Inquiry Driven Systems : Part 3

---

• Contents • Part 1 • Part 2 • Part 3 • Appendices • References • Document History •

---

Editing Note. This Part is somewhat draftier than the previous two.

Part 3.

3.1. Outlook of the Project : All Ways Lead to Inquiry

I am using the word inquiry in a way that is roughly synonymous with the term scientific method. Use of inquiry is more convenient, aside from being the shorter term, because of the following advantages:

1. It allows one to broaden the scope of investigation to include any form of proceeding toward knowledge that merely aims at such a method.
2. It allows one to finesse the issue, for the time being, of how much "method" there is in science.

This Subdivision and the next deal with opposite aspects of inquiry. In many ways it might have been better to interlace the opposing points of comparison, taking them up in a parallel fashion, but this plan was judged to be too distracting for a first approach. In other ways, the negative sides of each topic are prior in point of time to the positive sides of the issue, but sensible people like to see the light at the end of the tunnel before they trouble themselves with the obscurities of the intervening journey. Thus, this Subdivision of the text emphasizes the positive features of inquiry and the positive qualities of its objective, while the next Subdivision is reserved to examine the negative aspects of each question.

In the order of nature, the absence of a feature naturally precedes the full development of its presence. In the order of discussion, however, positive terms must be proposed if it is desired to say anything at all.

The discussion in this Subdivision is placed to serve a primer, declaring at least the names of enough positive concepts to propose addressing the negative conditions of knowledge in which inquiry necessarily starts.

In this Subdivision I stand back once again from the problem of inquiry and allow myself take a more distant view of the subject, settling into what I think is a comfortable and a natural account of inquiry, the best that I have at my command, and attending to the task of describing its positive features in a positive light. I present my personal view of inquiry as I currently understand it, without stopping to justify every concept in detail or to examine every objection that might be made to this view. In the next Subdivision I discuss a few of the more obvious problems that stand in the way of this view and I try to remove a few of the more tractable obscurities that appear ready to be cleared up. The fact that I treat them as my "personal insights" does not mean that all of these ideas about inquiry originate with me, but only that I have come to adopt them for my personal use. There will be many occasions, the next time that I go over this ground, to point out the sources of these ideas, so far as I know them.

The reader may take my apology for this style of presentation to be implicit in its dogmatic character. It is done this way in a first approach for the sake of avoiding an immense number of distractions, each of which is not being slighted but demands to be addressed in its own good time. I want to convey the general drift of my current model, however conjectural, naive, uncritical, and unreflective it may seem.

3.1.1. The Matrix of Inquiry

Thus when mothers have children suffering from sleeplessness, and want to lull them to rest, the treatment they apply is to give them, not quiet, but motion, for they rock them constantly in their arms; and instead of silence, they use a kind of crooning noise; and thus they literally cast a spell upon the children (like the victims of a Bacchic frenzy) by employing the combined movements of dance and song as a remedy.

(Plato, Laws, VII, 790D).

Try as I might, I do not see a way to develop a theory of inquiry from nothing: To take for granted nothing more than is already given, to set out from nothing but absolutely certain beginnings, or to move forward with nothing but absolutely certain means of proceeding. In particular, the present inquiry into inquiry, \(y_0 = y \cdot y,\) ought not to be misconstrued as a device for magically generating a theory of inquiry from nothing. Like any other inquiry, it requires an agent to invest in a conjecture, to make a guess about the relevant features of the subject of interest, and to choose the actions, the aspects, and the attitudes with regard to the subject that are critical to achieving the objectives of the study.

I can sum all this up by saying that an inquiry requires an inquirer to suggest a hypothesis about the subject of interest and then to put that particular model of the subject to the test. This in turn requires one to devote a modicum of personal effort to the task of testing the chosen hypothesis, to put a quantum of personal interest at stake for the sake of finding out whether the model fits the subject, and, overall, to take the risk of being wrong. Any model that is feasible is also defeasible, at least, where it concerns a contingent subject of inquiry.

The first step, then, of an inquiry into inquiry, is to put forth a tentative model of inquiry, to make a hypothesis about the features of inquiry that are essential to explaining its experienced characteristics, and thus, in a sense, to make a guess at the very definition of inquiry. This requirement seems both obvious and outrageous at the same time. One is perfectly justified in objecting that there is much that precedes this so-called "first step", namely, the body of experience that prepares one to see it and the mass of observation that prompts one to take it. I can deal with this objection by making a distinction between mundane experience and olympian theory, and then by saying that the making of a conjecture is really the first "theoretical" step, but this is a hedge that covers the tracks of theory in a deceptive way, hiding how early in the empirical process the "cloven hoof" of theory actually enters.

Leaving behind the mythical conditions of pure experience and naive observation, and at least by the time that one comes to give a name to the subject of investigation, one's trek through the data is already half-shod, half-fettered by the connotations of the name, and in turn by all of the concepts that it invokes in its train. The name, the concepts that it suggests, and the tacit but vague definition of the subject that this complex of associations is already beginning to constellate, attract certain experiences to the complex and filter out other observations from having any bearing on the subject matter. By this point, one is already busy translating one's empirical acquaintance with the subject into an arrangement of concepts that is intended to define its essential nature.

An array of concepts that is set up to capture the essence of a subject is a provisional definition of it, an implicit model of the subject that contains the makings of an explicit theory. It amounts to a selection from the phenomenal aspects of the subject, expresses a guess about its relevant features, and constitutes a hypothesis in explanation of its experienced characteristics. This incipient order of model or theory is tantamount to a definition because it sets bounds on the "stretches" and the "holds" of a term — its extension, intension, and intention — but this is not the kind of definition that has to be taken on faith, or that constitutes the first and the last word on the subject. In other words, it is an empirical definition, one that is subject to being falsified in reference to its intended subject, by failing to indicate the necessary, the pertinent, or the relevant features that account for the presence of its phenomena or the persistence of its process.

If I reflect on the conduct of inquiry, seeking to fix it in a fitting image and trying to cast it in a positive light, the best I can do is this:

Inquiry is a process that aims at achieving belief or knowledge.

But even this simple a description already plunges the discussion deep into a number of obscurities. Most prominently, there is the disjunction between belief and knowledge that cries out to be explained or resolved. Stirring beneath the surface, and not quite fading into the background, many of the other terms that are invoked in the description are capable of hiding the entire contents of the original ignorance that the image as a whole is aimed to dispel. And yet, there is nothing that I can do in this avowedly positive context but to mark these points down as topics for future discussion.

There is already a model of inquiry that is implicit, at least partially, in the text of the above description. Let me see if I can tease out a few of its tacit assumptions.

3.1.1.1. Inquiry as Conduct

First of all, inquiry is conceived to be a form of conduct. This invokes the technical term conduct, referring to the species of prototypically human action that is both dynamic and deliberate, or conceived to fall under a form of purposeful control, usually conscious but possibly not. For the sake of clarity, it helps to seek a more formal definition of conduct, one that expresses the concept in terms of abstract features rather than trying to suggest it by means of typical examples.

Conduct is action with respect to an object. The distinction between action and conduct, reduced to the level of the most abstract formal relations that are involved, can be described in the following manner.

Action is a matter of going from A to B, whereas conduct is matter of going from A to B in relation to C. In describing particular cases and types of conduct, the phrase "in relation to" can be filled out in more detail as "on account of", "in the cause of", "in order to bring about", "for the sake of", "in the interests of", or in many other ways. Thus, action by itself has a dyadic character, involving transitions through pairs of states, while conduct has a triadic character, involving the kinds of transactions between states that relate throughout to an object.

With regard to this distinction, notice that "action" is used inclusively, to name the genus of which "conduct" names a species, and thus depicts whatever has the aspect of action, even if it is actually more complex.

This creates the difficulty that the reputed "genus" is less than fully "generative", "generic", "genetic", or even "genuine" -- and so it is necessary to remain on guard against this source of misunderstanding.

What does this definition of conduct say about the temporal ordering of the object with respect to the states? The states are conceived to be ordered in time, but so far nothing has been said to pin down where in relation to these states the object must be conceived to fall in time. Nor does the definition make any particular specification necessary. This makes the question of relative time a secular parameter of the definition, allowing the consideration of the following options:

1. If the object is thought to precede the action of the conduct, then it tends to be regarded as a creative act, an initial intention, an original stimulus, a principal cause, or a prime mover.
2. If the object is thought to succeed the action of the conduct, then it tends to be regarded as an end, a goal, or a purpose, in other words, a state envisioned to be fulfilled.
3. If the object is thought to be concurrent, immanent, or transcendent throughout the action of the conduct, then it tends to be regarded as falling under one of the following possibilities: a prevailing value, a controlling parameter, a universal system of effective forces, a pervasive field of potentials, a ruling law, or a governing principle.

A prevailing value or a controlling parameter, which guides the temporal development of a system, is a term that fits into a law or a principle, which governs the system at a higher level. The existence of a value or a law that rules a system, and the information that an agent of the system has about its parameters and its principles, are two different matters. Indeed, a major task of development for an inquiring agent is to inform itself about the values and the laws that form its own system. Thus, one of the objects of the conduct of inquiry is a description in terms of laws and values of the rules that govern and guide inquiry.

The elaboration of an object in terms of this rich vocabulary — as a cause, end, field, force, goal, intention, law, parameter, principle, purpose, system, or value — adds colorful detail and concrete sensation to the account, and it helps to establish connections with the arrays of terminology that are widely used to discuss these issues. From a formal and relational point of view, however, all of these concepts are simply different ways of describing, at possibly different levels of generality, the object of a form of conduct. With that in mind, I find it useful to return to the simpler form of description as often as possible.

This account of conduct brings to the fore a number of issues, some of them new and some of them familiar, but each of them allowing itself to be approached from a fresh direction by treating it as an implication of a critical thesis just laid down. I next examine these issues in accord with the tenets from which they stem.

1. Inquiry is a form of conduct.

This makes inquiry into inquiry a special case of inquiry into conduct.

Certainly, it must be possible to reason about conduct in general, especially if forms of conduct need to be learned, examined, modified, and improved.

Placing the subject of inquiry within the subject of conduct and making the inquiry into inquiry a subordinate part of the inquiry into conduct does not automatically further the investigation, especially if it turns out that the general subject of conduct is more difficult to understand than the specialized subject of inquiry. But in those realms of inquiry where it is feasible to proceed hypothetically and recursively, stretching the appropriate sort of hypothesis over a wider subject area can act to prime the pump of mathematical induction all the more generously, and actually increase the power of the recursion. Of course, the use of a recursive strategy comes at the expense of having to establish a more extended result at the base.

2. The existence of an object that rules a form of conduct and the information that an agent of the conduct has about the object are two different matters.

This means that the exact specification of the object can demand an order of information that the agent does not have available, at least, not for use in reflective action, or even require an amount of information that the agent lacks the capacity to store. No matter how true it is that the actual course of the agent's conduct exactly reflects the influence of the object, and thus, in a sense, represents the object exactly, the question is whether the agent possesses the equivalent of this information in any kind of accessible, exploitable, reflective, surveyable, or usable form of representation, in effect, in any mode of information that the agent can use to forsee, to modify, or to temper its own temporal course.

This issue may seem familiar as a repetition of the "meta" question.

Once again, there is a distinction between (a) the properties of an action, agent, conduct, or system, as expressible by the agent that is engaged in the conduct, or as representable within the system that is undergoing the action, and (b) the properties of the same entities, as evident from an "external viewpoint", or as statable by the equivalent of an "outside observer".

3. Reflection is a part of inquiry. Reflection is a form of conduct.

The task of reflection on conduct is to pass from a purely interior view of one's own conduct to an outlook that is, effectively, an exterior view.

What is sought is a wider perspective, one that is able to incorporate the sort of information that might be available to an outside observer, that ought to be evident from an external vantage point, or that one reasonably imagines might be obvious from an independent viewpoint. I am tempted to refer to such a view as a "quasi-objective perspective", but only so long as it possible to keep in mind that there is no such thing as a "completely outside perspective", at least, not one that a finite and mortal agent can hope to achieve, nor one that a reasonably socialized member of a community can wish to take up as a permanent station in life.

With these qualifications, reflection is a form of conduct that can serve inquiry into conduct. Inquiry and its component reflection, applied to a form of conduct, are intended to provide information that can be used to develop the conduct in question. The "reflective development" that occurs depends on the nature of the case. It can be the continuation, the correction, or the complete cessation of the conduct in question.

If it is to have the properties that it is commonly thought to have, then reflection must be capable of running in parallel, and not interfering too severely, with the conduct on which it reflects. If this turns out to be an illusion of reflection that is not really possible in actuality, then reflection must be capable, at the very least, of reviewing the memory record of the conduct in question, in ways that appear concurrent with a replay of its action. But these are the abilities that reflection is "pre-reflectively" thought to have, that is, before the reflection on reflection can get under way. If reflection is truly a form of conduct, then it becomes conceivable as a project to reflect on reflection itself, and this reflection can even lead to the conclusion that reflection does not have all of the powers that it is commonly portrayed to have.

First of all, inquiry is conceived to be a form of conduct. This invokes the technical term "conduct", referring to the species of prototypically human action that is both dynamic and deliberate, or conceived to fall under a form of purposeful control, usually conscious but possibly not. For the sake of clarity, it helps to seek a more formal definition of conduct, one that expresses the concept in terms of abstract features rather than trying to suggest it by means of typical examples.

Conduct is action with respect to an object. The distinction between action and conduct, reduced to the level of the most abstract formal relations that are involved, can be described in the following manner. Action is a matter of going from A to B, whereas conduct is matter of going from A to B in relation to C. In describing particular cases and types of conduct, the phrase "in relation to" can be filled out in more detail as "on account of", "in the cause of", "in order to bring about", "for the sake of", "in the interests of", or in many other ways. Thus, action by itself has a dyadic character, involving transitions through pairs of states, while conduct has a triadic character, involving the kinds of transactions between states that relate throughout to an object.

With regard to this distinction, notice that "action" is used inclusively, to name the genus of which "conduct" names a species, and thus depicts whatever has the aspect of action, even if it is actually more complex. This creates the difficulty that the reputed "genus" is less than fully "generative", "generic", "genetic", or even "genuine" - and so it is necessary to remain on guard against this source of misunderstanding.

What does this definition of conduct say about the temporal ordering of the object with respect to the states? The states are conceived to be ordered in time, but so far nothing has been said to pin down where in relation to these states the object must be conceived to fall in time. Nor does the definition make any particular specification necessary. This makes the question of relative time a secular parameter of the definition, allowing the consideration of the following options:

1. If the object is thought to precede the action of the conduct, then it tends to be regarded as a creative act, an initial intention, an original stimulus, a principal cause, or a prime mover.
2. If the object is thought to succeed the action of the conduct, then it tends to be regarded as an end, a goal, or a purpose, in other words, a state envisioned to be fulfilled.
3. If the object is thought to be concurrent, immanent, or transcendent throughout the action of the conduct, then it tends to be regarded as falling under one of the following possibilities: a prevailing value, a controlling parameter, a universal system of effective forces, a pervasive field of potentials, a ruling law, or a governing principle.

A prevailing value or a controlling parameter, which guides the temporal development of a system, is a term that fits into a law or a principle, which governs the system at a higher level. The existence of a value or a law that rules a system, and the information that an agent of the system has about its parameters and its principles, are two different matters. Indeed, a major task of development for an inquiring agent is to inform itself about the values and the laws that form its own system. Thus, one of the objects of the conduct of inquiry is a description in terms of laws and values of the rules that govern and guide inquiry.

The elaboration of an object in terms of this rich vocabulary — as a cause, end, field, force, goal, intention, law, parameter, principle, purpose, system, or value — adds colorful detail and concrete sensation to the account, and it helps to establish connections with the arrays of terminology that are widely used to discuss these issues. From a formal and relational point of view, however, all of these concepts are simply different ways of describing, at possibly different levels of generality, the object of a form of conduct. With that in mind, I find it useful to return to the simpler form of description as often as possible.

This account of conduct brings to the fore a number of issues, some of them new and some of them familiar, but each of them allowing itself to be approached from a fresh direction by treating it as an implication of a critical thesis just laid down. I next examine these issues in accord with the tenets from which they stem.

1. Inquiry is a form of conduct.

This makes inquiry into inquiry a special case of inquiry into conduct. Certainly, it must be possible to reason about conduct in general, especially if forms of conduct need to be learned, examined, modified, and improved.

Placing the subject of inquiry within the subject of conduct and making the inquiry into inquiry a subordinate part of the inquiry into conduct does not automatically further the investigation, especially if it turns out that the general subject of conduct is more difficult to understand than the specialized subject of inquiry. But in those realms of inquiry where it is feasible to proceed hypothetically and recursively, stretching the appropriate sort of hypothesis over a wider subject area can act to prime the pump of mathematical induction all the more generously, and actually increase the power of the recursion. Of course, the use of a recursive strategy comes at the expense of having to establish a more extended result at the base.

2. The existence of an object that rules a form of conduct and the information that an agent of the conduct has about the object are two different matters.

This means that the exact specification of the object can require an order of information that the agent does not have available, at least, not for use in reflective action, or even an amount of information that the agent lacks the capacity to store. No matter how true it is that the actual course of the agent's conduct exactly reflects the influence of the object, and thus, in a sense, represents the object exactly, the question is whether the agent possesses the equivalent of this information in any kind of accessible, exploitable, reflective, surveyable, or usable form of representation, in effect, any mode of information that the agent can use to foresee, to modify, or to temper its own temporal course.

This issue may seem familiar as a repetition of the "meta" question. Once again, there is a distinction between (a) the properties of an action, agent, conduct, or system, as expressible by the agent that is engaged in the conduct, or as representable within the system that is undergoing the action, and (b) the properties of the same entities, as evident from an "external viewpoint", or as statable by the equivalent of an "outside observer".

3. Reflection is a part of inquiry. Reflection is a form of conduct.

The task of reflection on conduct is to pass from a purely interior view of one's own conduct to an outlook that is, effectively, an exterior view. What is sought is a wider perspective, one that is able to incorporate the sort of information that might be available to an outside observer, that ought to be evident from an external vantage point, or that one reasonably imagines might be obvious from an independent viewpoint. I am tempted to refer to such a view as a "quasi-objective perspective", but only so long as it possible to keep in mind that there is no such thing as a "completely outside perspective", at least, not one that a finite and mortal agent can hope to achieve, nor one that a reasonably socialized member of a community can wish to take up as a permanent station in life.

With these qualifications, reflection is a form of conduct that can serve inquiry into conduct. Inquiry and its component reflection, applied to a form of conduct, are intended to provide information that can be used to develop the conduct in question. The "reflective development" that occurs depends on the nature of the case. It can be the continuation, the correction, or the complete cessation of the conduct in question.

If it is to have the properties that it is commonly thought to have, then reflection must be capable of running in parallel, and not interfering too severely, with the conduct on which it reflects. If this turns out to be an illusion of reflection that is not really possible in actuality, then reflection must be capable, at the very least, of reviewing the memory record of the conduct in question, in ways that appear concurrent with a replay of its action. But these are the abilities that reflection is "pre-reflectively" thought to have, that is, before the reflection on reflection can get under way. If reflection is truly a form of conduct, then it becomes conceivable as a project to reflect on reflection itself, and this reflection can even lead to the conclusion that reflection does not have all of the powers that it is commonly portrayed to have.

3.1.1.2. Types of Conduct

The chief distinction that applies to different forms of conduct is whether the object is the same sort of thing as the states or whether it is something entirely different, a thing apart, of a wholly other order. Although I am using different words for objects and states, it is always possible that these words are indicative of different roles in a formal relation and not indicative of substantially different types of things. If objects and states are but formal points and naturally belong to the same domain, then it is conceivable that a temporal sequence of states can include the object in its succession, in other words, that a path through a state space can reach or pass through an object of conduct. But if a form of conduct has an object that is completely different from any one of its temporal states, then the role of the object in regard to the action cannot be like the end or goal of a temporal development.

What names can be given to these two orders of conduct?

3.1.1.3. Perils of Inquiry

Now suppose that making a hypothesis is a kind of action, no matter how covert, or that testing a hypothesis takes an action that is more overt. If entertaining a hypothesis in any serious way requires action, and if action is capable of altering the situation in which it acts, then what prevents this action from interfering with the subject of inquiry in a way that undermines, with positive or negative intentions, the very aim of inquiry, namely, to understand the situation as it is in itself?

That making a hypothesis is a type of action may seem like a hypothesis that is too far-fetched, but it appears to follow without exception from thinking that thinking is a form of conduct, in other words, an activity with a purpose or an action that wants an end. The justification of a hypothesis is not to be found in a rational pedigree, by searching back through a deductive genealogy, or determined by that which precedes it in the logical order, since a perfectly trivial tautology caps them all. Since a logical tautology, that conveys no empirical information, finds every proposition appearing to implicate it, in other words, since it is an ultimate implication of every proposition and a conceivable conclusion that is implicit in every piece of reasoning, it is obvious that seeking logical precedents is the wrong way to go for empirical content.

In making a hypothesis or choosing a model, one appears to select from a vaster number of conceivable possibilities than a finite agent could ever enumerate in complete detail or consider as an articulate totality. As the very nature of a contingent description and the very character of a discriminate action is to apply in some cases but not in others, there is no escaping the making of a risky hypothesis or a speculative interpretation, even in the realm of a purely mental action. Thus, all significant thought, even thinking to any purpose about thought itself, demands a guess at the subject or a grasp of the situation that is contingent, dubious, fallible, and uncertain.

If all this is true — if inquiry begins with doubt, if every significant hypothesis is itself a dubious proposition, if the making and the testing of a hypothesis are instances of equally doubtful actions, and if every action has the potential to alter the very situation and the very subject matter that are being addressed — then it leads to the critical question: How is the conduct of inquiry, that begins by making a hypothesis and that continues by testing this description in action, supposed to help with the situation of uncertainty that incites it in the first place and that is supposed to maintain its motivation until the end is reached? The danger is that the posing of a hypothesis may literally introduce an irreversible change in the situation or the subject matter in question. The fear is that this change might be one that too conveniently fulfills or too perversely subverts the very hypothesis that engenders it, that it may obstruct the hypothesis from ever being viewed with equanimity again, and thus prevent the order of reflection that is needed to amend or discard the hypothesis when the occasion to do so arises.

If one fears that merely contemplating a special hypothesis is enough to admit a spurious demonstration into the foundations of one's reasoning, even to allow a specious demon to subvert all one's hopes of a future rationality and to destroy all one's chances of a reasonable share of knowledge, then one is hardly in a state of mind that can tolerate the tensions of a full-fledged, genuine inquiry. If one is beset with such radical doubts, then all inquiry is no more comfort than pure enchoiry. Sometimes it seems like the best you can do is sing yourself a song that soothes your doubts. Perhaps it is even quite literally true that all inquiry comes back at last to a form of "enchoiry", the invocation of a nomos, a way of life, or a song and a dance. But even if this is the ultimate case, it does no harm and it does not seem like a bad idea to store up in this song one or two bits of useful lore, and to weave into its lyric a few suggestions of a practical character.

Let us now put aside these more radical doubts. This putting aside of doubts is itself a form of inquiry, that is, a way of allaying doubts. The fact that I appear to do this by fiat, and to beg for tacit assent, tends to make me suspect the validity of this particular tactic. Still, it is not too inanely dismissive, as its appeal is based on an argument, the argument that continuing to entertain this type of doubt leads to a paralysis of the reason, and that paralyzing the ability to think is not in the interests of the agent concerned. Thus, I adopt the hypothesis that the relationship between the world and the mind is not so perverse that merely making a hypothesis is enough to alter the nature of either. If, in future, I or anyone sees the need to reconsider this hypothesis, then I see nothing about making it that prevents anyone from doing so. Indeed, making it explicit only renders it more subject to reflection.

Of course, a finite person can only take up so many causes in a single lifetime, and so there is always the excuse of time for not chasing down every conceivable hypothesis that comes to mind.

3.1.1.4. Forms of Relations

The next distinguishing trait that I can draw out of this incipient treatise is its emphasis on the forms of relations. From a sufficiently formal and relational point of view, many of the complexities that arise from throwing intentions, objectives, and purposes into the mix of discussion are conceivably due to the greater arity of triadic relations over dyadic relations, and do not necessarily implicate any differences of essence inhering in the entities and the states invoked. As far as this question goes, whether a dynamic object is essentially different from a deliberate object, I intend to remain as neutral as possible, at least, until forced by some good reason to do otherwise. In the meantime, the factors that are traceable to formal differences among relations are ready to be investigated and useful to examine. With this in mind, it it useful to make the following definition:

A conduct relation is a triadic relation involving a domain of objects and two domains of states. When a shorter term is desired, I refer to a conduct relation as a conduit. A conduit is given in terms of its extension as a subset C c XxYxZ, where X is the object domain and where Y and Z are the state domains. Typically, Y = Z.

In general, a conduct relation serves as a model of conduct (MOC), not always the kind of model that is meant to be emulated, but the type of model that captures an aspect of structure in a form of conduct.

The question arises: What is the relationship between signs and states? On the assumption that signs and states are comparable in their levels of generality, consider the following possibilities:

1. Signs are special cases of states.
2. Signs and states are the same sorts of things.
3. States are special cases of signs.

Depending on how one answers this question, one is also choosing among the following options:

1. Sign relations are special cases of conduct relations.
2. Sign relations and conduct relations are the same sorts of things.
3. Conduct relations are special cases of sign relations.

I doubt if there is any hard and fast answer to this question, but think that it depends on particular interpreters and particular observers, to what extent each one interprets a state as a sign, and to what degree each one recognizes a sign as a component of a state.

3.1.1.5. Models of Inquiry

The value of a hypothesis, or the worth of a model, is not to be given a prior justification, as by a deductive proof, but has to be examined in practice, as by an empirical probation. It is not intended to be taken for granted or to go untested, but its meaning in practice has to be articulated before its usefulness can be judged. This means that the conceivable practical import of the hypothesis or the model has to be developed in terms of its predicted and its promised consequences, after which it is judged by the comparison of these speculative consequences with the actual results. But this is not the end of the matter, for it can be a useful piece of information to discover that a particular kind of conception fails a particular kind of comparison. Thus, the final justification for a hypothesis or a model is contained in the order of work that it leads one to do, and the value of this work is often the same whether or not its premiss is true. Indeed, the fruitfulness of a suggestion can lie in the work that proves it untrue.

My plan then has to be, rather than trying to derive a model of inquiry in a deductive fashion from a number of conditions like \(y_0 = y \cdot y,\) only to propose a plausible model, and then to test it under such conditions. Each of these tests is a two-edged sword, and the result of applying a particular test to a proposed model can have either one of two effects. If one believes that a particular test is a hard and fast rule of inquiry, or a condition that any inquiry is required to satisfy, then the failure of a model to live up to its standard tends only to rule out that model. If one has reason to believe that a particular model of inquiry covers a significant number of genuine examples, then the failure of these models to follow the prescribed rule can reflect badly on the test itself.

In order to prime the pump, therefore, let me offer the following account of inquiry in general, the whole of which can be taken as a plausible hypothesis about the nature of inquiry in general.

My observations of inquiry in general, together with a few suggestions that seem apt to me, have led me to believe that inquiry begins with a "surprise" or a "problem". The way I understand these words, they refer to departures, differences, or discrepancies among various modalities of experience, in particular, among "observations", "expectations", and "intentions".

1. A surprise is a departure of an observation from an expectation, and thus it invokes a comparison between present experience and past experience, since expectations are based on the remembered disposition of past experience.
2. A problem is a departure of an observation from an intention, and thus it invokes a comparison between present experience and future experience, since intentions choose from the envisioned disposition of future experience.

With respect to these

With respect to this hypothetical

I now test this model of inquiry under the conditions of an inquiry into inquiry, asking whether it is consistent in its application to itself. This leaves others to test the models they like best under the same conditions, should they ever see the need to do so.

Does the inquiry into inquiry begin with a surprise or a problem concerning the process or the conduct of inquiry? In other words, does the inquiry into inquiry start with one of the following forms of departure: (1) a surprising difference between what is expected of inquiry and what is observed about it, or (2) a problematic difference between what is observed about inquiry and what is intended for it?

3.1.2. The Moment of Inquiry

Every young man — not to speak of old men — on hearing or seeing anything unusual and strange, is likely to avoid jumping to a hasty and impulsive solution of his doubts about it, and to stand still; just as a man who has come to a crossroads and is not quite sure of his way, if he be travelling alone, will question himself, or if travelling with others, will question them too about the matter in doubt, and refuse to proceed until he has made sure by investigation of the direction of his path.

(Plato, Laws, VII, 799C).

Observe the paradox of this precise ambiguity: That both the occasion and the impulse of inquiry are instances of a negative moment. But the immediate discussion is aimed at the positive aspects of inquiry, and so I convert this issue into its corresponding positive form.

The positive aim of inquiry is a state of belief, certainty, or knowledge. There are distinctions that can be made in the use of these words, but the question remains as to what kind of distinctions these are. In my opinion, the differences that arise in practice have more to do with the purely grammatical distinctions of "case", "mood", "number", "person", and "voice", and thus raise the issues of plurality and point of view, as opposed to indicating substantial differences in the relevant features of state, as actually experienced by the agent concerned.

It is often claimed that there are signficant differences between the conditions of belief and knowledge, but the way that I understand the distinction is as follows. One says that a person "knows" something when that person believes exactly the same thing that one believes. When one is none other than the person in question, then one says that one "knows" exactly what one believes. Differences arise between the invocations of "belief" and "knowledge" only when more than one person is involved in the issue. Thus, there is no occasion for a difference between belief and knowledge unless there is more than one person that is being consulted about the matter in question, or else a single person in a divided state of opinion, in any case, when there is more than one impulse, moment, or occasion that currently falls under consideration.

In any case, belief or knowledge is the feature of state that an agent of inquiry lacks at the moment of setting out. Inquiry begins in a state of impoverishment, need, or privation, a state that is absent the quality of certainty. It is due to this feature that the agent is motivated, and it is on account of its continuing absence that the agent keeps on striving to achieve it, at least, with respect to the subject in question, and, at any rate, in sufficient measure to make action possible.

3.1.3. The Modes of Inquiry

Let the strange fact be granted, we say, that our hymns are now made into "nomes" (laws), just as the men of old, it would seem, gave this name to harp-tunes, — so that they, too, perhaps, would not wholly disagree with our present suggestion, but one of them may have divined it vaguely, as in a dream by night or a waking vision: anyhow, let this be the decree on the matter: — In violation of public tunes and sacred songs and the whole choristry of the young, just as in violation of any other "nome" (law), no person shall utter a note or move a limb in the dance.

(Plato, Laws, VII, 799E–800A).

In the present section, I am concerned with the kinds of reasoning that might be involved in the choice of a method, that is, in discovering a way to go about inquiry, in constructing a way to carry it through, and in justifying the way that one chooses. If the choice of a method can be established on the basis of reasoning, if it can be rationalized or reconstructed on grounds that are commonly thought to be sensible, or if it is likely to be affected or influenced in any way by a rational argument, then there is reason to examine the kinds of reasoning that go into this choice. All of this requires a minimal discussion of different modes of reasoning.

In this work as a whole, each instance of inquiry is analyzed in accord with various modes of reasoning, the prospective "elements of inquiry", and its structure as an object of inquiry is articulated, rationalized, and reconstructed with respect to the corresponding "form of analysis", "form of synthesis", or "objective genre" (OG).

According to my current understanding, the elements of inquiry can be found to rest on three types of steps, called "abductive", "deductive", and "inductive" modes of inference. As a result of this opinion, I do not believe that I can do any better at present than to articulate the structure of each instance of learning or reasoning according to these three types of motions of the mind. But since this work as a whole is nowhere near complete, I cannot dictate these steps in a dogmatic style, nor will it do for me to to call the tune of this form of analysis in a purely ritual or a wholly routine fashion.

Since the complexity of reasoning about different modes of reasoning is enough of a complication to occupy my attention at the present stage of development in this work, it is proably best to restrain this discussion along the majority of its other dimensions. A convenient way to do this is to limit its scope to simple examples and concrete situations, just enough to illustrate the selected modes of reasoning.

With all of these considerations in mind, the best plan that I can find for addressing the tasks of the present section is to proceed as follows: I make it my primary aim to examine only a few of the simplest settings in which these different modes of reasoning are able to appear, and I try to plot my path through this domain by way of concrete examples. Along the way, I discuss a few of the problems that are associated with reasoning about different modes of reasoning. Given the present stage of development, the majority of these issues have to be put aside almost as quickly as they are taken up. If they are ever going to be subject to resolution, it is not within reach of the present moment of discussion. In the body of this section, I therefore return to the initial strategy: to examine a few of the simplest cases and situations that can serve to illustrate the distinctions among the chosen modes of reasoning.

In trying to initiate a general discussion of the different modes of reasoning that might be available, and thus to motivate a model of this subject matter that makes an initial kind of sense to me, I meet once again with all the old "difficulties at the beginning", the kinds of obstructions that always seem to arise on trying to open up any new subject for discussion or in trying to introduce any new model of an old subject area. Much of this gratuitous bedevilment is probably due to the inherent conservatism of the human mind. Everything familiar is taken for granted, but each new picture of the situation is immediately subjected to the severest suspicions.

Now, I cannot reason with necessary force that the mind must use these particular modes of reasoning, any more than I can say that it must use a given language in order to express itself. But I can argue, relative to a particular model of thinking that must be proposed hypothetically, that certain modes of reasoning are available to the mind and are likely to be evident in its operation, if one only takes the trouble to look.

Ultimately, the model of thinking that I plan to propose makes use of the proposition that all thinking takes place in signs, and thus that inquiry is the transformation of a sign relation. Relative to this hypothesis, it would be possible to discharge the current assumptions about the basic modes of reasoning, that is, to derive the elementary modes of inquiry from a sign relational model of inquiry, and then to compare them with the current suggestions. Until this work is done, however, the assumption that these really are the most basic modes of reasoning has to be treated as a still more tentative hypothesis.

When a subject matter is so familiar that the logical connections between its parts are known both forwards and backwards, then it is reasonable and convenient to organize its presentation in an axiomatic fashion. This would not be such a bad idea, if it did not make it so easy to forget the nature of the reorganization that goes into a representation, and it would not constitute such a deceptive conception of the subject, if it did not mean that the exposition of the subject matter is just as often the falsification of its actual development and the covering up of its real excavation. Indeed, the logical order of axioms and theorems may have little to do with the original order of discovery and invention. In practice, the deepest axioms are often the last to come to light.

Once again, the structure of a reflective context means that each mode of reasoning is able to appear in a double role, once as an object and once as an instrument of the same extended discussion. And once again, the discussion runs into an array of obstructions, whose structures are becoming, if not more clear, at least, more familiar with each encounter. In particular, a description of different modes of reasoning involves a classification, and a classification presupposes a basis of distinctive features that cannot be treated as categorical, or objectively neutral, but has to be regarded as hypothetical, or potentially biased. In other words, the language that I use to describe different modes of reasoning may already have a particular model of reasoning built into it, and this disposition to a particular conception of logic may be lodged in such a way that it makes it nearly impossible to reflect on the operations and the limitations of this model.

Inquiry begins when a law is violated. It marks a time when a certain peace of mind is breached, it reigns all the while that a common accord is broken, disturbed, forgotten, or lost, and it rules right up until the time when a former condition of harmony is restored or until the moment when a new state of accord is established. Of course, the word "law" is a highly equivocal choice, especially to convey the sense of a founding principle. It renders not just its own meaning irrevocably subject to interpretation, but delivers into a similar subjection all the forms of understanding that depend on it. But the letter must release its hold on the spirit, if the word "law" is meant to evoke the requisite variety of connotations, and yet to maintain a sensible degree of order among their concrete meanings. Only in this way can it rise above the many different kinds of law that come into play.

There are descriptive laws, that organize experiences into expectations. There are prescriptive laws, that organize performances into intentions.

Other names for descriptive laws are "declarative" or "empirical" laws. Other names for prescriptive laws are "procedural" or "normative" laws.

Implicit in a descriptive law is the connection to be found or made, discovered or created, between past experience and present expectation. What one knows about these connections is kept in a descriptive model.

Implicit in a prescriptive law is the connection to be found or made, discovered or created, between current conduct and future experience. What one knows about these connections is kept in a prescriptive model.

A violation of an expectation, the contravention of a descriptive law, occurs when a present experience departs from a predicted experience, which is what a past expectation or description projected to be present. This is a "surprise", a state of affairs that calls for an explanation. An explanation points to other descriptions that better predict the actual experience, and suggests an alteration to the descriptive model that generated the expectation from a past experience.

A violation of an intention, the contravention of a prescriptive law, occurs when a present experience departs from a desired experience, which is what a past intention or prescription projected to be present. This is a "problem", a state of affairs that calls for a plan of action. , A plan of action points to other actions that better achieve the desired experience, and suggests an alteration to the prescriptive model that generated the conduct toward a prospective experience.

In the rest of this section, I treat the different modes of reasoning according to the forms that Aristotle gave them, collectively referred to as the "syllogistic" model. The discussion is kept within the bounds of propositional reasoning by considering only those "figures of syllogism" that are "purely universal", that is, the forms of argument all of whose premisses, and therefore all of whose conclusions, involve nothing but universal quantifications.

If it were only a matter of doing propositional reasoning as efficiently as possible, I would simply use the cactus language and be done with it, but there are several other reasons for revisiting the syllogistic model. Treating the discipline that is commonly called "logic" as a cultural subject with a rich and varied history of development, and attending to the thread of tradition in which I currently find myself, I observe what looks like a critical transition that occurs between the classical and the modern ages. Aside from supplying the barest essentials of a historical approach to the subject, a consideration of this elder standard makes it easier to appreciate the nature and the character of this transformation. In addition, and surprisingly enough to warrant further attention, there appear to be a number of cryptic relationships that exist between the syllogistic patterns of reasoning and the ostensibly more advanced forms of analysis and synthesis that are involved in the logic of relations.

3.1.3.1. Deductive Reasoning

In this subsection, I present a trimmed-down version of deductive reasoning in Aristotle, limiting the account to universal syllogisms, in effect, keeping to the level of propositional reasoning. Within these constraints, there are three basic "figures" of the syllogism.

In order to understand Aristotle's description of these figures, it is necessary to explain a few items of his technical terminology. In each figure of the syllogism, there are three "terms". Each term can be read as denoting either (1) a class of entities or (2) all of the members of a class of entities, depending on which interpretation the reader prefers. These terms are ranked in two ways: With respect to the "magnitudes" that they have in relation to each other, there are "major", "middle", and "minor" terms. With respect to the "positions" that they take up within the figure, there are "first", "intermediate", and "last" terms. The figures are distinguished by how the magnitudes correlate with the positions. However, the names for these rankings are not always used or translated in a rigorously systematic manner, so the reader has to be on guard to guess which type of ranking is meant.

In addition to this terminology, it is convenient to make use of the following nomenclature:

1. The Fact is the proposition that applies the term in the first position to the term in the third or last position.
2. The Case is the proposition that applies the term in the second or intermediate position to the term in the third or last position.
3. The Rule is the proposition that applies the term in the first position to the term in the second or intermediate position.

Because the roles of Fact, Case, and Rule are defined with regard to positions rather than magnitudes they are insensitive to whether the proposition in question is being used as a premiss or is being drawn as a conclusion.

The first figure of the syllogism is explained as follows:

When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By "middle term" I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by "extremes" (a) that which is contained in another, and (b) that in which another is contained. For if A is predicated of all B, and B of all C, A must necessarily be predicated of all C. … I call this kind of figure the First.

(Aristotle, Prior Analytics, 1.4).

For example, suppose A is "animal", B is "bird", and C is "canary". Then there is a deductive conclusion to be drawn in the first figure.

There is the Case:

"All canaries are birds." (C => B)

There is the Rule:

"All birds are animals." (B => A)

One deduces the Fact:

"All canaries are animals." (C => A)

The propositional content of this deduction is summarized on the right. Taken at this level of detail, deductive reasoning is nothing more than an application of the transitive rule for logical implications.

The second figure of the syllogism is explained as follows:

When the same term applies to all of one subject and to none of the other, or to all or none of both, I call this kind of figure the Second; and in it by the middle term I mean that which is predicated of both subjects; by the extreme terms, the subjects of which the middle is predicated; by the major term, that which comes next to the middle; and by the minor that which is more distant from it. The middle is placed outside the extreme terms, and is first by position.

(Aristotle, Prior Analytics, 1.5).

For example, suppose M is "mammal", N is "newt", and O is "opossum". Then there is a deductive conclusion to be drawn in the second figure.

There is the Fact:

"All opossums are mammals." (O => M)

There is the Rule:

"No newts are mammals." (N.M = 0)

One deduces the Case:

"No newts are opossums." (N.O = 0)

The propositional content of this deduction is summarized on the right. Expressed in terms of the corresponding classes, it says that if O c M and if N intersects M trivially, then N must also intersect O trivially. Here, I use a raised dot "." to indicate either the conjunction of two propositions or the intersection of two classes, and I use a zero "0" to indicate either the identically false proposition or the empty class, leaving the choice of interpretation to the option of the reader.

The third figure of the syllogism is explained as follows:

If one of the terms applies to all and the other to none of the same subject, or if both terms apply to all or none of it, I call this kind of figure the Third; and in it by the middle I mean that of which both the predications are made; by extremes the predicates; by the major term that which is [further from] the middle; and by the minor that which is nearer to it. The middle is placed outside the extremes, and is last by position.

(Aristotle, Prior Analytics, 1.6).

It appears that this passage is only meant to mark out the limiting cases of the type. From the examples that Aristotle gives it is clear that he includes many other kinds of logical situation under this figure. Perhaps the phrase "applies to all or none" is intended to specify that a term applies "affirmatively or negatively" to another term, but is not meant to require that it applies universally so.

For example, suppose P is "poem", R is "rhapsody", and S is "sonnet". Then there is deductive conclusion to be drawn in the third figure:

There is the Fact:

"All sonnets are poems." (S => P)

There is the Case:

"Some sonnets are rhapsodies." (S.R > 0)

One deduces the Rule:

"Some rhapsodies are poems." (R.P > 0)

The propositional content of this deduction is summarized on the right. Expressed in terms of the corresponding classes, it says that if S c P and if R intersects S non-trivially then R must intersect P non-trivially.

3.1.3.2. Inductive Reasoning

(Aristotle, Prior Analytics, 2.23).

3.1.3.3. Abductive Reasoning

A choice of method cannot be justified by deduction or by induction, at least, not wholly, but involves an element of hypothesis. In ancient times, this mode of inference to an explanatory hypothesis was described by the Greek word "apagoge", articulating an action or a process that "carries", "drives", or "leads" in a direction "away", "from", or "off". This was later translated into the Latin "abductio", and that is the source of what is today called "abduction" or "abductive reasoning". Another residue of this sense survives today in the terminology for "abductor muscles", those that "draw away (say, a limb or an eye) from a position near or parallel to the median axis of the body" (Webster's).

If an image is needed, one may think of Prometheus, arrogating for the sake of an earthly purpose the divine prerogative of the gods, and then drawing the fire of their heavenly ire for the presumption of this act. This seems to sum up pretty well, not only the necessity and the utility of hypotheses, but also the risks that one incurs in making conjectures. In other guises, abductive reasoning is the mode of inference that is used to diagnose a complex situation, one that originally presents itself under a bewildering array of signs and symptoms, and fixes it subject to the terms of a succinct "nomen" or a summary predicate. Finally, by way of offering a personal speculation, I think it is likely that this entire trio of terms, "abduction", "deduction", and "induction", have reference to a style of geometric diagrams that the Ancients originally used to illustrate their reasonings.

Abductive reasoning has also been called by other names. C.S. Peirce at times called it "presumption", perhaps because it puts a plausible assumption logically prior to the observed facts, and at other times referred to it as "retroduction", because it reasons backwards from the consequent to the antecedent of a logical implication.

In its simplest form, abductive reasoning proceeds from a "fact" that A is true, using a "rule" that B => A, to presume a "case" that B is true. Thus, if A is a surprising fact that one happens to observe, and B => A is a rule to the effect that if B is true then A necessarily follows, then guessing the case that B is true is an instance of abductive reasoning. This is a backward form of reasoning, and therefore extremely fallible, but when it works it has the effect of reducing the amount of surprise in the initial observation, and thus of partially explaining the fact.

In a slightly more complicated version, abduction proceeds from a fact that C => A, using a rule that B => A, to presume a case that C => B. This is an inessential complication, since the rule of modus ponens and the rule of transitivity are essentially equivalent in their logical force, but it is often convenient to imagine that C is the "common subject" or the "current situation" that is implicit throughout the argument, namely, the existing entity that substantiates or instantiates all of the other predicates that are invoked in its course.

Suppose I have occasion to reason as follows:

"It looks like a duck, so I guess it is a duck."

Or even more simply:

"It looks blue, therefore it is blue."

These are instances in which I am using abductive reasoning, according to the pattern of the following schema:

I observe a Fact:

"It looks like X." (X')

I have in the back of my mind a general Rule:

"If it is X, then it looks like X." (X => X')

I reason my way back from the observed Fact and the assumed Rule to assert what I guess to be the Case:

"It is X." (X)

The abduction is a hypothetical inference that results in a diagnostic conclusion, that is, a statement of opinion as to what is conjectured to be the case. In each case the operation of abductive reasoning starts from a complex configuration, involving a number of explicit observations in the foreground and a class of implicit assumptions in the background, and it offers a provisional statement about certain possibility, one that is typically less conspicuous, obvious, or prominent, but still potentially present in the situation, and hopefully serving to explain the surprising or the problematic aspects of the whole state of affairs.

What results from the abductive inference is a concept and possibly a term, for instance, "duck" or "blue". The concept attempts to grasp a vast complex of appearances within a unitary form, and the term that connotes the concept is used to put explicit bounds on what it conveys. Working in tandem, they express an approximation or a simplification, "a reduction of the manifold of phenomena to a unified conception". Finite minds cannot operate for very long with anything more than this.

The reader may have noticed some obvious distinctions between the two examples of abductive reasoning that I gave above, between the case of "looking like a duck" and the case of "looking blue". Just to mention the most glaring difference: Although a person is occasionally heard to reason out loud after the fashion of the former example, it is rare to hear anyone naturally reasoning along the lines of the latter example. Indeed, it is more likely that any appearance of doing so is always an artificial performance and a self-conscious reconstruction, if not a complete fabrication, and it is doubtful that the process of arriving at a perceptual judgment can follow this rule in just so literal a fashion.

This is true and important, but it is beside the point of the immediate discussion, which is only to identify the logical form of the inference, that is, to specify up to informational equivalence the class of conduct that is involved in each example. Thus, considering the inference as an information process, I do not care at this point whether the process is implemented by a literal-minded variety of rule-following procedure, so long as it "follows", "obeys", or "respects" these rules in the form of what it does. One can say that an information process "obeys" a set of rules in a "figurative" and a "formal" sense if the transformation that occurs in the state of information between the beginning and the end of the process has the form of a relation that can be achieved by literally following these rules with respect to the prospective class of materials.

The general drift of the strategy that is being mapped out here, the "abstract", the "formal", or the "functional" approach, is now evident. Conceptually, one partitions the space of processes into "effective", "informational", or "pragmatic" equivalence classes and then adopts the inditement of a sequence of rules as a symbolic "nomen" for the class of processes that all achieve the same class of effects. At this level of functional abstraction, the conception of a process is indifferent to the particulars of its implemenation, so long as it lives within the means of the indicated constraints. Moreover, unless there is a way to detect the nature of the "actual" process without interfering too severely with it, that is, a path-sensitive but still unobtrusive measure that can sort out a finer structure from these equivalence classes, then it is not possible to inquire any further into the supposedly "actual" details.

Similar remarks apply to every case where one attributes "law-abiding" or "rule-governed" behavior to oneself, to another person, or even to a physical process. Across this diverse spectrum of cases, it ranges from likely but not certain to unlikely but still conceivable that the action in question depends on the agent "knowing" the laws that abide or the rules that are effectively being obeyed. With this in mind, I can draw this digression on appearances to a conclusion: When I say that agents are acting according to a particular pattern of rules, it only means that it "looks like" they are. In other words, they are acting "as if" they are consciously following these rules, or they are acting just like I act when I conscientiously follow such rules. A concise way to sum all of this up is to say that a pattern of rules constitutes a model of conduct, one that I can deliberately emulate, or one that I can attribute to others by way of explaining their conduct. In attributing this model to others, or even in using it to account for my own less deliberate behavior, I am making an abductive inference.

One way to appreciate the pertinence of this point is to notice that this entire digression, concerned with explaining the similarities between "looking like a duck" and "looking blue", is itself a form of argument, making a case of abductive inference to a case of abductive inference. In short, I am reasoning according to the following pattern:

It appears to be the making of an abductive inference,

so I guess it is the making of an abductive inference.

Anyone who thinks that this style of reasoning is too chancy to be tolerated ought to observe that it is only the pattern of inference that one follows in attributing minds to others, solely on the evidence that they exhibit roughly the same array of external behaviors in reaction to various external conditions as one employs to express one's experience of roughly the same conditions.

It goes without saying that abductive reasoning is extremely fallible. The fact that it looks like a duck does not necessarily mean that it is a duck - it might be a decoy. Moreover, in most cases of actual practice the implicit rule that serves to catalyze the abductive inference is not an absolute rule or a necessary truth in its own right but may be only a contingent rule or a probable premiss. For instance, not every case of being blue presents the fact of looking blue - the conditions of observation may be trickier than that. This brings to the fore another mark that distinguishes the two examples, highlighting a potentially important difference between "looking like a duck" and "looking blue". This is the amount of oversight, or awareness and control, that an agent has with regard to an inference, in other words, the extent to which an inference really does "go without saying".

The abductive inference from "it looks blue" to "it is blue" and the abductive inference from "it looks like a duck" to "it is a duck" differ in the degrees to which they exhibit a complex of correlated properties. These variations are summed up in one sense by saying that the first, more perceptual inference is more automatic, compulsive, habitual, incorrigible, and inveterate. The correlations are summed up in the opposite sense by saying that the second, more conceptual inference is more aware, controllable, correctable, critical, deliberate, guarded, and reflective. From a fully pragmatic standpoint, these differences are naturally of critical importance. But from a purely logical standpoint, they have to be regarded as incidental aspects or secondary features of the underlying forms of inference.

There is one thing yet missing from this description of abductive reasoning, and that is its creative aspect. The description so far is likely to leave the impression that the posing of a hypothesis always takes place against a narrowly circumscribed background of established terms that are available for describing cases, and thus that it amounts to nothing more original than picking out the right label for the case. Of course, the forming of a hypothesis may be bound by the generative potential of the language that is ultimately in force, but that is a far cry from a prescriptively finite list of more or less obvious choices.

How does all of this bear on the choice of a method? In order to make a start toward answering that question, I need to consider the part that abductive reasoning plays in the inquiry into method, which is, after all, just another name for the inquiry into inquiry.

There are times when choosing a method looks more like discovering or inventing a method, a purely spontaneous creation of a novel way to proceed, but normally the choice of a path picks its way through a landscape of familiar options and mapped out opportunities, and this presupposes a description of previously observed forms of conduct and a classification of different paths from which to choose. Hence the etymology of the word "method", indicating a review of means or a study of ways.

I would now like to examine several types situations where a choice of method is involved, paying special attention to the way that abductive reasoning enters into the consideration.

Example 1.

Suppose I have occasion to reason along the following lines:

This situation looks like one in which this method will work, therefore I will proceed on the hypothesis that it will work.

The current situation (C) looks amenable (A') to this method, so I guess it really is amenable (A) to this method.

In this type of situation, my observations of the situation are reduced to a form of description that portrays it in the light of a given method, amounting to an estimate of whether the situation is a case to which the method applies. The form of the entire argument hinges on the question of whether the assurance of this application is apparent or actual.

I express my observations of the situation as a Fact:

"The current situation looks amenable." (C => A')

I have in the back of my mind a general Rule:

"If it is amenable, then it looks amenable." (A => A')

I reason my way back from the observed Fact and the assumed Rule to assert what I guess to be the Case:

"The current situation is amenable." (C => A)

As far as it goes, this style of reasoning follows the basic pattern of abductive inference. Its obvious facticity is due to the fact that the situation is being described solely in the light of a pre-selected method. That is a relatively specious way to go about describing a situation, in spite of the fact that it may be inevitable in many of the most ultimate and limiting cases. The overall effect is noticeably strained, perhaps because it results from dictating an artificial setting, attempting to reduce a situation to the patterns that one is prepared to observe, and trying to fit what is there to see into a precut frame. A more natural way to describe a situation is in terms of the freely chosen perceptual features that inform a language of affects, impressions, and sensations. But here a situation is forced to be described in terms of the prevailing operational features that constitute a language of actions, forcing the description to be limited by the actions that are available within a prescribed framework of methods.

Instead of describing a situation solely in terms of its reactive bearing, that is, wholly in terms of how it reacts to the application of a method, one can try to describe it in terms that appear to be more its own, its independent, natural, observational, perceptual, or "proper" features. What the "proper" or "object-oriented" features are and whether they can be distinguished in the end from "reactive" or "method-oriented" features are questions that cannot be answered in the early phases of an investigation.

Example 2.

Suppose I find myself reasoning as follows:

If the current world (C) is a blessed world (B),

then it is a world in which my method works (A).

Here, I call to mind an independent property of being, B, that a world or a situation can have, and I use it as a middle term to reason along the lines of the following scheme:

I express my inquiry by questioning the possibility of a certain Fact, that is, by interrogating the following statement:

"The current world is amenable." (C =?> A)

I have in the back of my mind a general Rule:

"What is blessed, is amenable." (B => A)

I reason my way back from the interrogated Fact and the assumed Rule to guess that I ought to contemplate the chances of the following Case:

"The current world is blessed." (C =?> B)

Altogether, the argument that underlies the current question of method falls into line with the following example of abductive reasoning:

I hope that C is A, so I guess I hope that C is B.

