120 ideas
| 12330 | In ontology, logic dominated language, until logic was mathematized [Badiou] |
| 9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
| 12318 | The female body, when taken in its entirety, is the Phallus itself [Badiou] |
| 12325 | Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology [Badiou] |
| 12324 | Consensus is the enemy of thought [Badiou] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 14713 | Truth in a scenario is the negation in that scenario being a priori incoherent [Chalmers] |
| 12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 12342 | Topos theory explains the plurality of possible logics [Badiou] |
| 12341 | Logic is a mathematical account of a universe of relations [Badiou] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 12335 | Numbers are for measuring and for calculating (and the two must be consistent) [Badiou] |
| 12334 | There is no single unified definition of number [Badiou] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 12333 | Each type of number has its own characteristic procedure of introduction [Badiou] |
| 12322 | Must we accept numbers as existing when they no longer consist of units? [Badiou] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
| 12327 | The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 12329 | If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 12328 | Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 12331 | Logic is definitional, but real mathematics is axiomatic [Badiou] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 12340 | There is no Being as a whole, because there is no set of all sets [Badiou] |
| 9809 | Mathematics inscribes being as such [Badiou] |
| 12323 | Existence is Being itself, but only as our thought decides it [Badiou] |
| 12332 | The modern view of Being comes when we reject numbers as merely successions of One [Badiou] |
| 12326 | The primitive name of Being is the empty set; in a sense, only the empty set 'is' [Badiou] |
| 9811 | It is of the essence of being to appear [Badiou] |
| 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] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 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] |
| 12338 | We must either assert or deny any single predicate of any single subject [Badiou] |
| 9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |
| 12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 16427 | Presumably God can do anything which is logically possible [Chalmers] |
| 12317 | The God of religion results from an encounter, not from a proof [Badiou] |