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My wife will be angry, unless I'm home by 7.00.
In the sentence above the "unless" should not be used. The correct conjunction is supposed to be the "if". Compare this sentence:
I'll come at 5 unless there is a traffic jam.
Here "unless" is appropriate. Why is it not so in my example sentence?
The reason that one of these examples is better than the other is not about grammar, it is about implications.
An implication is an idea that you might give to somebody, but that you didn't actually properly say. For example, if you say Give me my book back or I'll punch you, you are saying that you will punch the person if they do not give you back your book. But you are only implying that you will not punch the person if they do give your book back. But notice that you did not actually say this at all. Maybe you will punch them if they don't give it back and you will punch them if they do!
When we use the word if we often give people the idea that the situation in the main clause will be caused by the situation in the if-phrase:
When we hear the sentence above, we understand something like:
Notice that that is just an implication. We did not actually say that!
When we use the word unless, we often give a different implication. Consider this sentence:
In the sentence above, I am implying that the normal situation is that I play badminton on Tuesdays. I am implying that the situation you should expect is that I play badminton on Tuesdays. And I am also implying that somehow "it's cold outside" is an exception. It isn't what you would expect to happen. For this reason it would be very strange for me to say I play badminton on Tuesdays unless it's cold outside if I lived in the Arctic!
Getting it wrong
Implications are not usually accidents. People use implications to give people extra information without needing to use more words. If we want to show that some situation will cause another situation, it is better to use if than unless. Remember that chair sentence? Well if we use unless the sentence will sound very strange:
Now, if we are saying this to someone who is thinking about sitting down on a chair, this is a bit odd. This doesn't give the same implications as the if-sentence at all. It presents the chair breaking as something we might expect to happen, and it makes our not sitting on it sound like an unusual exception. The other reason it is odd is because if we wanted to imply that sitting on the chair would break it, we could just use the word if instead! It would be clear and effective. There is nothing wrong with the grammar in the unless-sentence. It just presents the information in a strange way, and doesn't use the implications of if or unless effectively.
It's important to remember that if and unless do not give opposite implications. They just give different ones. There are many situations where we could use either word and the implications would be useful.
Another thing to remember is that implications are very context-dependent. When the situation we use them in changes, the implications often change too. Also, the way that we arrange information in a sentence can give also different implications. This can change the types of implication that individual words would otherwise have.
The Original Posters examples
I'll come at 5 unless there is a traffic jam.
My wife will be angry, unless I'm home by 7.00.
The first example gives the implication that the listener should interpret the traffic jam as an exception to what is expected. The second example is not ungrammatical or untruthful. But if the speaker wants to say that not getting home by 7.00 will cause his wife to be angry it might be more effective to say:
This is not the best example that Michael Swan could have given. But this is what he means.
My wife will be angry unless I'm home by 7
If I'm not home by 7, my wife will be angry
In some ways, these two sentences are equivalent. They mean that if you get home at 7:05, your wife will be angry.
However, there's a difference in the detail.
If I'm not home by 7, my wife will be angry
This assumes that your wife is not angry, and will only become angry if you are late.
My wife will be angry unless I'm home by 7
This assumes that your wife will be angry, and the only way to placate her is to arrive home early.
It's a fairly subtle distinction, and frankly I think your book is being over-zealous as any native speaker would understand the intended meaning without issue.
To transfer this to your other sentence
I'll be home by 5pm, unless there is a traffic jam
As above, the assumption is that you will be home at 5pm.
Again, "unless" gives the assumption that the former clause is always true with the exception of the situation in the second clause.
I will be home late if there is a traffic jam
Now the assumption is that the first phrase is only true if the second is also true.
In this example, both are relevant because the initial position is that you are home on time, not that your wife is angry.
The "wrong" version of this sentence would be something more like the following, which perhaps shows why it is wrong.
I will be home late unless I get home on time.
