36 ideas
| 5745 | Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine] |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 16966 | Philosophers tend to distinguish broad 'being' from narrower 'existence' - but I reject that [Quine] |
| 16965 | All we have of general existence is what existential quantifiers express [Quine] |
| 16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
| 16964 | Theories are committed to objects of which some of its predicates must be true [Quine] |
| 4216 | Express a theory in first-order predicate logic; its ontology is the types of bound variable needed for truth [Quine, by Lowe] |
| 18966 | Ontological commitment of theories only arise if they are classically quantified [Quine] |
| 14490 | You can be implicitly committed to something without quantifying over it [Thomasson on Quine] |
| 16961 | In formal terms, a category is the range of some style of variables [Quine] |
| 12056 | An ancestral relation is either direct or transitively indirect [Wiggins] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 12050 | Substances contain a source of change or principle of activity [Wiggins] |
| 12052 | We never single out just 'this', but always 'this something-or-other' [Wiggins] |
| 12055 | Sortal predications are answers to the question 'what is x?' [Wiggins] |
| 12059 | A river may change constantly, but not in respect of being a river [Wiggins] |
| 12063 | Sortal classification becomes science, with cross reference clarifying individuals [Wiggins] |
| 12051 | If the kinds are divided realistically, they fall into substances [Wiggins] |
| 12053 | 'Human being' is a better answer to 'what is it?' than 'poet', as the latter comes in degrees [Wiggins] |
| 12054 | Secondary substances correctly divide primary substances by activity-principles and relations [Wiggins] |
| 12047 | We refer to persisting substances, in perception and in thought, and they aid understanding [Wiggins] |
| 12057 | Matter underlies things, composes things, and brings them to be [Wiggins] |
| 12064 | The category of substance is more important for epistemology than for ontology [Wiggins] |
| 12049 | Naming the secondary substance provides a mass of general information [Wiggins] |
| 12065 | Seeing a group of soldiers as an army is irresistible, in ontology and explanation [Wiggins] |