logical form,
n. 1. the syntactic structure that may be shared by different expressions, as abstracted from their content and articulated by the logical constants of a particular logical system.
2. in particular, the least detailed structure of an argument by virtue of which it can be shown to be logically valid. Thus
has the same logical form as
namely
in sentential calculus. Although these can also be formalized as
in the predicate calculus, the latter is not in this sense the logical form of the given arguments as their validity is demonstrable at sentential level without recourse to analysis of the predicate structure. 3. by contrast, the most detailed structure at a particular level of analysis of a statement, this level of detail being required in order to anticipate all logical relationships that this statement may have with any others. For example,
is said to have logical form in sentential calculus
even although we would say that the logical form, in the preceding sense, of
is
This disparity arises because we may wish to infer, say, London is noisy from the same sentence, and wish its logical form to allow for this too. We could assign this sentence a more detailed form in sentential calculus, but there is no unique most detailed logical form, incorporating, for example, modal and tense logic analyses, as that would require assurance that there would be no future logical discoveries.
John is tall and thin.
so John is tall
so John is tall
has the same logical form as
London is large and dirty.
so London is large,
so London is large,
namely
P and Q
so P
so P
in sentential calculus. Although these can also be formalized as
Fa and Ga.
so Fa
so Fa
in the predicate calculus, the latter is not in this sense the logical form of the given arguments as their validity is demonstrable at sentential level without recourse to analysis of the predicate structure. 3. by contrast, the most detailed structure at a particular level of analysis of a statement, this level of detail being required in order to anticipate all logical relationships that this statement may have with any others. For example,
if London is big, noisy and dirty, it is noisy and dirty
is said to have logical form in sentential calculus
if(P and Q and R), then (Q and R)
even although we would say that the logical form, in the preceding sense, of
London is big, noisy and dirty.
so it is noisy and dirty
so it is noisy and dirty
is
P and Q; so Q.
This disparity arises because we may wish to infer, say, London is noisy from the same sentence, and wish its logical form to allow for this too. We could assign this sentence a more detailed form in sentential calculus, but there is no unique most detailed logical form, incorporating, for example, modal and tense logic analyses, as that would require assurance that there would be no future logical discoveries.