' properties are just any bizarre property you fancy [Lewis] |
15737 | To be a 'property' is to suit a theoretical role [Lewis] |
15742 | A disjunctive property can be unnatural, but intrinsic if its disjuncts are intrinsic [Lewis] |
15397 | If a global intrinsic never varies between possible duplicates, all necessary properties are intrinsic [Cameron on Lewis] |
15398 | Global intrinsic may make necessarily coextensive properties both intrinsic or both extrinsic [Cameron on Lewis] |
15741 | All of the natural properties are included among the intrinsic properties [Lewis] |
15752 | We might try defining the natural properties by a short list of them [Lewis] |
14996 | Natural properties give similarity, joint carving, intrinsicness, specificity, homogeneity... [Lewis] |
15744 | We can't define natural properties by resemblance, if they are used to explain resemblance [Lewis] |
15743 | Defining natural properties by means of laws of nature is potentially circular [Lewis] |
15740 | I don't take 'natural' properties to be fixed by the nature of one possible world [Lewis] |
16262 | Sparse properties rest either on universals, or on tropes, or on primitive naturalness [Lewis, by Maudlin] |
15739 | There is the property of belonging to a set, so abundant properties are as numerous as the sets [Lewis] |
10723 | A property is the set of its actual and possible instances [Lewis, by Oliver] |
15399 | The property of being F is identical with the set of objects, in all possible worlds, which are F [Lewis, by Cameron] |
15732 | Properties don't seem to be sets, because different properties can have the same set [Lewis] |
15733 | Accidentally coextensive properties come apart when we include their possible instances [Lewis] |
15734 | If a property is relative, such as being a father or son, then set membership seems relative too [Lewis] |
9655 | Trilateral and triangular seem to be coextensive sets in all possible worlds [Lewis] |
16290 | I believe in properties, which are sets of possible individuals [Lewis] |
9653 | It would be easiest to take a property as the set of its instances [Lewis] |
9657 | You must accept primitive similarity to like tropes, but tropes give a good account of it [Lewis] |
15750 | Tropes need a similarity primitive, so they cannot be used to explain similarity [Lewis] |
15749 | Trope theory (unlike universals) needs a primitive notion of being duplicates [Lewis] |
15748 | Trope theory needs a primitive notion for what unites some tropes [Lewis] |
15745 | Universals recur, are multiply located, wholly present, make things overlap, and are held in common [Lewis] |
15746 | If particles were just made of universals, similar particles would be the same particle [Lewis] |
15747 | Universals aren't parts of things, because that relationship is transitive, and universals need not be [Lewis] |
13787 | Doesn't each thing have an essence, just as it has other qualities? [Plato] |
9667 | Mereological composition is unrestricted: any class of things has a mereological sum [Lewis] |
13268 | There are no restrictions on composition, because they would be vague, and composition can't be vague [Lewis, by Sider] |
13774 | Things don't have every attribute, and essence isn't private, so each thing has an essence [Plato] |
13793 | An essential property is one possessed by all counterparts [Lewis, by Elder] |
13772 | Is the being or essence of each thing private to each person? [Plato] |
9663 | A thing 'perdures' if it has separate temporal parts, and 'endures' if it is wholly present at different times [Lewis] |
14737 | Properties cannot be relations to times, if there are temporary properties which are intrinsic [Lewis, by Sider] |
9664 | Endurance is the wrong account, because things change intrinsic properties like shape [Lewis] |
9665 | There are three responses to the problem that intrinsic shapes do not endure [Lewis] |
19280 | I can ask questions which create a context in which origin ceases to be essential [Lewis] |
15968 | Identity is simple - absolutely everything is self-identical, and nothing is identical to another thing [Lewis] |
15969 | Two things can never be identical, so there is no problem [Lewis] |
13788 | If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato] |
9660 | The impossible can be imagined as long as it is a bit vague [Lewis] |
9669 | There are no free-floating possibilia; they have mates in a world, giving them extrinsic properties [Lewis] |
16133 | Possible worlds can contain contradictions if such worlds are seen as fictions [Lewis] |
16132 | On mountains or in worlds, reporting contradictions is contradictory, so no such truths can be reported [Lewis] |
16283 | For me, all worlds are equal, with each being actual relative to itself [Lewis] |
12255 | For Lewis there is no real possibility, since all possibilities are actual [Oderberg on Lewis] |
9219 | Lewis posits possible worlds just as Quine says that physics needs numbers and sets [Lewis, by Sider] |
15022 | If possible worlds really exist, then they are part of actuality [Sider on Lewis] |
10469 | A world is a maximal mereological sum of spatiotemporally interrelated things [Lewis] |
16441 | Lewis rejects actualism because he identifies properties with sets [Lewis, by Stalnaker] |
16282 | Ersatzers say we have one world, and abstract representations of how it might have been [Lewis] |
16284 | Ersatz worlds represent either through language, or by models, or magically [Lewis] |
16286 | Linguistic possible worlds need a complete supply of unique names for each thing [Lewis] |
16287 | Maximal consistency for a world seems a modal distinction, concerning what could be true together [Lewis] |
9662 | Linguistic possible worlds have problems of inconsistencies, no indiscernibles, and vocabulary [Lewis] |
7690 | If sets exist, then defining worlds as proposition sets implies an odd distinction between existing and actual [Jacquette on Lewis] |
14404 | The counterpart relation is sortal-relative, so objects need not be a certain way [Lewis, by Merricks] |
5440 | A counterpart in a possible world is sufficiently similar, and more similar than anything else [Lewis, by Mautner] |
5441 | Why should statements about what my 'counterpart' could have done interest me? [Mautner on Lewis] |
16291 | In counterpart theory 'Humphrey' doesn't name one being, but a mereological sum of many beings [Lewis] |
11903 | Extreme haecceitists could say I might have been a poached egg, but it is too remote to consider [Lewis, by Mackie,P] |
15129 | Haecceitism implies de re differences but qualitative identity [Lewis] |
9670 | Extreme haecceitism says you might possibly be a poached egg [Lewis] |
16279 | General causal theories of knowledge are refuted by mathematics [Lewis] |
13792 | There can't be any knowledge if things are constantly changing [Plato] |
9661 | Induction is just reasonable methods of inferring the unobserved from the observed [Lewis] |
9652 | To just expect unexamined emeralds to be grue would be totally unreasonable [Lewis] |
9658 | An explanation tells us how an event was caused [Lewis] |
16280 | Often explanaton seeks fundamental laws, rather than causal histories [Lewis] |
16274 | If the well-ordering of a pack of cards was by shuffling, the explanation would make it more surprising [Lewis] |
13781 | Soul causes the body to live, and gives it power to breathe and to be revitalized [Plato] |
8901 | Abstraction is usually explained either by example, or conflation, or abstraction, or negatively [Lewis] |
8904 | The Way of Abstraction says an incomplete description of a concrete entity is the complete abstraction [Lewis] |
8938 | The Way of Example compares donkeys and numbers, but what is the difference, and what are numbers? [Lewis] |
8903 | Abstracta can be causal: sets can be causes or effects; there can be universal effects; events may be sets [Lewis] |
8902 | If abstractions are non-spatial, then both sets and universals seem to have locations [Lewis] |
8905 | If universals or tropes are parts of things, then abstraction picks out those parts [Lewis] |
8906 | If we can abstract the extrinsic relations and features of objects, abstraction isn't universals or tropes [Lewis] |
8907 | The abstract direction of a line is the equivalence class of it and all lines parallel to it [Lewis] |
8908 | For most sets, the concept of equivalence is too artificial to explain abstraction [Lewis] |
16289 | We can't account for an abstraction as 'from' something if the something doesn't exist [Lewis] |
16278 | A particular functional role is what gives content to a thought [Lewis] |
9654 | A proposition is a set of entire possible worlds which instantiate a particular property [Lewis] |
15736 | A proposition is the property of being a possible world where it holds true [Lewis] |
15738 | Propositions can't have syntactic structure if they are just sets of worlds [Lewis] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
13785 | 'Arete' signifies lack of complexity and a free-flowing soul [Plato] |
9659 | Causation is when at the closest world without the cause, there is no effect either [Lewis] |
9666 | It is quite implausible that the future is unreal, as that would terminate everything [Lewis] |
13779 | The natural offspring of a lion is called a 'lion' (but what about the offspring of a king?) [Plato] |
13783 | Even the gods love play [Plato] |