76 ideas
21634 | Metaphysics is (supposedly) first the ontology, then in general what things are like [Hofweber] |
16415 | Esoteric metaphysics aims to be top science, investigating ultimate reality [Hofweber] |
16413 | Science has discovered properties of things, so there are properties - so who needs metaphysics? [Hofweber] |
21666 | 'Fundamentality' is either a superficial idea, or much too obscure [Hofweber] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
21640 | 'It's true that Fido is a dog' conjures up a contrast class, of 'it's false' or 'it's unlikely' [Hofweber] |
17990 | Instances of minimal truth miss out propositions inexpressible in current English [Hofweber] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
21657 | Since properties can have properties, some theorists rank them in 'types' [Hofweber] |
21653 | Maybe not even names are referential, but are just by used by speakers to refer [Hofweber] |
10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
21636 | 'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber] |
21637 | If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber] |
16416 | The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber] |
21643 | The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber] |
10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
17988 | Quantification can't all be substitutional; some reference is obviously to objects [Hofweber] |
9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
21644 | Numbers are used as singular terms, as adjectives, and as symbols [Hofweber] |
21646 | The Amazonian Piraha language is said to have no number words [Hofweber] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
21665 | The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber] |
21649 | How can words be used for counting if they are objects? [Hofweber] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
21647 | Logicism makes sense of our ability to know arithmetic just by thought [Hofweber] |
21648 | Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber] |
10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
21664 | Supervenience offers little explanation for things which necessarily go together [Hofweber] |
21660 | Reality can be seen as the totality of facts, or as the totality of things [Hofweber] |
21661 | There are probably ineffable facts, systematically hidden from us [Hofweber] |
17989 | Since properties have properties, there can be a typed or a type-free theory of them [Hofweber] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
21652 | Our perceptual beliefs are about ordinary objects, not about simples arranged chair-wise [Hofweber] |
21663 | Counterfactuals are essential for planning, and learning from mistakes [Hofweber] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
10004 | Our minds are at their best when reasoning about objects [Hofweber] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
21654 | The "Fido"-Fido theory of meaning says every expression in a language has a referent [Hofweber] |
21641 | Inferential role semantics is an alternative to semantics that connects to the world [Hofweber] |
21638 | Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber] |
21658 | Properties can be expressed in a language despite the absence of a single word for them [Hofweber] |
21659 | 'Being taller than this' is a predicate which can express many different properties [Hofweber] |
21655 | Compositonality is a way to build up the truth-conditions of a sentence [Hofweber] |
21656 | Proposition have no content, because they are content [Hofweber] |
21635 | Without propositions there can be no beliefs or desires [Hofweber] |
21662 | Do there exist thoughts which we are incapable of thinking? [Hofweber] |
21645 | 'Semantic type coercion' is selecting the reading of a word to make the best sense [Hofweber] |
21639 | 'Background deletion' is appropriately omitting background from an answer [Hofweber] |
17991 | Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber] |