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Are all coherent inferences deductive, inductive or abductive? If I justify a belief (to some degree) to myself, and it is not the best explanation, I am not deducing it from any premise, and it is not an induction from something occurring to it occurring again, then is my justification a sham?

What about cases where I use a mixture of these inferences at different times: I deduce an equivalence, then infer similar events will happen again, then explain that. What is the status of my justification? In general, is it a bad form of reasoning to use, specifically if without the induction the abduction does not seem as appealing?

I would especially want to read an answer that mentions Bayes theory, if that makes sense, because even-though I do not routinely use it, I suspect it shores up my justification. Moreover, how much do we believe the best explanation: is it trivially over 50% (what about in the above example of using an induction too)? If so, does that mean that if we can't justify something over 50%, if it is not the best explanation, then the explanation has no role to play, and the degree of belief we can assign it can readily assume the certainty of just how improbable it seems.

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    "Abduction is normally thought of as being one of three major types of inference, the other two being deduction and induction." SEP. Mixtures are mixtures, one can surely have mixed inference trees. "Several authors have recently argued that not only is abduction compatible with Bayesianism, it is a much-needed supplement to it... Bayesians ought to determine their prior probabilities and, if applicable, likelihoods on the basis of explanatory considerations." SEP.
    – Conifold
    Apr 18 at 17:47
  • yes @Conifold it is quite a trivial question, execpt perhaps for the last bit about a collapsing inference "tree"
    – andrós
    Apr 18 at 17:48
  • Abduction is just a particular case of induction. It is already included in Bayesian inference. The "best explanation" that we "abduct" to is the explanation of minimum description length that agrees with the data. Bayesian inference selects this explanation already.
    – causative
    Apr 18 at 20:41
  • @causative Description length heavily depends on chosen means of description, and Bayesian inference puts probabilities on "agreement with the data" regardless of description length. Moreover, we do not associate explanatory value with minimalism or parsimony, those are separate considerations, so Bayesian inference as such is pretty disjoint from abduction. As SEP says, "Bayesian confirmation theory makes no reference at all to the concept of explanation". They can be combined, but there is no "inclusion".
    – Conifold
    Apr 18 at 23:46
  • @Conifold "Description length depends on means of description" - yes, but in practice we can just use a Solomonoff MDL prior and asymptotically the results provably don't depend too much on which prior we choose. "We do not associate explanatory value with minimalism or parsimony" - speak for yourself? I certainly do. The theoretically best explanation is the MDL one. "SEP says Bayesian confirmation theory makes no reference at all to the concept of explanation" - SEP can say whatever it likes, doesn't make it right. We explain the data by producing a short computer program that generates it.
    – causative
    Apr 19 at 0:04

2 Answers 2

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More than anything, the inferences we use in our daily lives are analogical. We try to bring to mind similar scenarios to what we currently face, and apply methods of inference that worked in those similar scenarios.

A "method of inference" could be any kind of calculation at all. Our brains are big, mushy neural networks perfect for producing very complex interactions between many many moving parts - interactions that cannot be neatly summarized as any sort of logical procedure. It is these mushy, messy calculations that form the backbone of our thinking.

Ideally, our mushy, messy calculations approximate Bayesian inference. But we do not actually use Bayesian inference. Bayesian inference is too computationally difficult to perform exactly. We rely almost entirely on heuristics and analogy.

A method of inference does not necessarily involve declarative propositions. When you're playing baseball, you don't think "the ball is at coordinates (100, 23, 4)." Your neurons represent the ball as an active mess of partially random neuron spikes, interacting with another active mess of neurons that are controlling your muscles. It is a dynamical system rather than anything corresponding to definite propositions. The best that can be said of it is that it has produced a positive result in the past and may work this time too.

Another very important aspect of our thinking is that of searching for consistency. Our thoughts are not all consistent with each other. To think more clearly it is necessary to take different lines of thought to their conclusions, find there is some contradiction or tension between these conclusions, and then try to revise the premises in such a way that the contradiction or tension goes away or is at least reduced. It is important not only to revise the premises when contradictions are found, but also to actively seek out such contradictions.

By contradictions, here, I am not speaking necessarily or usually of logical contradictions. We might use the words "tension" or "dissonance" instead. This tension is more of a feeling, and it has a magnitude rather than being binary.

Occam's razor is also fundamental. When an explanation has too many parts, this also creates a kind of tension, perhaps the same as the tension of contradiction, and we'd rather revise our premises to reduce this tension, to explain more with less. Occam's razor is fundamental to Bayesian inference as well.

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  • sounds simialr to (existential) guilt
    – andrós
    Apr 18 at 17:43
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This is not an answer to the question but I think it helps to frame the investigation of the meaning of coherence and the context of unconscious or conscious inference. Exploring the experience of "coherence" and "inference" in the context of The Impossible Triangle (4:26):

https://www.youtube.com/watch?v=gbOu6ArLItg

When I first saw the image of the impossible triangle (demonstrated in a similar video) I felt a cognitive sense of something that I will call my sense of incoherence. The image did not seem to be a possible instance of a proper 3-dimensional triangle. Hermann von Helmholtz has a theory of Unconscious Inference. This is when perceptions arise in the mind as the product of an unconscious process that would otherwise map to a conscious inference. I personally cannot trace the cause of my sense of coherence or incoherence, or of true or false evaluations, to any process in my conscious mind. What happens is I turn my attention to some domain of concepts and perceptions. Then the sense of coherence or incoherence, of true or false, arises in my mind as the product of an unconscious process. The video, for example, shows first how the incoherence of the impossible triangle can be explained by some conscious analysis (by inferences?), and then how further perceptive information makes the illusion in the image become coherent in the mind. The shift from incoherence to coherence occurs via further knowledge arising in the mind.

Note: Based on contemplations such as the above I reject the phrase "consciousness is an illusion". The only means to recognize an illusion seems to be a turning or transformation of perceptions arising in my consciousness. Calling consciousness an illusion or user-illusion only triggers my sense of incoherence.

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  • "It takes an illusion to catch an illusion", eh?
    – Scott Rowe
    Apr 18 at 21:37

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