41 ideas
8893 | For any given area, there seem to be a huge number of possible coherent systems of beliefs [Bonjour] |
7798 | There are three axiom schemas for propositional logic [Girle] |
7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle] |
7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |
7797 | Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle] |
7794 | There are seven modalities in S4, each with its negation [Girle] |
7793 | ◊p → □◊p is the hallmark of S5 [Girle] |
7795 | S5 has just six modalities, and all strings can be reduced to those [Girle] |
7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle] |
7787 | Possible worlds logics use true-in-a-world rather than true [Girle] |
7788 | Modal logic has four basic modal negation equivalences [Girle] |
7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
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] |
7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |
8888 | The concept of knowledge is so confused that it is best avoided [Bonjour] |
8887 | It is hard to give the concept of 'self-evident' a clear and defensible characterization [Bonjour] |
8897 | The adverbial account will still be needed when a mind apprehends its sense-data [Bonjour] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
8896 | Conscious states have built-in awareness of content, so we know if a conceptual description of it is correct [Bonjour] |
8891 | My incoherent beliefs about art should not undermine my very coherent beliefs about physics [Bonjour] |
8892 | Coherence seems to justify empirical beliefs about externals when there is no external input [Bonjour] |
8894 | Coherentists must give a reason why coherent justification is likely to lead to the truth [Bonjour] |
8889 | Reliabilists disagree over whether some further requirement is needed to produce knowledge [Bonjour] |
8890 | If the reliable facts producing a belief are unknown to me, my belief is not rational or responsible [Bonjour] |
8895 | If neither the first-level nor the second-level is itself conscious, there seems to be no consciousness present [Bonjour] |