63 ideas
21360 | Unobservant thinkers tend to dogmatise using insufficient facts [Aristotle] |
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] |
13212 | Infinity is only potential, never actual [Aristotle] |
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] |
13221 | Existence is either potential or actual [Aristotle] |
16100 | True change is in a thing's logos or its matter, not in its qualities [Aristotle] |
16101 | A change in qualities is mere alteration, not true change [Aristotle] |
12133 | If the substratum persists, it is 'alteration'; if it doesn't, it is 'coming-to-be' or 'passing-away' [Aristotle] |
13213 | All comings-to-be are passings-away, and vice versa [Aristotle] |
16185 | Causality indicates which properties are real [Cartwright,N] |
12134 | Matter is the substratum, which supports both coming-to-be and alteration [Aristotle] |
16572 | Does the pure 'this' come to be, or the 'this-such', or 'so-great', or 'somewhere'? [Aristotle] |
16573 | Philosophers have worried about coming-to-be from nothing pre-existing [Aristotle] |
13214 | The substratum changing to a contrary is the material cause of coming-to-be [Aristotle] |
13215 | If a perceptible substratum persists, it is 'alteration'; coming-to-be is a complete change [Aristotle] |
16717 | Which of the contrary features of a body are basic to it? [Aristotle] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
16182 | Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N] |
16184 | An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N] |
16167 | Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N] |
16169 | Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N] |
16176 | Covering-law explanation lets us explain storms by falling barometers [Cartwright,N] |
16177 | I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N] |
16180 | You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
16171 | The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N] |
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] |
16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
13216 | Matter is the limit of points and lines, and must always have quality and form [Aristotle] |
17994 | The primary matter is the substratum for the contraries like hot and cold [Aristotle] |
13224 | There couldn't be just one element, which was both water and air at the same time [Aristotle] |
16594 | The Four Elements must change into one another, or else alteration is impossible [Aristotle] |
13223 | Fire is hot and dry; Air is hot and moist; Water is cold and moist; Earth is cold and dry [Aristotle] |
13220 | Bodies are endlessly divisible [Aristotle] |
13210 | Wood is potentially divided through and through, so what is there in the wood besides the division? [Aristotle] |
13211 | If a body is endlessly divided, is it reduced to nothing - then reassembled from nothing? [Aristotle] |
16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
6781 | There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird] |
16166 | Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N] |
16179 | Good organisation may not be true, and the truth may not organise very much [Cartwright,N] |
16170 | To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N] |
16181 | Simple laws have quite different outcomes when they act in combinations [Cartwright,N] |
16178 | There are few laws for when one theory meets another [Cartwright,N] |
13228 | There is no time without movement [Aristotle] |
16595 | If each thing can cease to be, why hasn't absolutely everything ceased to be long ago? [Aristotle] |
13227 | Being is better than not-being [Aristotle] |
13226 | An Order controls all things [Aristotle] |