94 ideas
| 13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
| 13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
| 13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
| 13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
| 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] |
| 13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
| 13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
| 13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [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] |
| 13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
| 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] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 3509 | Externalism may be the key idea in philosophical naturalism [Papineau] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
| 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] |
| 12583 | Belief truth-conditions are normal circumstances where the belief is supposed to occur [Papineau] |
| 13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
| 7871 | Perceptual concepts can't just refer to what causes classification [Papineau] |
| 13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
| 7852 | The only serious mind-brain theories now are identity, token identity, realization and supervenience [Papineau] |
| 7864 | Maybe mind and body do overdetermine acts, but are linked (for some reason) [Papineau] |
| 7873 | Young children can see that other individuals sometimes have false beliefs [Papineau] |
| 7874 | Do we understand other minds by simulation-theory, or by theory-theory? [Papineau] |
| 7882 | Researching phenomenal consciousness is peculiar, because the concepts involved are peculiar [Papineau] |
| 7854 | Whether octopuses feel pain is unclear, because our phenomenal concepts are too vague [Papineau] |
| 7889 | Our concept of consciousness is crude, and lacks theoretical articulation [Papineau] |
| 7891 | We can’t decide what 'conscious' means, so it is undecidable whether cats are conscious [Papineau] |
| 7890 | Maybe a creature is conscious if its mental states represent things in a distinct way [Papineau] |
| 7885 | The 'actualist' HOT theory says consciousness comes from actual higher judgements of mental states [Papineau] |
| 7886 | Actualist HOT theories imply that a non-conscious mental event could become conscious when remembered [Papineau] |
| 7887 | States are conscious if they could be the subject of higher-order mental judgements [Papineau] |
| 7888 | Higher-order judgements may be possible where the subject denies having been conscious [Papineau] |
| 7860 | The epiphenomenal relation of mind and brain is a 'causal dangler', unlike anything else [Papineau] |
| 7862 | Maybe minds do not cause actions, but do cause us to report our decisions [Papineau] |
| 3513 | How does a dualist mind represent, exist outside space, and be transparent to itself? [Papineau] |
| 3514 | Functionalism needs causation and intentionality to explain actions [Papineau] |
| 7870 | Role concepts either name the realising property, or the higher property constituting the role [Papineau] |
| 7858 | If causes are basic particulars, this doesn't make conscious and physical properties identical [Papineau] |
| 3510 | Epiphenomenalism is supervenience without physicalism [Papineau] |
| 3511 | Supervenience requires all mental events to have physical effects [Papineau] |
| 7865 | Supervenience can be replaced by identifying mind with higher-order or disjunctional properties [Papineau] |
| 7892 | The completeness of physics is needed for mind-brain identity [Papineau] |
| 3515 | Knowing what it is like to be something only involves being (physically) that thing [Papineau] |
| 7879 | Mind-brain reduction is less explanatory, because phenomenal concepts lack causal roles [Papineau] |
| 20971 | Weak reduction of mind is to physical causes; strong reduction is also to physical laws [Papineau] |
| 7856 | It is absurd to think that physical effects are caused twice, so conscious causes must be physical [Papineau] |
| 7881 | Accept ontological monism, but conceptual dualism; we think in a different way about phenomenal thought [Papineau] |
| 3512 | If a mental state is multiply realisable, why does it lead to similar behaviour? [Papineau] |
| 7866 | Mary acquires new concepts; she previously thought about the same property using material concepts [Papineau] |
| 7850 | Thinking about a thing doesn't require activating it [Papineau] |
| 7851 | Consciousness affects bodily movement, so thoughts must be material states [Papineau] |
| 16369 | There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati] |
| 7884 | Most reductive accounts of representation imply broad content [Papineau] |
| 7863 | If content hinges on matters outside of you, how can it causally influence your actions? [Papineau] |
| 7883 | Verificationists tend to infer indefinite answers from undecidable questions [Papineau] |
| 13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |
| 7872 | Teleosemantics equates meaning with the item the concept is intended to track [Papineau] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 7869 | Truth conditions in possible worlds can't handle statements about impossibilities [Papineau] |
| 7868 | Thought content is possible worlds that make the thought true; if that includes the actual world, it's true [Papineau] |
| 3516 | The Private Language argument only means people may misjudge their experiences [Papineau] |
| 7853 | Causation is based on either events, or facts, or states of affairs [Papineau] |
| 7857 | Causes are instantiations of properties by particulars, or they are themselves basic particulars [Papineau] |
| 20976 | The completeness of physics cannot be proved [Papineau] |
| 20974 | Modern biological research, especially into the cell, has revealed no special new natural forces [Papineau] |
| 20970 | Determinism is possible without a complete physics, if mental forces play a role [Papineau] |
| 20975 | Quantum 'wave collapses' seem to violate conservation of energy [Papineau] |