He set two objectives/objects: to ensure peace and ...

[WilliamTaft]

Michael I is the first of a new, very long dynasty. But he inherits a devastated country, ruined by years of wars and instability. Groups of looters plunder the countryside, while Polish and Swedish armies still occupy Russian territories. In order to restore the state, he set two objectives: to ensure peace, and to stabilize the state’s finances.

Source: The Russian Empire - Summary on a map, YouTube

Can I say "objects" in this context? If so, what's the difference?

 

[jutfrank]

No. The word 'object' just does not have that same sense.

An objective is a goal.

 

[WilliamTaft]

The Merriam-Webster Dictionary:

3 a : the goal or end of an effort or activity : PURPOSE, OBJECTIVE

Their object is to investigate the matter thoroughly.

The object of the game is to score the most points.

 

[Tarheel]

The two words are used differently.

 

[jutfrank]

The word 'object' just does not have that same sense.

I now see what I said here was not quite right. Sometimes, 'object' does have a very similar sense as 'objective'. Both words have a basic sense of 'goal' or 'end point'. but there are key differences in meaning and use. This is where I'd begin in outlining them:

An objective is something that someone has, in a possessive way. I can say 'I have two objectives' or 'Your objective is to ...' but I can't say 'I have two objects' or ''Your object is to ... " Similarly, a game can have an object but not an objective.

This frame affords 'object' very well and 'objective' not so well:

the _______ of the ________

The phrase 'the object of the game' is almost a fixed expression in its own right. In fact, I wouldn't be surprised if that particular expression represents the majority of all uses of 'object' in this particular sense.

The word 'objective' has it's own set of collocates that 'object' doesn't share, and I think this helps to see differences in meaning. An obvious one in the original text is the verb 'set'. I think this reveals the sense that there's a temporariness in an objective and a permanence in an object. Another revealing collocation is 'main' (my main objective), which shows that there may be and often are multiple objectives held at the same time. Games, on the other hand, must have only one object.

These are just my thoughts. I'd be happy to hear anyone disagree with anything.