209 ideas
19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
15390 | Metaphysics attempts to give an account of everything, in terms of categories and principles [Simons] |
12865 | Analytic philosophers may prefer formal systems because natural language is such mess [Simons] |
10838 | To explain a concept, we need its purpose, not just its rules of usage [Dummett] |
17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
19067 | A successful proof requires recognition of truth at every step [Dummett] |
10837 | It is part of the concept of truth that we aim at making true statements [Dummett] |
10840 | We must be able to specify truths in a precise language, like winning moves in a game [Dummett] |
19171 | Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson] |
8166 | Truth is part of semantics, since valid inference preserves truth [Dummett] |
19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
16951 | It was realised that possible worlds covered all modal logics, if they had a structure [Dummett] |
16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
16960 | If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett] |
16958 | In S4 the actual world has a special place [Dummett] |
18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher] |
18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
12815 | Classical mereology doesn't apply well to the objects around us [Simons] |
12832 | Complement: the rest of the Universe apart from some individual, written x-bar [Simons] |
12834 | Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons] |
12819 | A 'part' has different meanings for individuals, classes, and masses [Simons] |
12822 | Proper or improper part: x < y, 'x is (a) part of y' [Simons] |
12824 | Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons] |
12827 | Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons] |
12823 | Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons] |
12825 | Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons] |
12826 | Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons] |
12828 | General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons] |
12829 | General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons] |
12830 | Universe: the mereological sum of all objects whatever, written 'U' [Simons] |
12831 | Atom: an individual with no proper parts, written 'At x' [Simons] |
12844 | Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons] |
12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
12846 | A 'group' is a collection with a condition which constitutes their being united [Simons] |
12848 | The same members may form two groups [Simons] |
12861 | 'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons] |
11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
8173 | Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett] |
8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
7334 | Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A] |
8179 | The law of excluded middle is the logical reflection of the principle of bivalence [Dummett] |
9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
18801 | Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett] |
12876 | Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons] |
9182 | Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett] |
19057 | Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett] |
9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
12845 | Some natural languages don't distinguish between singular and plural [Simons] |
19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
9896 | A prime number is one which is measured by a unit alone [Dummett] |
18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
9895 | A number is a multitude composed of units [Dummett] |
9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
12838 | Four-dimensional ontology has no change, since that needs an object, and time to pass [Simons] |
12842 | There are real relational changes, as well as bogus 'Cambridge changes' [Simons] |
12841 | I don't believe in processes [Simons] |
12836 | Fans of process ontology cheat, since river-stages refer to 'rivers' [Simons] |
8979 | Slow and continuous events (like balding or tree-growth) are called 'processes', not 'events' [Simons] |
8981 | Maybe processes behave like stuff-nouns, and events like count-nouns [Simons] |
12880 | Moments are things like smiles or skids, which are founded on other things [Simons] |
12883 | Moving disturbances are are moments which continuously change their basis [Simons] |
12881 | A smiling is an event with causes, but the smile is a continuant without causes [Simons] |
12882 | A wave is maintained by a process, but it isn't a process [Simons] |
12840 | I do not think there is a general identity condition for events [Simons] |
8973 | Einstein's relativity brought events into ontology, as the terms of a simultaneity relationships [Simons] |
12839 | Relativity has an ontology of things and events, not on space-time diagrams [Simons] |
12879 | Independent objects can exist apart, and maybe even entirely alone [Simons] |
10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
12847 | Mass nouns admit 'much' and 'a little', and resist 'many' and 'few'. [Simons] |
12863 | Mass terms (unlike plurals) are used with indifference to whether they can exist in units [Simons] |
12862 | Gold is not its atoms, because the atoms must be all gold, but gold contains neutrons [Simons] |
12858 | Mixtures disappear if nearly all of the mixture is one ingredient [Simons] |
12859 | A mixture can have different qualities from its ingredients. [Simons] |
22297 | Dummett saw realism as acceptance of bivalence, rather than of mind-independent entities [Dummett, by Potter] |
9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
15049 | Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett] |
8184 | Philosophers should not presume reality, but only invoke it when language requires it [Dummett] |
8185 | We can't make sense of a world not apprehended by a mind [Dummett] |
8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
3303 | For anti-realists there are no natural distinctions between objects [Dummett, by Benardete,JA] |
8163 | Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts [Dummett] |
8161 | We know we can state facts, with true statements [Dummett] |
21628 | To say reality itself is vague is not properly intelligible [Dummett] |
8180 | 'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not [Dummett] |
10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
10532 | We can understand universals by studying predication [Dummett] |
10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
10543 | Abstract objects must have names that fall within the range of some functional expression [Dummett] |
9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
12850 | To individuate something we must pick it out, but also know its limits of variation [Simons] |
12860 | Sortal nouns for continuants tell you their continuance- and cessation-conditions [Simons] |
12886 | A whole requires some unique relation which binds together all of the parts [Simons] |
12857 | Tibbles isn't Tib-plus-tail, because Tibbles can survive its loss, but the sum can't [Simons] |
12835 | Does Tibbles remain the same cat when it loses its tail? [Simons] |
12820 | Without extensional mereology two objects can occupy the same position [Simons] |
12866 | Composition is asymmetric and transitive [Simons] |
12867 | A hand constitutes a fist (when clenched), but a fist is not composed of an augmented hand [Simons] |
12864 | We say 'b is part of a', 'b is a part of a', 'b are a part of a', or 'b are parts of a'. [Simons] |
12814 | Classical mereology says there are 'sums', for whose existence there is no other evidence [Simons] |
12817 | 'Mereological extensionality' says objects with the same parts are identical [Simons] |
12833 | If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals [Simons] |
12849 | Sums are more plausible for pluralities and masses than they are for individuals [Simons] |
12877 | Sums of things in different categories are found within philosophy. [Simons] |
12888 | The wholeness of a melody seems conventional, but of an explosion it seems natural [Simons] |
12871 | Objects have their essential properties because of the kind of objects they are [Simons] |
12870 | We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence [Simons] |
12873 | Original parts are the best candidates for being essential to artefacts [Simons] |
12874 | An essential part of an essential part is an essential part of the whole [Simons] |
12837 | Four dimensional-objects are stranger than most people think [Simons] |
12856 | Intermittent objects would be respectable if they occurred in nature, as well as in artefacts [Simons] |
12885 | Objects like chess games, with gaps in them, are thereby less unified [Simons] |
12854 | An entrepreneur and a museum curator would each be happy with their ship at the end [Simons] |
12855 | The 'best candidate' theories mistakenly assume there is one answer to 'Which is the real ship?' [Simons] |
12872 | The zygote is an essential initial part, for a sexually reproduced organism [Simons] |
9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |
12889 | The limits of change for an individual depend on the kind of individual [Simons] |
8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
8178 | Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
8175 | A theory of thought will include propositional attitudes as well as propositions [Dummett] |
8174 | The theories of meaning and understanding are the only routes to an account of thought [Dummett] |
19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
10839 | You can't infer a dog's abstract concepts from its behaviour [Dummett] |
18883 | Any equivalence relation among similar things allows the creation of an abstractum [Simons] |
18884 | Abstraction is usually seen as producing universals and numbers, but it can do more [Simons] |
10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
8165 | To 'abstract from' is a logical process, as opposed to the old mental view [Dummett] |
19055 | Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett] |
19056 | If a sentence is effectively undecidable, we can never know its truth conditions [Dummett] |
8168 | To know the truth-conditions of a sentence, you must already know the meaning [Dummett] |
8193 | Verification is not an individual but a collective activity [Dummett] |
8181 | A justificationist theory of meaning leads to the rejection of classical logic [Dummett] |
8182 | Verificationism could be realist, if we imagined the verification by a superhuman power [Dummett] |
8183 | If truths about the past depend on memories and current evidence, the past will change [Dummett] |
19054 | Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett] |
8176 | We could only guess the meanings of 'true' and 'false' when sentences were used [Dummett] |
8170 | Sentences are the primary semantic units, because they can say something [Dummett] |
19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
9181 | The causal theory of reference can't distinguish just hearing a name from knowing its use [Dummett] |
9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
8169 | We can't distinguish a proposition from its content [Dummett] |
12843 | With activities if you are doing it you've done it, with performances you must finish to have done it [Simons] |
12875 | One false note doesn't make it a performance of a different work [Simons] |
16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |
18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
8186 | Time is the measure of change, so we can't speak of time before all change [Dummett] |
8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
8167 | If Presentism is correct, we cannot even say that the present changes [Dummett] |
8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |