Induction and Deduction: two sides of the same coin?
Why induction and deduction are both erroneous and why they rely on each other.
One of the main topics in the history of science has for long been the supposed struggle between rationalism and empiricism and which one is superior in acquiring knowledge. The latter, empiricism, seems to have won and many scientists claim that empiricism is what drives scientific research. This is correct in a certain sense, but I will argue that empiricism is just as liable to errors as rationalism. Moreover, I will argue that both rationalism and empiricism cannot go without each other. Let’s have a look at the methods employed by rationalism and empiricism: deduction and induction.
Deduction: as good as its premises.
A clear example of rationalism is the method called deduction. Deduction happens when you derive (or deduce) a new fact from other facts. The most famous example is as follows:
Premise 1) Socrates is a man;
Premise 2) all men are mortal;
Therefore the conclusion is 3) Socrates is mortal.
Without perceiving or testing that Socrates is indeed mortal, you can argue that it is very likely that Socrates is mortal. This is called a deduction. Logic is also attributed to rationalism. Deduction is a form of logic, but we can use the term logic in a broader sense. Rationalism claims that it is possible to discover new knowledge about the world by using reason alone. Mathematics is an example of this. The problem with deduction however is that you first need to know something about the premises. If one or both of the premises are false, your conclusions will be false as well. Yet how do you come by the knowledge that for example, ‘all men are mortal”? You must have either deduced this fact from some other facts, or you must have observed this fact yourself, what is called empiricism and lies outside rationalism. The problem with rationalism is that when you want to conclude facts about the real world out there, you at one point need to resort to empiricism. You can deduce facts about other deduced facts, but this can’t continue indefinitely. This is the problem of infinite regress: at one point you will need to rely on observations. Like for example the earlier mentioned premise, all men are mortal, will be founded itself on the premises 1) that no person has ever been seen living forever, each one of them eventually died. premise 2) if something has never happened in the past, then it will likely also not happen in the future , therefore 3) all men are mortal. Another way out is to rely on axioms. Axioms can be a premise or starting point for reasoning, yet they are statements that we cannot prove to be true or likely, but which we nonetheless accept as being true or likely. Mathematics for example makes use of axioms. Despite this disadvantage, deduction remains a very powerful tool to understand and explain the world.
Induction: or how a chicken can still be wrong.
Empiricism, in contrary to rationalism, requires that you observe the world, be it with your eyes, other senses or an instrument. Based upon your observations and consequent tests you draw conclusions about the world. This method is called induction (in contrast to deduction). Induction is when you see your neighbors making pictures of their house, then having a visit from an estate agent who puts a sign in the garden reading ‘for sale’, and some days later numerous people independently of each other making brief visits and inspecting the house. You can conclude by these different observations that the neighbors have likely put their house up for sale. Interestingly, this conclusion can also be called a deduction of various induced premises. The history of philosophy is filled with arguments and discussions for why rationalism is supposed to be superior to empiricism and vice versa. Rationalism and empiricism can be used alongside each other, or they can reinforce each other. Yet there is an overall consensus that it is empiricism that is best at discovering the world and therefore to conduct science.
Induction is in one sense superior because we can use it to test our hypotheses. This aspect of testability is in fact so important that this can be seen as the demarcation between science and non-science. [1] This means that a scientific theory cannot be called scientific when it can’t be tested, or when an experiment cannot be reproduced for example. This is where rationalism proves to be inadequate. You cannot test a theory to be true or false only by rational thought. It might be plausible or logical, but it cannot be considered as proof. Take for example the statement: Socrates is able to live forever. The premise 1) Socrates is a man, and premise 2) all men are mortal, will lead to the conclusion that Socrates is mortal, and thereby falsify the initial statement. This is plausible and logical. Yet what if one of the premises is false? You need to test the premises themselves as well, and this will again inevitably lead to the need for observations and thus empiricism.
However, some scientists and philosophers argue that induction too is false and inadequate. The problem of induction was once posed by the philosopher Bertrand Russel like this. When a chicken gets fed by the farmer every morning, each day of the year, it will predict that it will likely be fed tomorrow and the day after as well. The chicken has extrapolated its observations into a theory in which the farmer must be really fond of the chicken. Each observation seems to corroborate (ie. confirm) the theory. Yet one day, the farmer comes in and does not feed it but violently breaks the chickens neck. The chicken was unfortunately dead wrong about his theory of the behavior of the farmer. Conclusion: repeated observations cannot prove theories to be correct. This example also shows that although the original theory was able to make good predictions for most days of the year, it was founded upon a wrong explanation of the observations.
How then, do we acquire new knowledge? The philosopher Karl Popper proposed that we should not use induction to confirm our theory, but use it to falsify or refute our hypothesis. Popper explains this concept by the following thought experiment. Say that the hypothesis is that there exist only white swans. When you set out to observe and then only find white swans, your hypothesis will be confirmed. But as with Russels’ chicken, this does not prove the hypothesis correct for it might be possible we miss swans of a different color. Instead of looking for white swans, we should actively be looking for swans with a different color. When we then find a black swan, we have falsified the hypothesis that swans are always white. When we translate this to the realm of science, we should create and conduct experiments that aim at falsifying or refuting the hypothesis instead of confirming it. When we are unable to find any evidence that may refute the hypothesis, but we can test and thereby find evidence that corroborates the hypothesis, we can assume that our hypothesis is a good approximation of reality. However (!), we can never be certain. It might be possible that we just did not create the right experiment to falsify the hypothesis yet, or perhaps we lack some other crucial insights that are needed to falsify the current hypothesis in that we are possibly looking in the wrong place. We humans are fallible, which means we can be wrong, and thus never be certain.
How can both be two sides of the same coin? Well, as mentioned earlier, deductions need to rely on observations (ie. induction) somewhere down the line. We cannot deduce anything without first acquiring some knowledge by observations. You might think you are able to conjure up some imaginary thing in your mind, but this is most likely a product of existing impressions, experiences, or in other words: observations. Nothing comes from nothing. Deduction however also influences how we induce new things about the world or what we observe. As Karl Popper tells us, theory comes before observation. My earlier post on how our brains make models of the world also explains why we first deduce a model (based upon observations) which we then use to determine where to look henceforth. To conclude, without induction, there is no deduction possible and vice versa.
[1] If you can’t test your theory, then what proof can you give?