The scientific method: strengths and limitations (2)

Part Two: Deduction vs. induction

The first part introduced the essence of logics, syllogisms and the concepts of validity and soundness. It was intended to present a fundamental way of thinking philosophically about big words such as truth and certainty, and to emphasise that ‘logical’ does not necessarily mean ‘true’. I would strongly recommend that you read Part One before proceeding. I know it is a long text, but it is also essential to be familiar with the concepts that are discussed there. 

In Part Two, I want to take the discussion a step away from general philosophy and closer to concepts more relevant to science: deductive and inductive reasoning. These are still fundamental to many, if not all branches of philosophy, but inductive reasoning in particular is central to the natural sciences.

Deductive and inductive reasoning are both forms of extrapolation (which was discussed in Part One). Strictly speaking, deduction is the act of reasoning from the general to the particular, while induction is the act of reasoning from the particular to the general. Before you get a headache trying to understand what on Earth that even means, let me talk you through a few simple examples.

Deduction is thinking that if all bananas are sweet, the banana you are about to eat will taste sweet. Induction, on the other hand, would be the reverse: if you eat a banana and find it sweet, you can expect other bananas to be sweet as well. In this case, ‘the general’ refers to all bananas, and ‘the particular’ is the banana you have or ate.

So, knowing that the general (all bananas) has a certain feature or attribute (tasting sweet), you may deduce that the particular (the banana in your hand) might possess that attribute as well. Conversely, observing an attribute (sweet taste) in the particular (the banana you ate) may lead to the inductive conclusion that that feature may belong to the general (all bananas).

If you are observant, you may already be wondering: does induction come before deduction then? How would you know that all bananas are sweet, unless that is a conclusion you have reached inductively by tasting many bananas? Well noted – but do not jump to conclusions! Although that may be true in many cases, there are many exceptions as well. (Trick quiz: was that inductive or deductive thinking?)

The main type of deduction that does not rely on induction is based on definitions. A classical example of something that is true by definition is that all bachelors are unmarried men. This is because the word bachelor means unmarried man. Thus, if you meet someone you know is a bachelor (he may have presented himself as such), you can deduce that he (!) is an unmarried man. This is not because you have met many bachelors and they have all turned out to be unmarried men, but because if he is not an unmarried man, then he is not a bachelor (or… maybe he is lying to you).

You may recall this example from Part One as the first example of a syllogism. I repeat it here because it is not only a sound syllogism, but also one that illustrates deductive reasoning:

     P: All bachelors are unmarried men

     P: Peter is a bachelor

     C: Therefore, Peter is an unmarried man

Here, we go from the general (all bachelors) to the particular (Peter). We know something about the general, something that applies to all of them; and from that, we reason that this something is true also for every particular individual or unit in this general group. We reason from the general to the particular in deduction.

Recall that deduction and induction are inferences, and as such not necessarily true. Again, what we are concerned about is how we reason when we infer. We want the reasoning to be valid, so we can be certain that the deductive or inductive conclusion is as true as the initial premise. In the above example, the first premise is true by definition, and therefore unquestionable (the only grey area would be a widower, a man whose wife has died) – unless you want to challenge the definition, but then it becomes a matter of language, not the nature of the world. The second premise, however, may or may not be true. As a result, the conclusion is only as certain as the second premise. If Peter is not a bachelor, then he is either married or not a man.

Note that that example also can be written as:

     P: All unmarried men are bachelors

     P: Peter is a bachelor

     C: Therefore, Peter is an unmarried man

Or:

     P: All bachelors are unmarried men

     P: Peter is an unmarried man

     C: Therefore, Peter is a bachelor

And so on…

Both attributes (being a bachelor and being an unmarried man) are mutually inclusive. But there are deductive syllogisms that are not true both ways, so to speak. Consider an example:

     P: All tall people wear hats

     P: Gareth is a tall person

     C: Therefore, Gareth wears a hat

This cannot be written as:

     P: All tall people wear hats

     P: Gareth wears a hat

     C: Therefore, Gareth is tall

This is because the key word is not to be. They are not the same. Think about it. The first syllogism claims that all tall people wear hats (a ridiculous statement, perhaps, but let us take it as a true fact for the purpose of this explanation), but that does not imply what the second syllogism states: that all people that wear hats necessarily are tall. In contrast, bachelors are unmarried men, and as a consequence unmarried men are also bachelors!

Hopefully, you now understand the basics of deduction, and recognise that it has important set-backs (think about how much we actually can use deduction for…). Please have them in mind, as I will now explain induction, and later go on to compare deductive and inductive reasoning.

I have been struggling to formulate the following example of inductive reasoning as a sensible syllogism, but I think the message can go through as a simple statement anyway: All swans observed so far are white; therefore, all swans are probably white. This is a generalisation based on observations of the particular (the portion all swans that we have observed), which concludes that the general (all swans that exist) possesses the same traits (colour) as the particular. We reason from the particular to the general.

(As a side note, I might add that this particular example, although classical, becomes problematic when you think about swanlings, which have a dark grey plumage. For that inductive claim to be accurate, swanlings must be excluded from the definition of swans, meaning that sub-adults are not considered members of the species, which further suggests that infants are not humans, and that abortion must be ethical… Woah, maybe I should calm down a bit there, hahaha! Actually, that induction can be improved by specifying that adult swans are white!)

Naturally, you wonder how we can be sure that all swans are white, when we haven’t seen them all. How can we know there are not black, blue or pinkish red swans out there?

Of course, we cannot know that. We can only be fairly certain, or guess that it is so. It is simply a logical impossibility to be absolutely certain about a (non-defining) attribute of a group without having observed every single member.

However, unless we have a reason to suspect that there may be deviations from the observed pattern, we can be quite confident that the pattern will hold even for situations that we have not observed. Still, that is no guarantee, only a probability.

Induction reasoning may be regarded as the core of science. Scientists observe features of the world and then, by working out why these features are the way they are, try to predict what will happen in a similar situation, or, if their understanding is deeper, predict what can happen if the situation changes. This is all based on generalising from a limited number of observations about unobserved events, groups, things, whatever. These generalisations are then usually tested by observing more examples of the unobserved things, and if the generalisations appear true, hooray!

The reason for relying on induction is simply that we cannot observe the whole world. We simply do not have the time nor the labour to do it. If we want to say something about what we have not yet seen, we nearly always have to use inductive reasoning, based on what we have seen so far.

As long as we are all aware of the inescapable problem of uncertainty in induction (deduction may very well be uncertain too, but it is at least possible to be entirely certain of a deductive statement, while absolute confidence in an inductive claim is unfeasible), as long as we treat those conclusions with care, this way of reasoning is amazingly useful, because it allows us to at least approach a truth about something unknown. Deductive reasoning is limited to what we already know – mostly what we know because we defined it that way. We will discuss this more later, in the main comparison between these two ways of thinking. 

However, there is one problematic aspect of induction, one that causes trouble for all branches of science that deal with predicting the future, or understanding the past (e.g. predicting natural disasters such as climate change or volcanic eruptions; predicting evolution and genetic changes, including extinction or survival of species; calculating how much longer our resources will last, and the implications of their over-use; and all sorts of things that lie at the heart of what can be seen as one of the main utilities of science).

To illustrate this fundamental problem with the inductive way of reasoning, let us consider another example: 

P: The sun has risen every day since recorded history

P: Tomorrow is a day

C: Therefore, the sun will probably rise tomorrow

Intuitively, this seems correct, but it is actually not even valid. To make this reasoning valid, we must assume that the world will work the same way tomorrow that it did today and has in the observed past. In other words, we need to assume that the universe works in a consistent manner.

That is a very intuitive claim, since it seems silly to think otherwise: we have little or no evidence to suggest that the world will function differently tomorrow, or any time in the foreseeable future. In the same way, it is against common sense to think that the universal laws of nature were different in a time before our own. Scientific evidence suggests that there was a time when there was no sun, and a time when there was a sun but no Earth. Scientists use other evidence to predict that the sun will collapse one day, if it runs out of ‘fuel’. Hence the word ‘probably’ in the conclusion: it safeguards against the chance that the specific example might change.

Still, what we assume must assume in order to call inductive syllogisms of that nature valid, is that the fundamental laws of the universe – the laws about how things exist and behave – have always been the same, and forever will be. We can accept that particular examples may be different, but the underlying thought is that the basic features of the universe are constant. (I am implying that the sun and Earth are not basic features of the universe.)

But, the problem is, can we really justify that assumption? Based only on what we have seen in the past and present, can we justify the claim that the sun is more likely to rise than not? The painful problem is that the assumption that ‘what has happened every day until now is likely to happen tomorrow as well’ can only be justified if we assume that ‘the world always has and always will work the same way’, which is the very thing we want to show with the first assumption. Thus, we have one assumption that only can be justified by another assumption, which in turn is only justifiable by accepting the first assumption. This circular reasoning is a big bad fallacy, as you may recall from Part One.

I quote a handout from philosophy class:

If nature is uniform and regular in its behaviour, then events in the observed past and present are a sure guide to unobserved events in the unobserved past, present and future. But the only grounds for believing that nature is uniform are the observed events in the past and present. We can’t seem to go beyond the events we observe without assuming the very thing we need to prove – that is, that unobserved parts of the world operate in the same way as the parts we’ve observed.

This is the problem with attempting to extrapolate inductively about the past or future: the necessary assumption cannot be logically justified. Although it seems intuitive, it is actually a fallacy.

Another reason to question the validity of the assumption of the universal laws being constant across time is that scientists also seem to hold the belief that everything is constantly changing. Unless they mean ‘everything except the universal laws is constantly changing’, we are looking at a troublesome inconsistency here (inconsistency, in the philosophical sense, is holding beliefs that contradict one another). The universe cannot be the same and, at the same time, change, since remaining the same is the same thing as not changing, by definition. One of those beliefs must be discarded (except if the constancy solely refers to the universal laws, and the change refers to everything else), which is tricky since both ideas are rather intuitive. We see things changing with time every day, every week, every month, etc. But we also see that many things stay the same. 

Still, even though there are logical reasons for doubt, things that science has accomplished, using those very methods, seem (!) to have hit something right somehow. Although the reasoning seems limping, it appears to have reached the goal. Either, the assumption that the world works in a consistent way just happens to be true (note that circular reasoning does not imply falseness: that an argument is circular only means that is cannot be shown to be true or false, but it has no bearing on whether it is actually true or false – it is either true or false or somewhere in between, but it cannot be demonstrated logically, and is therefore not good reasoning, even though it might be correct, just by luck!), or it is almost true, or it simply does not matter whether it is true or not, and the logical analysis of the flaws of the method is wrong somewhere.

In Notes from Underground, Fyodor Dostoyevsky writes that “man has such a predilection for systems and abstract deductions that he is ready to distort the truth intentionally, he is ready to deny the evidence of his senses only to justify his logic”. I interpret it to be questioning the assumption (really) that our logic has anything to the natural world. How can we know that logics really describes how the world works, and not just the way we humans think? This is a really interesting topic, one which I hope we will come back to later. But, now I think it is about time we get on with comparing deduction and induction.

In general, it can be said that deduction is more certain but less informative, while induction is less certain but more informative. (Or, really, one should say that deduction has greater potential of preserving the certainty of its premises, while a great deal of certainty may be lost through inductive generalisation.)

This is really because of the nature of these ways of reasoning. When you argue from the general to the specific, you just apply what you know about a group to a particular member of that group. If I know that most rocks are hard, I can be fairly sure that if I touch a rock, it will feel hard. In contrast, when you argue from the specific to the general, you are dealing with the uncertainty of whether the feature you are reasoning about applies to the whole group or not. In deduction, you know it applies throughout the group, and can therefore be confident that any particular member will also possess that feature; but, in induction, you cannot be sure that the feature is something that applies to the whole group based on only one or a few particular examples. Although many rocks are grey, it happens to be that colour is not consistent among rocks – there are many rocks that are red, white, beige, green, black, etc., and many have multiple colours!

But, I hope you realise that you cannot reason deductively without knowing anything about the whole group! Therefore, deduction is really not very informative at all. Deduction can only tell you things about particular examples from a broader category of which you already have a lot of information, and the information you apply to these particular examples is already known. Deduction is a way of inferring information from broad category to a narrow part of that or a similar category, rather than discovering new information. It is a tool of inference, not investigation. Deduction is nearly useless in the face of an unknown group of things.

Induction is the method of choice when you want to learn about something new. By making (careful) generalisations about the whole group from a limited sample, it provides a platform for beginning to study this group. These generalisations are usually checked by observing additional examples from the category, and, if the generalisations seem to hold, you keep looking for more particular examples; if you find that there are too many exceptions to your generalisation, you should reconsider or discard that idea and start over, drawing new generalisations from the examples you have now studied. (This systematic approach is not part of the essence of induction, but rather the way it is used effectively in science to learn about the unknown.)

While induction makes it possible to explore, deduction cannot do much more than point.

(But, note well that induction does not allow us to explore completely unknown situations. We always need at least one example of the particular to make generalised or inductive statements. When faced with the complete absence of specific examples, loose inference based on educated guesswork is probably the best we could do. Ideally, these guesses should assume the same predicting nature of inductive generalisations: the guesses should encourage explorers to test the ideas, by finding examples of that unknown, and comparing the guesses with observations.)

As already mentioned before, deduction is often preceded by inductive investigations. Since deduction can only preserve certainty, never increase it, it follows that deductive conclusions made from inductive premises is only as certain as those inductive claims. This is a practical limitation of deduction.

However, induction alone does not take us far. It can help us learn about a category of entities in the world, but that is where it stops. Deduction is one way of making use of information gained from induction, by allowing us to apply the general knowledge to specific situations. If we have observed the consequences of earthquakes and learned about it through induction, we can put this general information to use by applying it deductively on earthquakes we experience now, and better know what to do when they occur and how to act after they have passed.

In other words, deduction and induction seem to come hand in hand, combined, in practice, although they are each others’ opposites, theoretically.

The final point I want to make in this comparison is about the role of language in deduction and induction. In one (philosophical) sense, language is based on inductive generalisations: we implicitly organise the world into general categories by putting names on them, based on common characteristics. We notice that some things have much in common with each other, but still are different from everything else, and call them something unique, e.g. dog, table, teacher. Dogs bark, but neither do tables, teachers or anything else, tables have a specific shape and function that make them tables, etc.

We also implicitly use deductive reasoning by expecting similar behaviour from members of the same ‘thing, which may be distinct from other ‘things’. For example, if you punch a dog, it will probably feel pain, and maybe bite you; if you punch a table, the table might take damage, but will not react, and you will surely hurt yourself; if you punch a teacher, you are in big trouble.

In that sense, by using language, you are implicitly also using deductive and inductive reasoning, often combined.

What is more important, however, is that deduction and induction effectively depend on that the world is organisable into discrete categories, i.e. things/words. What I am trying to argue is that language is not only a way of communicating ideas; language is also a way of organising the world into discrete categories, thus making deductive and inductive logics possible. Deduction is the art of reasoning from such categories to their specific members, and induction is the art of reasoning from specific members to broader categories. If the world is not organisable into discrete groups, such reasoning falls apart.

That is the main reason why many modern taxonomists (scientists who classify living organisms) are struggling with distinguishing different species. The more the biologists learn about the diversity of living organisms, the more they realise that the concept of a ‘species’ is more a made-up grouping than a real, natural unit. There is so much continuous variation within and between ‘species’ that the scientist must make rather arbitrary decisions on how to decide the ‘limit’ between closely related ‘species’. This is just one example of humans trying to impose order on something that apparently is not meant to be organisable.

I admit that this discussion might have been rather confusing, but I hope at least the general message has come across. Scientific research is based mainly on inductive reasoning, or generalisations, basically; scientific inference, on the other hand, relies on deduction, the opposite of induction. Deduction is the art of inferring from the general to the particular, while induction is about generalising from the particular to the general. Induction is less certain that deduction, but much more useful when it comes to investigating the world. Both are often used in combination, however, as they are not very meaningful in isolation.

Part Three will be about practical rather than theoretical issues with inductive reasoning: the limitations of sense perception – the link between our minds and the outside world –  and why we should have the fallibility of our senses close in mind when thinking about science, with its particular emphasis on observing the world.