Critical Thinking 2: Induction and deduction

There was a great response to my first post in this series, so thanks to everyone who contributed to that. For my second one I’ve decided to tackle an issue that’s quite crucial to how Critical Thinking relates to the Middle Way.

There are two types of argument, normally known as induction and deduction. Deductive argument is what is classically formulated as argument and abstracted into logic. Deductive argument begins with assumed claims known as premises, and draws a conclusion from those premises. Within the terms of interpretation and the beliefs it assumes, the logical link between the premises and conclusion in deductive argument is absolute. If the premises are correct, then the conclusion must be correct if the reasoning is valid (i.e. follows the laws of logic).

For example:

John is an engineer.Engineer at work Angelsman

All engineers are human beings.

So John must be a human being.

This valid argument must be correct if John is indeed an engineer, and if indeed all engineers are human beings. But I might have false information about John, and robotic engineers may be under development right now in Japanese laboratories. My assumptions may be false, but if they happen to be true then the conclusion must also be true.

That’s what we’re traditionally told about deductive argument. However, if you take into account embodied meaning, then we are all also going to have slightly different meanings for ‘John’, ‘engineer’, ‘human being’ etc. experienced in different bodies. It’s only if we further assume that these meanings are sufficiently shared and stable that a deductive argument can be ‘valid’ in this way.

The other type of argument, however, is far more common and far more useful. Inductive argument is imperfect argument that begins with limited information and draws further conclusions from it. Sometimes such reasoning can sometimes be grossly over-stated and prejudiced. For example:

My neighbour was burgled by a man from Norfolk.

Norfolk people are all criminals.

This is a crude example of prejudiced reasoning. It takes just one example and draws a conclusion about a whole class of people that are extremely varied. It’s obviously not taking into account all the reasons why it might be wrong.

However, inductive reasoning is what we rely upon constantly. If we take into account its limitations it can be a justified way of reasoning. For example:

Tom has failed to fulfil his promises to his mother on ten successive occasions within a month.

His mother should not place any further reliance on Tom’s promises.

It’s still possible that Tom is trustworthy, and has just had ten unfortunate sets of events that stopped him fulfilling his promises, or that he was at fault in the past but has now completely reformed. However, it’s unlikely. We are usually obliged to trust the weight of our experience in cases like this. We could have confidence in the conclusion here as long as we also took into account the possibility that we could be wrong.

So, my argument here is that deductive argument, though perfect in theory, is not really different from inductive in the way we should treat it in practice. Deductive logic, though it may be perfect in the abstract, is in practice dependent both on the assumptions made and on the interpretation of the words of the argument to be applied in our lives. In practice, then deductive reasoning is just as fallible as inductive. If we use inductive reasoning with awareness of its limitations, though, it can provide us with justified beliefs. This kind of reasoning is justified because of its fallibility, not in spite of it.

Exercise

How well justified are the following (inductive or deductive) arguments?

1. The no. 37 bus that I take to work has been more than ten minutes late on three successive days. This is an unacceptable standard of punctuality, and it has made me late for work. I shall write to the bus company to complain.

2. If the UK economy continues to grow at the rate it managed during the last quarter of 2013 (a rate unmatched since the crash of 2008) then we can conclude that economic recovery is well under way.

3. Romanians in the UK are arrested at seven times the rate of Britons (Daily Mail), so if more Romanians come to the UK we can expect an increase in crime.

4. If God exists and God is good, he would not allow people to suffer without making the truth available to them. So he must have sent divinely-inspired prophets to guide people.

5. I’ve been practising this difficult piano piece for two months now, but I seem to be making no progress. I keep making the same mistakes. I should give up this piece and learn something else.

