57 ideas
15169 | Metaphysics is clarifying how we speak and think (and possibly improving it) [Sidelle] |
15164 | We seem to base necessities on thought experiments and imagination [Sidelle] |
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] |
15180 | There doesn't seem to be anything in the actual world that can determine modal facts [Sidelle] |
15184 | Causal reference presupposes essentialism if it refers to modally extended entities [Sidelle] |
15172 | Clearly, essential predications express necessary properties [Sidelle] |
15181 | Being a deepest explanatory feature is an actual, not a modal property [Sidelle] |
15173 | That the essence of water is its microstructure is a convention, not a discovery [Sidelle] |
15185 | We aren't clear about 'same stuff as this', so a principle of individuation is needed to identify it [Sidelle] |
15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
15175 | Evaluation of de dicto modalities does not depend on the identity of its objects [Sidelle] |
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] |
15032 | Necessary a posteriori is conventional for necessity and nonmodal for a posteriority [Sidelle, by Sider] |
15179 | To know empirical necessities, we need empirical facts, plus conventions about which are necessary [Sidelle] |
15171 | The necessary a posteriori is statements either of identity or of essence [Sidelle] |
15167 | Empiricism explores necessities and concept-limits by imagining negations of truths [Sidelle] |
15177 | Contradictoriness limits what is possible and what is imaginable [Sidelle] |
15176 | The individuals and kinds involved in modality are also a matter of convention [Sidelle] |
15174 | A thing doesn't need transworld identity prior to rigid reference - that could be a convention of the reference [Sidelle] |
15183 | 'Dthat' operates to make a singular term into a rigid term [Sidelle] |
15165 | A priori knowledge is entirely of analytic truths [Sidelle] |
15168 | That water is essentially H2O in some way concerns how we use 'water' [Sidelle] |
15166 | Causal reference seems to get directly at the object, thus leaving its nature open [Sidelle] |
15182 | Because some entities overlap, reference must have analytic individuation principles [Sidelle] |
5954 | All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch] |
15178 | Can anything in science reveal the necessity of what it discovers? [Sidelle] |