The relation of classification to abductive reasoning

Deer tracks in the snow

Deer tracks in the snow.

In my last post, commentator DiscoveredJoys raised the question of abductive reasoning and how it relates to my claim that classification is basically pattern recognition. It’s a fair question. First I’ll repeat my response, and then go into it a little more.

In my view, abduction is larger in scope than pattern recognition (PR). PR provides the foundation, but abductive reasoning leaps (usually on the basis of very few observations) to a causal argument or inference, while I am merely talking about the PR itself. PR presents the explicandum for inductive, abductive and deductive explanation.

So I have a much smaller target here. However, I should have thought (and written) about abductive reasoning more. Let me now. Abduction is sometimes called “inference to the best explanation”. Recognition of species, for example, is not, I think, explanatory, but it sets up a problem for the pattern recogniser: why is that pattern there? The usual answer (leapt to immediately on the basis of prior knowledge) is that there is some reproductive power that makes progeny resemble parents. This is the abduction, not the recognition of a pattern. It is the “best explanation” based on a host of prior assumptions and knowledge claims. If we had never seen a living thing (if we were a Matrix style computer), we might not leap to the explanation, but I think we would still recognise the pattern.

Of course the economic argument would not apply, and would rely upon other criteria of salience (maybe the Matrix needs to categorise objects that have functional roles in the simulation).

First of all, what is abduction? The Stanford entry is quite complete and comprehensible (see this also), but basically it is leaping to an explanation from a single or few observations. It is called by the late Peter Lipton Inference to the Best Explanation (IBE). IBE is a principle that you should choose to explain an observation based on the best causal explanation, the most likely based on background knowledge. My commenter suggested that pattern recognition is a form of IBE. I think it is not.

For a start, to make a pattern recognition-based classification does not require positing an explanation. It requires explanation once you have one, which is to say, it sets up an explicandum. To make an IBE, one needs already to know enough to make some explanations more likely than others. Lipton (1991) calls this assessing the “loveliness” of competing hypotheses. But while pattern recognition involves prior knowledge – of the domain and its general properties, mostly what to look for – it doesn’t involve assessing the loveliness of hypotheses. Instead it involves assessing the salience of differing stimuli.

In order to make an IBE, you have to recognise things. Take for example an IBE about what made footprints in the snow. First you have to recognise the pattern of footprints. This is something you have learned to do, not least by making footprints. Second, in order to make an IBE that a deer made these particular tracks, you need to recognise the difference between bipedal and quadrupedal tracks (gotten from years of observing them), and between claws and hoofs (likewise) and so on. With all that categorical apparatus in play, you “leap” to the hypothesis that of the likely animals in the area, it was a deer, not a cat or horse.

But classification is different to that, at least initially when the domain under investigation (DUI) is unexplored. You know about the wider domains in which the DUI is situated, so you are primed to see some sorts of things. But you get an idea of what is in the DUI by looking, a lot. Experience trains you to see patterns, and then, and only then, can you make IBEs. Hence my response above.

There are those who think taxa are explanations. One author, Kirk Fitzhugh (2005, 2009) thinks species are explanations, a view I cannot make sense of. An explanation of why a species is a species is something independent of recognising the species. Others have argued that phylogenies are explanations or hypotheses, in a Popperian fashion. Again, I cannot make sense of this. In the case of phylogenies, the explanation is the theory of common descent (or, in some cases, lateral transfer and introgression through hybridisation), but the phylogenies themselves are patterns in data. If a systematist works out a phylogeny of a group, then there is an IBE of common ancestry (or perhaps a Bayesian inference, which is distinct in the eyes of IBE advocates from abductive inferences), but common ancestry is not the same thing as working out the phylogeny, again, at least initially. Then background information can come into play to revise and refine the phylogenetic systematics, for instance by using molecular clocks or distributional properties, but again, these are further inferential activities to classification.

The relations of different kinds of cognitive activities here are not simple. While it helps us to classify them as distinct activities, in practice we shift and change from one to another, or do them simultaneously. Science is not done by recipe. However, it pays to be clear about the differences between them.

References

Fitzhugh, Kirk. 2005. The inferential basis of species hypotheses: the solution to defining the term ‘species’. Marine Ecology 26 (3-4):155-165.
———. 2009. Species as Explanatory Hypotheses: Refinements and Implications. Acta Biotheoretica 57 (1):201-248.

Lipton, Peter. 1991. Inference to the best explanation. London: Routledge.

8 thoughts on “The relation of classification to abductive reasoning

  1. Since you mention phylogeny, I’m able to make some sense of your argument. Without such familiar examples, I have problems.

    But you did, so here. I do think of a phylogenetic tree as IBE, to use your jargon. The way phylogenetic algorithms work does suggest such a categorization. We examine a great many possible trees and in fact consider them potential explanations of the data, and we pick the one with best fit to the data by some criterion (e.g. “parsimony”). That’s the tree that’s the best explanation of the data. (There are of course complications; we go on to judge whether “best” is enough better that we want to assert it, using various statistical and quasi-statistical tests. But the principle is unchanged.)

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  2. This is good stuff. Thanks for clarifying. The previous comment about abductive reasoning, your response, and this post all took place while I was reading Iain McCalman’s book “Darwin’s Armada,” in which he recounts how Darwin, Hooker, Huxley, and Wallace all took long voyages during which they were gathering data, recognizing patterns, and toying with abductive reasoning. They were, in other words, grappling with all these issues when confronted with the messy realities of the world. If you haven’t read the book, I recommend it. The Aussie in you should much appreciate it.

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  3. triggered by the footprints in the snow.

    I think one of the problems is resolving what is seen as the “rightness” or “wrongness” of various types of reasoning (and I include pattern recognition or descriptive efforts as reasoning) in science. I’ve always been a bit mystified by the distinction between “a priori” and “a posteriori” statistical tests – why does the same test on the same data produce a different answer if you haven’t declared first that you were going to do it?

    A lot of time seems to be spent on the wrong sort of “correctness”.

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    1. To answer your question: because if you don’t specify what you’re testing before you test it, there are many possible results you could have seized on as a supported hypothesis. In other words, a posteriori tests implicitly must correct for multiple tests.

      To fall back on a phylogenetic example, suppose you have a tree with 22 taxa, and you predict that taxa A and B should go together. If you perform some statistical test of this assertion and you get P<=.05, there's only a 5% chance you would have a result like that given the null hypothesis of the test. But if instead you had just analyzed the data, tested every one of the 20 internal branches on that tree, you would average one branch supported with P<=.05 even if the null hypothesis were true, so you could trumpet that result in Nature and impress everyone who had no understanding of statistics.

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  4. Fitzhugh kind of agrees with you, I think ;). He says

    http://link.springer.com/article/10.1007%2Fs11692-008-9015-x?LI=true

    “…I will refer to all aspects of biological nomenclature, species, and phylogenetics, under the heading of systematics, rather than
    classification…The distinction between systematics and
    classification is relevant given that the former is the process
    of performing systematization, i.e., the organization of
    observations into a system of concepts, in the form of
    hypotheses, according to theory, in contrast to the mere
    segregation of objects into classes based on specified
    properties.

    Further:

    “…The ‘general lineage concept of species;’ de Queiroz 1998, 1999; Wilkins 2007…can only be interpreted as referring to the products of human inference, in the form of explanatory hypotheses. As such, the relations that exist between our observations of the properties
    of organisms and those hypotheses can only be described in
    terms of abductive inference.”

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  5. Wilkins posted this:

    “For a start, to make a pattern recognition-based classification does not require positing an explanation. It requires explanation once you have one, which is to say, it sets up an explicandum. To make an IBE, one needs already to know enough to make some explanations more likely than others. Lipton (1991) calls this assessing the “loveliness” of competing hypotheses. But while pattern recognition involves prior knowledge – of the domain and its general properties, mostly what to look for – it doesn’t involve assessing the loveliness of hypotheses. Instead it involves assessing the salience of differing stimuli.”

    But hang about, consider pattern-matching as practised by biological organisms. What property of pattern-matching allows a lion to match a wildebeeste to the pattern of “prey”? Precisely because the pattern-matching module in its brain has already incorporated the “explanation” of “catchable and good to eat”.

    If you exclude the explanation from the process, then the pattern-matching module would constantly misfire, and lions would catch thorn bushes as often as they catch food.

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    1. This is exactly inverted. We infer the explanation – the lion merely does what works, and that involves both a pattern recognition system based on neural network architecture and whatever dispositions to identify kinds of things that evolution has bequeathed it (see my series on evospychopathy for exploration of this).

      It is very common for humans, and occasionally scientists, to think that the conceptual elements take priority; this is because in humans, and especially scientists, it often does (not a often as we might think). But explanation here is something that arises out of there being an exploring mind. Pattern recognition is very primitive (in the sense of being evolutionarily deep) and does not involve any explanation as such. Consider a jellyfish that is able, in the absence of any neural network, to respond to gradients of light and pressure. It does what it does because it is built that way by evolution on the basis that those who did it less well reproduced less. A lion is able to do what it does because its ancestors were better at what was needed to reproduce than competing systems. The idea they have “explanations” of the patterns they recognise is as silly as the claim (made by William Calvin) that hominids calculate trajectories of thrown objects, when instead they simply practice throwing.

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  6. I get it John, at is least I think I do.

    I am simply saying that in natural systems like lion/wildebeeste, the pattern-matching process (“this thing I am looking at matches the template for prey”) AND the template pattern of the meaning of prey (the “explanation”) must have evolved together, if they are to provide any adaptive benefit.

    This helps us not at all in understanding how humans construct explanations for connecting cause and effect.

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