Would you tell me the difference between object and objective as a noun?

I am very confused. Could you possibly elaborate (in detail) the reason why:

My object is to improve my English as much as possible. [WRONG it should be 'objective']

My object is to learn English. [RIGHT]

The object of the game is to improve children's math skill. [RIGHT]

So, why has Longman written the following:

! Do not use object to mean 'the thing you are working towards and hope to achieve'. Use objective: We have not yet achieved our objective (NOT our object).

Is Longman here wrong?

All of the expressions and examples which I have provided are extracted from Longman (see link below) and Common Errors from Longman too.

http://www.ldoceonline.com/Grammar-topic/object_1

Solution 1:

If Longman says "Do not use object to mean 'the thing you are working towards and hope to achieve" and provided "My object is to learn English" as an example, then it is contradicting itself. As for the object-objective distinction, I can only offer an opinion:

1. Objective can be used in any situation where object can be used, i.e. "what's the objet of the game" → "what's the objective of the game"
2. Object can only be used to describe the main goal of something. For this reason, you can say "the object of my visit is to return your book" or "the object of the game is to pick up the most sticks" but not "my object is to learn English" because in the first two, you are describing the central goal of the visit or game, while in the third, you are only describing one of your many goals.

Solution 2:

The distinction Longman draws is entirely artificial and does not reflect actual use in any register. Object has been used continuously since the 17th century to mean ‘the thing you are working towards and hope to achieve’, and it is used so today. You may satisfy yourself of this by searching Google Books for 21st-century instances of "our object is to"; alongside reprinted older works you will find scores of uses—in mathematics, philosophy, history, law, politics, art, literary criticism, and fiction. You will find similar results with various combinations of achieve and object.

If you are of a prescriptivist bent, consult Fowler, Modern English Usage. He says nothing about a distinction between object and objective; but his parade sentence for discussion of the split infinitive is

Our object is to further cement trade relations.

The best advice you have seen here is John Lawler’s:

Following this and similar overfussy advice about "correctness" only produces needless anxiety. Once you learn that anybody can write anything at all about what's "correct" in English—no matter how silly it is—and somebody will read and believe it—no matter how silly it is—you will understand that you needn't care about things like this.

Solution 3:

An objective is something you want to pursue.

My objective is to improve my coordination.

An object of a thing is the purpose for which it exists.

The object of billiards in school is to teach coordination.

An object is internal to the thing. An objective is something that can come from a being. So only people and persons can have objectives whereas objects and people can have an object.

This is exactly what is expressed by the quote from Longman:

Do not use object to mean 'the thing you are working towards and hope to achieve'. Use objective: We have not yet achieved our objective (NOT our object).

Your attempts to produce sentences with this grammar are basically wrong.

My object is to improve my English as much as possible (probably comprehensible but wrong)

Unless you are a being that exists solely to improve English, then this is wrong. You should use objective.

My object is to learn English (incorrect)

Again, unless you exist to maximize your English learning, then this is wrong.

The object of the game is to improve children's math skill. (correct)

This is correct because the game is made for this purpose, so we can call that purpose its object.