* The sun will rise at 6.30 tomorrow
* We will buy a new car next month
* I will meet my mother at the airport tomorrow
* The train will depart in 10 minutes
All perfectly fine.
Here's an example where "will" cannot be substituted with "going to".
"If you sit down then the movie will start." <-- makes sense
"If you sit down then the movie is going to start." <-- ???
In the earlier list, that's "will" because it's a prediction or statement of fact.
Also, "The movie will start when you sit down" is probably better form all 'round.
https://en.wikipedia.org/wiki/Future_tense#English and https://en.wikipedia.org/wiki/Going-to_future are clear that there are differences between the uses of the different ways to express the future tense in English.
Quoting the latter link, "in some contexts the different constructions are interchangeable, while in others they carry somewhat different implications."
Do you disagree with that assessment? If so, why?
"Don't get close to the bomb, it will explode." implies the bomb will explode if someone gets close to it.
"Don't get close to the bomb, it's going to explode." implies it's going to explode (no matter what) and that people shouldn't be nearby.
http://esl.fis.edu/grammar/rules/future.htm comments that the future tense "is a very difficult aspect of English grammar", with several different forms:
- auxiliary verb will for predictions/statements of fact ("The sun will rise at 6.30 tomorrow")
- auxiliary verb going to for intentions ("We're going to buy a new car next month.")
- present continuous for arrangements; arrangement = a plan for the future that you have already thought about and discussed with someone else. ("I'm meeting my mother at the airport tomorrow")
- present simple for scheduled events ("The train departs in 10 minutes.")
That's in addition to the future continuous ("Don't call me after 10 o'clock. I'll be sleeping." and future perfect ("I hope my mother will have finished cooking dinner by the time I get home.")
Your Cartesian doesn't include negatives, where English uses the auxiliary verb do. (Compare "I do not know Spanish." with "I know not Spanish".)