Will the sun rise tomorrow? The problem of induction – 01/02/2016

In his Treatise on Human Nature (1739), the philosopher David Hume argued that it is not reasonable to believe that the sun will rise tomorrow.

I wonder if Hume was always such a gloomy character. I for one wouldn’t be inclined to invite a friend to my party if he would preach to everyone that they should give up the belief that the sun will rise tomorrow. That’d kill the party mood.

But is Hume right? Here’s why he thinks it’s not reasonable to believe the sun will rise tomorrow.

Let’s first start asking the question: why do we believe the sun will rise tomorrow? Well, you might say, it has risen every day until now. Therefore, it is reasonable to believe that the sun will rise tomorrow as well.

But Hume doesn’t think so. He argues that induction cannot lead us to this conclusion.

What is induction?
Suppose you find a raven. It is black. You look for another raven. It is also black. You go on a trip through the country, looking out for as many ravens you can find. All ravens you see are black. At the end you’ve seen many ravens and all of them are black. Based on these observations, you draw the conclusion: the next raven I’ll see will be black. Is this a valid inference?

An inference is valid if (and only if) the truth of all premises guarantees the truth of the conclusion. In this case, there are many premises:

p1. Raven no. 1 is black
p2. Raven no. 2 is black
p3. Raven no. 3 is black

pn. Raven no. n is black
——————
conclusion: Raven no. n+1 will be black.

raven

But do these premises guarantee the conclusion? No. Even if you’ve seen 23786 black ravens, and none of another colour, it is still possible that the next raven is an albino raven, and therefore white. So the conclusion is not valid…

…unless you add another premise. The key premise you need to add to make the inference valid is: the future resembles the past. So you get:

p1. Raven no. 1 is black
p2. Raven no. 2 is black
p3. Raven no. 3 is black

pn. Raven no. n is black
and
pm. The future resembles the past.
——————
conclusion: Raven no. n+1 will be black.

raven2

But remember that the conclusion only follows if the premises are true. Is the premise ‘the future resembles the past’ true? Well, you might say, the future has so far resembled the past, because during my entire trip, the next raven was black all the time. But then you get the same problem:

p1. At t1, the future turned out to resemble the past.
p1. At t2, the future turned out to resemble the past.

pn At tn, the future turned out to resemble the past.
——————-
conclusion: The next time, the future will also resemble the past.

raven3

This is, again, an induction, so you’ll need ‘the future resembles the past’ as a premise, again. But that leads to a fallacy of circularity: one of the premises is the same as the conclusion. Circularity doesn’t prove anything, so we can’t say with certainty that it’s true that the future will resemble the past. Therefore, we can’t use it in our induction about the ravens, and therefore we can’t conclude that the next raven will be black.

albino raven

But what have these ravens to do with the sunrise?

According to Hume, the same applies to the sun. Just because it has risen every morning, doesn’t mean we can conclude that it will rise again tomorrow.

Why should I care?

Science, and indeed our daily conduct, would be impossible if we didn’t rely on inductive reasoning. So what do we do now? We have a problem!

 

Resources

This video explains the above in a slightly different way.

More info on Hume’s philosophy can be found in this episode of BBC’s In Our Time.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s