127 ideas
19504 | My modus ponens might be your modus tollens [Pritchard,D] |
14713 | Truth in a scenario is the negation in that scenario being a priori incoherent [Chalmers] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
17824 | The master science is physical objects divided into sets [Maddy] |
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
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] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
2401 | All facts are either physical, experiential, laws of nature, second-order final facts, or indexical facts about me [Chalmers] |
16424 | Strong metaphysical necessity allows fewer possible worlds than logical necessity [Chalmers] |
16425 | Metaphysical necessity is a bizarre, brute and inexplicable constraint on possibilities [Chalmers] |
16426 | How can we know the metaphysical impossibilities; the a posteriori only concerns this world [Chalmers] |
19503 | An improbable lottery win can occur in a nearby possible world [Pritchard,D] |
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] |
16473 | Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker] |
19258 | Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya] |
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] |
19505 | Moore begs the question, or just offers another view, or uses 'know' wrongly [Pritchard,D, by PG] |
14712 | A sentence is a priori if no possible way the world might actually be could make it false [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] |
19499 | We can have evidence for seeing a zebra, but no evidence for what is entailed by that [Pritchard,D] |
19500 | Favouring: an entailment will give better support for the first belief than reason to deny the second [Pritchard,D] |
19502 | Maybe knowledge just needs relevant discriminations among contrasting cases [Pritchard,D] |
19498 | Epistemic internalism usually says justification must be accessible by reflection [Pritchard,D] |
19506 | Externalism is better than internalism in dealing with radical scepticism [Pritchard,D] |
19496 | Disjunctivism says perceptual justification must be both factual and known by the agent [Pritchard,D] |
19497 | Metaphysical disjunctivism says normal perceptions and hallucinations are different experiences [Pritchard,D] |
19495 | Epistemic externalism struggles to capture the idea of epistemic responsibility [Pritchard,D] |
19501 | We assess error against background knowledge, but that is just what radical scepticism challenges [Pritchard,D] |
19507 | Radical scepticism is merely raised, and is not a response to worrying evidence [Pritchard,D] |
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] |
2389 | Sometimes we don't notice our pains [Chalmers] |
2419 | Why should qualia fade during silicon replacement? [Chalmers] |
2402 | It seems possible to invert qualia [Chalmers] |
2415 | In blindsight both qualia and intentionality are missing [Chalmers] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
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] |
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] |
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] |
14739 | 'Water' is two-dimensionally inconstant, with different intensions in different worlds [Chalmers, by Sider] |
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] |
16427 | Presumably God can do anything which is logically possible [Chalmers] |