Logical syntax description of the forms of the expressions of a language in virtue of which the expressions stand in logical relations to one another. Implicit in the idea of logical syntax is the assumption that all – or at least most – logical relations hold in virtue of form: e.g., that ‘If snow is white, then snow has color’ and ‘Snow is white’ jointly entail ‘Snow has color’ in virtue of their respective forms, ‘If P, then Q’, ‘P’, and ‘Q’. The form assigned to an expression in logical syntax is its logical form. Logical form may not be immediately apparent from the surface form of an expression. Both (1) ‘Every individual is physical’ and (2) ‘Some individual is physical’ apparently share the subjectpredicate form. But this surface form is not the form in virtue of which these sentences (or the propositions they might be said to express) stand in logical relations to other sentences (or propositions), for if it were, (1) and (2) would have the same logical relations to all sentences (or propositions), but they do not; (1) and (3) ‘Aristotle is an individual’ jointly entail (4) ‘Aristotle is physical’, whereas (2) and (3) do not jointly entail (4). So (1) and (2) differ in logical form. The contemporary logical syntax, devised largely by Frege, assigns very different logical forms to (1) and (2), namely: ‘For every x, if x is an individual, then x is physical’ and ‘For some x, x is an individual and x is physical’, respectively. Another example: (5) ‘The satellite of the moon has water’ seems to entail ‘There is at least one thing that orbits the moon’ and ‘There is no more than one thing that orbits the moon’. In view of this, Russell assigned to (5) the logical form ‘For some x, x orbits the moon, and for every y, if y orbits the moon, then y is identical with x, and for every y, if y orbits the moon, then y has water’.
See also GRAMMAR , LOGICAL FORM, THE- ORY OF DESCRIPTION. T.Y.