I have a statement here in yellow,
which, for the sake of this video,
we will assume is true, that eating spinach makes
you stronger.
And then after this, in white, I've
written a bunch of other statements.
And I want to figure out if these are reasonable things
to say, given the assumption that this first statement is
true, that eating spinach makes you stronger.
And we could even put it over here.
"Eating spinach makes you stronger."
So let's read this first sentence.
"If you eat spinach, then you will get stronger."
So this is just really a rephrasing of the first one.
This is really just putting it in if-then form.
You have your "if" and your "then," but it's
really saying the same thing.
If you eat spinach-- that's the same thing as eating
the spinach-- then you will become stronger,
then you will be stronger.
You get stronger.
So this is saying the exact same thing.
I will say that if we assume this first statement is true,
then the second statement is definitely true.
Now, this third statement.
"If you don't eat spinach, then you will not get stronger."
So this is interesting.
This is kind of assuming that the only way to get stronger
is by eating spinach.
But that's not what that first statement says.
That first statement says eating spinach
is a way to get you stronger.
So if we think about ways to get stronger,
there are other ways to get stronger.
You could lift weights.
And maybe you don't want to eat any spinach at all.
Maybe you eat eggs.
Who knows?
There's a million, you know-- maybe you have a-- drink milk.
Who knows what?
There are a lot of options that will get you stronger.
Drink milk.
So eating spinach is not the only way.
So if you don't eat spinach, you still
might be able to get stronger.
They're not ruling out that you can't get stronger.
So I would say, I would not go with this statement
right over there.
Let me do it in red so that I can mark it off.
This one is not necessarily true.
You can get stronger other ways.
Now, if you eat spinach, you will definitely get stronger,
if you believe that statement.
But you can get stronger other ways.
So just by not eating spinach, if you lift weights, eat eggs,
who knows what else, you could still get stronger.
So we'll rule out the second statement.
Now, this third statement.
"You are not stronger.
Therefore, you must not have eaten spinach."
Now, this is where we really have to put our logician hats.
And a logician is just someone who has really,
really, really good logic.
"You are not stronger.
Therefore, you must not have eaten spinach."
And we have to be very careful to separate
our everyday experience versus what
we're trying to deduce logically.
So in our everyday experience, I'm not stronger,
but maybe I did eat spinach.
And we'd say, hey, you know, maybe sometimes spinach
doesn't make me stronger, et cetera, et cetera.
But we have to remember, we're assuming this first statement
is true.
We're assuming this first statement is absolutely true.
Eating spinach makes you stronger.
If you had eaten spinach, by definition,
this first statement says you will be stronger.
If you're not stronger, then there's
no way that you ate some spinach.
So this is actually true.
This is actually true if we assume
this first statement is true.
Now, this last statement.
"You are stronger.
Therefore, you must have eaten spinach."
Well, this goes back to this idea.
That first statement didn't say spinach is the only way
to get stronger, or the second statement wasn't if
and only if you eat spinach, then you'll get stronger.
There's other ways to get stronger.
You could lift weights, eat eggs, drink milk.
So this last statement-- you are stronger.
Therefore, you must have eaten spinach--
isn't necessarily true.
You could have drank-- lifted weights,
or ate eggs, or anything like that.
So I will rule this one out, as well.
You cannot make this conclusion given this first statement.