68 ideas
| 9456 | Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette] |
| 7689 | The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 9457 | The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette] |
| 7681 | Logic describes inferences between sentences expressing possible properties of objects [Jacquette] |
| 9463 | Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette] |
| 12430 | Classical logic is our preconditions for assessing empirical evidence [Kitcher] |
| 12431 | I believe classical logic because I was taught it and use it, but it could be undermined [Kitcher] |
| 7682 | Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette] |
| 7697 | On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette] |
| 9466 | Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette] |
| 9465 | Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette] |
| 9458 | Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette] |
| 9461 | Intensionalists say meaning is determined by the possession of properties [Jacquette] |
| 7701 | Can a Barber shave all and only those persons who do not shave themselves? [Jacquette] |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| 7707 | To grasp being, we must say why something exists, and why there is one world [Jacquette] |
| 7687 | Existence is completeness and consistency [Jacquette] |
| 7692 | Being is maximal consistency [Jacquette] |
| 7679 | Ontology is the same as the conceptual foundations of logic [Jacquette] |
| 7678 | Ontology must include the minimum requirements for our semantics [Jacquette] |
| 7683 | Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette] |
| 7684 | Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette] |
| 7703 | If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette] |
| 7685 | An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 7699 | Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette] |
| 12428 | Many necessities are inexpressible, and unknowable a priori [Kitcher] |
| 12429 | Knowing our own existence is a priori, but not necessary [Kitcher] |
| 7691 | The actual world is a consistent combination of states, made of consistent property combinations [Jacquette] |
| 7688 | The actual world is a maximally consistent combination of actual states of affairs [Jacquette] |
| 7695 | Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette] |
| 7694 | We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette] |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| 7706 | If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 7704 | Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette] |
| 9460 | Extensionalist semantics forbids reference to nonexistent objects [Jacquette] |
| 9459 | Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette] |
| 7702 | The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette] |
| 7258 | The forefather of modern intuitionism is Richard Price [Price,R, by Dancy,J] |