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The types of reasoning: 1. Deduction - given premises and inferential rules, produces conclusions; as certain as possible. 2. Induction - given premises and c

The types of reasoning: 1. Deduction - given premises and inferential rules, produces conclusions; as certain as possible. 2. Induction - given premises and conclusions, produces inferential rules; statistically probable, but a single counterfactual observation means throwing out the whole thing (e.g. black swans). 3. Abduction - given conclusions and inferential rules, produces premises; no guarantee of certainty. Any time we retrospectively tell a story of how something came to be, that we did not immediately observe, we're applying abductive reasoning. It relies on the same inferential rules as deduction and induction, but applied in reverse.

riedel 4y ago
Thanks, never thought about it this way: It seems like the NP of reasoning. If you know the solution everything seems much easier.
michael_j_ward 4y ago
For others like me that wondered "Wait is proof by induction not induction?" > Although its name may suggest otherwise, mathematical induction should not be confused with inductive reasoning as used in philosophy (see Problem of induction). The mathematical method examines infinitely many cases to prove a general statement, but does so by a finite chain of deductive reasoning involving the variable n, which can take infinitely many values. https://en.wikipedia.org/wiki/Mathematical_induction https://en.wikipedia.org/wiki/Mathematical_induction
- ebingdom 4y ago
  I think there might be a loose connection. When you want to prove something using mathematical induction, you must come up with an "induction hypothesis". This requires cleverness which could possibly be described as the product of inductive reasoning (in the philosophical sense). Essentially it amounts to finding a general principle that can be specialized to prove each of the inductive steps. The main difference to me is that, with inductive reasoning (in the philosophical sense), you converge on a general principle but it might be wrong—it is only probable. Mathematical induction is the tool needed to close the gap—to turn a hypothesis which could be wrong into a bulletproof mathematical theorem. Of course, if your induction hypothesis didn't turn out to be right, you won't be able to complete the proof. I use the Coq theorem prover to write induction proofs all the time, and often you have to try out different induction hypotheses until you get one that finally works. The process my brain goes through to come up with these induction hypotheses feels like "inductive reasoning" in the philosophical sense as I understand it.
  - routerl 4y ago
    Yeah, I think you nailed the reason why they both use the same word: "mathematical induction" is deductive once the proof is finished, but coming up with the proof is absolutely an inductive process.
joe_the_user 4y ago
I was looking at that. It seems like induction and abduction are pretty much that same thing but framed differently. Abduction looks for the "simplest explanation: and induction uses statistical machinery to argue for an explanation, which, if you break down the statistical machinery, is something like the lowest entropy, the most efficient encoding of the data, the ... simplest explanation.
- jfarmer 4y ago
  The term "abduction" was coined by CS Peirce to describe the process that puts hypotheses on the docket to be tried by induction and deduction. Sometimes folks use it to mean something like "inference to best explanation", but that's not how Peirce meant it. > Proposals for hypotheses inundate us in an overwhelming flood, while the process of verification to which each one must be subjected before it can count as at all an item, even of likely knowledge, is so very costly in time, energy, and money -- and consequently in ideas which might have been had for that time, energy, and money, that Economy would override every other consideration even if there were any other serious considerations. In fact there are no others. For abduction commits us to nothing. It merely causes a hypothesis to be set down upon our docket of cases to be tried. — CS Peirce (Collected Papers §5.602)
  - routerl 4y ago
    > abduction commits us to nothing. It merely causes a hypothesis to be set down upon our docket of cases to be tried. This is the perfect phrasing. Consider the contrast with deduction: if I have a premise, P, there are many deductive inferential rules I could apply to that premise to produce a new truth. E.g. Given P, we can infer "not not P", and if we're also given "P implies Q" we can infer Q Abduction flips this on its head: we have Q. And Q could be just the double negation of a P we weren't given. Or it could be the consequence of "P implies Q". There's really no way to know with certainty. This is forensics. It's exactly the reasoning used in courtrooms: from the evidence (or "consequences"), we need to use science and logic to figure out how we got there (i.e. what were the antecedents). This is why the most famous fictional user of "abduction" is Sherlock Holmes. But really it's what every forensic investigator (including a detective) is doing. Abduction is most common in judicial settings (i.e. when we are trying to assign blame).
adrian_b 4y ago
While the name "abduction" has been chosen to resemble the traditional terms "deduction" and "induction", the name does not make sense. The name for this kind of reasoning should suggest a reverse direction when compared to "deduction", but "abduction" has the same direction as "deduction". The preposition "ab" is related to the English "off" and "of" and it can usually be translated by "from". The preposition "de" means the same thing as "ab" (which is why in most Romance languages, like French, "de" corresponds to English "of"), except that it suggests a vertical movement from up towards down, while "ab" suggests a horizontal movement. I do not know which might have been a better word, maybe they should just have stuck with "reverse deduction", because "reduction" is widely used with other meanings, or maybe they could have used "adduction", which has an opposite direction to "abduction" ("ad" corresponds to English "at"). The names "deduction" and "abduction" make grammatical sense when their direct objects are the premises (i.e. the action is "lead from premises"), while the name "adduction" makes grammatical sense when the direct objects of this action are the conclusions (i.e. the action is "lead at conclusions").
- routerl 4y ago
  IIRC the original English-language author who coined the term (C. S. Pearce) did use the verb form "adduce" as analogous to "deduce", so perhaps the original offending term, "abduction", is a poor back-formation.
- vkreso 4y ago
  From Latin abductiō (“robbing; abduction”), from abdūcō (“take or lead away”), from ab (“away”) + dūcō (“to lead”)[1]. Equivalent to abduct +‎ -ion. "Away" and "to lead" indead does imply a reverse direction. https://en.wiktionary.org/wiki/abduction https://en.wiktionary.org/wiki/abduction
  - adrian_b 4y ago
    It does not imply a reverse direction with respect to "deduction", which was the intention of the name, as used in the book discussed here. Both "abdūcō" and "dēdūcō" mean "lead away", except that the latter implies that the origin of the movement was somewhere above, i.e. the movement was descendant (the prefix "dē-" in descend is the same as the prefix "dē-" in deduce). "Abduction" implies a reverse direction only vs. "adduction", which means leading towards something, not away of something, like "abduction". The words "abduction" and "adduction" are frequently used to describe the movements of the human arms and legs, where the place that is the initial point of the movement for abduction or the final point of the movement for adduction is understood to be the median axis of the body. Thus there are abductor muscles and adductor muscles. (For example the abductor muscles of the thigh raise the thigh laterally, away from the other thigh, while the adductor muscles of the thigh bring the two thighs together.) "Induction" also implies the same direction of movement as "adduction", i.e. towards something, and opposite of deduction/abduction, but "induction" implies that the final point of the movement is inside the target.
russellbeattie 4y ago
Given this definition, abduction seems to me to be the source of many, many arguments between significant others. "I know you! You must think [some random opinion] because of [some past unrelated event]." In theory, you know the final opinion, and you know how your partner thinks, so you can logically guess what the source of the opinion is. So abduction is armchair psychology?
dandanua 4y ago
This doesn't make a lot of sense because when you're trying to infer premises from conclusions the conclusions are your current premises. And premises you're searching will be your conclusions.
qikInNdOutReply 4y ago
Its also a great part of the "success"stories. Somebodys subconcious drags up a great idea or he is plain lucky, and then gets ask about the how and why. And the subconcious puzzles together a semi-plausible story, to explain away the heuristics in the head working and the statistics washing an outliar to shore.
YeGoblynQueenne 4y ago
Sometimes I understand abduction, other times, not. I'm a bit of a fan of logic programming so I try to describe the three inference modes using definite clauses. Deduction: we go from facts (positive literals) and rules (definite clauses) to facts: swan(alice). white(X) ← swan(X). ---------------------------------- white(alice) (If we know that Alice is a swan, and all swans are white, we can infer that alice is white). Induction: we go from facts and rules to new rules: has_feathers(X) ← bird(X). bird(X) ← swan(X). ---------------------------------------------- has_feathers(X) ← swan(X). (If we know that all birds have feathers and all swans are birds, we can infer that all swans have feathers). Abduction: we go from facts and rules to _goals_ (negative literals): white(alice). white(X) ← swan(X). ----------------------------------- swan(alice) (If we know that Alice is white and all swans are white, we can infer that Alice is a swan). The last inference is of course not sound, as such - Alice could be white because she's a yogurt, say. But, if we operate under the assumption that only what we can prove is true (the so-called "closed world assumption") and the only rule we have about the concept of "white" is that "all swans are white", then the reasoning step becomes sound: the only way that we know for Alice to be white is for her to be a swan. What if we know multiple ways for an "X" to be white? For example, what if we have the rule "white(X) ← yogurt(X)"? Well then, we can make this inference also: white(alice). white(X) ← yogurt(X). ------------------------------------- yogurt(alice) And now we have two contradictory hypotheses about Alice: either she's a swan, or she's a yogurt^. We can resolve the contradiction when we learn more about yogurts and swans, and Alice. For example, if we have the information that Alice has feathers, we can figure out that Alice is a swan. The closed world assumption is the simplest way to handle uncertainty (or in any case there are no simpler methods). It is also non-monotonic, in that new facts and rules can change the truth value of facts inferred from a theory. Which is great because that way we 're not stuck with the conclusions of initial premises. Anyway, that's my logic-programmer's model for abduction. And it may be horribly wrong at places (my model for logic programming was horribly wrong the first ten years so...). _______________ ^Correction: Actually... alice can be a swan _and_ a yogurt. swan(alice) and yogurt(alice) are not contradictory unless we have some proof that they are.
- dreamcompiler 4y ago
brightball 4y ago
Any reason not to just call that “speculation”?

riedel 4y ago

Thanks, never thought about it this way: It seems like the NP of reasoning. If you know the solution everything seems much easier.

michael_j_ward 4y ago

For others like me that wondered "Wait is proof by induction not induction?" > Although its name may suggest otherwise, mathematical induction should not be confused with inductive reasoning as used in philosophy (see Problem of induction). The mathematical method examines infinitely many cases to prove a general statement, but does so by a finite chain of deductive reasoning involving the variable n, which can take infinitely many values. https://en.wikipedia.org/wiki/Mathematical_induction https://en.wikipedia.org/wiki/Mathematical_induction

ebingdom 4y ago
I think there might be a loose connection. When you want to prove something using mathematical induction, you must come up with an "induction hypothesis". This requires cleverness which could possibly be described as the product of inductive reasoning (in the philosophical sense). Essentially it amounts to finding a general principle that can be specialized to prove each of the inductive steps. The main difference to me is that, with inductive reasoning (in the philosophical sense), you converge on a general principle but it might be wrong—it is only probable. Mathematical induction is the tool needed to close the gap—to turn a hypothesis which could be wrong into a bulletproof mathematical theorem. Of course, if your induction hypothesis didn't turn out to be right, you won't be able to complete the proof. I use the Coq theorem prover to write induction proofs all the time, and often you have to try out different induction hypotheses until you get one that finally works. The process my brain goes through to come up with these induction hypotheses feels like "inductive reasoning" in the philosophical sense as I understand it.
- routerl 4y ago
  Yeah, I think you nailed the reason why they both use the same word: "mathematical induction" is deductive once the proof is finished, but coming up with the proof is absolutely an inductive process.

joe_the_user 4y ago

I was looking at that. It seems like induction and abduction are pretty much that same thing but framed differently. Abduction looks for the "simplest explanation: and induction uses statistical machinery to argue for an explanation, which, if you break down the statistical machinery, is something like the lowest entropy, the most efficient encoding of the data, the ... simplest explanation.

jfarmer 4y ago
The term "abduction" was coined by CS Peirce to describe the process that puts hypotheses on the docket to be tried by induction and deduction. Sometimes folks use it to mean something like "inference to best explanation", but that's not how Peirce meant it. > Proposals for hypotheses inundate us in an overwhelming flood, while the process of verification to which each one must be subjected before it can count as at all an item, even of likely knowledge, is so very costly in time, energy, and money -- and consequently in ideas which might have been had for that time, energy, and money, that Economy would override every other consideration even if there were any other serious considerations. In fact there are no others. For abduction commits us to nothing. It merely causes a hypothesis to be set down upon our docket of cases to be tried. — CS Peirce (Collected Papers §5.602)
- routerl 4y ago
  > abduction commits us to nothing. It merely causes a hypothesis to be set down upon our docket of cases to be tried. This is the perfect phrasing. Consider the contrast with deduction: if I have a premise, P, there are many deductive inferential rules I could apply to that premise to produce a new truth. E.g. Given P, we can infer "not not P", and if we're also given "P implies Q" we can infer Q Abduction flips this on its head: we have Q. And Q could be just the double negation of a P we weren't given. Or it could be the consequence of "P implies Q". There's really no way to know with certainty. This is forensics. It's exactly the reasoning used in courtrooms: from the evidence (or "consequences"), we need to use science and logic to figure out how we got there (i.e. what were the antecedents). This is why the most famous fictional user of "abduction" is Sherlock Holmes. But really it's what every forensic investigator (including a detective) is doing. Abduction is most common in judicial settings (i.e. when we are trying to assign blame).

adrian_b 4y ago

While the name "abduction" has been chosen to resemble the traditional terms "deduction" and "induction", the name does not make sense. The name for this kind of reasoning should suggest a reverse direction when compared to "deduction", but "abduction" has the same direction as "deduction". The preposition "ab" is related to the English "off" and "of" and it can usually be translated by "from". The preposition "de" means the same thing as "ab" (which is why in most Romance languages, like French, "de" corresponds to English "of"), except that it suggests a vertical movement from up towards down, while "ab" suggests a horizontal movement. I do not know which might have been a better word, maybe they should just have stuck with "reverse deduction", because "reduction" is widely used with other meanings, or maybe they could have used "adduction", which has an opposite direction to "abduction" ("ad" corresponds to English "at"). The names "deduction" and "abduction" make grammatical sense when their direct objects are the premises (i.e. the action is "lead from premises"), while the name "adduction" makes grammatical sense when the direct objects of this action are the conclusions (i.e. the action is "lead at conclusions").

