Ordinary language, meta-language, and logically perfect language

The world is divided into many facts and each fact displays some kind of structure. To describe the structure we need an appropriate language that is termed as first order language or ordinary language or natural language. It assists us to express about the objects and/or facts of the world. We use this language to share our thoughts, desires, cravings, passions etc. with others. Thus, it is also known as object language. Logically speaking, the language in which we shall be characterizing the language of logic is known as ordinary language (Singh and Goswami, 1998, 1), and an extended version of ordinary language is known as meta-language. Meta-language can't be explained on its own. It needs the ordinary language for its elucidation.

Etymologically speaking, the language through which we speak or express the object of the phenomenal world is called object language. Meta-language on the other hand, is one through which we can formulate statements of object language. In meta-language, sentences embrace semantic concepts.

There are two components found in the meta-language. They are as follows:

1. Semantic part
2. Non-semantic part

The non-semantic part furnishes an expressive potential which is as rich as that of object language. Thus, there is a correspondence relation found between the non-semantic part of the meta-language and the object language, while no such correspondence is sought in the semantic part of the meta-language.

Meta-language must meet the following requirements.

1. It must allow for all expressions of the object language to be explicable in it.
2. It must contain semantic concepts in relation to the object language that can't be formulated in the object language.