Clarifying the Process of Abduction and

Understanding “Inductive” Generalization

The aim of this paper is to support Peirce’s understanding of abduction as a third form of logical inference that is separate and distinct from both deduction and induction.  To do this, I will draw heavily upon the work of Josephson and Josephson (1996).  While attacking their suggestion that abduction can be best understood as an inference to the best explanation (IBE), with an argument that parallels the work of Minnameier (2004), I do want to support the Josephsons’ suggestion that inductive generalizations are abductive inferences, while inductive projections are not.

Traditional Paper Submission

           

Peirce on Abduction

            Throughout his work, Peirce worked to establish a third form of logical inference to support deduction and induction.  Peirce called this third form retroduction or abduction, and described it as a type of hypothesis formation (CP, 7.202).  Not only is abduction the only type of logical inference that is ampliative (in that it adds new information to the “proof”), but abduction is also the logical inference of discovery, in that it works to explain the facts before us.  Peirce describes his “logical triad” as,

Abduction is the process of forming an explanatory hypothesis.  It is the only logical operation which introduces any new idea; for induction does nothing but determine a value, and deduction merely evolves the necessary consequences of a pure hypothesis.

Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be (CP, 5.171.)

 

With the role for the two “traditional” elements of logic in place, Peirce also describes abduction in a syllogistic form:

The surprising fact C is observed.

But if A were true, C would be a matter of course.

Hence there is some reason to suspect that A is true (CP, 5.189, italics added).

 

It is critically important to note that for deductive logic, this argument is an affirmation of the consequent, and is invalid.  However, this is a natural form of abductive logic.  Whatever “surprising fact C” may be, novel information, unexpected scientific data, etc., there is new information that requires an explanation. 

For Peirce, abduction works from these surprising facts to determine a possible, plausible explanation.  Furthermore, Peirce stresses the fact that the logic of abduction is fallible – abductive inferences, like induction, can, and do, lead us to the wrong result (CP, 5.189, 5.197, 6.532).  However, as a part of the triad, abduction is able to correct itself, once it is investigated by deduction and tested by induction (CP 5.574).  Because of this, we should never take the conclusion of an abductive inference to be a fact in and of itself until it is tested.  Until that point “abduction commits us to nothing…it merely causes a hypothesis to be set down upon our docket of cases to be tried” (CP, 5.602).  Furthermore, by hypothesis, Peirce does not just mean scientific hypotheses.  Abduction certainly includes the more formalized, conscious cognitive process of deliberately searching for an explanation to a set of particular facts; however, abduction is also a logical inference used in everyday life from crude hypotheses (his Catholic priest example) to perceptual judgments (understanding the information that we receive from our senses) (CP 7.202, 5.180, 5.184). 

In using this broader definition of hypothesis, abduction becomes the process of generating a hypothesis, or discovering some possible explanation for the facts at hand.  In the case of perceptual judgments, we are presented with a wave of incoming sense-data: we are able to sense the color, texture and shape of the wood, the hardware, the door handle, but until we are able to create some explanation for why we are seeing all of these separate elements in one discrete package of visual input, we are not able perceive a door as a door.  It is abduction that provides fragmentary elements of “everyday life” with a unified character, and it is the ampliative nature of abductive inference that allows us to collect separate sensory experiences under one simple perception.  This allows Peirce to call perceptual judgments an “extreme case of abductive inferences” (CP, 5.180).  Furthermore, Peirce notes that the perceptual judgment only differs from crude or scientific abduction in the tenacity with which we hold onto the conclusion of the inference.  For instance, it is a matter of course that we test any and all scientific conclusions.  However, very few of us ever doubt our perceptions, even under extreme duress (CP 5.180).

 

The Josephson Artificial Intelligence Project, and Abduction as IBE

Josephson and Josephson suggest a refinement of the Peircean definition of abduction.  The Josephsons’ understand abduction to be the same as the inference to the best explanation.  As a matter of course they simply define abduction as,

Abduction, or inference to the best explanation, is a form of inference that goes from data describing something to a hypothesis that best explains or accounts for the data (Josephson, 5).

 

Furthermore they suggest that a successful abduction uses a body of data to provide a hypothesis, or more particularly an explanation, for that data, “better than the explanatory alternatives” (Josephson, 5).  Furthermore, like Peirce, the Josephsons provide a syllogistic form for abductive inferences:

D is a collection of data (facts, observations, givens).

H explains D (would if true, explain D).

No other hypothesis can explain D as well as H does.

Therefore, H is probably true (Josephson, 5).

