110 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] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 14308 | We can bring dispositions into existence, as in creating an identifier [Dennett, by Mumford] |
| 7384 | Words are fixed by being attached to similarity clusters, without mention of 'essences' [Dennett] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 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] |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| 7366 | It is arbitrary to say which moment of brain processing is conscious [Dennett] |
| 4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
| 7380 | Visual experience is composed of neural activity, which we find pleasing [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] |
| 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] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |
| 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] |