50 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] |
22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
22301 | The Identity Theory says a proposition is true if it coincides with what makes it true [Potter] |
22324 | It has been unfortunate that externalism about truth is equated with correspondence [Potter] |
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] |
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |
4638 | The principle of bivalence distorts reality, as when claiming that a person is or is not 'thin' [Baggini /Fosl] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
22295 | Modern logical truths are true under all interpretations of the non-logical words [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter] |
22298 | Why is fictional arithmetic applicable to the real world? [Potter] |
22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
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] |
10709 | Priority is a modality, arising from collections and members [Potter] |
4646 | Is 'events have causes' analytic a priori, synthetic a posteriori, or synthetic a priori? [Baggini /Fosl] |
22281 | A material conditional cannot capture counterfactual reasoning [Potter] |
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] |
22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter] |
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] |
22273 | Traditionally there are twelve categories of judgement, in groups of three [Potter] |
22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter] |
22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter] |
22282 | 'Direct compositonality' says the components wholly explain a sentence meaning [Potter] |
22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |