57 ideas
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
10635 | Second-order quantification and plural quantification are different [Linnebo] |
10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
9464 | One of their own prophets said that Cretans are always liars [Anon (Titus)] |
22886 | The modern idea of 'limit' allows infinite quantities to have a finite sum [Bardon] |
23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
22914 | An equally good question would be why there was nothing instead of something [Bardon] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
22902 | Why does an effect require a prior event if the prior event isn't a cause? [Bardon] |
22905 | Becoming disordered is much easier for a system than becoming ordered [Bardon] |
22913 | The universe expands, so space-time is enlarging [Bardon] |
22889 | We should treat time as adverbial, so we don't experience time, we experience things temporally [Bardon, by Bardon] |
22900 | How can we question the passage of time, if the question takes time to ask? [Bardon] |
22898 | What is time's passage relative to, and how fast does it pass? [Bardon] |
22897 | The A-series says a past event is becoming more past, but how can it do that? [Bardon] |
22901 | The B-series needs a revised view of causes, laws and explanations [Bardon] |
22896 | The B-series is realist about time, but idealist about its passage [Bardon] |
22903 | The B-series adds directionality when it accepts 'earlier' and 'later' [Bardon] |
22910 | To define time's arrow by causation, we need a timeless definition of causation [Bardon] |
22909 | We judge memories to be of the past because the events cause the memories [Bardon] |
22904 | The psychological arrow of time is the direction from our memories to our anticipations [Bardon] |
22906 | The direction of entropy is probabilistic, not necessary, so cannot be identical to time's arrow [Bardon] |
22907 | It is arbitrary to reverse time in a more orderly universe, but not in a sub-system of it [Bardon] |
22883 | It seems hard to understand change without understanding time first [Bardon] |
22890 | We experience static states (while walking round a house) and observe change (ship leaving dock) [Bardon] |
22884 | The motion of a thing should be a fact in the present moment [Bardon] |
22892 | Experiences of motion may be overlapping, thus stretching out the experience [Bardon] |
22911 | At least eternal time gives time travellers a possible destination [Bardon] |
22912 | Time travel is not a paradox if we include it in the eternal continuum of events [Bardon] |
22882 | We use calendars for the order of events, and clocks for their passing [Bardon] |