This is a part of a sentence:
As many of you will have seen yesterday, . . .
What does it mean? The words will and yesterday seem to be in contradiction.
Is that a correct sentence?
I think this is incorrect, but it's complicated. My best guess is that this a manager-speak corruption of a conditional perfect clause, with some inbuilt assumptions.
If you had read the news yesterday, you would have seen…
This is a standard conditional perfect construction. However, I think that the speaker in your example is making a tacit assumption that everyone has read the news, and therefore drops the first part.
You would have seen yesterday…
But that seems to lack conviction, so they trade up from a “would” to a “will”, and in doing so wreck the grammar of the whole.
You will have seen yesterday…
(In my experience this is exactly the kind of thing that senior executives say when discussing company-wide restructures.)
This use of the future perfect is a standard construction used in English to express an assumption, expectation or presumption.
If someone asks, "Where is Fred?", then I might respond:
He has gone to the bank.
This would indicate that I know for certain where he has gone - perhaps he told me so. However, if he didn't say anything, but I happen to know that he usually goes to the bank on a Thursday, I might instead say:
He will have gone to the bank.
The reason the tense is used in this way (to my mind, at least) is as follows: we are implying that, at the point in the future when we discover for certain where he has gone, we will discover "he has gone to the bank" - and hence the construction is roughly equivalent to [When we find out where he has gone] he will have gone to the bank.
The usage in the question is similar. If the speaker had said
As many of you saw yesterday...
that would imply that he knows that the audience saw [whatever it was] yesterday - again, perhaps he spoke to the people concerned, or was there at the time. Instead, by saying
As many of you will have seen yesterday...
he conveys that he does not know for certain, but confidently assumes this to be the case based on habit, common sense or some such: perhaps he knows that many of the audience were in the right place at the right time to see [whatever this momentous spectacle happened to be].
The British National Corpus reports many examples of such use - searching for "you will have *d", there are plenty of examples of the future perfect being used with this meaning, including You will have noted/noticed (24), you will have gathered/found (16), and plenty more with other verbs; searching with other subjects reveals many more examples, but it gets harder to filter out those that use the future perfect in this way rather than other uses. Even so, searching for "will have *d" and looking through the first page of results reveals that this construction is extremely common, perhaps even the most common use of the future perfect.
(I also tried checking COCA for US usage, to see if this is more common in the UK, but alas I was unable to due to "database errors".)
As has been noted elsewhere on ELU, English doesn't really have a "future tense". But just because we normally use the modal/auxiliary verb "will" to indicate future, doesn't mean that's all it can do. To claim that OP's example is illogical or ungrammatical is just spurious pedantic rationalisation.
When talking about an imaginary event, or a past event that might not have happened (i.e. - we don't know, or it's conditional), we normally use the form "would have" + past participle.
To indicate that a past event actually happened, we normally use "will have" + past participle...
[Edited: In short, as you will have seen yesterday is technically correct and natural in speech; but, since the same meaning could be conveyed in fewer words, and because it may be slightly confusing at times, perhaps as you saw yesterday would be better in a polished text. ]
1.) As many of you saw yesterday, she sucked.
This is a simple situation, in which I describe what you saw yesterday.
2.) As many of you will agree, she sucked.
Here I presume that you will agree that she sucked, if I ask your opinion at some point in the fture. The "if I ask your opinion" is implicit. You will agree is equivalent in meaning to "it will turn out that you agree".
3.) As many of you will have seen, she sucked yesterday.
Now how should this be parsed? The use of will to indicate future probability is quite unremarkable on its own, as seen in (2.) above.
It is the combination with have seen that makes it complex. At some point in the future, if I ask, it will turn out that you saw that she sucked yesterday. So there is actually no real problem.
4.) As many of you will have seen yesterday, she sucked.
I parse this similarly to (3.), but with yesterday in a different position: at some point in the future, if I ask, it will turn out that you saw yesterday that she sucked.
Here yesterday modifies only (that) you say, not it will turn out; this different scope of yesterday is invisible in will have seen, but it is there. The cause of confusion is that our subconscious might want to apply yesterday to the whole clause, including will, while in fact it applies only to (that) you saw. ]
Added Note: My answer to the stated question begins following this indented paragraph. Several other answers treat the questioned sentence part (As many of you will have seen yesterday) strictly as a current utterance. In my answer I treat the case where the given part appears in a recorded message, written or spoken. For that particular case, without commenting on other cases, I submit that the sentence part is correct and easily understood. My answer does not address, nor is it intended to address, the current-utterance issues treated at length in other replies and comments. Whether the questioned usage is "common and natural in speech, where the audience hear the words as soon as they are said" is outside the scope of this answer. The reason for addressing only the recorded message case is that it is a case not treated in other answers, in spite of falling within the purview of the question, which does not say if the sentence part is recorded or is current utterance.
Such constructions are (or were) commonly found in magazine articles, where writers' deadlines fall a few weeks in advance of the publication being in the hands of readers. The following is a typical example of correct use in this manner. In the InfoWorld 27 Oct 1986 issue, R. X. Cringely wrote,
Then he told me that by the time this paper hits the streets, AST Research will have announced a desktop publishing system...
In examples like this, writer and speakers presume that when their recorded communications are read or heard, some event will have occurred.
On the one hand, this seems to be accepted usage; I'm sure I've heard it, and it doesn't sound horrible, at least. (Although, as maniacyak points out in his excellent answer, it is probably incorrect grammar.)
On the other hand, simply saying "As many of you saw yesterday" seems so much more obvious. At worst, "As many of you should have seen yesterday" is grammatically correct and expresses the apparently intended meaning adequately.
It's not incorrect - in the future (one second from now as I complete my sentence) you will reflect on the past event. Tense wise it's logical, but it's pretty unnecessary. No meaning is lost by saying "As many of you have seen yesterday,..." Even changing it to "As many of you saw yesterday,..." doesn't mean anything different.
If you say that in speech, there's nothing wrong with it - rules of grammar are more important in writing since you have more time to consider what you're going to write and have the opportunity to edit.
I want to answer the question of "Max" and argue that the use of "will" is not only perfectly correct, but that it serves a rhetorical function. Its grammatical correctness derives not so much from adherence to grammatical rules as from its precise although somewhat elusive rhetorical function. What I want propose is a psychologico-rhetorical interpretation.
"As many of you will have seen yesterday ..." strikes me in the first place by its rhetorical effect. The speaker shows that they presume something about their audience. In our case, the speaker presumes that the listeners know a certain thing.
If the speaker said "As many of you ____ have seen yesterday", this would sound bold as it would mean that the speaker is certain that his audience saw something the day before. The fact that he adds "will" betrays that the speaker is actually making only an assumption - although one which, the speaker believes, is quite probable. "Will" in this sentence could be easily replaced with "must" without altering the meaning of the sentence: "As many of you MUST have seen yesterday ..." The phrase tells us that the speaker believes (or makes us want to believe) that they have a reason on which they ground this assumption.
It seems open to interpretation whether this "will" attenuates the boldness of the speaker's claim or is a false display of modesty.