I never thought about the connection between logic and probability before, though now it seems obvious. I’ve read a few introductory logic texts and deductive reasoning always seemed a bit pointless to me (in RL premises are usually inferred from something). -
To draw from a literary example, Sherlock Holmes use of the phrase “deduce” always seemed a bit deceptive. You can say “that color of dirt exists only in spot x in London. Therefore, that Londoner must have come in contact with spot x if I see that dirt on his trouser knee.” This is presented as a deduction, but really, the premises are induced and he assumes some things about how people travel.
It seems more likely that we make inferences, not deductions, but convince ourselves that the premises must be true, without bothering to put real information about likelihood into the reasoning. An induction is still a logical statement, but I like the idea of using probability to quantify it.
I agree that Holmes is neither deducing nor “inducing”, but I don’t like this concept of “abductive inference”.
It’s obvious that what we’re after is the best explanation of the data we’ve collected, so it’s never wrong to attempt to find the best explanation, but as advice, or as a description of how a rational agent proceeds, it’s as useless as the advice to win a game of football by scoring more goals than the opposing side.
Perhaps yes… but… I have found over time that paying attention to interesting but weird features of a domain leads interesting places. The tractability problems inherent to some computational models of bayesian reasoning makes me suspect that “something else” is being used as “the best that can be physically realized for now” to do whatever it is that brains do. When evolutionary processes produce a result it generally utilizes principles that are shockingly beautiful and simple once you see them.
I had not previously heard of the term “abductive reasoning” but catching terms like this is one of the reasons I love this community. The term appears to connect with something I was in a discussion about called “cogent confabulation”. (Thanks for the heads up, Jayson!)
The obvious thing that jumps out is that what Hecht-Neilson called “cogency” is strikingly similar to both Jayne’s police example and the example of Sherlock Holmes. I’m tempted to speculate that the same “architectural quirk” in human brains that supports this (whatever it turns out to be) may also be responsible (on the downside) for both the Prosecutor’s Fallacy and our notoriously crappy performance with Modus Tollens.
Given the inferential distance between me and the many handedhorror, this makes me think there is something clever to be said for whatever that quirk turns out to be. Maybe storing your “cause given evidence” conditional probabilities and your causal base rates all packed into a single number is useful for some reason? If I were to abduct a reason, it would be managing “salience” when trying to implement a practically focused behavior generating system that has historically been strongly resource limited. Its just a guess until I see evidence one way or the other… but that would be my “working hunch” until then :-)
I never thought about the connection between logic and probability before, though now it seems obvious. I’ve read a few introductory logic texts and deductive reasoning always seemed a bit pointless to me (in RL premises are usually inferred from something). -
To draw from a literary example, Sherlock Holmes use of the phrase “deduce” always seemed a bit deceptive. You can say “that color of dirt exists only in spot x in London. Therefore, that Londoner must have come in contact with spot x if I see that dirt on his trouser knee.” This is presented as a deduction, but really, the premises are induced and he assumes some things about how people travel.
It seems more likely that we make inferences, not deductions, but convince ourselves that the premises must be true, without bothering to put real information about likelihood into the reasoning. An induction is still a logical statement, but I like the idea of using probability to quantify it.
As far as I can tell, Holmes actually engages in, what Charles Sanders Peirce called, “abduction”. It is neither deduction nor induction.
I agree that Holmes is neither deducing nor “inducing”, but I don’t like this concept of “abductive inference”.
It’s obvious that what we’re after is the best explanation of the data we’ve collected, so it’s never wrong to attempt to find the best explanation, but as advice, or as a description of how a rational agent proceeds, it’s as useless as the advice to win a game of football by scoring more goals than the opposing side.
Perhaps yes… but… I have found over time that paying attention to interesting but weird features of a domain leads interesting places. The tractability problems inherent to some computational models of bayesian reasoning makes me suspect that “something else” is being used as “the best that can be physically realized for now” to do whatever it is that brains do. When evolutionary processes produce a result it generally utilizes principles that are shockingly beautiful and simple once you see them.
I had not previously heard of the term “abductive reasoning” but catching terms like this is one of the reasons I love this community. The term appears to connect with something I was in a discussion about called “cogent confabulation”. (Thanks for the heads up, Jayson!)
The obvious thing that jumps out is that what Hecht-Neilson called “cogency” is strikingly similar to both Jayne’s police example and the example of Sherlock Holmes. I’m tempted to speculate that the same “architectural quirk” in human brains that supports this (whatever it turns out to be) may also be responsible (on the downside) for both the Prosecutor’s Fallacy and our notoriously crappy performance with Modus Tollens.
Given the inferential distance between me and the many handed horror, this makes me think there is something clever to be said for whatever that quirk turns out to be. Maybe storing your “cause given evidence” conditional probabilities and your causal base rates all packed into a single number is useful for some reason? If I were to abduct a reason, it would be managing “salience” when trying to implement a practically focused behavior generating system that has historically been strongly resource limited. Its just a guess until I see evidence one way or the other… but that would be my “working hunch” until then :-)