47 ideas
12463 | Unlike correspondence, truthmaking can be one truth to many truthmakers, or vice versa [Jacobs] |
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
5791 | Reduction is either by elimination, or by explanation [Searle] |
5799 | Eliminative reduction needs a gap between appearance and reality, as in sunsets [Searle] |
14375 | If structures result from intrinsic natures of properties, the 'relations' between them can drop out [Jacobs] |
5790 | A property is 'emergent' if it is caused by elements of a system, when the elements lack the property [Searle] |
14378 | Science aims at identifying the structure and nature of the powers that exist [Jacobs] |
12467 | Powers come from concrete particulars, not from the laws of nature [Jacobs] |
14377 | Possibilities are manifestations of some power, and impossibilies rest on no powers [Jacobs] |
14376 | States of affairs are only possible if some substance could initiate a causal chain to get there [Jacobs] |
14379 | Counterfactuals invite us to consider the powers picked out by the antecedent [Jacobs] |
14372 | Possible worlds are just not suitable truthmakers for modality [Jacobs] |
12466 | All modality is in the properties and relations of the actual world [Jacobs] |
14371 | We can base counterfactuals on powers, not possible worlds, and hence define necessity [Jacobs] |
12465 | Concrete worlds, unlike fictions, at least offer evidence of how the actual world could be [Jacobs] |
12464 | If some book described a possibe life for you, that isn't what makes such a life possible [Jacobs] |
12469 | Possible worlds semantics gives little insight into modality [Jacobs] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
5792 | Explanation of how we unify our mental stimuli into a single experience is the 'binding problem' [Searle] |
5786 | A system is either conscious or it isn't, though the intensity varies a lot [Searle] |
5794 | Consciousness has a first-person ontology, which only exists from a subjective viewpoint [Searle] |
5795 | There isn't one consciousness (information-processing) which can be investigated, and another (phenomenal) which can't [Searle] |
5788 | The use of 'qualia' seems to imply that consciousness and qualia are separate [Searle] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
5789 | I now think syntax is not in the physics, but in the eye of the beholder [Searle] |
5798 | Consciousness has a first-person ontology, so it cannot be reduced without omitting something [Searle] |
5787 | There is non-event causation between mind and brain, as between a table and its solidity [Searle] |
5797 | The pattern of molecules in the sea is much more complex than the complexity of brain neurons [Searle] |
5796 | If tree rings contain information about age, then age contains information about rings [Searle] |