Abductive reasoning

Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference which starts with an observation or set of observations then seeks to find the simplest and most likely explanation for the observations. This process, unlike deductive reasoning, yields a plausible conclusion but does not positively verify it. Abductive conclusions are thus qualified as having a remnant of uncertainty or doubt, which is expressed in retreat terms such as 'best available' or 'most likely.' One can understand abductive reasoning as inference to the best explanation, although not all usages of the terms abduction and inference to the best explanation are exactly equivalent.Looking out my window this lovely spring morning, I see an azalea in full bloom. No, no! I don't see that; though that is the only way I can describe what I see. That is a proposition, a sentence, a fact; but what I perceive is not proposition, sentence, fact, but only an image, which I make intelligible in part by means of a statement of fact. This statement is abstract; but what I see is concrete. I perform an abduction when I so much as express in a sentence anything I see. The truth is that the whole fabric of our knowledge is one matted felt of pure hypothesis confirmed and refined by induction. Not the smallest advance can be made in knowledge beyond the stage of vacant staring, without making an abduction at every step. M is P S is M ∴ {displaystyle herefore } S is P. S′, S′′, S′′′, &c. are taken at random as M's; S′, S′′, S′′′, &c. are P: ∴ {displaystyle herefore } Any M is probably P.Any M is, for instance, P′, P′′, P′′′, &c.; S is P′, P′′, P′′′, &c.: ∴ {displaystyle herefore } S is probably M.Rule: All the beans from this bag are white. Case: These beans are from this bag. ∴ {displaystyle herefore } Result: These beans are white.Case: These beans are from this bag. Result: These beans are white. ∴ {displaystyle herefore } Rule: All the beans from this bag are white.Rule: All the beans from this bag are white. Result: These beans are white. ∴ {displaystyle herefore } Case: These beans are from this bag.The surprising fact, C, is observed; Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.It allows any flight of imagination, provided this imagination ultimately alights upon a possible practical effect; and thus many hypotheses may seem at first glance to be excluded by the pragmatical maxim that are not really so excluded.Methodeutic has a special interest in Abduction, or the inference which starts a scientific hypothesis. For it is not sufficient that a hypothesis should be a justifiable one. Any hypothesis which explains the facts is justified critically. But among justifiable hypotheses we have to select that one which is suitable for being tested by experiment..... What is good abduction? What should an explanatory hypothesis be to be worthy to rank as a hypothesis? Of course, it must explain the facts. But what other conditions ought it to fulfill to be good? .... Any hypothesis, therefore, may be admissible, in the absence of any special reasons to the contrary, provided it be capable of experimental verification, and only insofar as it is capable of such verification. This is approximately the doctrine of pragmatism.Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine with reference to the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of heuristic and is the first question of heuristic, is to be governed by economical considerations.The mind seeks to bring the facts, as modified by the new discovery, into order; that is, to form a general conception embracing them. In some cases, it does this by an act of generalization. In other cases, no new law is suggested, but only a peculiar state of facts that will 'explain' the surprising phenomenon; and a law already known is recognized as applicable to the suggested hypothesis, so that the phenomenon, under that assumption, would not be surprising, but quite likely, or even would be a necessary result. This synthesis suggesting a new conception or hypothesis, is the Abduction.Thus, twenty skillful hypotheses will ascertain what 200,000 stupid ones might fail to do. The secret of the business lies in the caution which breaks a hypothesis up into its smallest logical components, and only risks one of them at a time. Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference which starts with an observation or set of observations then seeks to find the simplest and most likely explanation for the observations. This process, unlike deductive reasoning, yields a plausible conclusion but does not positively verify it. Abductive conclusions are thus qualified as having a remnant of uncertainty or doubt, which is expressed in retreat terms such as 'best available' or 'most likely.' One can understand abductive reasoning as inference to the best explanation, although not all usages of the terms abduction and inference to the best explanation are exactly equivalent. In the 1990s, as computing power grew, the fields of law, computer science, and artificial intelligence research spurred renewed interest in the subject of abduction.Diagnostic expert systems frequently employ abduction. Deductive reasoning allows deriving b {displaystyle b} from a {displaystyle a} only where b {displaystyle b} is formal logical consequence of a {displaystyle a} . In other words, deduction derives the consequences of the assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. For example, given that 'Wikis can be edited by anyone' ( a 1 {displaystyle a_{1}} ) and 'Wikipedia is a wiki' ( a 2 {displaystyle a_{2}} ), it follows that 'Wikipedia can be edited by anyone' ( b {displaystyle b} ). Inductive reasoning allows inferring b {displaystyle b} from a {displaystyle a} , where b {displaystyle b} does not follow necessarily from a {displaystyle a} . a {displaystyle a} might give us very good reason to accept b {displaystyle b} , but it does not ensure b {displaystyle b} . For example, if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. (Indeed, it turns out that some swans are black.) Abductive reasoning allows inferring a {displaystyle a} as an explanation of b {displaystyle b} . As a result of this inference, abduction allows the precondition a {displaystyle a} to be abduced from the consequence b {displaystyle b} . Deductive reasoning and abductive reasoning thus differ in the direction in which a rule like ' a {displaystyle a} entails b {displaystyle b} ' is used for inference. As such, abduction is formally equivalent to the logical fallacy of affirming the consequent (or Post hoc ergo propter hoc) because of multiple possible explanations for b {displaystyle b} . For example, in a billiard game, after glancing and seeing the eight ball moving towards us, we may abduce that the cue ball struck the eight ball. The strike of the cue ball would account for the movement of the eight ball. It serves as a hypothesis that explains our observation. Given the many possible explanations for the movement of the eight ball, our abduction does not leave us certain that the cue ball in fact struck the eight ball, but our abduction, still useful, can serve to orient us in our surroundings. Despite many possible explanations for any physical process that we observe, we tend to abduce a single explanation (or a few explanations) for this process in the expectation that we can better orient ourselves in our surroundings and disregard some possibilities. Properly used, abductive reasoning can be a useful source of priors in Bayesian statistics. In logic, explanation is accomplished through the use of a logical theory T {displaystyle T} representing a domain and a set of observations O {displaystyle O} . Abduction is the process of deriving a set of explanations of O {displaystyle O} according to T {displaystyle T} and picking out one of those explanations. For E {displaystyle E} to be an explanation of O {displaystyle O} according to T {displaystyle T} , it should satisfy two conditions: In formal logic, O {displaystyle O} and E {displaystyle E} are assumed to be sets of literals. The two conditions for E {displaystyle E} being an explanation of O {displaystyle O} according to theory T {displaystyle T} are formalized as: Among the possible explanations E {displaystyle E} satisfying these two conditions, some other condition of minimality is usually imposed to avoid irrelevant facts (not contributing to the entailment of O {displaystyle O} ) being included in the explanations. Abduction is then the process that picks out some member of E {displaystyle E} . Criteria for picking out a member representing 'the best' explanation include the simplicity, the prior probability, or the explanatory power of the explanation.