The next essay in “Sherlock Holmes and Philosophy” is “Action Man or Dreamy Detective” by Sami Paavola and Lauri Jarvilehto, and has to win for the most abstract title of a chapter ever because the essay itself is about Holmes’ ability to reason and what that conforms to, which doesn’t really have all that much to do with the title. The essay looks at two of Charles Peirce’s ideas on reasoning, but I’m only going to look at the first of them, which is abduction. They claim that Holmes uses abduction as opposed to either deduction or induction, and define them all thusly:
Deduction, the pattern of reasoning by clarifying logical necessities.
Induction, reasoning on the basis of what “actually is”.
Abduction, the main kind of reasoning we use for coming up with new ideas.
The first thing we can see from these definitions is that, well, they’re all pretty much useless, except for maybe the one for deduction. The other two seem more like a definition someone would espouse if they wanted to denigrate deduction … which fits in with this essay. After all, deduction clarifies “logical necessities”, but according to the other definitions it wouldn’t focus on what “actually is” — as that’s induction — and wouldn’t be what we’d use for coming up with new ideas, as that’s abduction. Both of those definitions talk much about what they can do or are used for — implicitly saying why they’re superior to deduction — but neither of them give any clarity on what that sort of reasoning actually is. So let’s redefine them:
Deduction: the form of reasoning that proceeds from premises to a conclusion following standard logical operations.
Induction: the form of reasoning that proceeds from instances and generalizes to propositions outside of the direct scope of the available data.
This leaves abduction, so let me try to summarize it as best I can from what they seem to say about it:
Abduction: the form of reasoning that proceeds from hypotheses about the given data through testing the hypotheses to see if they hold.
So, given this, does Holmes use deduction, induction, or abduction?
Holmes doesn’t really generalize outside of the data he has. Even in their example of Holmes’ assessment of Watson when they first meet, he takes things that he knows and applies them to Watson, and so instead of moving from specific instances to the general he moves from the general to the specific instance. Thus, he’s not using induction.
So, given that, I think the key to determining which he does is to ask: does Holmes form hypotheses that he then tests to see if they are accurate, or does he just operate on the data he has and sees what follows from it? Note that gathering more data — ie going back to look at the scene again, or even going to the scene — wouldn’t count in favour of abduction, because in all forms of reasoning discovering that you need more data and even what specific data you need is a key part of it; none of them must draw conclusions from insufficient data. So let’s look at the reasoning they summarized from “Silver Blaze”:
Did the dog bark? No. Why does a watchdog not back in the middle of the night, if something odd is happening? Because whatever was happening in the night-time, the perpetrator must have been someone the dog knew well enough not to be disturbed by him.
So, for this to count as abductive, Holmes would have had to come up with that hypothesis and then go out to test it, to make sure that the reasoning held. Holmes usually doesn’t do that. Also, it would have to be expressed, as the authors put it, in maybes and mights, but in the quote provided — and in general — Holmes never thinks of things that way. In fact, his main catchphrase aims more at certainty than at maybes: When you have eliminated the impossible, whatever remains, no matter how improbable, must be the truth. This even strike at the Bayesian interpretation of abduction because Holmes makes it clear that he doesn’t care about probabilities if it’s the only explanation left. So it really looks like Holmes uses deduction, not abduction.
They even themselves hint at this by talking about the analytic/synthetic distinction, and claiming that Holmes’ approach is analytic. Analytic reasoning is deductive, synthetic reasoning would fit in with their definition of inductive. Neither, as it turns out, fit either their or my definitions of abductive. Well, abductive reasoning would be a form of synthetic reasoning, which doesn’t help their case at all.
I think the confusion here is the idea that deduction can only work on things that are true by definition. But deduction isn’t that way, really. Deduction simply is proceeding from the premises to a conclusion that follows logically and directly from the premises. So what Holmes does is gather lots and lots of data through his powers of observation and his experiments, and given all of those facts, he simply sees what conclusion necessarily follows given those premises. If he has all of the relevant facts and the conclusion logically follows from the premises — ie if the premises are true the conclusion cannot be false — then he has his answer. No testing required, and no room for maybes.
The problem is that too many people over-emphasize what deduction needs to work, which is that it has to know that the premises are true. Sure, you can establish that if the premises are true the conclusion must be as well, but you have to know that the premises are true before you can say that the conclusion is true. And so you can come up with logically valid arguments that are, in fact, ridiculous. This is what gets people yearning for something like induction or abduction to save the day, demanding that we actually go and look at the world, which they claim deduction can’t do. But is going out to verify the premises testing (and so abduction) or simply gathering more data (and so deduction)? I’d say that, from the perspective of deduction, it’s gathering more data: I need to know this fact, so let me go see if this fact is true. For Holmes, who starts with more facts and usually the facts that he needs, he rarely has to actually go and look to see if his premises are true, and so when he does go out and check things it’s not him forming a hypothesis and then testing it, but him merely going to find out the facts that he’s missing to fill in the blanks in his deduction.
You can decide for yourself in Holmes is a dreamy detective or action man.