 

This account provides two significant changes from the traditional understanding provided by Peirce: 1) abduction changes from an inference that provides any hypothesis to one that provides the “best” hypothesis, and 2) abduction is now fundamentally responsible for providing an explanatory hypothesis. 

            The Josephsons suggest that these modifications are necessary to the (correct) understanding of abduction and further support their claims by offering pragmatic concerns for the selection or adoption of hypotheses.  They suggest that the form of the argument, albeit in the particular form of diagnostic tool, follows five main steps,

  1. There is a finding that must be explained.
  2. The finding may be explained in a number of ways.
  3. Some of these ways are judged to be implausible because expected consequences do not appear.
  4. Some ways are judged to be irrelevant or implausible because they do not explain important findings.
  5. Of the plausible explanations that remain, the best is the conclusion (Josephson, 10).

 

These five steps suggest a pattern that is natural to all abductive inferences.  First and foremost, like Peirce, they suggest that abduction works to explain some novel occurrence of data, then a series hypotheses are generated that explain these data.  Out of all the possible hypotheses, one “best” hypothesis is selected as the tentative conclusion.  However, because of this particular characterization of the argument, the Josephsons suggest that abduction is best understood as the “whole process of generation, criticism, and acceptance of explanatory hypotheses,” opposed to being merely restricted to the “hypothesis generation phase” (Josephson, 8).  They support this claim on two pragmatic concerns: 1) that most abductive inferences are complicated or compound hypotheses and 2) it seems that separating the generation and selection of hypotheses would drastically alter and therefore increase the computational demands of abductive inference.  Both of these concerns are inter-related.  If it were true that most abductions, including “everyday” abductions, are compound hypotheses, then the number of possible, reasonable explanations for a set of data vastly increases.  Furthermore, according to the Josephsons, by separating the abductive process into two ‘phases’ (one for hypothesis generation, another for selection and testing) there must be some “preselection phase” that eliminates improbable or junk theories from even the most basic levels of consideration (Josephson, 9).  Even if the preselection phase is minimally demanding on a cognitive level, the sheer number of hypotheses that must be eliminated must create a considerable burden for cognitive resources.  When the number of potential hypotheses escalates due to a single compound hypothesis, the maxim of “everything counts in large numbers” must swamp all available cognitive resources and, “reasonably sized problems would take cosmological amounts of time” (Josephson, 9).

            The above concerns along with the Josephsons’ form of the abductive inference do find some purchase in the canon surrounding abduction.  Not only does Peirce suggest some notions like economy in the process of selecting the hypothesis, but also in the hypothesis itself.  Peirce notes that

In those subjects, we may, with great confidence, follow the rule that one of all admissible hypotheses which seems the simplest to the human mind ought to be take up for examination first…This rule has another advantage, which is that the simplest hypotheses are those of which the consequences are most readily deduced and compared with observation; so that, if they are wrong, they can be eliminated at less expense than any others (CP, 6.532).

 

First and foremost this passage does appear to suggest that the process of abduction does indeed include not only hypothesis formation but also the process of testing and selection (to some extent) in the abductive inference.  This is important to note, simply because Peirce frequently suggests that abduction is a formally distinct process from deduction and induction which are later used to determine the (logical) consequences of the hypothesis and test those consequences versus the world.  Furthermore, Pierce acknowledges that there is an inherent need for both cognitive and material economy during the selection and testing of a hypothesis.  Here, good hypotheses are those that appear simple in and of themselves.  If the hypothesis proves successful, it allows us to explain a large body of data with a minimal number of theories while committing the theory to the fewest number of necessarily testable consequences.  This produces a two-fold benefit: by default, time, energy, and resources are saved by having to conduct as few tests as possible to confirm the theory (which allows us to eliminate junk hypotheses rapidly and quickly move onto other viable theories), and the theory is widely applicable, saving the need to generate and test other hypotheses in the future.  This directly relates to the Josephsons’ six rules for evaluating abductive inferences,

  1. how decisively does H surpasses the alternatives.
  2. how good H is all by itself.
  3. judgments of the reliability of the data.
  4. how much confidence there is that all plausible explanations have been considered.
  5. pragmatic considerations including the costs of being wrong and the benefits of being right.
  6. how strong the need is to come to a conclusion at all (Josephson, 14).

