38 ideas
| 8472 | Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein] |
| 8476 | Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein] |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| 8480 | S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein] |
| 8474 | Unlike elementary logic, set theory is not complete [Orenstein] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| 8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
| 8452 | Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein] |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| 8475 | The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein] |
| 8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| 8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| 8458 | Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein] |
| 20339 | Classes rarely share properties with their members - unlike universals and types [Wollheim] |
| 8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
| 20338 | We often treat a type as if it were a sort of token [Wollheim] |
| 8477 | People presume meanings exist because they confuse meaning and reference [Orenstein] |
| 8471 | Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein] |
| 8484 | If two people believe the same proposition, this implies the existence of propositions [Orenstein] |
| 20343 | A love of nature must precede a love of art [Wollheim] |
| 20342 | Interpretation is performance for some arts, and critical for all arts [Wollheim] |
| 20348 | A criterion of identity for works of art would be easier than a definition [Wollheim] |
| 20347 | If beauty needs organisation, then totally simple things can't be beautiful [Wollheim] |
| 20345 | Some say art must have verbalisable expression, and others say the opposite! [Wollheim] |
| 20331 | It is claimed that the expressive properties of artworks are non-physical [Wollheim] |
| 20336 | Style can't be seen directly within a work, but appreciation needs a grasp of style [Wollheim] |
| 20337 | The traditional view is that knowledge of its genre to essential to appreciating literature [Wollheim] |
| 20333 | If artworks are not physical objects, they are either ideal entities, or collections of phenomena [Wollheim] |
| 20334 | The ideal theory says art is an intuition, shaped by a particular process, and presented in public [Wollheim] |
| 20335 | The ideal theory of art neglects both the audience and the medium employed [Wollheim] |
| 20340 | A musical performance has virtually the same features as the piece of music [Wollheim] |
| 20341 | An interpretation adds further properties to the generic piece of music [Wollheim] |
| 20332 | A drawing only represents Napoleon if the artist intended it to [Wollheim] |