Sherlock Holmes, ‘inference to the best explanation’, false dichotomies and God

There’s a way of thinking called abductive reasoning, commonly referred to as “the inference to the best explanation”. Sherlock Holmes famously uses it, and his use is fallacious. There are many structures of argument that would fall under abductive reasoning, which this post will look at, briefly, focussing on their errors. It will then focus on abductive reasoning in the context of using a false dichotomy. At the end, the post will then look at applying these concepts to an argument for the existence of God (which, as it turns out, fails).

Holmes says he uses deductive reasoning, but he doesn’t; he uses abductive reasoning. Taking an example from the TV series with Benedict Cumberbatch ― A Study in Pink (2010) ― Holmes tries to identify a deceased lady, and concludes that because the lady’s coat is wet and she has an umbrella, she has come from somewhere it has been recently raining but too windy to use the umbrella. The series portrays this as cast-iron logic, even though there are other possibilities as to how her coat got wet. Not that it is the point of this post, but here’s a brief list of other explanations: she bought the umbrella after it started raining, and hence got wet before she bought it; she was splashed by a vehicle; the rain began very suddenly and so she got wet before she pulled out the umbrella; she forgot she had the umbrella; she was in a rush and so didn’t stop to pull out the umbrella.

This often happens. Also in A Study in Pink, when Holmes meets Watson, Holmes “deduces” (abducts) that Watson’s phone was given to him by an alcoholic. His observation that leads him to this conclusion is scratches around the power port, something Holmes decides is only present on an alcoholic’s phone. Again, there are other explanations: a lack of coordination; putting the phone on charge at night, in the dark; putting the phone on charge without looking, because the current or previous owner is compulsively busy; Watson is the alcoholic. In both cases, my proposed alternative explanations are unlikely to be exhaustive; they are only meant to be illustrative of the problem.

In scripts, this doesn’t matter. You simply write the script in such a way that Holmes is right and the flawed reasoning can be glossed over. But, here’s a brief look at the form of that alcoholic’s phone:

Given an observation, C (observation: scratches around the charging port)

If A (the phone belonged to an alcoholic), then C (scratches around the charging port).

C (scratches around the charging port), therefore good reason to believe A (the phone belonged to an alcoholic).

(derived from Wikipedia contributors, 2017)

Also within Holmes, there is another flawed use of abductive reasoning: “If you’ve eliminated all other possibilities whatever remains must be the truth”. Logically, this would follow:

The options are A, B or C

It is not B or C

Therefore it is A

The problem is premise 1. What if A, B and C are not all your options. That leaves the possibility that it is not A, B or C. The problem it leads to is this: I have explored option B, and it’s not that; I have explored option C, and it’s not that; I therefore do not have to explore option A, it just is that. But if it is actually option D ― some option that it has not occurred to you is a possibility ― then which option you decide it is (A, B or C) depends quite literally on the order you explore the options.

Premise 1 is rejected, not because it is false, but because it cannot be demonstrated to be true. All premise 1 does is express the imagination ― or its limitations ― of the person making the argument. It is possible that option D hasn’t occurred to the arguer, or their interlocutor, and therefore is never mentioned. But that is an artefact of the ignorance of the people, not an artefact of reality to be put into a logical argument. Premise 1 is a false dichotomy.

There are attempts to save this kind of argument, which is what the “inference to the best explanation” is. But they also fail. The argument ends up looking more like this:

The best candidates for an explanation are A, B or C

Of those, A is the best

Therefore, we should accept A

Even in this new formulation, premise 1 is an expression of the current state of knowledge and not all actual explanations. But now, premise 2 becomes problematic as well. And the reason is a little complicated.

To establish which candidate is “best”, the process is one of assessing the confidence held in each candidate, so the probability that a candidate is true. But, that poses a number of very big challenges.

The claim “I will roll a 3 with a fair 6-sided dice” has a 16.7% chance of being true. The claim “I will roll an even number with a fair 6-sided dice” has a 50% chance of being true. This is simple, as the number of faces on the dice and the probability distribution are well defined. However, if a person presents a raffle ticket and makes the claims “I will win the charity raffle with this ticket”, the probability of that being true is impossible to state on the information given: we don’t know how many tickets were sold; we don’t know if it’s a fair raffle; we don’t even know that the presented ticket is a part of the discussed raffle. This leads to complete agnosticism on the probability of that claim being true. And, contrary to what your intuitions may be, complete agnosticism is not the same as 50% confidence; it is an undefined confidence.

Taking the Study in Pink example, again, how could Holmes assess the probability of three different claims purporting to explain why the dead lady’s coat is wet? She could have come from a wet and windy place, rendering the umbrella useless; she could have gotten wet before she bought the umbrella; she could have forgotten she had the umbrella. How could Holmes reliably assess their probability, compare them, and then claim certainty on something that is, by definition of this type of argument, a gamble?

Even if we play Devil’s advocate, and assume he can assess the probability of each of those claims, we may still end up with a problem:

A – She came from somewhere wet and windy (40% probability)

B – She got wet before she bought the umbrella (30% probability)

C – She forgot she had an umbrella (15% probability)

(Leaving 15% chance for unthought of explanations ― because we’re open minded.)

Even if this task could be completed, it is still more likely that it is not A (45%) than it is A (40%). And, even more importantly, 40% confidence is not confident. Let alone certain (see graph).

It may be that these criticisms don’t really hit ‘abductive reasoning’ as hard as I’m implying here. This is because the discussed purpose of abductive reasoning was to formulate a hypothesis that is to be later tested before it’s held with any level of confidence (Harman, 1965). However, you will note that is not how Holmes uses it. And neither is this how it is used in the following popular argument: The Teleological Argument for God

Let us explore this argument in more detail. The observation the argument tries to explain is the “fine tuning” in the universe. What this means is that certain values in the maths that represents natural laws appear arbitrary, meaning they are not derived or explained from a deeper understanding. At the same time, if any one of these values were anything different, the universe wouldn’t exist. For the purposes of this post, we are ignoring some important facts: a universe may still exist is a number of these values were different; the reason none of the values in the natural laws are derived from a deeper understanding is because there currently isn’t a deeper understanding.

(As a fun side note, there is a “former” fine-tuned natural law: the expansion rate of the early universe. The naive calculation of the probability of that value was “within 1 part in 1060” (Craig, 2015). But, using General Relativity equations, the probability becomes 1. What once appeared as “fine tuning” turned out to be “necessity”.)

The argument goes like this:

The fine tuning of the universe can be explained by design, necessity or chance.

It is not necessity or chance

Therefore it is design

We can even improve this for the rational debater, by expressing the premises more weakly, even though this is not an improvement according to the theologian:

The best candidates for the explanation of fine tuning in the universe are design, necessity or chance

The best of these options is design

Therefore we should accept design as the best explanation

Okay, so what problems that we’ve already discussed still apply to this argument?

Premise 1 is still a false dichotomy, in both examples. It is limited to our imagination of what the candidates could be, not any actual fact about what the candidates are.

Premise 2, in both cases, is not established and may even be demonstrably false. There is at least 1 example of the appearance of fine tuning being explained by necessity (the expansion rate of the universe). Whereas the other two should have an undefined probability: we don’t know the chances a designer could exist; we don’t know how many universes there are to assess “chance”; we don’t know whether each possible universe has an equal likelihood (the probability distribution issue).

The conclusion does follow in the first example (even though it follows problematic premises). But in the second example, the conclusion doesn’t really follow: even if the premises are sound, we could be looking at another 40%, 30%, 15% confidence issue; it may be that no explanation is really a reliable one, and that each premises is still more likely not to be true than to be true.

Holmes’ use of fallacious abductive reasoning gets past most people’s rationality detectors for two reasons: it appears sound, and it’s authored to always work. However, in the real world where these processes don’t have authors, the mistakes carry intellectual risks; there is no author to make sure bad conclusions are validated. And so, it pays to be properly prepared to assess why the very structure of the logic is flawed.

Craig, W.L. (2015) God and Cosmology: The Existence of God in Light of Contemporary Cosmology | Reasonable Faith. Available from: [Accessed 15 November 2017].

Harman, G.H. (1965) The Inference to the Best Explanation. The Philosophical Review. 74 (1), pp. 88–95.

Wikipedia contributors (2017) Abductive reasoning. Available from: [Accessed 15 November 2017].

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