58 ideas
9108 | From an impossibility anything follows [William of Ockham] |
16676 | Why use more things when fewer will do? [William of Ockham] |
6806 | Do not multiply entities beyond necessity [William of Ockham] |
9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
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] |
9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
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] |
9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
16608 | Ockham was an anti-realist about the categories [William of Ockham, by Pasnau] |
16654 | Our words and concepts don't always correspond to what is out there [William of Ockham] |
18529 | Relations are expressed either as absolute facts, or by a relational concept [William of Ockham] |
22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
9103 | A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham] |
15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
16779 | Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham] |
16757 | Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham] |
16599 | Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau] |
16681 | Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham] |
9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
16792 | If parts change, the whole changes [William of Ockham] |
9089 | Knowledge is a quality existing subjectively in the soul [William of Ockham] |
9091 | Sometimes 'knowledge' just concerns the conclusion, sometimes the whole demonstration [William of Ockham] |
9100 | Our intellect only assents to what we believe to be true [William of Ockham] |
9090 | Knowledge is certain cognition of something that is true [William of Ockham] |
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] |
9101 | Abstractive cognition knows universals abstracted from many singulars [William of Ockham] |
9102 | If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
9114 | There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham] |
9104 | A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham] |
9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
16675 | Every extended material substance is composed of parts distant from one another [William of Ockham] |
19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |
9115 | To love God means to love whatever God wills to be loved [William of Ockham] |
16679 | Even an angel must have some location [William of Ockham, by Pasnau] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |