79 ideas
| 2797 | As coherence expands its interrelations become steadily tighter, culminating only in necessary truth [Dancy,J] |
| 2768 | The correspondence theory also has the problem that two sets of propositions might fit the facts equally well [Dancy,J] |
| 2765 | Rescher says that if coherence requires mutual entailment, this leads to massive logical redundancy [Dancy,J] |
| 2769 | If one theory is held to be true, all the other theories appear false, because they can't be added to the true one [Dancy,J] |
| 2766 | Even with a tight account of coherence, there is always the possibility of more than one set of coherent propositions [Dancy,J] |
| 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] |
| 2781 | Realism says that most perceived objects exist, and have some of their perceived properties [Dancy,J] |
| 2745 | A pupil who lacks confidence may clearly know something but not be certain of it [Dancy,J] |
| 2755 | If senses are fallible, then being open to correction is an epistemological virtue [Dancy,J] |
| 5677 | Naïve direct realists hold that objects retain all of their properties when unperceived [Dancy,J] |
| 5678 | Scientific direct realism says we know some properties of objects directly [Dancy,J] |
| 5681 | Maybe we are forced from direct into indirect realism by the need to explain perceptual error [Dancy,J] |
| 5682 | Internal realism holds that we perceive physical objects via mental objects [Dancy,J] |
| 5683 | Indirect realism depends on introspection, the time-lag, illusions, and neuroscience [Dancy,J, by PG] |
| 2778 | Phenomenalism includes possible experiences, but idealism only refers to actual experiences [Dancy,J] |
| 5684 | Eliminative idealists say there are no objects; reductive idealists say objects exist as complex experiences [Dancy,J] |
| 2777 | Extreme solipsism only concerns current experience, but it might include past and future [Dancy,J] |
| 2794 | Knowing that a cow is not a horse seems to be a synthetic a priori truth [Dancy,J] |
| 2780 | Perception is either direct realism, indirect realism, or phenomenalism [Dancy,J] |
| 5679 | We can't grasp the separation of quality types, or what a primary-quality world would be like [Dancy,J] |
| 5680 | For direct realists the secondary and primary qualities seem equally direct [Dancy,J] |
| 2782 | We can be looking at distant stars which no longer actually exist [Dancy,J] |
| 2775 | It is not clear from the nature of sense data whether we should accept them as facts [Dancy,J] |
| 2784 | Appearances don't guarantee reality, unless the appearance is actually caused by the reality [Dancy,J] |
| 2785 | Perceptual beliefs may be directly caused, but generalisations can't be [Dancy,J] |
| 2788 | If perception and memory are indirect, then two things stand between mind and reality [Dancy,J] |
| 2787 | Memories aren't directly about the past, because time-lags and illusions suggest representation [Dancy,J] |
| 2791 | Phenomenalism about memory denies the past, or reduces it to present experience [Dancy,J] |
| 2790 | I can remember plans about the future, and images aren't essential (2+3=5) [Dancy,J] |
| 2754 | Foundations are justified by non-beliefs, or circularly, or they need no justification [Dancy,J] |
| 2749 | For internalists we must actually know that the fact caused the belief [Dancy,J] |
| 2770 | Internalists tend to favour coherent justification, but not the coherence theory of truth [Dancy,J] |
| 2752 | Foundationalism requires inferential and non-inferential justification [Dancy,J] |
| 2771 | Foundationalists must accept not only the basic beliefs, but also rules of inference for further progress [Dancy,J] |
| 2756 | If basic beliefs can be false, falsehood in non-basic beliefs might by a symptom [Dancy,J] |
| 2753 | Beliefs can only be infallible by having almost no content [Dancy,J] |
| 2773 | Coherentism gives a possible justification of induction, and opposes scepticism [Dancy,J] |
| 2779 | Idealists must be coherentists, but coherentists needn't be idealists [Dancy,J] |
| 2786 | For coherentists justification and truth are not radically different things [Dancy,J] |
| 2767 | If it is empirical propositions which have to be coherent, this eliminates coherent fiction [Dancy,J] |
| 2776 | Externalism could even make belief unnecessary (e.g. in animals) [Dancy,J] |
| 2746 | How can a causal theory of justification show that all men die? [Dancy,J] |
| 2747 | Causal theories don't allow for errors in justification [Dancy,J] |
| 2772 | Coherentism moves us towards a more social, shared view of knowledge [Dancy,J] |
| 2743 | What is the point of arguing against knowledge, if being right undermines your own argument? [Dancy,J] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 2751 | Probabilities can only be assessed relative to some evidence [Dancy,J] |
| 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] |
| 2757 | The argument from analogy rests on one instance alone [Dancy,J] |
| 2758 | You can't separate mind and behaviour, as the analogy argument attempts [Dancy,J] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 2744 | Verificationism (the 'verification principle') is an earlier form of anti-realism [Dancy,J] |
| 2760 | Logical positivism implies foundationalism, by dividing weak from strong verifications [Dancy,J] |
| 2761 | If the meanings of sentences depend on other sentences, how did we learn language? [Dancy,J] |
| 2763 | There is an indeterminacy in juggling apparent meanings against probable beliefs [Dancy,J] |
| 2762 | Charity makes native beliefs largely true, and Humanity makes them similar to ours [Dancy,J] |
| 7260 | If there are intuited moral facts, why should we care about them? [Dancy,J] |
| 7261 | Internalists say that moral intuitions are motivating; externalist say a desire is also needed [Dancy,J] |
| 7262 | Obviously judging an action as wrong gives us a reason not to do it [Dancy,J] |
| 7265 | Moral facts are not perceived facts, but perceived reasons for judgements [Dancy,J] |
| 18681 | The base for values has grounds, catalysts and intensifiers [Dancy,J, by Orsi] |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |