116 ideas
| 3798 | An overexamined life is as bad as an unexamined one [Dennett] |
| 3801 | Rationality requires the assumption that things are either for better or worse [Dennett] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 14308 | We can bring dispositions into existence, as in creating an identifier [Dennett, by Mumford] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 7384 | Words are fixed by being attached to similarity clusters, without mention of 'essences' [Dennett] |
| 2526 | Philosophers regularly confuse failures of imagination with insights into necessity [Dennett] |
| 3802 | Why pronounce impossible what you cannot imagine? [Dennett] |
| 7374 | Light wavelengths entering the eye are only indirectly related to object colours [Dennett] |
| 2523 | That every mammal has a mother is a secure reality, but without foundations [Dennett] |
| 3795 | Causal theories require the "right" sort of link (usually unspecified) [Dennett] |
| 7369 | Brains are essentially anticipation machines [Dennett] |
| 4608 | Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil] |
| 7393 | We can't draw a clear line between conscious and unconscious [Dennett] |
| 7367 | Perhaps the brain doesn't 'fill in' gaps in consciousness if no one is looking. [Dennett] |
| 4880 | Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett] |
| 2528 | Does consciousness need the concept of consciousness? [Dennett] |
| 2525 | Maybe language is crucial to consciousness [Dennett] |
| 7394 | Conscious events can only be explained in terms of unconscious events [Dennett] |
| 7391 | We can know a lot of what it is like to be a bat, and nothing important is unknown [Dennett] |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| 2527 | Unconscious intentionality is the foundation of the mind [Dennett] |
| 6624 | Dennett denies the existence of qualia [Dennett, by Lowe] |
| 4873 | What is it like to notice an uncomfortable position when you are asleep? [Dennett] |
| 7387 | "Qualia" can be replaced by complex dispositional brain states [Dennett] |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| 7376 | We can't assume that dispositions will remain normal when qualia have been inverted [Dennett] |
| 7372 | In peripheral vision we see objects without their details, so blindsight is not that special [Dennett] |
| 7373 | Blindsight subjects glean very paltry information [Dennett] |
| 3797 | I am the sum total of what I directly control [Dennett] |
| 7385 | People accept blurred boundaries in many things, but insist self is All or Nothing [Dennett] |
| 4881 | Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett] |
| 7383 | The psychological self is an abstraction, not a thing in the brain [Dennett] |
| 7386 | Selves are not soul-pearls, but artefacts of social processes [Dennett] |
| 7381 | We tell stories about ourselves, to protect, control and define who we are [Dennett] |
| 7382 | We spin narratives about ourselves, and the audience posits a centre of gravity for them [Dennett] |
| 7370 | The brain is controlled by shifting coalitions, guided by good purposeful habits [Dennett] |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| 3800 | You can be free even though force would have prevented you doing otherwise [Dennett, by PG] |
| 3803 | Can we conceive of a being with a will freer than our own? [Dennett] |
| 3791 | Awareness of thought is a step beyond awareness of the world [Dennett] |
| 3794 | Foreknowledge permits control [Dennett] |
| 7379 | If an epiphenomenon has no physical effects, it has to be undetectable [Dennett] |
| 7365 | Dualism wallows in mystery, and to accept it is to give up [Dennett] |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| 3796 | The active self is a fiction created because we are ignorant of our motivations [Dennett] |
| 3161 | If mind is just an explanation, the explainer must have beliefs [Rey on Dennett] |
| 3986 | The 'intentional stance' is a way of interpreting an entity by assuming it is rational and self-aware [Dennett] |
| 2530 | Could a robot be made conscious just by software? [Dennett] |
| 7371 | All functionalism is 'homuncular', of one grain size or another [Dennett] |
| 4875 | We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett] |
| 4879 | There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett] |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 7366 | It is arbitrary to say which moment of brain processing is conscious [Dennett] |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| 7380 | Visual experience is composed of neural activity, which we find pleasing [Dennett] |
| 4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
| 4878 | The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett] |
| 3177 | You couldn't drive a car without folk psychology [Dennett] |
| 3987 | Like the 'centre of gravity', desires and beliefs are abstract concepts with no actual existence [Dennett] |
| 4874 | The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett] |
| 2524 | A language of thought doesn't explain content [Dennett] |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| 23803 | States have content if we can predict them well by assuming intentionality [Dennett, by Schulte] |
| 3984 | The nature of content is entirely based on its functional role [Dennett] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 4882 | Concepts are things we (unlike dogs) can think about, because we have language [Dennett] |
| 2529 | Maybe there can be non-conscious concepts (e.g. in bees) [Dennett] |
| 3983 | Learning is evolution in the brain [Dennett] |
| 4872 | Most people see an abortion differently if the foetus lacks a brain [Dennett] |
| 7368 | Originally there were no reasons, purposes or functions; since there were no interests, there were only causes [Dennett] |
| 3985 | Biology is a type of engineering, not a search for laws of nature [Dennett] |
| 4877 | Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett] |
| 3804 | Darwin's idea was the best idea ever [Dennett] |