56 ideas
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| 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] |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 20712 | God is 'eternal' either by being non-temporal, or by enduring forever [Davies,B] |
| 20701 | Can God be good, if he has not maximised goodness? [Davies,B] |
| 20702 | The goodness of God may be a higher form than the goodness of moral agents [Davies,B] |
| 20703 | How could God have obligations? What law could possibly impose them? [Davies,B] |
| 20694 | 'Natural theology' aims to prove God to anyone (not just believers) by reason or argument [Davies,B] |
| 20706 | A distinct cause of the universe can't be material (which would be part of the universe) [Davies,B] |
| 20707 | The universe exhibits design either in its sense of purpose, or in its regularity [Davies,B] |
| 20708 | If God is an orderly being, he cannot be the explanation of order [Davies,B] |
| 20710 | Maybe an abnormal state of mind is needed to experience God? [Davies,B] |
| 20711 | A believer can experience the world as infused with God [Davies,B] |
| 20709 | The experiences of God are inconsistent, not universal, and untestable [Davies,B] |
| 20697 | One does not need a full understanding of God in order to speak of God [Davies,B] |
| 20699 | Paradise would not contain some virtues, such as courage [Davies,B] |