Logical operations

@article{McGee1996LogicalO,
  title={Logical operations},
  author={Vann McGee},
  journal={Journal of Philosophical Logic},
  year={1996},
  volume={25},
  pages={567-580}
}
  • Vann McGee
  • Published 1996
  • Philosophy
  • Journal of Philosophical Logic
Tarski and Mautner proposed to characterize the “logical” operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively “logical”, this lends support to… 
Logical Operations and Invariance
TLDR
A notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski–Sher criterion for logicality is presented and the invariant operators are characterized as definable in a fragment of the first-order language.
Logic, Logics, and Logicism
TLDR
An examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain and a new notion of homomorphism invariant operation over functional type structures is introduced.
Extensionality and logicality
TLDR
This paper defines the logical terms of a language as those terms whose extension can be determined by their form, and defines purely logical languages as “sub-extensional”, namely, as concerned only with form, to obtain a wider perspective on both logicality and extensionality.
A completeness theorem for unrestricted first- order languages
Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an
Invariance and Definability, with and without Equality
TLDR
This paper generalizes a correspondence due to Krasner between invariance under groups of permutations and definability in $\La_{\ infty\infty}$ so as to cover the cases (quantifiers, logics without equality) that are of interest in the logicality debates, getting McGee's theorem about quantifiers invariant under all permutation and Definability in pure $\La_infty$ as a particular case.
Logical Indefinites∗
The best extant demarcation of logical constants, due to Tarski, classifies logical constants by invariance properties of their denotations. This classification is developed in a framework which
LOGICALITY AND MODEL CLASSES
Abstract We ask, when is a property of a model a logical property? According to the so-called Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to
Which Quantifiers Are Logical? A Combined Semantical and Inferential Criterion
TLDR
A combined semantical and inferential criterion for logicality is offered and it is shown that any quantifier that is to be counted as logical according to that criterion is definable in first order logic.
Logicality and Invariance
  • D. Bonnay
  • Philosophy
    Bulletin of Symbolic Logic
  • 2008
TLDR
The standard arguments in favor of invariance under permutation, which rely on the generality and the formality of logic, should be modified and shown to support an alternative to Tarski's criterion, according to which an operation is logical iff it is invariant under potential isomorphism.
LOGICALITY AND MEANING
  • Gil Sagi
  • Philosophy
    The Review of Symbolic Logic
  • 2018
TLDR
It is proposed that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension, and it is shown that this leads to a graded account of logicality: the less structure a term requires in order to be fixed, the more logical it is.
...
...