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Full Idea
A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains.
Gist of Idea
In proof-theory, logical form is shown by the logical constants
Source
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2)
A Reaction
You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus.
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |