Does Abductive Reasoning really exist?
Salutations,
I have been a regular reader (and big fan) of LessWrong for quite some time now, so let me just say that I feel honoured to be able to share some of my thoughts with the likes of you folks.
I don’t reckon myself a good writer, nor a very polished thinker (as many of the veterans here), so I hope you’ll bear with me and be gentle with your feedback (it is my first time after all).
Without further ado, I have been recently wrestling with the concept of abductive reasoning. I have been perusing for good definitions and explanations of it, but none persuade me that abductive reasoning is actually a needed concept.
The argument goes as follows: “Any proposed instance of abductive reasoning can be fully explained by a combination of inductive and deductive reasoning. Therefore, abductive reasoning is unnecessary — i.e., it does not « exist » as a form of reasoning.”
Now, the idea that a form of reasoning that has been accepted wisdom for over a century might be bogus sounds a bit far-fetched. (That much more so because I very much respect the work of Charles Sanders Peirce, who first proposed the concept). I am sure that I am missing something, but for the love of logic, it’s not coming to me. So I am hoping that some clever comment might help me figure it out.
But first, here’s a more detailed explanation of my argument.
Deductive reasoning can be defined as constructing formal logical arguments, such that if the premises are true, then the conclusion must be true. (Formally, I see this as mathematical logic, or more broadly as reasoning in the absence of new empirical evidence).
Example: “Humans are fragile. I am a human. Therefore, I am fragile.”
Inductive reasoning is about generalising a body of observations to formulate general principles. (Formally, I see this as inferential statistics, or more broadly as reasoning to incorporate new empirical evidence).
Example: “For the past 7 days it has been raining. Therefore, tomorrow it will probably also rain.”
It is often said that: “The conclusions of deductive reasoning are certain, whereas those of inductive reasoning are probable”. I think this contrast is somewhat misleading and imprecise, as the certainty of deductive conclusions just means that they necessarily follow from the premises (they are implied by the premises), but the conclusion itself might still be probabilistic.
Example: “If I have a fever, there’s a 65% probability that I have the flu. I have a fever. Therefore, there’s a 65% probability that I have the flu.”
Finally, abductive reasoning (also known as “inference to the best explanation”) is about finding the most likely explanation for one or few observations.
Example: “I have a fever, cough and I am feeling weak. Therefore, I most likely have the flu”.
Now let’s attack the example of abductive reasoning, starting with the conclusion “I most likely have the flu”.
This is logically equivalent to “Among the potential explanations for my symptoms that I could come up with, having the flu has the highest probability of being true”.
But where are the probabilities coming from? They must come from inductive reasoning (looking at past instances of symptoms and diseases) or deductive reasoning (e.g., from your existing knowledge).
Note that we don’t really care if the probabilities are right. We also don’t care if I am examining all the possible diseases or just a handful that came to mind (and maybe none of them is right).
The point is that you can reconstruct the argument as:
Inductive reasoning: Given past data, the probability of having a given disease given symptom X are [...]
Deductive reasoning: the probabilities are [...] → I have symptom X → I have disease Y with probability > 50% == “I most likely have disease Y”
There’s no “leap of faith”, no “abduction” happening. Just inducting probabilities and then deducting the most likely outcome.
What if there is no prior data about this event to use to induce probabilities?
It doesn’t matter; you can still deduce your way to probability estimates from other beliefs, analogous events, and adjacent knowledge. (Curiously, I haven’t seen a LessWrong article on how to correctly make probability estimates in the absence of direct data, can anyone point me to it?)
The point is that you must arrive at some probability distribution of explanations to be able to declare one as the “most likely” (which is in the definition of abductive reasoning).
If you had absolutely no prior knowledge (e.g., you were dropped in a completely new universe), then the rational stance would be to consider all outcomes as equally likely—which means none can be considered the most likely.
In conclusion, to paraphrase Eliezer, abductive reasoning is starting to sound a lot like “magical reasoning”. It’s unclear what it actually means, and I suspect it just came to represent a mix of subconscious search over the hypothesis space and estimation of the probability distribution of possible explanations. But just because some reasoning is subconscious, it doesn’t make it a new form of reasoning.
But as I said, simply based on the historical endurance of this term, I’m probably missing something here.
Update: I now believe this argument to be somewhat redundant, as it is simply trying to reconcile the historical classification of “reasoning” with more modern scientific understanding of computation and logic. There is truly only one form of computation, although I do find it practically useful to distinguish between Bayesian Statistics (to incorporate empirical evidence into models) and Mathematical Logic (using existing evidence to infer additional information).
Abductive reasoning results from the abduction of one’s reason.
Couldn’t resist the quip. To speak more seriously: There is deduction, which from true premises always yields true conclusions. There is Bayesian reasoning, which from probabilities derives probabilities. There is no other form of reasoning. “Induction” and “abduction” are pre-Bayesian gropings in the dark, of no more account than the theory of humours in medicine.
I am not sure what your definition of Bayesian reasoning is, but I personally think of:
Induction as somewhat equivalent to inferential statistics.
I am not sure where most people would place Bayes’ theorem itself, but Bayesian statistics is usually considered a subfield of (or rather an approach to) inferential statistics.
Imagine a world with thousand different diseases, all of them comparably frequent, that all cause fever, cough, and weakness. Flu would be one of them.
In such world, this kind of reasoning would be clearly wrong. You have symptoms that correspond to thousand different diseases; that is no reason to suspect a specific one among them.
This reasoning is okay in our world, because we have the prior that among diseases that have these three symptoms, flu is most frequent. But this is an extra information that is not included in the quote. That means that the form of reasoning in the example will be sometimes correct and sometimes wrong, depending on circumstance, which means that it is unreliable in general.
...is my guess.
There’s something off about this example. In deductive reasoning, if A implies B, then A and C together also imply B. But if A is “I have a fever” and C is “I have the flu” then A and C do not imply “there’s a 65% probability that I have the flu” (since actually there is a 100% chance).
I think what is going on here is that the initial statement “If I have a fever, there’s a 65% probability that I have the flu” is not actually an instance of material implication (in which case modus ponens would be applicable) but rather a ceteris paribus statement: “If I have a fever, then all else equal there’s a 65% probability that I have the flu.” And then the “deductive reasoning” part would go “I have a fever. And I don’t have any more information relevant to whether I have the flu than the fact that I have a fever. Therefore, there’s a 65% probability that I have the flu.”
Inference to this best explanation is broader than inference to the most likely explanation. Simplicity and consistency are also factors in “best”.
I think “best” is a bit of a generic term, but in regard to beliefs, it seems safe to say that the “quality” of a belief should be judged exclusively on its probability of being true.
Simplicity and consistency are then factors that positively affect the probability of a belief being true, but they are not in themselves determinants of the “best” explanation.
Given:
- Belief A, which is 51% likely to be true but very complex and somewhat discordant with existing beliefs (this is included in the probability estimation)
- Belief B, which is 49% likely to be true but very simple and elegant
Assuming the probabilities are correct, I think Belief A should be considered the “best”. Would you agree with this?
P.S. Quantum field theory is an example of a very complex theory and inconsistent with other accepted theories (e.g. General Relativity), but still the “best” explanation for empirical evidence.
If that is so, you no longer have an argument that abduction is merely a form of induction, because you have admitted to two sources of probability other than induction.
The underlying issue is that what we are trying to do with abduction is find the hidden mechanism behind the directly observable, the force of gravity that makes the apple fall. Since induction is limited to inferring futures observations from past ones, it is limited to the observable and silent about behind-the-scenes mechanisms. And so it is limited compared to abduction, and so abduction is not a form of induction. ( The classic argument against induction is that it is not a form of deduction...within classical loguic. It could still be a form of probabilistic reasoning).
Bayes allow you to confirm hypotheses that would generate the observable evidence, but doesn’t mechanically generate them for you , and also.doesn’t allow you to distinguish equally predictive ones. You can solve the first problem by creatively positing hypotheses, and the second with the criteria of simplicity and consistency. That gives you full abductive reasoning . Bayes is a subset of full abductive reasoning.
Science uses abductive reasoning , plus (dis)confirmation. Deduction is needed for these, because you need to deduce the expected consequences of a theory to observe them.
I would need to know where you are getting your likelihoods from. Are they hard observational data, or subjective priors?
Simplicity is a relative measure, not an absolute. QFT can both a complex theory, and the simplest that does the job.
@Viliamand
Yes, we need to know where the likelihood is coming from.
@Richard_Kennaway
Probabilistic reasoning is also induction, so long as induction isn’t required to be certain: observing multiple instances of something in the past raises the probability that it occur again in the future.
@AnthonyCand
Not really. they have standard definitons you can just look up. You don’t have to guess.
@speck1447
Well, Bayesian updates are no good unless you have the right hypothesis. That might be what you mean.
It’s naive to assume that explanations are suggested by the data. They are conjectured.
I appreciate that point, yes, and I have looked up standard definitions. I’m probably not looking in the right places, though, because they ones I have found are either too vague and imprecise for me to make sense of, or focus on generating hypotheses/explanations/models. If you do have a good source for a better explanation, I’d actually really like to learn more.
My argument was never that abduction is a subset of induction, but that it can always be replaced by a combination of deduction and induction.
The effect of simplicity and consistency on probabilities can both be classified as deductions:
the former as a correct application of probabilistic logic (every additional assumption reduces the probability of the conclusion being true due to probability product)
the latter as a correct application of Bayes’ theorem or other types of logic (when [belief A] implies [not belief B])
I don’t think this is generally correct. Induction is about moving probability mass to both parameters and models that best explain the evidence. So it both improves your existing models and makes you choose better models (aka new “mechanisms” as you call them).
(This is a Machine Learning friendly way to see induction; more generally, you could consider any model-parameter combination as a separate model.)
I also don’t think this is quite correct. Simplicity and consistency should be considered evidence in your application of Bayes’ theorem. Namely, Bayes is complete: there is no other theorem or formula required to achieve the most accurate estimate of probability for beliefs. (Also, Bayesian statistics is considered a subset of inferential statistics, which is the formal mathematics associated with induction. Whether you think Bayes Theorem itself fits under induction or deduction, I don’t think most people would consider it abduction).
Besides this, if I understand correctly, you are proposing that the core of abduction is about generating hypotheses rather than evaluating the evidence for or against them. This I find intriguing.
I was originally considering the standpoint of an “optimal Bayesian” who simultaneously evaluates all hypotheses at once by shifting probability mass, but this is far from the human experience.
I do wonder whether this still happens subconsciously or whether hypothesis search constitutes in some way its own form of reasoning. But I’m afraid I haven’t thought enough about this, so I won’t be able to argue about it.
Thank you for the inspiration though, quite useful.
Is it? That isn’t the classic definition. The classic definition is fairly limited, more like:-
Ie, just more of the same , not an infinite variety of models
It does sounds like Bayes,...but Bayes could be a superset of induction.
And where are you getting your models from? If you are creating them , that’s abduction, even if you are calling it induction. If they they are already there, in some oracular database, that’s uncomputable ideal reasoning.
Or it’s something in ML that has been mislabelled “induction”, like “hallucination”
Complete what? It isn’t complete epistemology as I have shown.
What does “associated with” mean? If inferential stats is a superset of induction it’s pretty unsurprising that it could contain abduction. If your models are being created on the fly, it actually does.
Indeed. If ideal Bayesians don’t need abduction, that doesn’t mean humans don’t.
@AnthonyC
Why is that a bad thing?
Yes. Hypothesis generation isn’t mechanical or algorthmic. That may be “bad”, but there’s not much alternative—you can’t actually use Solomonoff Induction, or whatever.
I don’t think I implied it was a bad thing? I certainly didn’t intend to imply that.
Not quite, prior to this. We could say, for example, that having a scratchy throat is evidence that one has a cold. Bayes allows us to formalize this claim somehow. But it does not actually tell us what a “scratchy throat”, or indeed a “cold”, is. A perfect reasoner does not need this—they need the possible laws of physics, a sensible prior, and very good computational skills, and concept formation is not relevant to them. But a bounded Bayesian does not have this luxury—we cannot actually draw the boundary in concept-space around these terms, we certainly cannot quantify how fuzzy the boundary is, and yet we find ourselves able to do mostly-sensible probability updates anyway, because prior to a Bayesian approach, we are somehow good at concept-grouping.
Incidentally, this is why I say metaphysics is harder for a Bayesian—a perfect reasoner, or a bounded inferrentialist, does not require that their concept formation is perfect. Making metaphysical categories is helpful but optional for them. But a bounded Bayesian needs to do it and do it well, and it’s not clear how this is possible—you do not get it from priors and you do not get it from the update rule, and indeed these two things alone are not sufficient materials for a bounded Bayesian update.
I find it’s good practice to be deeply suspicious of the word “just.” Small words in arguments are often load-bearing in ways that hide much of the meaning from casual readers. E.g. LLMs are just applied arithmetic, biology is just applied chemistry, chemistry is just applied physics, etc. There is a sense in which this is ‘true’ in each case, but that does not make the less-fundamental concepts useless or unnecessary, and straightforwardly ‘believing’ such ‘just’ statements tends to cause poor thinking down the line in a variety of ways.
In this case, my own (not at all formal, just my sense) understanding is that while induction and deduction are largely about interpreting and reasoning regarding facts/data, abduction is largely about applying, proposing, and evaluating models and heuristics. At some level, yes, we can say that this is unnecessary. But in practice, keeping these as interrelated-but-separate mental objects helps people track which is which, notice when we need to reconsider and re-evaluate what models and assumptions we’re applying, and not get lost in our own ontologies. My mental model/example of this is any of the times SSC/ACX takes a useful analogy/metaphor and pushes it just that much farther than any sane normie would go, in order to find out whether it breaks or provides useful insight.
Apologies, I am not sure I understood.
Is it that:
- Induction/Deduction fit data to existing models
- Abduction is about proposing new models?
Basically, yeah. Most times I see abduction discussed, it’s less about drawing conclusions and more about hypothesis generation. That implies different permissible levels of making and breaking assumptions, choosing and changing models. It’s more fluid, less rule-bound, more willing to accept being knowingly wrong in some ways, less tied to formalisms and precise methods.
I’m not sure you’re characterizing deductive and inductive reasoning right here in Bayesian terms. Bayes factors come from metaphysical assumptions and concept groupings, neither of which seems meaningfully described as “inductive reasoning” here
I find it useful to think in terms of failure modes: inductive reasoning is the sort of reasoning that tends to fail because you overestimated the strength of the existing evidence, abductive reasoning is the sort of reasoning that tends to fail because you didn’t evaluate the direction of the existing evidence well (maybe you over-weighted something, maybe you’re missing a possible hypothesis and hence a direction in possibility space, etc.) Of course if you’re simultaneously thinking about all priors and all pieces of evidence these are the same type of error, and a perfect Bayesian update avoids both problems. Indeed a perfect Bayesian doesn’t recognize a distinction between these at all. The problem is that a perfect Bayesian needs perfect Bayesian metaphysics for concept formation and identifying reference classes—metaphysics is already very hard, but it’s much harder if you also want to be a Bayesian with it. The upshot is that members of this community should probably not worry about this distinction, because the accepted approach around here obviates it (as you oberve here) and gives you very different (but equally hard!) things to think about instead.