To proceed with the application of a given method on the basis of such a piece of reasoning is tantamount to the faith, the hope, or the wish that there is already the right kind of justice in the world that would make the prejudices of one's favorite method turn out to be right, that one is just lucky enough to be playing in accord with a pre-established harmony. If such a confidence is all that allows one to go on inquiring, then there is no harm in assuming it, so long as one reserves the right to question every particular of its grant, should the occasion arise.

If one abstracts from the specific content of this example and examines its underlying structure, it reveals itself as the pattern of abductive reasoning that occurs in relating complex questions to simpler questions or in reducing difficult problems to easier problems. Furthermore, the iteration of this basic kind of step motivates a downward recursion from questions of fact to questions of cases, in a hopeful search for a level of cases where most of the answers are already known.

The previous examples of inquiry into method are not very satisfactory. Indeed, their schematic forms have an absurdly sketchy character about them, and they fail to convey the realistic sorts of problems that are usually involved in reasoning about the choice of a method. The first example characterizes a situation wholly in terms of a selected method. The second example characterizes a situation in terms of a property that is nominally independent of the method chosen, but the ad hoc character of this property remains obvious. In order to reason "properly" about the choice of method, it is necessary to contemplate properties of the methods themselves, and not just the situations in which they are used.

Example 3.

If I reason that scientific method is wise because wise people use it, then I am making the hypothesis that they use it because they are wise. Here, my reasoning can be explained according to the following pattern:

I observe a fact:

"A certain conduct is done by wise people." (C => X)

I have in mind a rule:

"If a wise act, then done by wise people." (A => X)

I abduce the case:

"A certain conduct is a wise act." (C => A)

Example 4.

If I reason that scientific method is a good method on account of the fact that it works for now, then I am guessing that it works for now precisely because it is good.

I observe a fact:

"Scientific method works for now." (C => X)

I have in mind a rule:

"What is good, works for now." (A => X)

I abduce the case:

"Scientific method is good." (C => A)

As always, the abductive argument is extremely fallible. The fact that scientific method works for now can be one of its accidental features, and not due to any essential goodness that it might be thought to have.

Finally, it is useful to consider an important variation on this style of argument, one that exhibits its close relation to reasoning by analogy or inference from example. Suppose that the above argument is presented in the following manner:

Scientific method (C) has many of the features that a good method needs to have, for instance, it works for now (X), so I reason that it has all of the features of a good method, in short, that it is a good method (A).

So far, the underlying argument is exactly the same. In particular, it is important to notice that the abductive argument does not depend on the prior establishment of any known cases of good methods. As of yet, the phrase "good method" is a purely hypothetical description, a term that could easily turn out to be vacuous. One has in mind a number of properties that one thinks a good method ought to have, but who knows if there is any thing that would satisfy all of these requirements? There may be some sort of subtle contradiction that is involved in the very juxtaposition of the terms "good" and "method". In sum, it can happen that scientific method is the very first method that is being considered for membership in the class of good methods, and so it is still unknown whether the class labeled "good methods" is empty or not.

But what if an example of a good method is already known to exist, one that has all of the commonly accepted properties that appear to define what a good method ought to be? In this case, the abductive argument acquires the additional strength of an argument from analogy.

3.1.3.4. Analogical Reasoning

The classical treatment of analogical reasoning by Aristotle explains it as a combination of induction and deduction. More recently, C.S. Peirce gave two different ways of viewing the use of analogy, analyzing it into complex patterns of reasoning that involve all three types of inference. In the appropriate place, it will be useful to consider these alternative accounts of analogy in detail. At the present point, it is more useful to illustrate the different versions of analogical reasoning as they bear on the topic of choosing a method.

The next example, ostensibly concerned with reasoning about a choice of method, is still too artificial to be taken seriously for this purpose, but it does serve to illustrate Aristotle's analysis of analogical reasoning as a mixed mode of inference, involving inductive and deductive phases.

Example 5.

Suppose I reason as follows. I think I can establish it as a fact that scientific method is a good method by taking it as a case of a method that always works and by using a rule that what always works is good. I think I can establish this rule, in turn, by pointing to one or more examples of methods that share the criterial property of always working and that are already acknowledged to be good. In form, this pattern of reasoning works by noticing examples of good methods, by identifying a reason why they are good, in other words, by finding a property of the examples that seems sufficient to prove them good, and by noticing that the method in question is similar to these examples precisely in the sense that it has in common this cause, criterion, property, or reason.

In this situation, I am said to be reasoning by way of analogy, example, or paradigm. That is, I am drawing a conclusion about the main subject of discussion by way of its likeness to similar examples. These cases are like the main subject in the possession of a certain property, and the relation of this critical feature to the consequential feature of interest is assumed to be conclusive. The examples that exhibit the criterial property are sometimes known as "analogues" or "paradigms". For many purposes, one can imagine that the whole weight of evidence present in a body of examples is represented by a single example of the type, an exemplary or typical case, in short, an archetype or epitome. With this in mind, the overall argument can be presented as follows:

Suppose that there is an exemplary method (E) that I already know to be a good method (A). Then it pays to examine the other properties of the exemplary method, in hopes of finding a property (B) that explains why it is good. If scientific method (C) shares this property, then it can serve to establish that scientific method is good.

The first part of the argument is the induction of a rule:

I notice the case:

"The exemplary method always works." (E => B)

I observe the fact:

"The exemplary method is a good method." (E => A)

I induce the rule:

"What always works, is good." (B => A)

The second part of the argument is the deduction of a fact:

I notice the case:

"Scientific method always works." (C => B)

I recall the rule:

"What always works, is good." (B => A)

I deduce the fact:

"Scientific method is good." (C => A)

Example 6.

Example 7.

Suppose that several examples (S1, S2, S3) of a good method are already known to exist, ones that have a number of the commonly accepted properties (P1, P2, P3) that appear to define what a good method is. Then the abductive argument acquires the additional strength of an argument from analogy.

The first part of the argument is the abduction of a case:

I observe a set of facts:

"Scientific method is P1, P2, P3." (C => P)

I recall a set of rules:

"Bona fide inquiry is P1, P2, P3." (B => P)

I abduce the case:

"Scientific method is bona fide inquiry." (C => B)

The second part of the argument is the induction of a rule:

I notice a set of cases:

"S1, S2, S3 exemplify bona fide inquiry." (S => B)

I observe a set of facts:

"S1, S2, S3 exemplify good method." (S => A)

I induce the rule:

"Bona fide inquiry is good method." (B => A)

The third part of the argument is the deduction of a fact:

I recall the case:

"Scientific method is bona fide inquiry." (C => B)

I recall the rule:

"Bona fide inquiry is good method." (B => A)

I deduce the fact:

"Scientfic method is good method." (C => A)

Now, logically and rationally in the purest sense, the argument by analogy to an example has no more force than the abductive argument, but, empirically and existentially, the example serves, not only as a model of the method to be emulated, but as an object of experimental variation and a source of further experience.

It is time to ask the question: Why do these examples continue to maintain their unrealistic character, their comical and even ridiculous appearance, in spite of all my continuing attempts to reform them in a sensible way? It is not merely their simplicity. A simple example can be telling, if it grasps the essence of the problem, that is, so long as it captures even a single essential feature or highlights even a single critical property of the thing that one seeks to understand. It is more likely due to the circumstance that I am describing agents, methods, and situations all in one piece, that is, without any analysis, articulation, or definition of what exactly constitutes the self, the scientific method, or the world in question. It is not completely useless to consider cases of this type, since many forms of automatic, customary, and unreflective practice are underlain by arguments that are not much better that this. Of course, on reflection, their "commedius" character becomes apparent, and all deny or laugh off the suggestion that they ever think this way, but that is just the way of reflection.

In order to improve the character of the discussion on this score …

3.2. Obstacles to the Project : In the Way of Inquiry

The discussion in this Chapter addresses a set of conceptual and methodological obstacles that stand in the way of the current inquiry, threatening to undermine a reasonable level of confidence in the viability of its proceeding, all of which problems I think can be overcome.

Often the biggest obstacle to learning more is the need to feel that one already knows. And yet there are some things that a person knows, at least, in comparison to other things, and it makes sense to use what one already knows best in order to learn what one needs to know better. The question is, how does one know which is which? What test can tell what is known so well that it can be trusted in learning what is not?

One way to test a supposed knowledge is to try to formulate it in such a way that it can be taught to other people. A related test, harder in some ways but easier in others, is to try to formalize it so completely that even a computer could go through the motions that are supposed to be definitive of its practice. Both proposals for testing a supposition of knowledge invoke the critical notion of putting knowledge into a form that is communicable or transportable from one system or one medium of interpretation to another. If the knowledge is conceived to be residing already in one form or another, then this requirement simply points to a "reformation" or a "transformation" of knowledge, otherwise it demands a more radical metamorphosis, from a wholly disorganized condition to an incipiently communicable facility or an initially portable formulation.

3.2.1. The Initial Unpleasantness

Inquiry begins in doubt, a debit of certainty and a drought of information that is never a pleasant condition to acknowledge, and one of the primary obstacles to inquiry can be reckoned as owing to the onus that everyone feels on owning up to this debt. Human nature vastly prefers to revel in the positive features of the scientific knowledge it already possesses, and the mind defers as long as possible the revolt it feels arising on facing the uncertainties that still persist, the "nots" and "not yets" that as yet it cannot and ought not deny.