routerl 4y ago
IIRC the original English-language author who coined the term (C. S. Pearce) did use the verb form "adduce" as analogous to "deduce", so perhaps the original offending term, "abduction", is a poor back-formation.
vkreso 4y ago
From Latin abductiō (“robbing; abduction”), from abdūcō (“take or lead away”), from ab (“away”) + dūcō (“to lead”)[1]. Equivalent to abduct +‎ -ion. "Away" and "to lead" indead does imply a reverse direction. https://en.wiktionary.org/wiki/abduction https://en.wiktionary.org/wiki/abduction
- adrian_b 4y ago
  It does not imply a reverse direction with respect to "deduction", which was the intention of the name, as used in the book discussed here. Both "abdūcō" and "dēdūcō" mean "lead away", except that the latter implies that the origin of the movement was somewhere above, i.e. the movement was descendant (the prefix "dē-" in descend is the same as the prefix "dē-" in deduce). "Abduction" implies a reverse direction only vs. "adduction", which means leading towards something, not away of something, like "abduction". The words "abduction" and "adduction" are frequently used to describe the movements of the human arms and legs, where the place that is the initial point of the movement for abduction or the final point of the movement for adduction is understood to be the median axis of the body. Thus there are abductor muscles and adductor muscles. (For example the abductor muscles of the thigh raise the thigh laterally, away from the other thigh, while the adductor muscles of the thigh bring the two thighs together.) "Induction" also implies the same direction of movement as "adduction", i.e. towards something, and opposite of deduction/abduction, but "induction" implies that the final point of the movement is inside the target.

russellbeattie 4y ago

Given this definition, abduction seems to me to be the source of many, many arguments between significant others. "I know you! You must think [some random opinion] because of [some past unrelated event]." In theory, you know the final opinion, and you know how your partner thinks, so you can logically guess what the source of the opinion is. So abduction is armchair psychology?

dandanua 4y ago

This doesn't make a lot of sense because when you're trying to infer premises from conclusions the conclusions are your current premises. And premises you're searching will be your conclusions.

qikInNdOutReply 4y ago

Its also a great part of the "success"stories. Somebodys subconcious drags up a great idea or he is plain lucky, and then gets ask about the how and why. And the subconcious puzzles together a semi-plausible story, to explain away the heuristics in the head working and the statistics washing an outliar to shore.

YeGoblynQueenne 4y ago

Sometimes I understand abduction, other times, not. I'm a bit of a fan of logic programming so I try to describe the three inference modes using definite clauses. Deduction: we go from facts (positive literals) and rules (definite clauses) to facts: swan(alice). white(X) ← swan(X). ---------------------------------- white(alice) (If we know that Alice is a swan, and all swans are white, we can infer that alice is white). Induction: we go from facts and rules to new rules: has_feathers(X) ← bird(X). bird(X) ← swan(X). ---------------------------------------------- has_feathers(X) ← swan(X). (If we know that all birds have feathers and all swans are birds, we can infer that all swans have feathers). Abduction: we go from facts and rules to _goals_ (negative literals): white(alice). white(X) ← swan(X). ----------------------------------- swan(alice) (If we know that Alice is white and all swans are white, we can infer that Alice is a swan). The last inference is of course not sound, as such - Alice could be white because she's a yogurt, say. But, if we operate under the assumption that only what we can prove is true (the so-called "closed world assumption") and the only rule we have about the concept of "white" is that "all swans are white", then the reasoning step becomes sound: the only way that we know for Alice to be white is for her to be a swan. What if we know multiple ways for an "X" to be white? For example, what if we have the rule "white(X) ← yogurt(X)"? Well then, we can make this inference also: white(alice). white(X) ← yogurt(X). ------------------------------------- yogurt(alice) And now we have two contradictory hypotheses about Alice: either she's a swan, or she's a yogurt^. We can resolve the contradiction when we learn more about yogurts and swans, and Alice. For example, if we have the information that Alice has feathers, we can figure out that Alice is a swan. The closed world assumption is the simplest way to handle uncertainty (or in any case there are no simpler methods). It is also non-monotonic, in that new facts and rules can change the truth value of facts inferred from a theory. Which is great because that way we 're not stuck with the conclusions of initial premises. Anyway, that's my logic-programmer's model for abduction. And it may be horribly wrong at places (my model for logic programming was horribly wrong the first ten years so...). _______________ ^Correction: Actually... alice can be a swan _and_ a yogurt. swan(alice) and yogurt(alice) are not contradictory unless we have some proof that they are.

dreamcompiler 4y ago

brightball 4y ago

Any reason not to just call that “speculation”?