Introduction

The sun will rise tomorrow.  This seems to be an uncontroversial statement.  The sun came up today, and the sun came up yesterday, and the day before that.  Just as it has for millions of days before that.  Gravity held today, just as it has held since the formation of the universe.  This is, again, another uncontroversial statement.  We often predict future events based on generalisations of past experiences.  It is how science works, and it is how science creates laws of nature.  Science forms hypotheses based off of past observations, and creates predictions about the future.  It works, and we are gifted by technological advances and medical advances.  However, science is based inductive reasoning and inductive principles.  It is based on the idea that the future will continue on in the same manner as the past.  Is this a rational and reasonable stance though?  What is the problem of induction?

Most people make claims every day about particular things, such as ‘the car started this morning’.  We also make general claims about various things too, such as ‘the car will start when I turn the ignition’.  These claims are also made about various things in nature, such as ‘there are cherry blossoms on that tree’ and ‘the cherry tree will blossom this spring’.  These general claims are known as empirical generalisations.  Science is a source of, and based on, these empirical generalisations.  Many of the empirical generalisations made by science are deeper and richer in detail than we would have if we simply relied on common sense.  The tools it has given us has allowed us to make greater and more detailed investigations than our senses alone would allow, and has allowed us to build up a greater depth of knowledge than our senses alone would allow.

Empirical Generalisations

However, if we were to ponder about the nature of empirical generalisations then we would see that there is something of a problem with them.  If we were to ask what kind of evidence supports these kinds of empirical generalisations, then the only answer that we could give is our past experiences.  Our empirical generalisations are derived from the past experiences we have with particular instances.  Meaning that they rest on an assumption, the assumption that the future will always continue on as the past has.  Why is it an assumption?  Well, because there is no way to prove that the empirical generalisations made from past events will continue on in the future.  This is the problem of induction as put forward by David Hume, and as philosophers like Bertrand Russell, AJ Ayer, and Karl Popper have argued, it is a problem that is unsolvable. 

Using Logic to Solve the Problem

There are philosophers, like Aristotle and Descartes, that have tried to use logic to solve the problem.  Their claims are that universal generalisations can be deduced by logic from very general claims such as ‘Events in nature occur in a regular law-like manner’ and ‘Nature behaves in a uniform manner’.  These claims are treated as logical truths or tautologies, they are accepted as true by definition.  These serves as the basis of a deduction similar to:

P1) Events in nature occur in regular law-like manner
P2) The blossoming of a cherry tree is an event in nature
C1) Therefore the blossoming of a cherry tree will occur in a regular law-like manner

However, this can be criticised in a couple of ways.  First, we can doubt that the claims about the uniformity in nature are actually logical truths or tautologies.  If the claims were actually tautologies, then its denial or negation would be self-contradictory.  Yet, it is not obvious that the statement ‘it is not the case that events in nature always occur in a regular law-like manner’ is self-contradictory.  If it was a contradiction then there are certain claims that scientists make, and take seriously, that would have to be rejected as nonsense.

We can also argue that all that can be deduced from logical truths and tautologies are further logical truths or tautologies.  A main feature of tautologies is that their subject matter is not real-world events and objects, their subject matter is themselves.  Tautologies do not succeed in conveying truth about the world itself.  A statement like ‘cherry trees blossom in spring’ is a statement about events in the world, and not merely confined to the meanings of words.

Real World Claims

Empirical generalisations made by science are real world claims though.  They are claims about how the world has worked, and how the world will work.  Other philosophers, like JS Mill and Francis Bacon, have claimed universal generalisations can be justified by treating such claims as empirical claims, claims that can be considered true or false.  If they are treated as empirical claims, then we can assume that past events can be a reliable guide to future experiences.  As these past events can be seen to consistently occur in a regular way, then we have good reason to believe they will consistently occur in a regular way in the future.  How would we go about proving something like that though?  The only way we can prove inductive reasoning to be accurate is through inductive reasoning, making the enterprise circular.  We are proving it to be true by using it, and making predictions based off it, and then using those predictions to prove it again.  We are essentially begging the question; we are assuming the claim is true while proving the claim to be true.

Consider a conversation as such:

A: ‘Why should we trust inductive arguments?’
B: ‘We should trust them because scientists have made many successful predictions using inductive arguments.’
A: ‘And how do we know that the inductive arguments of science are successful?’
B: ‘We know by showing how successful science has been in the past.’
A: ‘But how can we guarantee that this regularity will hold in the future, and that successes will continue?’
B: ‘By using inductive reasoning to show past successes.’
A: ‘And why should we trust inductive arguments?’

Circular Reasoning

The conversation can be brought round into circles.  The only justification for the successes of inductive reasoning is the success of the inductive reasoning.  There are of course times when inductive reasoning fails too.  Consider the case of the black swan.  If we only ever came across white swans for centuries, would this be a good guarantee that we will never come across a black swan.  Is it rational to say that because we have only ever encountered white swans in the past that we will only ever come across white swans in the future?  It would seem not, considering the experience of the black swan.  There are many instances such as this where it could be shown that inductive reasoning fails to continue to hold in the future.  Whether the agent wishes to admit it or not, there is a certain level of faith necessary in inductive reasoning.  ‘The future will continue on as the past, because the past has always continued on in such a way… except in all of these examples, but we know that these other examples will continue on because they always have.’

There will be many who read this now, angered, spitting out statements like ‘science works, we don’t need faith in it, we know it works’; and one should agree.  Science does work, but that is not the question, or the argument.  The argument is about whether or not science will work, and whether or not our empirical generalisations will hold true in the future simply because they hold true in the past.  For those arguing that there is no faith necessary, they should pause and ponder for a moment on what justification beyond ‘it has worked in the past so it will work in the future’ that they have.  What good rational and logical reasons do they hold beyond this that the predictions of science will consistently hold in the future?

AJ Ayer took the view that problems can only count as genuine philosophical problems if there is actually some solution to the problem.  As stated earlier, Ayer took the stance that the problem is not one that is solvable.  As it cannot be solved either empirically or logically, some philosophers have concluded that the problem itself is a fictional one.  As pointed out by AJ Ayer, scientists will continue to rely on inductive arguments regardless of such a problem, and they will also continue to flourish regardless of such a problem.  No claims about the unsolvable nature of the problem of induction will stop scientists from doing science, nor will it stop those fans of science from claiming that science can give us the answer to any problem.

A More Pragmatic View

We can, as Ayer did, take a more pragmatic view to the justification of science and how it relies on induction.  It can be argued that science only has to satisfy its success in practice, and it passes that kind of test quite often.  The gains it makes are often significant gains, giving it the right for it to be taken seriously.  A scientific hypothesis or theory has a right to be taken seriously if it can be shown to work or have practical application.  We have the very technology that was used to write and read this article to show that science can very successfully be applied to make our lives better, and we have advancements in medical sciences as evidence that it can be successfully applied.  If science is doing the work it should be doing, and it is doing it successfully, then it is reasonable to have faith in it.  It is reasonable to see it as a meaningful, and important, branch of knowledge.  It could even be referred to as a paradigm of knowledge, on that appears to be progressing successful when it comes to predicting future experiences and events.  It also gives us the ability to control and organise our environment in ways that reach pre-determined ends.

However, the sceptic can still be sceptical even of the pragmatic approach.  It still holds true that they can simply argue that just because it has had success in the post does not guarantee it will continue to have that success.  We could, as Ayer might, simply call it a pointless objection.  Arguing that it is a waste of time trying to guarantee something that it is not logically possible to guarantee.  Just because a guarantee cannot be provided it does not follow that it is irrational to expect science to continue to deliver in the future as it has done in the past.  After all, part of what is meant by saying that humans are rational is their ability to recognise and act on the relevant guidance of past experience and past knowledge.

There is one point in favour of the pragmatic approach that can be put forward, one that will appeal to scientists and fervent fans of science.  It might be seen as slightly ridiculous, at least from the point of common sense, that this sceptical question mark hangs over science while a logical guarantee of the uniformity of nature and reliability of induction cannot be provided.  We must be honest in the fact that it is able to make successful predictions about the future in a better way than many other human activities.  Astrology, fortune telling, palm reading, revelations from religion, none of these have the success rate at making predictions that science does, nor could they give us the medical and technical advances that science is able to give us.  Science can be relied on to provide the theoretical reasoning that is behind our ability to produce machines and other technologies on a vast scale, and technology that works.

A High Price to Pay

Disregarding, or even stopping the use of, science simply because of its use of inductive reasoning would be more detrimental to us than the admission that there may be an element of faith necessary in the use of inductive reasoning.  It could even be said that if we were to drop inductive reasoning entirely that it would be impossible to lead a normal human life.  If we only acted on beliefs that we were knew were absolutely true, then we could never cross a bridge, we could never plan ahead for tomorrow, and we could never eat knowing that food will give us sustenance.  These things all rely on some form of induction.  In fact, understanding that there is some element of faith involved, and that the past experiences may not always resemble future events, gives us good cause to be more cautious about our predictions, and to never become complacent about our knowledge.  The pragmatist counts on the fact that sane people will think all of these things are simply too high a price to pay for rejecting induction, and living according to very strict demands of logic.

Another line of thinking that concerns the pragmatic approach is its common sense and practical attitude towards rationality.  It could be argued that those extreme sceptics, like Russell and Descartes, treat rationality in a very limited way.  For people like that, rationality means being prepared to believe and act only on principles that can be proven beyond any shadow of a doubt.  Principles that cannot be doubted, and that logic has proven to be absolutely the case.  According to this approach it would not be rational to accept principles that might be true, and could only be regarded as probably true.  The pragmatist wants us to agree that this is too narrow and restricting a view of what everyday rationality amounts to.  In order to lead a regular human life then we must place trust in the assumption that the past is a reliable guide to future experiences, and future expectations.  It is rational because by behaving in this manner a human being can lead a varied and meaningful life.

The Sceptic be Scepticking

It is unlikely that the person that is sceptical about inductive reasoning will ever give up that scepticism about inductive reasoning though, just as those that put complete trust in the scientific method will ever admit to there being a level of faith involved.  The sceptic will always be able to level criticism at the pragmatic approach, and those that put complete trust in the scientific method will always be able to point to its successes.  The sceptic, and the pragmatist, both already accept that any empirical defence of induction is simply begging the question, and the argument defending the pragmatist simply goes around in circles.

If we accept that induction is not deduction though, and understand that we should not expect the same of inductive reasoning as we expect of deductive reasoning, then we can still speak of a certain kind of certainty with inductive arguments.  As long as we are clear that what we are referring to is not ‘logical certainty’.  The word ‘certain’ can be gathered from context and the circumstances we use it in.  If we step out in front of a bus, or a speeding train, we can say that we are certain that we will be hit by it, and we can say that we can be certain that we will burn our hands if we hold it in fire.  A colleague of AJ Ayers at Oxford, Peter Strawson, approached the problem of induction by trying to show that philosophers have created the problem by misrepresenting everyday uses of ‘reason’ and ‘rationality’ in his book Introduction to Logical Theory.

Peter Strawson’s View

The argument can be summarised as the following.  It generally makes sense to ask if we are justified in holding a particular belief.  In the case of some beliefs, we appeal to and apply inductive principles.  Is there are further standard that can be appealed to so the inductive reasoning can be justified?  Yes, the inductive principle itself.  All things being equal, it is reasonable to suppose that nature will continue to behave in the future just as it has in the past.  Can we appeal to some more fundamental standard to justify our appeal to the general inductive principle?  Is our appeal to uniformity justified or grounded?  There are two responses that are given here.  We can show our faith in the certainty of the inductive principle by appealing to its reliability.  By doing so though we give a circular response.  Or we can state that it makes no sense as a question because there is no answer.

To settle disputes we appeal to standards, but to suppose these standards themselves can be justified is senseless.  They are axiomatic, they are the standards we just happen to have.  Strawson argues that a question like ‘Is the sun going to come up tomorrow?’ is similar to ‘Is it against the law to shop in the nude?’.  Our grounds for settling the first is the inductive principle, and our grounds for settling the second is the law.  The question ‘Is there a justification for induction in general?’ is the same as ‘Is the law legal?’.  Strawson’s conclusion being that searching for a general justification for induction is a mistaken endeavour.

In Conclusion

So, as we can see, the problem of induction is itself a tricky one.  The sceptic of induction will always be just that, and as we can see they have good reason to be sceptical.  Perhaps it is even necessary, because by remaining sceptical of the inductive method we can remain honest about it.  As pointed out by people like Ayer though, science will go on using the inductive method regardless of what issues sceptic raises.  Fervent fans of science will go on being fervent fans of science, because science brings us results, and often amazing results.  It appears to be one of the best tools in our toolbox for understanding the world around us, and for adapting the world around us in useful and beneficial ways.  The sceptic allows us the ability to never become complacent about the knowledge gained using science, and to keep questioning and fine tuning the scientific method, as people like Popper and Kuhn have done.  The fervent fans of science, and those that ignore the sceptics, allow us to continue doing science, and to continue getting results, and advancements.  Just as the sceptic needs to accept that the pragmatic approach works, the fervent fan of science needs to accept that there is some level of faith necessary in science.  The New Atheist may have a problem with this, because faith is one of those words that feels dirty in their minds and mouths, and is a word only worthy of disdain; but faith it is.  And there is nothing strictly wrong with that, accepting it can keep us honest and help stop science becoming dogmatic and followed with a religious like sense of reverence.  Long live the problem of induction, and long live science.