56 ideas
17266 | Using modal logic, philosophers tried to handle all metaphysics in modal terms [Correia/Schnieder] |
17263 | Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder] |
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] |
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] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
17270 | Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder] |
17268 | Grounding is metaphysical and explanation epistemic, so keep them apart [Correia/Schnieder] |
17267 | The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder] |
17377 | All descriptive language is classificatory [Dupré] |
17376 | We should aim for a classification which tells us as much as possible about the object [Dupré] |
17390 | Natural kinds don't need essentialism to be explanatory [Dupré] |
17389 | A species might have its essential genetic mechanism replaced by a new one [Dupré] |
17388 | It seems that species lack essential properties, so they can't be natural kinds [Dupré] |
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] |
17374 | The possibility of prediction rests on determinism [Dupré] |
17378 | Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré] |
17381 | Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré] |
17385 | Kinds don't do anything (including evolve) because they are abstract [Dupré] |
17375 | Natural kinds are decided entirely by the intentions of our classification [Dupré] |
17379 | Borders between species are much less clear in vegetables than among animals [Dupré] |
17384 | Even atoms of an element differ, in the energy levels of their electrons [Dupré] |
17387 | Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré] |
17382 | Cooks, unlike scientists, distinguish garlic from onions [Dupré] |
17380 | Wales may count as fish [Dupré] |
17383 | Species are the lowest-level classification in biology [Dupré] |
17386 | The theory of evolution is mainly about species [Dupré] |