37 ideas
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| 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] |
| 7374 | Light wavelengths entering the eye are only indirectly related to object colours [Dennett] |
| 7369 | Brains are essentially anticipation machines [Dennett] |
| 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] |
| 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] |
| 7387 | "Qualia" can be replaced by complex dispositional brain states [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] |
| 7385 | People accept blurred boundaries in many things, but insist self is All or Nothing [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] |
| 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] |
| 7371 | All functionalism is 'homuncular', of one grain size or another [Dennett] |
| 7380 | Visual experience is composed of neural activity, which we find pleasing [Dennett] |
| 7366 | It is arbitrary to say which moment of brain processing is conscious [Dennett] |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| 7368 | Originally there were no reasons, purposes or functions; since there were no interests, there were only causes [Dennett] |