 

Picture: Engineer at work by Angelsman (Wikimedia Commons)

 

About Robert M Ellis

Robert M Ellis is the founder and chair of the Middle Way Society, and author of a number of books on Middle Way Philosophy, including the introductory 'Migglism' and the more in-depth 'Middle Way Philosophy' series. He has a Christian background, and about 20 years' past experience of practising Buddhism, but it was his Ph.D. studies in Philosophy that set him on the track of developing a systematic account of the Middle Way beyond any specific tradition. He has earned his living mainly by teaching, and more recently by online tutoring.

5 thoughts on “Critical Thinking 2: Induction and deduction

  1. I have made an attempt to answer the questions.
    1. An inductive argument, not well justified.
    2. Also inductive reasoning, probably justified.
    3. Deductive logic (an absolute claim) not well justified. No matter what theorythe Daily Mail supports
    4. Also deductive and not well jusified.
    5. Inductive argument which is not well jsutified, hard peices take longer to learn.
    I’ll post this now, but will have another think about my answers.

  2. Hi,

    I’m going to rate the justification of each argument from 0 (not justified at all) to 10 (as justifiable as is possible).

    1. Rate = 4. This seems fairly justified, but three times in a row does not seem excessive and might not indicate a systemic problem with the bus company. It is quite probable that three separate and unavoidable random events took place, causing the bus to be late each time.

    2. Rate = 6. I found this difficult. The argument only states that the economy continues to grow, but not for how long. It also says that the recovery is well under way, rather than just under way. Either way, since it has not grown as much since 2008, if it continues to then it is reasonable to claim that a recovery is well under way.

    3. Rate = 4. This one is challenging. It does not take into account the possibility of discrimination by the police, or the fact that Romanians might not be as good as evading arrest. However, I can understand how – presented as it is – this conclusion can be reached.

    4. Rate = 1. This one scores low because the conclusion seems quite wild – it assumes that revelation of the truth can only be achieved by God, via prophets.

    5. Rate = 3. It would be reasonable to wish to give up but making the same mistake for two months does not mean that you will continue to make this mistake, and the best way to enable oneself to overcome this difficulty is to practice.

    :( I feel a bit upset that I have given my highest score to the daily mail example, but I suppose this is an emotional, rather than logical response.

  3. Hi Robert,
    1. Using Rich’s 1-10 ratings I would say this is fairly justified: Rating 6 out of 10. There are arguably more mitigating circumstance for a bus to be late than say a train, such as heavy early morning traffic, passengers searching for change while paying etc. One should also take into account to what degree the bus service guarantees punctuality. However, given the fact that the person uses the present simple tense to express habitual action (the bus I take to work), I feel one can make the reasonable assumption that the person normally relies on this service rather than other forms of transport to get them to work on time and that reliability has to be backed up by a certain degree of confidence (presumably base on experience) in the punctuality of the service, otherwise they would choose another mode of transport. My degree of justification in this example has also been influenced by the fairly punctual timetable that buses operate to in my neck of the woods.

    2. I found this a difficult one as I don’t have a good grasp of economics and to what degree of confidence one can have in an upward economic trend continuing and for what period. You’ve mentioned that Nicholas Taleb in his book “Antifragile” suggests that , economists and market analysts often put far too much faith in their economic predictions that don’t take sufficient account of the complexity of market forces and other unpredictable influencing factors . Also, why should it be a given that the UK will remain one of the top world economies, especially if you take into account the rise of economies such as India, Brazil, Russia etc. So I think I’ll giving this a rating of 4.

    3. At first glance this argument appears strong in a deductive sense. However, one would need to question what these Romanians were arrested for eg. maybe for being illegal immigrants? – which now would be no longer the case, given the new EU Law. Also, what size of control group did they use, 7 people out of 10, or 70,000 out of 100,000 and where did they take that control group from and what deciding factors did they use? Arguably, in any argument as well, one needs to take into account to some extent not just what is being judged, but also the judger. Does the Daily Mail place great importance in providing their readers with a balanced view when putting forward an argument? Would the Daily Mail possibly have a vested interest in wanting their readers to feel that 70% of Romanians living this country are criminals? Is this me employing an Ad Hominim argument though? Rating 2 out of 10

    4. Another example of a seductive deductive argument, if the premises are true then the conclusion must be true. However, I think what’s important is how well the premises stand up. It’s a bit like saying, If all polar bears could play the piano, and were classically trained then at some stage in the training they would most likely learn “Fur Elise” by Beethoven. I think I can say with a strong degree of justification that there is no way of knowing whether God exists or not (given that concept is not subject to experience), so any hypothesizing about it is arguably irrelevant (unless one is playing safe of course). Rating 0 out of 10

    5. I feel this is fairly well justified and give it a rating of 7 out of 10. Admittedly, the piano player could conceivably be giving up too early as Norma and Rich point out . However, given the fact that they are attempting a difficult piece (‘difficult’ is also relative of course), one could make the reasonable assumption that they are fairly proficient and would not have reached that degree of proficiency without plenty of practice and some experience of when to accept that some pieces at their stage of learning are too challenging (and therefore potentially demotivating) for them. I feel it is quite reasonable to assume that they have reached that point here and are making a pragmatic decision to move on.

  4. ‘I feel a bit upset that I have given my highest score to the daily mail example, but I suppose this is an emotional, rather than logical response’

    Interestingly, this is a false statement. I believed it at the time of writing my last post (above), but having read my answer again I can see that I gave a rating of 6 to the economy argument and only 4 to the daily mail argument. It is amazing how quickly a false memory can occur. Giving a 4 to the daily mail argument was enough to disturb me into this error!!

  5. Whether the arguments are inductive or deductive is rather less open to argument here than how well justified they are! Part of the point of the exercise, though, is to think about the different ways that inductive and deductive arguments are justified. These are my answers:

    1. This is an inductive argument, generalising from three occasions. If you compare it with generalisation from three examples elsewhere, it becomes clearer how weak this is. For example, if I went to a business conference and met three Russian businessmen, and concluded from this experience that all Russians were businessmen. I think this argument is weaker than Rich or Barry are recognising.

    2. This is a deductive argument. It is entirely hypothetical, stating that *if* one thing is the case then the other must be. The two things are “the economy continues to grow at the same rate it managed in the last quarter of 2013” and “economic recovery is well under way”. This seems to me obviously the case. No assumptions are being made about whether the recovery will continue – the hypothetical event is just being re-described. This can be seen as a valid deductive argument, regardless of whether you know anything about economics, and regardless of whether you agree with the hypothesis.

    3. You could interpret this either inductively or deductively. Inductively, it would be arguing from a higher rate of arrests amongst Romanians already in the UK to an overall increase in crime if further Romanians arrive in future. If you take it this way it is weak, because the new Romanians might be quite different from the current Romanians. The rate of arrests amongst current Romanians compared to the rest of the population also tells you nothing about how many arrests have been made (there might be a very small number), so even if it was true (as no doubt many Daily Mail readers assume) that Romanians in general are 7 times more inclined to criminality than average, the impact on crime rates in general might still be negligible because the number of Romanians is very small when compared to the numbers in the general population.

    If you take this as a deductive argument, it’s even worse. It certainly doesn’t follow from the arrest rates of current Romanians that there will necessarily be an increase in crime of future Romanians.

    4. This is a deductive argument that seems entirely valid. As Barry points out, however, it’s only of any relevance if you accept the assumptions it begins with.

    5. This is inductive. I was interested in the variety of responses this got, as this is a real dilemma that I have encountered as an amateur pianist! How strong it is depends on other assumptions, I think, such as how much you really want to learn the piece, particularly when compared to others that you could more realistically learn. In general (on the basis of individual experience) I’m inclined to agree with Barry that it’s quite a strong argument (though not overwhelmingly so). If I’ve made little progress with a piece in two months then I may be ‘flogging a dead horse’ to continue.

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