48 ideas
| 3993 | Arguments are nearly always open to challenge, but they help to explain a position rather than force people to believe [Lewis] |
| 22271 | Aristotle was the first to use schematic letters in logic [Aristotle, by Potter] |
| 11060 | Aristotelian syllogisms are three-part, subject-predicate, existentially committed, with laws of thought [Aristotle, by Hanna] |
| 18909 | Aristotelian sentences are made up by one of four 'formative' connectors [Aristotle, by Engelbretsen] |
| 8080 | Aristotelian identified 256 possible syllogisms, saying that 19 are valid [Aristotle, by Devlin] |
| 13912 | Aristotle replaced Plato's noun-verb form with unions of pairs of terms by one of four 'copulae' [Aristotle, by Engelbretsen/Sayward] |
| 8071 | Aristotle listed nineteen valid syllogisms (though a few of them were wrong) [Aristotle, by Devlin] |
| 13819 | Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs [Bostock on Aristotle] |
| 9403 | There are three different deductions for actual terms, necessary terms and possible terms [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] |
| 11148 | Deduction is when we suppose one thing, and another necessarily follows [Aristotle] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 18896 | Aristotle places terms at opposite ends, joined by a quantified copula [Aristotle, by Sommers] |
| 3300 | Aristotle's logic is based on the subject/predicate distinction, which leads him to substances and properties [Aristotle, by Benardete,JA] |
| 11149 | Affirming/denying sentences are universal, particular, or indeterminate [Aristotle] |
| 8079 | Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin] |
| 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] |
| 3990 | The whole truth supervenes on the physical truth [Lewis] |
| 3991 | Where pixels make up a picture, supervenience is reduction [Lewis] |
| 14641 | A deduction is necessary if the major (but not the minor) premise is also necessary [Aristotle] |
| 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] |
| 3995 | A mind is an organ of representation [Lewis] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 18911 | Linguistic terms form a hierarchy, with higher terms predicable of increasing numbers of things [Aristotle, by Engelbretsen] |
| 3994 | Human pain might be one thing; Martian pain might be something else [Lewis] |
| 3989 | I am a reductionist about mind because I am an a priori reductionist about everything [Lewis] |
| 3992 | Folk psychology makes good predictions, by associating mental states with causal roles [Lewis] |
| 3996 | Folk psychology doesn't say that there is a language of thought [Lewis] |
| 3998 | If you don't share an external world with a brain-in-a-vat, then externalism says you don't share any beliefs [Lewis] |
| 3997 | Nothing shows that all content is 'wide', or that wide content has logical priority [Lewis] |
| 3999 | A spontaneous duplicate of you would have your brain states but no experience, so externalism would deny him any beliefs [Lewis] |
| 4000 | Wide content derives from narrow content and relationships with external things [Lewis] |