Barker notices that introduction rules reveal the canonical grounds for use of a logical constant
: what characterizes an inference-rule as an introduction rule are certain cognitive and epistemic asymmetries that are linked to the idea of a canonical ground.
The Treatise's Grundgedanke is that the propositions of logic do not represent at all (that's why there is no 'logical constant
--, 1976, "What Is a Logical Constant
?", Journal of Philosophy, vol.
When an expression, including a logical constant
, is introduced
74); hence the way in which the rules governing each logical constant
were given, and in particular, the introduction rules, would have to be immediately connected with its intuitive meanings.
A second kind of model for understanding a primitive expression is provided by the logical constants
. The condition for understanding a logical constant
is plausibly given by alluding to some kind of grasp of certain introduction and/or elimination rules involving it.
Sher focuses on the fact that my quantifier '[Q.sup.*]' is "unnatural: it behaves like one familiar logical constant
in some universes, like another in others" (2001, 250), and she goes on to assert:
(All the paradoxes in Group Bii do this and some of the paradoxes in Group A, notably Russell's, but not the paradoxes in Bi or the other paradoxes in Group A.) For each paradox of this kind, we can form a new paradox by replacing [logical not][alpha] uniformly with [alpha][right arrow][beta], where [beta] is an arbitrary formula, or, more simply, with [alpha][right arrow][perpendicular to], where [perpendicular to] is some logical constant
. The standard account of logical constants
is hybrid: on the one hand it contains a highly informative, precise, and systematic criterion for logical connectives, namely, the Boolean or truth-functional criterion; on the other hand it contains an altogether uninformative and unsystematic definition of logical constants
other than connectives, namely, a definition by enumeration--C is a logical constant
(other than connective) iff: C is `[for all]' or C is `[there exists]' or C is `=' (or C is definable from constants on this list and/or logical connectives).
On the Sense and Reference of a Logical Constant
, HAROLD HODES
Necessity when thought of as truth in all possible worlds is also arguably a logical constant
as natural extensions of "all" and "some." McGinn does not tell us what logical concepts have in common, and in denying the use of quantifiers in explaining identity and necessity, rules out a credible way of saying what they have in common and share with "all," "some," "and," and "or."