The question is: do you agree that abductive reasoning is a specific type of inductive reasoning? — Magnus Anderson
I'm not getting too hung up on the divisions. There is the more familiar dichotomy of deductive vs inductive argument - necessary inferences vs probable inferences. That kind of works in the sense that deduction proceeds from the general to the particular with syntactic certainty while induction does the reverse of going from the particular to the general with provisional hopefulness.
But then a triadic view - one where a dichotomistic separation resolves itself into a hierarchical structure - is the special twist that Peirce brings to everything. It is the next step which completes the metaphysics.
So that is why it is a neat result - one that hierarchical structuralism predicts - that the actual process of human reasoning splits itself so cleanly into a trichotomistic process. It makes reasoning not an arbitrary business but one that works in the same basic way as the nature it wants to describe.
This is obviously a huge metaphysical deal - for those who still have faith in metaphysics as a grand unifying project.
So is abduction a specific form of induction? The Peircean question is instead where does abduction fit in the basic semiotic triad.
And it slots in as Firstness. A hypothesis is the first free and spontaneous act, which then leads to the "deductive" secondness that is mechanically determined reaction, and followed then by the thirdness which is the generalisation of such individual reactions to the form of some regular and enduring global habit.
Here's an example of abductive reasoning:
1. The grass is wet.
2. If it rains, the grass gets wet.
3. Therefore, it rained. — Magnus Anderson
But is it?
The classical deductive syllogism is:
Major premise (or the general rule: All M are P.
Minor premise (or the particular case): All S are M.
Conclusion (or result): All S are P.
Abduction then rearranges the order so that the argument is: All Ms are Ps (rule); all Ss are Ps (result); therefore, all Ss are Ms (case).
So you would have to say something like:
- Rain makes things wet.
- This grass is wet.
- Therefore, the grass was (probably) left out in the rain last night.
It is quite apparent to me that abductive reasoning is a very narrow form of reasoning. By definition, it only forms conclusions regarding events that took place in the past. This means that abductive reasoning is restricted to making "predictions" about the past. In other words, it can only be used to create retrodictions. This is unlike induction which can be used to form beliefs of any kind. This suggests to me the possibility of you defining the concept of induction narrowly as pertaining only to making assumptions about the future. — Magnus Anderson
I'm not sure why it seems a problem that abduction is retroductive - that the past is being assumed to hold the key to the future. To the degree the world has actually developed some stable intelligible being, it will have developed those general constraints which serve to restrict freedom and spontaneity to give the world its predictable shape.
This is the point concerning the metaphysics. Rather than going with the classical metaphysics which thinks reality is some God-given realm of law and deterministic material action, Peirce is up-ending that view to build a logic that arises out of a completely probabilistic model of existence.
So again, induction is not a problem as it sits on the side of probability. Deduction is now the problem as the shallowness of a deterministic or mechanical metaphysics stands exposed. The issue is really why would deduction function at all? And clearly - just as we find with computers and other machines - they can't stand alone. They are helpless if it weren't for us to bookend them and makes sense of their furious syntactical whirrings.
So if you sit on the side of a probabilistic ontology, now the whole picture can snap into place properly. Abduction seeks out the constraints that must underly any observable regularity in the world. A classical/deductive/mechanical/deterministic/atomistic world is merely the emergent limit on this probabilistic description. So the task is to guess at the rules that stabilise things sufficiently that the probability of causal certainty approaches arbitrarily near 1 (or 0) for the things we might care about as fundamental facts of the world.
Will we always fall down rather than up when stepping off that cliff? Well thermodynamics says all our atoms could fluctuate upwards at that precise moment and give us a surprise. Yet also, that is almost surely never going to happen - even given a really vast number of lifetimes for our Universe.
Thus abduction does seek to recover rules already formed. And inductive confirmation seeks to show our guesses are correct. And it is all couched in probabilistic language. We no longer believe in a classical Cosmos - the one of Newton and Hume. We are presciently already into a quantum reality where concrete classicality is an emergent and inherently probabilistic limit state.
When I guess that the next value in the sequence 1 2 3 4 is number 5 I do not necessarily do so because I am aware of the underlying pattern. Rather, in most cases, we do so because we know that the superset {1, 2, 3, 4, 5} has the highest degree of similarity to the superset {1, 2, 3, 4} among the supersets that have the form {1, 2, 3, 4, *}. — Magnus Anderson
I'm sure the rule you abduce is the simper one - 1+1=2. And so on, ad infinitum.
So you abduce a deductive rule, an algorithm that blindly constructs. You are recovering the set theoretic approach that is already the axiomatic basis for number theory.
A cherry-picked example which is a textbook case of deductive thought is hardly a good way to illustrate an argument about the true nature of induction.
:-}
Regarding AGI research, most of the research has been dedicated to modelling how the world works rather than to modelling how thinking works. I think that's the problem. Rather than having a programmer create a model of reality, an ontology, for the computer to think within, it is better for a programmer to create a model of thinking which will allow machines to create models of reality -- ontologies -- on their own from the data that is given to them. — Magnus Anderson
Well that is why I always say forget Turing Machines and symbolic logic. It is neural networkers who have been thinking about how to properly mimic the Bayesian principles by which a brain actually makes inductive predictions.