- Hi, everyone, Jade here.
What if I told you that the observation of a white shoe
can support the hypothesis that all ravens are black?
You'd probably think I was talking complete nonsense, right?
And to be fair, that's a pretty reasonable response.
What could a white shoe possibly have to do
with all Ravens being black?
Well.
This is a video about a phenomenon called the Raven Paradox.
It came about in the early 20th century,
when a hopeful group of scientists and philosophers
were trying to understand the world.
They called themselves the Logical Empiricists.
And as the name suggests,
they thought the only things you needed
to understand the world were logic and empiricism,
which is basically observations of the world
we all agree on.
In a nutshell,
their philosophy was that any meaningful statement
about the world could be understood by looking at the world.
That's the empiricist part.
And then we could use logic to make conclusions.
The name the Logical Empiricists
gave their way of understanding the world
might be familiar to some of you.
It's called the scientific method.
And as you can imagine,
it's greatly influenced the way that we think about science.
But things didn't go as smoothly as they imagined,
as the Raven Paradox soon flew into the face
of their neat little method.
Hopefully by the end of this video
you'll see that the ways that we go about doing science,
aren't always as straightforward as you might think.
To demonstrate this,
let's take inspiration from the Logical Empiricists
and try to do some science with just logic and empiricism.
Imagine you have the hypothesis: All ravens are black.
It seems like a reasonable hypothesis to make, right?
So as a logical empiricist what kind of steps
would you take to investigate this hypothesis?
Well, to gather some empirical evidence,
you could go out into the world and simply find some ravens,
check the color of their feathers and see if they're black.
So you do this, and every raven you find is black.
This is good news for your hypothesis.
Logical empiricism tells us
that with every new black raven you see,
you should become more confident in your hypothesis
that all ravens are black.
So now that we've gathered some empirical evidence,
it's time to introduce some logic.
Basic inference and deduction tells us that the fact
that we've only seen black ravens support our hypothesis
that all ravens are black.
We can formalize this logic by saying,
observing lots of As with property B
supports the hypothesis that all As are B.
We can replace A with raven and B with black,
or we can replace them with anything for that matter.
And that logic should still hold.
Now we can use the rules of logic to change this statement
in such a way so that it is logically equivalent.
What I mean by logically equivalent
is that there could be two sentences
that look different on the surface,
but are really saying the same thing.
For example, the two sentences,
"I'll meet you at the cafe at noon."
And, "I'll see you at the shop which sells coffee
when the sun is highest in the sky."
One might sound a little bit weird,
but ultimately they mean the same thing.
They're logically equivalent.
To make this clearer, it's often really helpful
to draw Venn diagrams to help visualize what we're saying.
Let's draw a circle to represent all black things,
and another disconnected circle
to represent all non-black things.
Remember our original hypothesis
is that all ravens are black,
which means that assuming our hypothesis is true,
ravens only exist in the all-black thing circle.
But if we stop and think about it for a second,
we can see that it's logically equivalent
to say that there are no ravens in the non-black circle,
or in other words, all non-black things are not ravens.
All ravens are black is logically equivalent to saying,
all non-black things are not ravens.
If you're not convinced,
take a bit of time to let this sink in,
because this should be a non-controversial statement.
Now, can you think of a non-black non-raven?
Well, what about a white shoe?
It fits the description.
It's not black, it's white.
And it's not a raven, it's a shoe.
Now let's apply some inductive logic.
Take the same formerly logical statement from before.
Observations of A with property B support the hypothesis
that all As are B.
We can replace A with non-black things
and B with not ravens.
So the observation of a white shoe
gives support to the statement,
all non-black things are not ravens.
But hang on a minute, we showed that the statement,
all non-black things are not ravens
is logically equivalent to the statement,
all ravens are black.
So we can swap it in without changing
the meaning of the sentence.
And what do we get?
An observation of a white shoe
gives support to the hypothesis that all ravens are black.
Now I don't know about you,
but I don't remember the last time of bird scientist
published their results on the observation of white shoes.
And I like to keep up with my bird science.
But all they used to construct their argument
was logic and empiricism.
So what went wrong?
This is the question that puzzled philosoph...
This is the question that puzzled philosophers of science
for years and still does today.
There are many responses to the paradox,
but here I'll give the three most well-known ones.
And who knows?
They may even inspire you
to come up with a theory of your own.
One potential response which our logical empiricist friend,
Carl Hempel actually gave,
is to just bite the bullet and say that an observation
of a white shoe does help confirm the hypothesis
that all ravens have black.
Even if only by a minuscule amount.
End of story.
The advantage of this response is that the scientific method
stays safely intact and there is no paradox.
But it doesn't really gel with our intuition
of how the world works.
Philosopher of science, Nelson Goodman
said that if this approach were true,
we could do a lot of indoor ornithology.
In other words, we could sit in comfy armchairs
and further the study of birds
by pointing at colorful objects.
Not only that, but if you think about it,
an observation of a white shoe
also helps confirm the hypothesis that all ravens are blue
or green or purple.
Let's see what other options there are.
The next response comes from another famous name
in the philosophy of science, Karl Popper.
