| 11033 | Predications of predicates are predications of their subjects [Aristotle] |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| 8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
| 10014 | Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes] |
| 10828 | Quantifying over predicates is treating them as names of entities [Quine] |
| 13639 | Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro] |
| 10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| 21657 | Since properties can have properties, some theorists rank them in 'types' [Hofweber] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [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] |