55 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 18915 | If facts are the truthmakers, they are not in the world [Engelbretsen] |
| 18919 | There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen] |
| 18913 | Traditional term logic struggled to express relations [Engelbretsen] |
| 18907 | Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 13331 | Part and whole contribute asymmetrically to one another, so must differ [Fine,K] |
| 18912 | Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 18922 | Logical syntax is actually close to surface linguistic form [Engelbretsen] |
| 18905 | Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen] |
| 18908 | Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 18917 | Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 18916 | Facts are not in the world - they are properties of the world [Engelbretsen] |
| 18921 | Individuals are arranged in inclusion categories that match our semantics [Engelbretsen] |
| 13332 | Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K] |
| 13333 | The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K] |
| 13326 | A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K] |
| 13327 | A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K] |
| 13329 | An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K] |
| 13330 | An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K] |
| 13328 | Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 18918 | Terms denote objects with properties, and statements denote the world with that property [Engelbretsen] |
| 18920 | 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen] |
| 18906 | Negating a predicate term and denying its unnegated version are quite different [Engelbretsen] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |