34 ideas
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 8492 | Relations are functions with two arguments [Frege] |
| 15091 | Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| 15095 | A property's causal features are essential, and only they fix its identity [Shoemaker] |
| 15097 | I claim that a property has its causal features in all possible worlds [Shoemaker] |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| 15094 | I now deny that properties are cluster of powers, and take causal properties as basic [Shoemaker] |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| 15099 | If something is possible, but not nomologically possible, we need metaphysical possibility [Shoemaker] |
| 15101 | Once you give up necessity as a priori, causal necessity becomes the main type of necessity [Shoemaker] |
| 15098 | Empirical evidence shows that imagining a phenomenon can show it is possible [Shoemaker] |
| 15100 | Imagination reveals conceptual possibility, where descriptions avoid contradiction or incoherence [Shoemaker] |
| 15096 | 'Grue' only has causal features because of its relation to green [Shoemaker] |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| 15093 | We might say laws are necessary by combining causal properties with Armstrong-Dretske-Tooley laws [Shoemaker] |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |