55 ideas
| 14273 | Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 12205 | There are two families of modal notions, metaphysical and epistemic, of equal strength [Edgington] |
| 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] |
| 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] |
| 12790 | Generalisations must be invariant to explain anything [Leuridan] |
| 12789 | Biological functions are explained by disposition, or by causal role [Leuridan] |
| 14388 | Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan] |
| 14386 | Mechanisms are ontologically dependent on regularities [Leuridan] |
| 12787 | Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan] |
| 14384 | We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan] |
| 14389 | There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan] |
| 14387 | Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan] |
| 14382 | Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan] |
| 14385 | Strict regularities are rarely discovered in life sciences [Leuridan] |
| 14383 | A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan] |