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Full Idea
The defining features of a pure logic are its absolute generality (the objects of discourse are irrelevant), and its formality (logical truths depend on form, not matter), and its cognitive primacy (no extra-logical understanding is needed to grasp it).
Gist of Idea
A pure logic is wholly general, purely formal, and directly known
Source
Øystein Linnebo (Plural Quantification [2008], 3)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.10
A Reaction
[compressed] This strikes me as very important. The above description seems to contain no ontological commitment at all, either to the existence of something, or to two things, or to numbers, or to a property. Pure logic seems to be 'if-thenism'.
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |