75 ideas
7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
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] |
7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
6346 | The main epistemological theories are foundationalist, coherence, probabilistic and reliabilist [Pollock/Cruz] |
6351 | Most people now agree that our reasoning proceeds defeasibly, rather than deductively [Pollock/Cruz] |
6374 | To believe maximum truths, believe everything; to have infallible beliefs, believe nothing [Pollock/Cruz] |
6355 | Direct realism says justification is partly a function of pure perceptual states, not of beliefs [Pollock/Cruz] |
6359 | Phenomenalism offered conclusive perceptual knowledge, but conclusive reasons no longer seem essential [Pollock/Cruz] |
6366 | Perception causes beliefs in us, without inference or justification [Pollock/Cruz] |
6362 | Sense evidence is not beliefs, because they are about objective properties, not about appearances [Pollock/Cruz] |
6371 | Bayesian epistemology is Bayes' Theorem plus the 'simple rule' (believe P if it is probable) [Pollock/Cruz] |
6373 | Internalism says if anything external varies, the justifiability of the belief does not vary [Pollock/Cruz] |
6353 | People rarely have any basic beliefs, and never enough for good foundations [Pollock/Cruz] |
6361 | Foundationalism requires self-justification, not incorrigibility [Pollock/Cruz] |
6357 | Reason cannot be an ultimate foundation, because rational justification requires prior beliefs [Pollock/Cruz] |
6363 | Foundationalism is wrong, because either all beliefs are prima facie justified, or none are [Pollock/Cruz] |
6365 | Negative coherence theories do not require reasons, so have no regress problem [Pollock/Cruz] |
6354 | Coherence theories fail, because they can't accommodate perception as the basis of knowledge [Pollock/Cruz] |
6367 | Coherence theories isolate justification from the world [Pollock/Cruz] |
6370 | Externalism comes as 'probabilism' (probability of truth) and 'reliabilism' (probability of good cognitive process) [Pollock/Cruz] |
6358 | One belief may cause another, without being the basis for the second belief [Pollock/Cruz] |
6364 | We can't start our beliefs from scratch, because we wouldn't know where to start [Pollock/Cruz] |
6352 | Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
6372 | Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz] |
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] |
6360 | Scientific confirmation is best viewed as inference to the best explanation [Pollock/Cruz] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |