58 ideas
11147 | Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence] |
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] |
15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
15427 | The Cut Rule expresses the classical idea that entailment is transitive [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] |
15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [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] |
15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
15412 | Models leave out meaning, and just focus on truth values [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] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
15419 | General consensus is S5 for logical modality of validity, and S4 for proof [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] |
11141 | Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence] |
11142 | Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence] |
11121 | Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence] |
11120 | Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence] |
11122 | A computer may have propositional attitudes without representations [Margolis/Laurence] |
11124 | Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence] |
11123 | Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence] |
11125 | The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence] |
11140 | Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence] |
11128 | Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence] |
11129 | The classical theory explains acquisition, categorization and reference [Margolis/Laurence] |
11130 | Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence] |
11131 | It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence] |
11134 | People don't just categorise by apparent similarities [Margolis/Laurence] |
11136 | Many complex concepts obviously have no prototype [Margolis/Laurence] |
11133 | Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence] |
11135 | Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence] |
11132 | The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence] |
11137 | The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence] |
11138 | The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence] |
11139 | Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence] |
11146 | People can formulate new concepts which are only named later [Margolis/Laurence] |