Induction has been held in high regard as the spirit of scientific enquiry. Science is in the business of going from the known to the unknown, and indeed, these are the kind of inferences that are what we mean by induction.
We have, for instance, general relativity, a theory
that gravitation is a geometric property of spacetime. This is ‘unknowable’,
but as an explanation fits with ‘known’ data most strongly, such as the
observed light deflection during the Eddington Eclipse. Similarly, biological variation (known) supports evolution (unknown). Hubble-type expansion (known) supports the big bang (unknown). And so on and so on.
On the other hand, however, we have the rather concerning news that induction is unreliable!
Russell famously asked us to imagine a chicken that noticed every day the farmer came and fed him like clockwork. The chicken therefore assumed the farmer must be a benevolent man, and predicted he would continue to bring food every day. According to an inductive line of thinking, the chicken had ‘extrapolated’ observations into a theory, and each feeding time added further justification. Until one day, the farmer came and wrung the chicken’s neck.
How can it be that induction cannot be justified as being reliable, and yet it reliably gets such great results for us in science?
This apparent dichotomy is the essence of the 'problem of induction', however, it is based on an equivocation.
Notice that the kind of induction that Russell (and incidentally other critics of induction) are referring to, is what can be known as 'more of the same' type inferences. e.g. if the sun has always risen, it will continue to rise. It's this expectation that reality is uniform that is in error.
When I referred earlier to certain prized theories in science that go from the known to the unknown, however, they were not more of the same type inferences. They were a different kind of 'going from the known to the unknown', one where the unknown is the best explanation for the known (this is called inference to the best explanation). In fact, look to any prized scientific theory and I suggest you will on trend find this kind of inference.
They are called narrow induction (more of the same type inferences) and broad induction (inference to the best explanation).
Through our distinction then we can dissolve the dichotomy. Narrow induction bears inconsistent and unreliable results, but it is not needed by science. We can throw it out and it appears we can do fine with broad induction alone.
Now, I may here appear to abandon an expectation of uniformity too quickly. What about laws of nature such as 'all copper conducts electricity' surely here narrow induction has it's place? But no. The scientific explanation for why copper conducts electricity is that we have a theory that copper contains electrons, which is evident in its physical characteristics. This too is broad induction.
I purpose that the importance of narrow induction is nothing but a myth, kept alive by nothing more than an equivocation Let's be done with it and give the credit where it's due.