 

Criterion 1, 2, and 5 are directly addressed by Peirce above.  The remaining criterion are the more interesting suggestions.  The Josephsons echo Peirce’s earlier statements that abduction, at best, is considered a fallible process.  Within the Peircean logical triad of abduction, deduction, and induction, all three types of logical inference are required for the acceptance of a hypothesis.  If faulty or irrelevant information is used as the basis for the generation of a (tentative) hypothesis, then it becomes highly probable that a faulty or bad abduction will occur (this is a classic case “garbage in, garbage out”).  While this part of the Josephsons’ suggested additions do not directly relate to the particulars of Peirce’s writing, they do make excellent “common sense” suggestions that one ought to consider when evaluating the quality of an abductive inference.

Minnameier’s attack on abduction as IBE

            Gerhard Minnameier directly attacks the understanding of abduction as IBE, and challenges the Josephsons’ conception of the abductive process. Minnameier’s and the Josephsons’ work, however, talk past each other in some respects. Minnameier states,

Peirce characterizes abduction as the only type of inference that is creative in the sense that it leads to new knowledge, especially to (possible) theoretical explanations of surprising facts.  As opposed to this, IBE is about the acceptance (or rejection) of already established explanatory suggestions.  Thus while abduction marks the process of generating theories, IBE concerns their evaluation (Minnameier, 75).

 

This suggests that Minnameier not only wants to consider abduction as strictly generating hypotheses, but also that the process must be discrete enough to exclude the evaluation of the potential theories.  The second condition of the previous statement is critically important, especially as Minnameier continues to discuss the place of induction in the triad of logical inference.

Minnameier suggests that the “mature” Peirce quickly changes his opinion of induction and this form of inference designates the evaluation of abduction, or more specifically, of hypotheses.  For Minnameier, Peircean induction is “only about evaluating the suggested hypothesis” and therefore, “this establishes an entirely new role for induction, because now it is seen as an inference from theory to facts, rather than from facts to theory” (Minnameier, 79).  Furthermore, Minnameier quotes the Collected Papers of Charles Sanders Peirce to drive a wedge between the process of hypothesis formation and evaluation; here we use induction to determine,

whether the hypothesis should be regarded as proved, or as well on the way toward being proved, or as unworthy of further attention, or whether it ought to receive a definite modification in the light of the new experiments and be inductively reexamined ab ovo, or where finally, that while not true it probably resents some analogy to the truth, and that the results of the induction may help to suggest a better hypothesis (Minnameier, 80; CP, 2.759)

 

These three statements, plus his later comments that Peirce understands induction as “forming habits or warranted expectations about the future,” and “the projection of certain features from one entity to another... what are projected are the features (qualities) implied by the theory” to data observed in the future, suggest that induction is strictly responsible for the distinct process of evaluating the hypothesis created by abduction (Minnameier, 80, 82). 

            It seems that Minnameier has a strong argument against the case of abduction as IBE.  However, as he notes none of the logical inferences are truly meant to stand alone, they exist as part of Peirce’s logical triad.  Abduction first generates a hypothesis, deduction traces out the necessary conclusions of the theory, and these consequences are tested and evaluated via induction.  It is important to note, as Minnameier does, that the process simply does not “end” with the inductive test, all three forms of logical inference establish a “feedback” and “feedforward” loop (Minnameier, 76, 80).  While there may be distinct differences between each step, and each logical inference has its own “niche” and unique task, there are no clear distinctions or necessary stages in “real world” practices of hypothesis formation and selection.  While abduction is certainly a viable form of logical inference, it does not (and was never meant) to provide a serious “logic of discovery.”  Peirce, himself, notes this as he frequently uses romantic descriptions of abduction as il lume naturale or even as an instinctual, natural “function” of human nature (CP, 1.80, 5.171-5.174).