His approach to science can basically be summed up as,
"The job of science and the scientific method
is to show whether or not a hypothesis is wrong.
That's it."
This idea of showing something as false using observation
is called falsifiability.
And it's what Popper thought
was the key feature of a scientific hypothesis.
On the surface,
this seems like a reasonable way of looking at science.
It always leaves us open to the possibility
that we might be wrong.
But if we look a bit closer, things get a bit funny.
Remember when we said that many observations of black ravens
would support our hypothesis that all ravens of black?
Well, Popper completely disagreed with this approach.
He thought the business of science was to falsify theories
and only falsify them,
not make us more confident in anything being true.
An observation of a white shoe
wouldn't support the hypothesis that all ravens are black,
but neither would a black raven.
To Popper, the notion of support or confirmation
was not the way science should operate.
If all we find are black ravens, all this means
is that our hypothesis is yet to be falsified.
This last response, I must tell you
is the one I agree with most
Just so you know my biases up front.
It has to do with the context surrounding an observation.
Let's demonstrate this with some strange
but instructive examples.
Imagine you have someone come up to you and say,
"Behind my back is a raven.
Would you like me to show it to you?"
You're a bit creeped out,
but as someone interested in the hypothesis,
all ravens of black, you should say yes,
since if it's a blue or a purple raven,
that would refute your hypothesis.
Popper would be proud.
Now, imagine someone comes up to you and says,
"Behind my back, I have a black object.
Would you like me to show it to you?"
You figure the people here are just a bit weird.
So you go to say yes.
But if you think about it for a minute,
whatever is behind their back
could never refute the hypothesis that all ravens are black.
Since even if it is a black raven,
not much would be learned since you knew the object
was going to be black given the circumstance.
Finally, a more subtle example.
Imagine a third person comes up to you and says,
"Behind my back is a non-black object.
Would you like me to show it to you?"
Here, you should definitely say yes.
Since it could be a blue raven,
which could refute your hypothesis.
But if this person pulls out a white shoe,
in a roundabout way, it gives support to your hypothesis
that all ravens are black.
Since given the particular situation,
a different outcome could have refuted it.
But the crucial point to make here
is whether or not we care about the observation
of a white shoe, depends on the wider context.
If this person said they have a non raven behind their back,
then pulling out a white shoe
should not matter to you in the slightest,
since we only care about ravens.
Whereas you should care
if they say they have a non-black object
since then it has the chance to be a non black raven.
So the takeaway with this response
is that sometimes a white shoe
does add confidence to your hypothesis,
and sometimes it doesn't.
You need more information about
how the observation was carried out to make that call.
So there are just three theories about how the Raven Paradox
could potentially be resolved.
The historical development after the advent
of the logical empiricists was incredibly fascinating.
With its fair share of heated disagreements
and skirmishes between scientists and philosophers.
Some had more radical approaches to the scientific method,
like Paul Feyerabend's total rejection
of any kind of universal methodology.
Complete scientific anarchy.
Other approaches like Bayesian Analysis were developed
and is still being widely used to this day.
But that is a topic for another video.
What the Raven Paradox tells me personally,
is that you can't remove science
from the specific context in which it's done,
even in principle and especially in practice.
I think this paradox serves as a really good introduction
to the counter-intuitive intricacies
of the scientific method.
It challenges our assumptions about how science is done,
and in doing so makes us understand it
and hopefully appreciate it all the more.
But I wanna know what you think.
Does the observation of a white shoe support the hypothesis
that all ravens are black?
Let me know your thoughts in the comments below.
Being exposed to paradoxes and brain teasers like this
is great for improving your lateral thinking
and training your powers of reasoning.
But what's even better
is trying to answer these problems yourself.
With today's sponsor, Brilliant, you can do just that.
The daily challenges are a fun and interactive way
to improve your problem solving skills.
This one was one of my favorites,
as I've always been fascinated by the unintuitive nature
of probability and how numbers can be so sneaky.
I've found that trying to answer questions
is the best way to learn
because it forces you to truly think about the problem.
If you want to know more about any challenge,
you can click on the accompanying course
where you'll find similar questions
and helpful explanations for when you get stuck.
Brilliant has loads of courses available in math, physics
and computer science.
They're all interactive, complete with fun questions like,
how phase synchronization of oscillators
helps firefly courtship
or how to get the best hand at blackjack.
All their courses are available in offline mode.
So you can get deep into concentration.
If you want to support Up and Atom
and get unlimited access to all of Brilliant's
in-depth math and science courses.
Head over to brilliant.org/upandatom
to get 20% of their annual premium subscription.
I'm doing my first ever live stream
to celebrate the channel reaching 100,000 subscribers.
It's going to be on the 19th of May 8:00 PM
Eastern Standard Time.
I'll also be reminding you guys about it on my social media.
So make sure to follow me on there as well.
It'd be awesome if you could make it along.
You'll get to see how awkward I am in real life
when I don't have any prepared lines to say.
It's probably gonna be a Q and A so nothing too exciting.
If you have any suggestions
of things I can do to make it interesting,
please leave them in the comments below.
I feel like I need to entertain.
Anyway, that's the end of the video.
Thanks for watching.
Bye.
(upbeat music)