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**1 - 4**of**4**### 2004] Intensional Logic and the Irreducible Contrast between de dicto and de re

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### Logical Form

"... Abstract. The notion of the logical form of an expression E is shown to be a semantic notion that can be derived from the notion of the structured meaning of E. This simple idea can be traced to categorial grammars, and it is implicitly used by Richard Montague. We argue that a most fine-grained too ..."

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Abstract. The notion of the logical form of an expression E is shown to be a semantic notion that can be derived from the notion of the structured meaning of E. This simple idea can be traced to categorial grammars, and it is implicitly used by Richard Montague. We argue that a most fine-grained tool for defining structured meaning can be found in Pavel Tichý’s Transparent Intensional Logic (TIL). Structured meanings of expressions are identified with abstract procedures, known as TIL constructions, expressed by the expressions. We construe concepts as closed constructions, and present a method of seeking the best semantic analysis (identical to the structured meaning) of a given expression. The method terminates in a complete lattice over the set of possible analyses; which analysis is the best one must, however, be relativized to a conceptual system. This relativization concerns primitive concepts of the conceptual system within which the semantic analysis is set. Our main thesis is: Every well-formed expression E of the language under analysis can be associated with a logical form that is unambiguously derived from the structured meaning of E. 1 The problem of adequate explication

### Two Concepts of Validity and Completeness

"... Abstract. A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. Th ese are ‘natural ’ concepts of validity and completeness, which were, however, in the course of the hist ..."

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Abstract. A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. Th ese are ‘natural ’ concepts of validity and completeness, which were, however, in the course of the history of modern logic, stealthily replaced by their formal descen-dants: formal validity and completeness. A formula is formally valid iff it is true under all interpretations in all universes; and an axiomatic system is called formally sound and complete iff it proves all and only formulas valid in this sense. Th ough the step from material to formal validity and completeness may seem to be merely an unproblematic case of explication, I argue that it is not; and that mistaking the latter concepts for the former ones may lead to serious conceptual confusions. 1. Regimentation and its completeness To start with, let us summarize some obvious facts about common logical calculi. Th e passage from a natural language sentence, such as (1) Mickey is a mouse and Donald is a duck to the corresponding formula of such a calculus, e.g. (1') P1(T1) ∧ P2(T2), can be analyzed as proceeding along two diff erent dimensions, which we can call regimentation and abstraction. Th e logical vocabulary of natural language becomes regimented: disambiguated, unifi ed and standardized – a cluster of ‘improvements ’ for which we will use the umbrella term idealization. In this way, for example, the natural