37 ideas
| 4643 | The Principle of Sufficient Reason does not presuppose that all explanations will be causal explanations [Baggini /Fosl] |
| 4633 | You cannot rationally deny the principle of non-contradiction, because all reasoning requires it [Baggini /Fosl] |
| 4635 | Dialectic aims at unified truth, unlike analysis, which divides into parts [Baggini /Fosl] |
| 4632 | 'Natural' systems of deduction are based on normal rational practice, rather than on axioms [Baggini /Fosl] |
| 4631 | In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use [Baggini /Fosl] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 4638 | The principle of bivalence distorts reality, as when claiming that a person is or is not 'thin' [Baggini /Fosl] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 4640 | If identity is based on 'true of X' instead of 'property of X' we get the Masked Man fallacy ('I know X but not Y') [Baggini /Fosl, by PG] |
| 4647 | 'I have the same car as you' is fine; 'I have the same fiancée as you' is not so good [Baggini /Fosl] |
| 4639 | Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects [Baggini /Fosl] |
| 4646 | Is 'events have causes' analytic a priori, synthetic a posteriori, or synthetic a priori? [Baggini /Fosl] |
| 4645 | 'A priori' does not concern how you learn a proposition, but how you show whether it is true or false [Baggini /Fosl] |
| 4582 | Basic beliefs are self-evident, or sensual, or intuitive, or revealed, or guaranteed [Baggini /Fosl] |
| 4644 | A proposition such as 'some swans are purple' cannot be falsified, only verified [Baggini /Fosl] |
| 4584 | The problem of induction is how to justify our belief in the uniformity of nature [Baggini /Fosl] |
| 4583 | How can an argument be good induction, but poor deduction? [Baggini /Fosl] |
| 4634 | Abduction aims at simplicity, testability, coherence and comprehensiveness [Baggini /Fosl] |
| 4637 | To see if an explanation is the best, it is necessary to investigate the alternative explanations [Baggini /Fosl] |
| 4629 | Consistency is the cornerstone of rationality [Baggini /Fosl] |
| 14080 | Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J] |