123 ideas
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 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] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 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] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [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] |
| 18149 | There are many criteria for the identity of numbers [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] |
| 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] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [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] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [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] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
| 5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
| 2392 | Properties supervene if you can't have one without the other [Chalmers] |
| 2393 | Logical supervenience is when one set of properties must be accompanied by another set [Chalmers] |
| 2394 | Natural supervenience is when one set of properties is always accompanied by another set [Chalmers] |
| 2398 | Reduction requires logical supervenience [Chalmers] |
| 16048 | Physicalism says in any two physically indiscernible worlds the positive facts are the same [Chalmers, by Bennett,K] |
| 2401 | All facts are either physical, experiential, laws of nature, second-order final facts, or indexical facts about me [Chalmers] |
| 13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
| 457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
| 16425 | Metaphysical necessity is a bizarre, brute and inexplicable constraint on possibilities [Chalmers] |
| 16424 | Strong metaphysical necessity allows fewer possible worlds than logical necessity [Chalmers] |
| 16426 | How can we know the metaphysical impossibilities; the a posteriori only concerns this world [Chalmers] |
| 13956 | Kripke is often taken to be challenging a priori insights into necessity [Chalmers] |
| 13963 | Maybe logical possibility does imply conceivability - by an ideal mind [Chalmers] |
| 2407 | One can wrongly imagine two things being non-identical even though they are the same (morning/evening star) [Chalmers] |
| 2390 | We attribute beliefs to people in order to explain their behaviour [Chalmers] |
| 2397 | 'Perception' means either an action or a mental state [Chalmers] |
| 2422 | The structure of the retina has already simplified the colour information which hits it [Chalmers] |
| 462 | One vision is produced by both eyes [Empedocles] |
| 2396 | Reductive explanation is not the be-all and the end-all of explanation [Chalmers] |
| 2426 | Why are minds homogeneous and brains fine-grained? [Chalmers] |
| 2391 | Can we be aware but not conscious? [Chalmers] |
| 2412 | Can we explain behaviour without consciousness? [Chalmers] |
| 2386 | Hard Problem: why brains experience things [Chalmers] |
| 2416 | What turns awareness into consciousness? [Chalmers] |
| 2423 | Going down the scale, where would consciousness vanish? [Chalmers] |
| 2403 | Nothing in physics even suggests consciousness [Chalmers] |
| 2400 | Is intentionality just causal connections? [Chalmers] |
| 2419 | Why should qualia fade during silicon replacement? [Chalmers] |
| 2389 | Sometimes we don't notice our pains [Chalmers] |
| 2402 | It seems possible to invert qualia [Chalmers] |
| 2415 | In blindsight both qualia and intentionality are missing [Chalmers] |
| 2414 | When distracted we can totally misjudge our own experiences [Chalmers] |
| 2409 | Maybe dualist interaction is possible at the quantum level? [Chalmers] |
| 2411 | Supervenience makes interaction laws possible [Chalmers] |
| 2424 | It is odd if experience is a very recent development [Chalmers] |
| 22765 | Wisdom and thought are shared by all things [Empedocles] |
| 2413 | If I can have a zombie twin, my own behaviour doesn't need consciousness [Chalmers] |
| 2417 | Does consciousness arise from fine-grained non-reductive functional organisation? [Chalmers] |
| 2428 | Maybe the whole Chinese Room understands Chinese, though the person doesn't [Chalmers] |
| 2418 | The Chinese Mind doesn't seem conscious, but then nor do brains from outside [Chalmers] |
| 2406 | H2O causes liquidity, but no one is a dualist about that [Chalmers] |
| 2405 | Perhaps consciousness is physically based, but not logically required by that base [Chalmers] |
| 2395 | Zombies imply natural but not logical supervenience [Chalmers] |
| 9318 | Phenomenal consciousness is fundamental, with no possible nonphenomenal explanation [Chalmers, by Kriegel/Williford] |
| 2404 | Nothing external shows whether a mouse is conscious [Chalmers] |
| 2429 | Temperature (etc.) is agreed to be reducible, but it is multiply realisable [Chalmers] |
| 1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
| 18403 | Indexicals may not be objective, but they are a fact about the world as I see it [Chalmers] |
| 14708 | Rationalist 2D semantics posits necessary relations between meaning, apriority, and possibility [Chalmers, by Schroeter] |
| 13958 | The 'primary intension' is non-empirical, and fixes extensions based on the actual-world reference [Chalmers] |
| 2399 | Meaning has split into primary ("watery stuff"), and secondary counterfactual meaning ("H2O") [Chalmers] |
| 13959 | The 'secondary intension' is determined by rigidifying (as H2O) the 'water' picked out in the actual world [Chalmers] |
| 13957 | Primary and secondary intensions are the a priori (actual) and a posteriori (counterfactual) aspects of meaning [Chalmers] |
| 13961 | We have 'primary' truth-conditions for the actual world, and derived 'secondary' ones for counterfactual worlds [Chalmers] |
| 13962 | Two-dimensional semantics gives a 'primary' and 'secondary' proposition for each statement [Chalmers] |
| 13960 | In two-dimensional semantics we have two aspects to truth in virtue of meaning [Chalmers] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
| 589 | 'Nature' is just a word invented by people [Empedocles] |
| 21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
| 2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
| 6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
| 13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
| 13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
| 459 | All change is unity through love or division through hate [Empedocles] |
| 13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
| 460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
| 5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
| 466 | God is pure mind permeating the universe [Empedocles] |
| 461 | God is a pure, solitary, and eternal sphere [Empedocles] |
| 1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
| 16427 | Presumably God can do anything which is logically possible [Chalmers] |
| 1522 | It is wretched not to want to think clearly about the gods [Empedocles] |