If yesterday were tomorrow, then today would be Friday. (S) If yesterday were tomorrow, then today would be Friday.
Question: What day is today?

This seems to be an old puzzle, and depending on the interpretations, the answers are Wednesday or Sunday (or perhaps Friday as well?). I would like to understand the logic required to analyze and answer the above question.
The following is my attempt in formalizing the analysis. Please let me know if (and where) I err.
Model
Let the actual &quot;today&quot; be $t$, so that &quot;yesterday&quot; in the antecedent of (S) is $t-1$ and &quot;tomorrow&quot; in the antecedent is $t+1$.
Let $D(\tau)$ denote the day of week of date $\tau$.
The subjunctive &quot;today&quot; in the consequent of (S) can be formalize in two ways: as (i) &quot;the yesterday of tomorrow&quot;, or (ii) &quot;the tomorrow of yesterday&quot;.
The two interpretations thus lead to two ways to translate (S):
$$(t-1)=(t+1) \quad\Rightarrow\quad D(t+1)-1=\text{Friday}\tag{1}$$
$$(t-1)=(t+1) \quad\Rightarrow\quad D(t-1)+1=\text{Friday}\tag{2}$$
From $(1)$, we have $D(t-1)=\text{Saturday}\Rightarrow D(t)=\text{Sunday}$.
From $(2)$, we have $D(t+1)=\text{Thursday}\Rightarrow D(t)=\text{Wednesday}$.
But both interpretations also seem to suggest Friday as a solution, which is implausible (?) and indicates that the model I've proposed has flaws.
What's wrong, and how can we improve the model?
Yesterday was not tomorrow.  From a false assumption, any conclusion is possible.

But one interpretation of the puzzle goes like this. The only day of the week $x$ for which is would be correct to say "If yesterday was $x$, then today would be Friday"
is Thursday.  So on that interpretation, $x = $Thursday, which actually happens to be tomorrow, so today is Wednesday.

Alternatively, "If $y$ was tomorrow, then today would be Friday" is true if $y$ is Saturday.  On that interpretation, Saturday is actually yesterday instead of tomorrow, and today is Sunday.
As mentioned by others, yesterday is never tomorrow, assuming a linear timeline. Thus, it has no bearing on the question.

In other words, the answer is the same as "Zip-A-Dee-Doo-Dah. What day is today?"

According to my phone, today is February 3rd. In general, the answer is "[insert today's date here]".