51 ideas
| 7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle] |
| 7798 | There are three axiom schemas for propositional logic [Girle] |
| 7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |
| 14273 | Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington] |
| 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] |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| 7787 | Possible worlds logics use true-in-a-world rather than true [Girle] |
| 7788 | Modal logic has four basic modal negation equivalences [Girle] |
| 7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| 7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| 12205 | There are two families of modal notions, metaphysical and epistemic, of equal strength [Edgington] |
| 7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
| 12207 | Metaphysical possibility is discovered empirically, and is contrained by nature [Edgington] |
| 12206 | Broadly logical necessity (i.e. not necessarily formal logical necessity) is an epistemic notion [Edgington] |
| 12185 | Logical necessity is epistemic necessity, which is the old notion of a priori [Edgington, by McFetridge] |
| 12208 | An argument is only valid if it is epistemically (a priori) necessary [Edgington] |
| 7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
| 13857 | Truth-functional possibilities include the irrelevant, which is a mistake [Edgington] |
| 14281 | A thing works like formal probability if all the options sum to 100% [Edgington] |
| 14284 | Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington] |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| 13853 | It is a mistake to think that conditionals are statements about how the world is [Edgington] |
| 14270 | Simple indicatives about past, present or future do seem to form a single semantic kind [Edgington] |
| 14269 | Maybe forward-looking indicatives are best classed with the subjunctives [Edgington] |
| 13770 | There are many different conditional mental states, and different conditional speech acts [Edgington] |
| 14275 | Truth-function problems don't show up in mathematics [Edgington] |
| 13764 | Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington] |
| 13765 | 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington] |
| 14274 | Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism [Edgington] |
| 14276 | The truth-functional view makes conditionals with unlikely antecedents likely to be true [Edgington] |
| 14290 | Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! [Edgington] |
| 13855 | A conditional does not have truth conditions [Edgington] |
| 13859 | X believes 'if A, B' to the extent that A & B is more likely than A & ¬B [Edgington] |
| 14271 | Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF [Edgington] |
| 14272 | I say "If you touch that wire you'll get a shock"; you don't touch it. How can that make the conditional true? [Edgington] |
| 13854 | Conditionals express what would be the outcome, given some supposition [Edgington] |
| 14282 | On the supposition view, believe if A,B to the extent that A&B is nearly as likely as A [Edgington] |
| 14278 | Truth-functionalists support some conditionals which we assert, but should not actually believe [Edgington] |
| 14287 | Does 'If A,B' say something different in each context, because of the possibiites there? [Edgington] |
| 7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |