The Audacity of Induction

A zealous Intelligent Design proponent once offered the following proof of design in the universe.

  1. Every beautiful thing we have ever seen was produced by a creative being.
  2. The universe contains beautiful things.
  3. Therefore, those things, [that is, the beautiful things in the universe] were produced by a creative being.

While are so many things wrong with this logic, my first comment to him was to say that #1 needed to be proven first.  He answered with, “#1 is arrived at through Induction, which is a valid logical operation.”  He offered that almost all scientific theories contain premises arrived at through Induction. He is correct on both counts, that induction is a valid logical operation and is unavoidable in scientific theories.  But he is wrong about how it is applied.

What is Induction

“What is good for the goose is good for the gander”, would be an example of inductive reasoning.  But what is more interesting is universal induction, such as “what is good for these few geese is good for all ganders”.  Universal Induction is when we take what we believe is true for a limited set of cases and apply it to all other similar cases (few goose, all ganders).

If induction seems a bit sketchy to you your instincts are good.  It seems a bit audacious to make just a few observations, then wave your hands, make a bold claim about everything and just walk away.  But consider something like geometry.  We can create geometric proofs about a perfect circle and declare it true for all perfect circles by induction. For example, “The longest line that can be drawn between two points on a circle goes through the center of the circle.  This is true for all perfect circles.”  We can do this because a perfect circle is something that we characterized completely such that all perfect circles have the exact same properties.

But when we come back to making claims about nature, we don’t get to make the definitions.  Our claims about nature are not absolute like they are in geometry, rather they are “empirical” meaning all we can do is observe nature with our senses and hope we are finding something universal in those observations.  What we can observe about a few geese may not necessarily be true about all geese.  Geese come from nature, not from our own definitions.  All we can do is try to discover the universal essence of geese-ness through observations.

Why is induction necessary in science?  Because we will never be able to observe everything for all time everywhere in the universe.  If your theory is about geese, you will never be able to exhaustively prove it by examining all geese that have ever lived, that are now living, and will live in the future.  But how can science be so successful if most of it is based on what seems to be  a house of cards of exaggeration?  It would seem that one could “prove” just about anything by just declaring it “induction!”

The answer to this lies in risk.  Science will only allow inductive premises for those things that have a possibility of failing if the induction is wrong.  Although you cannot test all geese, any universal claim you make about geese can be proven wrong by just one geese that does not live up to your claim.  Suppose you have observed that all the geese in your town are white.  Let’s call that the “range” of your observations that support your geese theory. By induction you impose your observation on a much larger “domain”, let’s say all geese everywhere, ever are white.

Once you do that, you can now test your geese theory by observing more geese.  Each new white goose you observe adds more confidence to your theory.   Each successful new observation moves one more geese from the domain to your range of actual observations. But it would take only one observation of a non-white goose to come across to explode your theory completely.  The important thing here is that there is a huge imbalance of audacity vs risk.

In science, our geese theory would be considered a kind of prediction engine that predicts the color of all geese everywhere.   Prediction is used in a formal sense in that our predictions have to hold for all new observations whether they are about geese in the past, present, or the future.
It would be considered a scientific theory because the prediction is said to be “falsifiable” meaning it can readily fail if the theory is wrong.  Scientific theories are engines of falsifiable prediction.  Our geese theory is falsifiable because it forbids geese of any other color but white. And so we build confidence the fastest in risky falsifiable theories that demand things and forbid things in their predictions but manage to “fail to fail” in predicting the outcome of ever more novel observations in the world in their subject matter.

This requirement for testing a theory on the basis of its falsifiable prediction allows for our initial theory to be wrong but detectably wrong as it starts to fail in its predictive power.  A theory that fails predictions is one that can be improved or replaced over and over again until it no longer fails for the moment.  Then we continue the process forever.  We don’t only do this ourselves.  What scientists do is to publish their work in professional journals with enough explanation to allow others to test the predictions on their own.  So if our range is all geese in our hometown, we can enlist professional geese watchers all around the world to try to find a non-white goose.  Those scientists in turn publish their findings in professional journals and cite our original article.  And the science community keeps track of all of those articles and citations.  In this way a public record for predictive range and success accumulates over time from many different independent observers.

If you want to examine that public record at anytime, you can do a literature search in the professional journals and you will find a reference to all article that cite our article on geese theory.  At any time we can examine how well the theory is holding up all around the world.

This is what gets us from a flat Earth to a spherical Earth to an egg-shaped Earth in our ever improving theories about the universe.  Bold theories are proposed and then thrown against the wall of nature day in and day out to see if they continue to stick.   Any slight discrepancies in what they predict vs what we see is seen as an opportunity by scientists to perhaps discover something new, even at the expense of this theory that has been so successful so far.  You won’t win a prize for reporting the next white goose, but your name may be made on being the first to discover a non-white goose.

Our acceptance of scientific theories have to always be provisional because of this, but while it looks like a weakness, risk and falsifiable prediction is the rubber meeting the road of nature.  Its what gives us traction to climb the hill of better and better explanations for things we see in nature.

 

 

I have been involved in science and engineering since probably before you were born. I am interested in writing about science, its conceptions and misconceptions.

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