Home Philosophy Advances in Proof-Theoretic Semantics

## An Overview of the Theory of ConstructionsVersions of the Theory of Constructions were presented by Kreisel [25, 26], and Goodman [16–18]. The details of the notation and formal systems formulated in these papers differ in several respects. Our goal here will thus not be to present a systematic exposition of the different formalisms proposed by Kreisel and Goodman, nor even to provide a complete formulation of any one of them. Rather we shall simply attempt to set down some of the common characteristics of these systems with the dual goals of explaining how Kreisel and Goodman proposed to use the language of the Theory of Constructions to formalize Kreisel's reformulation of the BHK clauses and also to be able to reconstruct as closely as possible the reasoning of the Kreisel-Goodman paradox. In so doing, we will adhere as closely as possible to the notation and terminology of the (I) The system (II) Using the theory it is possible to define a decidable predicate intended interpretation “construction (III) Statements of the latter form are themselves treated by the theory as propositions which may themselves admit to proof. In particular, it is possible within the theory to formulate statements such as It would appear that the ability to iterate the application of the predicate is necessary if we are to formalize clauses such as (P2 → ). But note that if this is allowed, it must also be acknowledged that the constructions must play a dual role in then |

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