On Double Quantification
Georg Henrik von Wright · 2017
The study of the fragment of the lower functional calculus, which contains only formulae of the first degree, might be called the theory of simple quantification. The study of the fragment of the lower functional calculus, which contains only formulae of the second degree, might be called the theory of double quantification. The decision problem can be effectively solved for formulae of the first degree. The solution of the problem is implicit in some of the classical treatments of the syllogism, using diagrams. The first systematic solution is due to Lowenheim. The decision problem can be effectively solved also for formulae of the second degree. The decision problem for formulae of the second degree has now become &s;reduced&s; to the problem of giving effective criteria for the solvability of the two problems which people have called the Fitting-in-Problem and the Completing-Problem.