Translating Natural Language into L

5 Translating Natural Language into L

5.1 Introduction

5.1.1 For any Interpretation I,

5.1.1.1 ‘Ds’ is true under I iff the object I assigns to ‘s’ belongs to the set that I assigns to ‘D’

5.1.1.2 ‘-Ds’ is true under I iff the object I assigns to ‘s’ does not belong to the set that I assigns to ‘D’

5.1.1.3 ‘(∃x)Dx’ is true under I iff some element of the domain of I belongs to the set that I assigns to ‘D’.

5.1.1.4 ‘Ds \(\implies) (∃x)Dx’ is true under I iff either the object that I assigns to ‘s’ does not belong to the set that I assigns to ‘D’ or some element of the domain of I belongs to the set that I assigns to ‘D’, or both

5.2 Interpretation and Translation

5.2.1 Given the sense, the denotation(if any) is thereby fixed, but converse does not hold.

5.3 Translating connectives and quantifiers

5.3.1 Only relative to an interpretation do the expressions of L have denotations

5.3.1.1 Futile to translate unless an interpretation is given

5.3.2 If an Interpretation is given a standard translation con be obtained.

5.3.3 No simple correspondence between the form of an ordinary sentence and its counterpart in L exists.

5.3.4 Two formal sentences equivalent in L may not be equivalently represented in Natural Language.