reductionism, explanatory See METHODOLOGICAL. HOLIS. reduction sentence, for a given predicate Q3 of space-time points in a first-order language, any universal sentence S1 of the form: (x) [Q1x / (Q2x / Q3 x)], provided that the predicates Q1 and Q2 are consistently applicable to the same space-time points. If S1 has the form given above and S2 is of the form (x) [Q4x / (Q5 / — Q6)] and either S1 is a reduction sentence for Q3 or S2 is a reduction sentence for -Q3, the pair {S1, S2} is a reduction pair for Q3. If Q1 % Q4 and Q2 % — Q5, the conjunction of S1 and S2 is equivalent to a bilateral reduction sentence for Q3 of the form (x) [Q1 / (Q3 S Q2)].
These concepts were introduced by Carnap in ‘Testability and Meaning,’ Philosophy of Science (1936–37), to modify the verifiability criterion of meaning to a confirmability condition where terms can be introduced into meaningful scientific discourse by chains of reduction pairs rather than by definitions. The incentive for this modification seems to have been to accommodate the use of disposition predicates in scientific discourse. Carnap proposed explicating a disposition predicate Q3 by bilateral reduction sentences for Q3. An important but controversial feature of Carnap’s approach is that it avoids appeal to nonextensional conditionals in explicating disposition predicates.
See also CARNAP, REDUCTION , VERIFICA — TIONIS. I.L.