If yesterday were tomorrow, then today would be Friday.

Question

(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 "today" be $t$, so that "yesterday" in the antecedent of (S) is $t-1$ and "tomorrow" in the antecedent is $t+1$.

Let $D(\tau)$ denote the day of week of date $\tau$.

The subjunctive "today" in the consequent of (S) can be formalize in two ways: as (i) "the yesterday of tomorrow", or (ii) "the tomorrow of yesterday". 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?

Answer 1

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.

Answer 2

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]".

Answer 3

In my opinion the problem is not well defined:let the REAL today be $t_0$.

• The problem does not specify if we are in a situation where our hypothetical tomorrow (relative to a new "today" $t_1$) is the REAL yesterday (aka $t_0-1$)

(S) If [the REAL]yesterday($t_0-1$) were tomorrow($t_1+1$), then today($t_1$) would be Friday.

Question: What day is today($t_0$)?

$OR$

• if we have to imagine that our hypothetical yesterday (so a yesterday $t_1-1$ because is relative to $t_1$) is the REAL tomorrow ($t_0+1$)

(S) If yesterday($t_1-1$) were [the REAL]tomorrow($t_0+1$), then today($t_1$) would be Friday.

Question: What day is today($t_0$)?

So there can be two interpretations (Friday is $w_5$)

$1)$ if $t_0-1=t_1+1$ and $t_1=w_5$ find $t_0$

$2)$ if $t_1-1=t_0+1$ and $t_1=w_5$ find $t_0$

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• By definition $t_1=\operatorname{Friday}$

• In the first interpretation $t_0-1=t_1+1$ so $t_0=t_1+2$

• In the second interpretation $t_1-1=t_0+1$ so $t_0=t_1-2$

so if Friday is $w_5$ and $\{w_i\}_{i\in\{1,2,...,7\}}$ are the days of the week then

$t_0=w_5+2=w_7$ that is Sunday

$t_0=w_5-2=w_3$ that is Wednesday

Answer 4

Yesterday was some day. What if that day was tomorrow? If it was, today would be Friday. That means, find what day implies it would be Friday.

Yesterday was Saturday. If Saturday was tomorrow, today would be Friday.

Answer 5

If you are interested in a logic which can handle this kind of conditionals, you might be interested in the field of Conditional Logic. These kinds of logics can be used to analyse conditionals with false antecedent. See

• the Wikipedia entry,
• the SEP entry,
• this survery article (which I think can also be found on the web somewhere), or
• e.g. this book (which again I think can also be found on the web in full).

Enjoy!

Answer 6

If yesterday were tomorrow, then today would be Friday. What day is today?

(Deleted my previous answer and starting over.)

Let $d$ be any date, past or present or future, expressed as an integer, with the natural ordering of days.

Let $d_0$ be the supposed current date.

Let $D(x)$ be the day of the week for date $x$ (Monday, Tuesday, etc.).

We are given:

$d-1=d_0+1$ and $D(d)=Friday$

Can there be any other meaningful interpretations?

Then the day of the week for the supposed current date would be $D(d_0)$ where

$D(d_0)=D(d-2)=Wednesday$

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Edit

A tabular approach...

CURRENT DATES AND DAYS:

..............................................Date...........Day..............

Today..............................$x_0$...............Wednesday.

Tomorrow.....................$x_0+1$........Thursday.......

Day After Tomorrow..$x_0+2$........Friday...........

NEW DATES AND DAYS:

..............................................Date...........Day..............

Yesterday.......................$x_0+1$.......Thursday.......

Today...............................$x_0+2$......Friday...........

First, fill in the current dates with today's date of $x_0$. Then fill in the new dates with yesterday's date of $x_0+1$. Then fill in the new days with today's day of Friday. Finally, fill in the current days with day-after-tomorrow's day of Friday.

Answer 7

If yesterday was tomorrow (tomorrow being Saturday as today is Friday) then it was spoken on Sunday as yesterday was Saturday. It all hinges on the word "if" so don't read any more into it than that?

Answer 8

You are going back 2 days in the week. So, it would be a Wednesday.

In Hindi, there is one word for tomorrow and yesterday,so in this case no answer possible.