Minnameier does have some valid criticisms of the basic character of the Josephsons’ work.  However, these criticisms do not seem to be damning. Given the above distinction between the states of logical inference, the Josephsons seem to blur the lines between the purely creative aspects of abduction and the whole complimentary, recursive nature of the logical triad.  At best, we ought to caution the Josephsons against being too loose with their language and adopting a liberal understanding of boundaries between hypothesis formation and selection.  At worst, it seems as if the Josephsons’ project of trying to create an abductive machine, or an AI that perform abductive inferences, has forced them to adopt a peculiar understanding of abductive inference.  From this perspective, the Josephsons are guilty of trying to force abduction to do too much, and are attempting to subsume both induction and deduction under abduction, thus giving abduction too high of a priority.  In this light, abduction becomes the capital mechanism of logical inference, while the other two forms work only to evaluate and support abductive arguments.  Clearly, this is not the case, as one can perform either for their own sake, and to their own ends without the pretense of hypothesis selection.  I think it is more likely, given the particular stress they place on cognitive resources, that the Josephsons are merely trying too hard to accelerate and encapsulate the abductive process to make it possible for machine intelligence(s).  To be perfectly clear, abduction and inference to the best explanation are not identical.  However, they are closely related.  It may seem reasonable in some cases to use the term ‘abduction’ in the loose sense, like the Josephsons, to designate the whole process of hypothesis formation and selection.  This does not designate Peirce’s original use of the term, and for good reason.  Peirce intended the term to focus strictly on the creative and ampliative aspects of hypothesis formation, and later clearly discusses the distinct role that both deduction and induction play in the selection of a hypothesis.  As it stands, it is best to leave the term ‘abduction’ to this strict usage and abandon the epistemology that comes to the fore with the idea of IBE.  It is, perhaps, unfortunate that Peirce uses the terms ‘abduction’ and ‘retroduction’ interchangeably; otherwise, we would be able to simply keep abduction as an “inference to a (or any) explanation” and allow ‘retroduction’ to refer to the whole process of formation and selection.

The success of the Josephsons

With these points in mind, Josephsons’ suggestion that inductive generalization is a veiled form of abduction still remains a positive contribution.  The Josephsons characterize inductive generalization in its syllogistic form as,

All observed A’s are B’s.

            Therefore, all A’s are B’s (Josephson, 19).

 

They note that under this form, the inductive generalization is clearly ampliative; the inference moves from a statement about observed A’s and B’s to all instances of those entities. Furthermore, they note that the traditional understanding of this syllogism as a pure inductive inference does not stand to provide an explanation of the premise on the observed state the world.  If we understand this purely as move towards a generalization of the facts, the conclusion does not provide a lasting explanation as to why these, or future, A’s are B’s (Josephson, 20, 21).  Under this construction, as an inductive argument, it is not quite clear what work the generalization is trying to accomplish.  There are, however, reasons to suggest that the generalization is, in fact, an abductive argument and not inductive.  As per both Minnameier’s and the Josephsons’ descriptions above, the argument appears to be abductive: it is ampliative, creates new information, and the conclusion seeks to explain the premise (all observed A’s are B’s, because all A’s are B’s).  Furthermore, it maintains the form of an abductive inference because it is moving from observed facts about the world towards a theory, unlike inductive arguments that move from the theory to facts.  

            Finally, as a means of clarification and conclusion, if we reject the Josephsons’ suggestion and take abduction in the strict sense, as an ampliative process of hypothesis formation, we are able to see how see how inductive projection cannot be an abductive inference and observe the whole process of hypothesis formation and selection in Peircean logical triad.  Inductive projection, described below in its syllogistic form, is a predictive inference that moves from the (tentatively) accepted hypothesis towards data to be observed in the future

All A’s are B’s.

            The next observed A will be a B (Josephson, 22).

 

Again, the Josephsons, Minnameier, and Peirce would agree the inference must hold the form of an inductive argument, despite the fact that it appears to draw novel information into the conclusion.  It is important to note that while it may appear ampliative, the premise in the argument actually explains the conclusion (The next observed A will be a B because All A’s are B’s).  Furthermore, while the argument may also appear deductive, i.e. the decomposition of a universal, the inference cannot remain deductive and retain its predictive power. All three of the logical inferences interact to create an inductive projection and create Peirce’s recursive triad in this rough outline of process of hypothesis formation, deduction, and the inductive selection (and/or confirmation) of the hypothesis,

All observed A’s are B’s.

          Therefore, all A’s are B’s

Abduction (Inductive Generalization)

All A’s are B’s.

          Therefore, all observed A’s are B’s.

Deduction

All observed A’s are B’s.

          Therefore, the next observed A will be a B.

Induction (Inductive Projection)

 

The process begins with an abductive inference that explains the observed phenomena, continues to determine the necessary conclusion of the explanatory hypothesis, and culminates in formulation of testable statement that will help to determine the truth of the original hypothesis.  This process of hypothesis formation and selection (or confirmation) is markedly different than the original process of abduction that Pierce describes.  While I must disagree with the Josephsons on this point, they do provide helpful insights into discrete aspects of abduction, the Peircean logical triad, and the nature of inductive generalization. 

 

Works Cited:

Josephson, John, and Susan Josephson (1996).  Abductive Inference, Cambridge

University Press.

Minnameier, Gerhard (2004).  “Peirce-suit of Truth,” Erkennis, 60, pages 75-105.

Peirce, C.S. (1958).  The Collected Works of Charles Sanders Peirce, Harvard University

Press.