45 ideas
| 23770 | Reductive analysis makes a concept clearer, by giving an alternative simpler set [Williams,NE] |
| 23769 | Promoting an ontology by its implied good metaphysic is an 'argument-by-display' [Williams,NE] |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 23783 | Change exists, it is causal, and it needs an explanation [Williams,NE] |
| 23784 | Processes don't begin or end; they just change direction unexpectedly [Williams,NE] |
| 23790 | Processes are either strings of short unchanging states, or continuous and unreducible events [Williams,NE] |
| 23786 | The status quo is part of what exists, and so needs metaphysical explanation [Williams,NE] |
| 23768 | A metaphysic is a set of wider explanations derived from a basic ontology [Williams,NE] |
| 23773 | Humeans say properties are passive, possibility is vast, laws are descriptions, causation is weak [Williams,NE] |
| 23779 | We shouldn't posit the existence of anything we have a word for [Williams,NE] |
| 23780 | Every possible state of affairs is written into its originating powers [Williams,NE] |
| 23789 | Naming powers is unwise, because that it usually done by a single manifestation [Williams,NE] |
| 23775 | Powers are 'multi-track' if they can produce a variety of manifestations [Williams,NE] |
| 23771 | Fundamental physics describes everything in terms of powers [Williams,NE] |
| 23776 | Rather than pure powers or pure categoricals, I favour basics which are both at once [Williams,NE] |
| 23777 | Powers are more complicated than properties which are always on display [Williams,NE] |
| 23774 | There are basic powers, which underlie dispositions, potentialities, capacities etc [Williams,NE] |
| 23791 | Dispositions are just useful descriptions, which are explained by underlying powers [Williams,NE] |
| 23772 | If objects are property bundles, the properties need combining powers [Williams,NE] |
| 23788 | Four-Dimensional is Perdurantism (temporal parts), plus Eternalism [Williams,NE] |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 23785 | Causation needs to explain stasis, as well as change [Williams,NE] |
| 23782 | Causation is the exercise of powers [Williams,NE] |
| 23787 | If causes and effects overlap, that makes changes impossible [Williams,NE] |
| 23778 | Powers contain lawlike features, pointing to possible future states [Williams,NE] |