Introduction to non-deductive arguments
The famous fictional detective Sherlock Holmes is always talking about deducing his conclusions from the evidence, but actually the kind of reasoning he engages in is not deductive reasoning.
Here is an extract from the Sherlock Holmes story “A Scandal in Bohemia.”
Dr Watson visits Holmes after a long absence. Holmes figures out that Watson has started practising medicine again, and that he has been out in bad weather lately, and that he has an incompetent servant, even though Watson hasn’t told him any of these things.
“My eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts. Obviously they have been caused by someone who has very carelessly scraped round the edges of the sole in order to remove crusted mud from it. Hence, you see, my double deduction that you had been out in vile weather, and that you had a particularly malignant boot-slitting specimen of the London slavery. As to your practice, if a gentleman walks into my rooms smelling of iodoform, with a black mark of nitrate of silver upon his right forefinger, and a bulge in the side of his top hat to show where he has secreted his stethoscope, I must be dull indeed if I do not pronounce him to be an active member of the medical profession.”
In this passage, Holmes draws three conclusions:
- Watson has been out in bad weather.
- Watson has an incompetent servant.
- Watson has started practicing medicine again.
The evidence presented for 1 and 2 is that the leather on the inside of Watson’s left shoe is scored by six almost parallel cuts. The evidence presented for 3 is that Holmes smells of iodoform, has a black mark of nitrate of silver upon his right forefinger, and has a bulge in the side of his top hat.
Even if these are good reasons to believe the conclusions, surely they do not guarantee them. There are other logically possible reasons why Watson might have six cuts on his shoe, smell of iodoform, etc. There is an unstated premise that the hypothesis that Watson has started practising medicine again is the best explanation for the iodoform smell, black mark on his finger and bulge in the side of his top hat. And that this is the best explanation of the observed facts is intended as a reason to believe it. Such arguments can never guarantee the truth of their conclusion – it’s always possible that some other explanation is actually the correct one. So they are not deductive arguments. Nevertheless, such non-deductive arguments can provide very good reasons to believe their conclusions. We will be discussing a number of different kinds of non-deductive arguments in this chapter, concluding with arguments like the Sherlock Holmes one, which is called an inference to the best explanation.
One way to signal that your argument is non-deductive is to put [Probably] in front of the conclusion – this shows that you are not intending to guarantee that the conclusion is true, only to make it likely (probable). And one test of whether an argument is deductive or non-deductive is to think about whether it would make sense to put a [Probably] in front of the conclusion. For example, if someone argued that since all mice have tails and Minnie is a mouse, Minnie has a tail, it would make no sense to put [Probably] in front of the conclusion “Minnie has a tail.” The premises, if true, make it certain that Minnie has a tail, not just probable. On the other hand, if the argument instead went “Almost all mice have tails, and Minnie is a mouse, so Minnie has a tail,” it makes very good sense to put a [Probably] in front of “Minnie has a tail,” and that’s a sign that the argument is non-deductive.
Non-deductive arguments are never valid, and therefore never sound. But, since they’re not trying to be, we don’t tend to complain about them being invalid and unsound– that’s the wrong standard to hold a non-deductive argument to. The terms we use when evaluating a non-deductive argument are “strong” and “cogent”.
Strength plays the same role in the evaluation of non-deductive arguments as validity plays in the evaluation of deductive arguments. To say that a non-deductive argument is strong is to say that its premises, if they were true, would provide good reason to believe the conclusion, although (since it’s not a deductive argument) they do not guarantee the truth of the conclusion. Like validity, strength is to do with how strong the connection is between the premises and the conclusion. Like validity, strength has nothing to do with whether or not the premises are actually true.
An argument is cogent if it is strong and all of its premises are true.
We ask the same two questions when evaluating non-deductive arguments as we did when evaluating deductive arguments:
- What is the connection between the premises and the conclusion?
- Are the premises true?
In the case of non-deductive arguments, we answer the first question by talking about strength. When we talk about cogency, we are answering both questions.
There is an important difference between validity and strength. Validity is all-or-nothing. A deductive argument is either invalid or invalid; it cannot be a little bit valid or partly valid or almost valid. Strength is not like this: it is a matter of degree. Some non-deductive arguments provide almost complete support for the conclusion, some provide a bit of support for the conclusion, and some provide hardly any or no support for the conclusion.
Consider the following three arguments:
Argument One:
P1. 96% of politicians are dishonest.
P2. Winston is a politician.
C. Winston is dishonest.
Argument Two:
P1. 75% of politicians are dishonest.
P2. Winston is a politician.
C. Winston is dishonest.
Argument Three:
P1. Most politicians are dishonest.
P2. Winston is a politician.
C. Winston is dishonest.
The first is very strong, the second is less strong, the third is even less strong. Strength is a matter of degree.
Summary
A strong argument is one in which the premises provide a lot of support (although not conclusive support) for the conclusion: if the premises were all true, the conclusion would be likely to be true.
Strength is a matter of degree (unlike validity).
A cogent argument is a strong argument which does in fact have all true premises.
Here’s an everyday example of non-deductive reasoning. There used to be a film critic on National radio called Jonathan Dennis. He was a rather harsh critic – he didn’t like many movies, and in particular, he very rarely liked a commercial, Hollywood movie. So, since I do like some such movies, when Jonathan said that a particular movie was bad, I didn’t necessarily abandon my plans to go and see it. But if Jonathan raved about a movie that I wasn’t planning to go to, I was quite likely to decide to go and see it after all.
My reasoning went like this:
P1. In cases W, X, Y and Z, when Jonathan liked a movie, I liked it too.
P2. There haven’t been any cases when Jonathan liked a movie and when I saw it I didn’t like it.
P3. Jonathan liked movie P.
[Probably] C. I will like movie P as well.
Do you think I was reasoning well, or badly?
Some of you might have said that four cases (movies W, X, Y and Z) are not enough to generalise from. Certainly, on the basis of this amount of evidence, I wouldn’t go so far as to say that any movie that Jonathan Dennis liked, I would also like. If I was thinking of making any such strong claim, I’d want to test it further. If I was going to be scientific about it – if I was going to set about trying to test the claim – I’d go to more movies recommended by Jonathan Dennis and see if I liked them.
But think about the context. All I’m trying to decide about is whether to go to a movie. The most I stand to lose if I get it wrong is one evening and $15. I think the evidence on which I am deciding to go to the movies is good enough, under the circumstances. That is to say, even if the argument doesn’t make the probability of the conclusion very high, it’s good enough for my purposes.
If something more serious was at stake, we would want better evidence, more cases, something which gave us reason to think the conclusion had a very high likelihood of being true. Suppose my child is diagnosed with cancer and I am choosing between conventional medical treatments such as chemotherapy and some alternative treatment like “quantum vibrational therapy,” which involves passing an electric current through the body. I should want a lot more than four cases in which the alternative therapy has been successful before I’ll think I have good reason to use it. In a case in which so much is at stake, I need much stronger reasons to believe the conclusion than in a case in which I am merely deciding whether or not to go to a movie.