3.2.2. The Justification Trap

There is a particular type of "justification trap" that a person can fall into, of trying to prove the scientific method by solely deductive means, that is, of trying to show that the scientific method is a good method by starting from the simplest possible axioms, that everybody would accept, about what is good.

Often this happens, in spite of the fact that one really knows better, simply in the process of arranging one's thoughts in a rational order, say, from the most elementary and independent to the most complex and derivative, as if for the purposes of a logical and summary exposition. But when does this rearrangement cease to be a rational reconstruction and start to become a destructive rationalization, a distortion of the genuine article, and a falsification of the authentic inquiry that it attempts to recount?

Sometimes people express their recognition of this trap, and their appreciation of the factor that it takes to escape it, by saying that there is really no such thing as "the scientific method", that the very term "scientific method" is a misnomer and does not refer to any kind of method at all, in sum, that the development of knowledge cannot be reduced to any fixed method because it involves in an essential way such a large component of non-methodical activities. If one's idea of what counts as method is fixed on the ideal of a deductive procedure, then it is no wonder that one draws this conclusion.

3.2.3. A Formal Apology

Using "form" in the sense of "abstract structure", I can state that the focus of my interest in this research is limited to the formal properties of inquiry processes. Among their chief constituents these include all the thinking and unthinking processes that support the ability to learn and to reason.

This "formal apology", that is, the apologetics of declaring a decidedly formal intent, will be used on numerous occasions to beg off a host of material difficulties and thus to avoid the perceived necessity of meeting a multitude of conventional controversies.

The next several subsections enumerate a few of the ways that I plan to make use of this "formal apologetics".

3.2.3.1. Category Double-Takes

The first use of the formal apology is to rehabilitate certain classes of associations between concepts that would otherwise go down as category mistakes. This conversion can be achieved in each detailed case by flipping from one side of the concept's dual aspect to the other as the context demands. Thus it is possible in selected cases to reform the characters of category mistakes in the manner of categorical "retakes" or "double-takes".

3.2.3.2. Conceptual Extensions

The second use of the formal apology is to permit the tentative extension of concepts to novel areas, giving them experimental trial beyond the cases and domains where their use is already established in the precedents of accustomed habit and successful application.

This serves to dissipate the essential or "in principle" objection that any category distinction puts a prior constraint on the recognition of similar structure between materially dissimilar domains. As a result, it leaves this issue as a matter to be settled by a post hoc judgment, one that is directed to the question of what fits best "in practice".

3.2.3.3. Explosional Recombinations

Another obstacle to inquiry is posed by the combinatorial explosion of questions that can arise in complex cases. This embarrassment of riches is deceptively deadly to the ends of inquiry in the very measure that it seems so productive at first. The formalist strategy provides a way to manage this wealth of material diversity by identifying formal similarities among materially different domains, permitting the same formal answer to unify many contentious questions under a single roof, overall reducing the number of distinct topics that need to be covered.

3.2.3.4. Interpretive Frameworks

Iterations of this recombinatorial process will generate an alternative hierarchy of categories that helps to control the explosion of parts in the domain under inquiry. If by some piece of luck this alternative framework is uniquely suited to the natural ontology of the domain in question, then it would be advisable to reorganize the whole inquiry along the lines of its topic headings. However, a complex domain seldom falls out this neatly. The new interpretive framework will not preserve all the information in the object domain, but typically capture only another aspect of it. In order to take the maximal advantage of all the different frameworks that might be devised, it is best to quit depending on any one of them exclusively. Thus, a rigid reliance on a single hierarchy to define the ontology of a given domain passes over into a flexible application of interpretive frameworks to make contact with particular aspects of one's object domain.

3.2.4. A Material Exigency

On the other hand, I have cast this project as an empirical inquiry, proposing to represent experimental hypotheses in the form of computer programs. At the heart of this empirical attitude is a feeling that all formal theories should arise from and bear on experience.

Every season of growth in empirical knowledge begins with a rush to the sources of experience. Every fresh-thinking reed of intellect is raised to pipe up and chime in with the still-viable canons of inquiry in one glorious paen to the personal encounter with natural experience. But real progress in the community of inquiry depends on observers being able to orient themselves to objects of common experience, and so the uncontrolled exhaltation of individual phenomenologies leads as a rule to the disappointment and the disillusionment that befalls the lot of unshared enthusiasms and fragmented impressions. Look again at the end of the season and see it faltering to a close, with every young scribe being rapped on the knuckles for departing from that uninspired identification with impersonal authority that expresses itself in third-person passive accounts of one's own experience.

It is easy to decry this turn of events, but anything that happens so often must have a cause, a force of reason to explain the dynamics of its recurring moment in the history of ideas. It appears that the heart of the developmnt that transpires is not born on the sleeve of its first and last stages, where the initial explosion and final collapse march along their inevitable course in a lockstep fashion, but is embodied more naturally in the middle of the above narrative.

Experience exposes and explodes expectations. How can experiences impinge on expectations unless these two types of entities are both reflected in the same medium, for instance, and perhaps without loss of generality, in the form of representation that constitutes the domain of signs? However complex its world may be, internal or external to itself, or on the boundaries of its being, a finite creature can only describe it in a finite number of finite terms, or in a finite sketch of finite lines. Finite terms and lines are signs. What they indicate need not be finite, but what they are, must be.

The common sensorium.

The common sense and the senses of "common".

This is point where the empirical and the rational meet. I describe as "empirical" any method that exposes theoretical descriptions of an object to further experiences with that object.

3.2.5. A Reconciliation of Accounts

The reader may share with the author a feeling of discontent at this juncture, attempting to reconcile the formal intentions of this inquiry with the cardinal contentions of experience. Let me try to express this difficulty in the form of a question: What is the nature of the bond between form and content in experience, between the abstract formal categories and the concrete material contents that exist in experience?

Here is the tentative answer that I will entertain, seeking to test its usefulness in this work. I take there to be a primitive category of "form-in-experience" that presently lacks a compact name, but that from the standpoint of a given agent often passes from the "structure of experience" to the "experience of structure".

My personal definition of mathematical understanding has long been expressed in the chiasmatic figure of speech: "the form of experience and the experience of form". This is not the place to argue for the virtues of this concept, but I thought it would clarify a few points to share it here.

3.2.6. Objections to Reflexive Inquiry

Inquiry begins when an automatic routine or a normal course of activity is interrupted, when agents are thrown into a state of doubt about what is best for them to do next and what is really true of their situation. If this model applies at level of self-application, then an occasion for inquiry into inquiry arises when an ongoing activity of inquiry into any special area becomes obstructed and agents are obligated to initiate a new order of inquiry in order to obviate the problem. At such moments, agents must acknowledge the higher order of uncertainty that prevails and accept the interruption of a special inquiry in order to examine their accepted conventions and their antecedent convictions about the appropriate conduct of any inquiry at all. The new order demands that agents pause and reflect on the assumptions embodied in their previous inquiry, criticizing with a deliberate and reconstructive intent aspects of an activity that formerly proceeded through its paces untroubled by any articulate concern.

An agent may be able to articulate these apprehensions in the form of a pair of questions: What actions are advisable to adopt and apply in order to achieve the aim of the current activity? What assumptions among those accepted already are ready to be adapted or abandoned in order to advance this course of affairs?

Thus there is this negative aspect to the object of inquiry, a feature captured in the Greek word pragma for "object", whose manifold of senses and derivatives includes among its connotations the ideas of purposeful objectives and problematic objections, of booming inquiries and buzzing expositions.

The fact that an episode of inquiry has the style of an interlude, that it begins and ends "in medias res" with respect to a circumstantial action, is a feature of inquiry that is important to remember and a contingency of its process that has a couple of consequences:

First, it means that genuine inquiry does not touch on the inciting action at points of total doubt or absolute certainty. An incident of inquiry does not begin or end in absolute totalities but only in the differential and relative measures that actually occasion its departures and resolutions. Inquiry is not a process that demands an absolutely secure foundation from which to set out or any place to stand from which to judge the totality of onrushing events. It never requires more than it does in fact have at the outset: assumptions that were not in practice doubted just a moment before and a circumstance of conflict that will force the whole situation to be reviewed before returning to the normal course of affairs.

Second, the interruptive character or escapist interpretation of inquiry is especially significant when contemplating programs of inquiry with recursive definitions, like the motivating case of inquiry into inquiry. It means that the termination criterion for an inquiry subprocess is whatever allows continuation of the calling process.

3.2.7. Empirical Considerations

The use of computer programs to represent empirical hypotheses brings with it a number of novel considerations about the nature of hypotheses and the status of theories in relation to phenomena. It forces a re-examination of several issues whose traditional answers have long been taken for granted.

3.2.8. Computational Considerations

3.2.8.2. A Power of Abstraction

Here's a scenario that often occurs. Inquiry begins with a question that leads to a number of further questions. After several iterations of this development a sense of despair sets in that the nominal progress of inquiry is doing more to multiply the tension of uncertainty than to clarify its issues. The only saving grace that rescues the effort comes from noticing that several groups of materially distinct questions have in fact similar forms.

---

• Contents • Part 1 • Part 2 • Part 3 • Appendices • References • Document History •

---

<sharethis />