A further development of what I want to claim will be retrospectively recognizable as the same line of thought can be found in Frege. His use of Latin letters and his logical sign of generality (used in conjunction with the notation for hypotheticals) express relations between concepts. It has always been an embarrassment for the anachronistic extensional quantificational reading of this notation (due originally to Russell) that Frege says of it, when he first introduces it in the that it is the right way to express relations of necessitation. For it Begriffsschrift, causal is a commonplace of the later logistical tradition that merely quantificational relations between concepts cannot distinguish between contingent regularities and lawlike, necessary ones. For that, explicit modal operators must be applied to the quantified conditionals. But Frege deploys his notation so that the relations between concepts expressed by generalized conditionals have modal force. Relations between concepts of the sort logic already lets us express have consequences for relations between their extensions, of the sort our quantificational notation expresses, but his generality locutions (the use of Latin letters and the codify relations we think of as intensional. Fregean logical concepts are concavity with German ones) indeed second- and higher-order concepts, but more than that, the universality they express is rulish. They are in the first instance principles in accordance with which to reason, and only derivatively premises from which to reason. In addition to permitting the formulation of purely logical relations among logical concepts, Frege’s logical vocabulary permits us to assert necessary connections among empirical concepts that themselves can only be discovered empirically: physically or causally necessary connections. In the Preface to the Begriffsschrift, Frege says: It seems to me to be easier still to extend the domain of this concept-script [Begriffsschrift] to include geometry. We would only have to add a few signs for the intuitive relations that occur there…The transition to the pure theory of motion and then to mechanics and physics could follow at this point. The latter two fields, in which besides rational necessity [Denknotwendigkeit] natural necessity [Naturnotwendigkeit] asserts itself, are the first for which we can predict a further development of the notation as knowledge progresses.
A further development of what I want to claim will be retrospectively recognizable as the same line of thought can be found in Frege. His use of Latin letters and his logical sign of generality (used in conjunction with the notation for hypotheticals) express relations between concepts. It has always been an embarrassment for the anachronistic extensional quantificational reading of this notation (due originally to Russell) that Frege says of it, when he first introduces it in the Begriffsschrift, that it is the right way to express causal relations of necessitation. For it is a commonplace of the later logistical tradition that merely quantificational relations between concepts cannot distinguish between contingent regularities and lawlike, necessary ones. For that, explicit modal operators must be applied to the quantified conditionals. But Frege deploys his notation so that the relations between concepts expressed by generalized conditionals already have modal force. Relations between concepts of the sort logic lets us express have consequences for relations between their extensions, of the sort our quantificational notation expresses, but his generality locutions (the use of Latin letters and the concavity with German ones) codify relations we think of as intensional. Fregean logical concepts are indeed second- and higher-order concepts, but more than that, the universality they express is rulish. They are in the first instance principles in accordance with which to reason, and only derivatively premises from which to reason. In addition to permitting the formulation of purely logical relations among logical concepts, Frege’s logical vocabulary permits us to assert necessary connections among empirical concepts that themselves can only be discovered empirically: physically or causally necessary connections. In the Preface to the Begriffsschrift, Frege says: It seems to me to be easier still to extend the domain of this concept-script [Begriffsschrift] to include geometry. We would only have to add a few signs for the intuitive relations that occur there…The transition to the pure theory of motion and then to mechanics and physics could follow at this point. The latter two fields, in which besides rational necessity [Denknotwendigkeit] natural necessity [Naturnotwendigkeit] asserts itself, are the first for which we can predict a further development of the notation as knowledge progresses.
Analytic%20Pragmatism%20Expressivism%20and%20Modality%2014-10-2%20a.docx