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==Part 3.==
==Part 3.==
===3.1. Outlook of the Project : All Ways Lead to Inquiry===
===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:
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:
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.
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=====
=====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.
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.
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.
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.
1. Inquiry is a form of conduct.
This makes inquiry into inquiry a special case of inquiry into conduct.
This makes inquiry into inquiry a special case of inquiry into conduct.
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.
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.
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 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.
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".
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.
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.
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.
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.
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.
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.
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.
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.
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 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".
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.
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.
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.
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.
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=====
=====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.
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?
What names can be given to these two orders of conduct?
=====3.1.1.3. Perils of Inquiry=====
=====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?
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?
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.
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=====
=====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:
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:
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.
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=====
=====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.
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.
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?
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====
====3.1.2. The Moment of Inquiry====
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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.
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====
====3.1.3. The Modes of Inquiry====
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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.
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=====
=====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 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.
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.
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=====
=====3.1.3.2. Inductive Reasoning=====
(Aristotle, ''Prior Analytics'', 2.23).
(Aristotle, ''Prior Analytics'', 2.23).
=====3.1.3.3. Abductive Reasoning=====
=====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).
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).
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.
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=====
=====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 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.
In order to improve the character of the discussion on this score …
In order to improve the character of the discussion on this score …
===3.2. Obstacles to the Project : In the Way of Inquiry===
===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.
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.
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.
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====
====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.
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====
====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.
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.
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.
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====
====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.
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.
The next several subsections enumerate a few of the ways that I plan to make use of this "formal apologetics".
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=====
=====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".
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=====
=====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.
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".
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=====
=====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.
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=====
=====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.
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====
====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.
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.
I describe as "empirical" any method that exposes theoretical descriptions of an object to further experiences with that object.
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====
====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?
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?
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.
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====
====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.
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.
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.
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====
====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.
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. Computational Considerations====
=====3.2.8.1. A Form of Recursion=====
=====3.2.8.1. A Form of Recursion=====
=====3.2.8.2. A Power of Abstraction=====
=====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.
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.
===3.3. Orientation of the Project : A Way Into Inquiry===
===3.3. Orientation of the Project : A Way Into Inquiry===
I have used the word "inquiry" to signify my object, and acknowledged that mere use of the word does not indicate much knowledge of it.
I have used the word "inquiry" to signify my object, and acknowledged that mere use of the word does not indicate much knowledge of it.
By itself, a name points to nothing at all, or nothing beyond itself, at least. There must be adduced an interpretive framework (IF) if any bit of language is to get a meaning in practice. But there is nothing in the beginning that could distinguish one potential IF from all the others, and thus arises the issue of alternate paradigms and plural interpreters. Nothing in this excludes the possibility that a text of suitable character could perforce of its content lead any viable candidate interpreter from an otherwise vague initial state to the point of becoming the text's own ideal reader, but nothing makes this obviously so.
By itself, a name points to nothing at all, or nothing beyond itself, at least. There must be adduced an interpretive framework (IF) if any bit of language is to get a meaning in practice. But there is nothing in the beginning that could distinguish one potential IF from all the others, and thus arises the issue of alternate paradigms and plural interpreters. Nothing in this excludes the possibility that a text of suitable character could perforce of its content lead any viable candidate interpreter from an otherwise vague initial state to the point of becoming the text's own ideal reader, but nothing makes this obviously so.
====3.3.1. Initial Description of Inquiry====
====3.3.1. Initial Description of Inquiry====
At first approach, I describe inquiry as a process that brings an agent, identical or analogous to a thinking human being, from a state of information that most people experience as doubt or uncertainty to a state of information that most people would describe as a condition of certainty and could express in the form of a determinate proposition, like those that represent settled beliefs or fixed items of knowledge.
At first approach, I describe inquiry as a process that brings an agent, identical or analogous to a thinking human being, from a state of information that most people experience as doubt or uncertainty to a state of information that most people would describe as a condition of certainty and could express in the form of a determinate proposition, like those that represent settled beliefs or fixed items of knowledge.
I will refer to this as the "initial description" (ID) of inquiry, characterizing the relationship of the process of inquiry to the states of its systematic agents and to the symbolic expressions of these states. Simply to clarify the grounds on which the ID is stated will require me to address a number of constituent topics, seemingly trifling in the offing but hiding a host of stumbling blocks in their train.
I will refer to this as the "initial description" (ID) of inquiry, characterizing the relationship of the process of inquiry to the states of its systematic agents and to the symbolic expressions of these states. Simply to clarify the grounds on which the ID is stated will require me to address a number of constituent topics, seemingly trifling in the offing but hiding a host of stumbling blocks in their train.
====3.3.2. Terms of Analysis====
====3.3.2. Terms of Analysis====
A sign, by itself, points to nothing at all — nothing beyond itself, at least. An interpretive framework (IF) must be adduced to give a sign a meaning in practice. So the simple name of "inquiry" and the complex expression of its ID indicate by themselves nothing beyond themselves. If an IF is adduced, then the ID can begin to take on meaning, at first by assigning tentative meanings to the ID's constituent terms and then testing the effects on the whole ID. But there is nothing unique about the interpretive framework that might be adduced, at least, nothing that can be distinguished at first. And so discussion is forced to take up the relations between interpretive frameworks that turn on the different senses of signs, the different directions they give to activity.
A sign, by itself, points to nothing at all — nothing beyond itself, at least. An interpretive framework (IF) must be adduced to give a sign a meaning in practice. So the simple name of "inquiry" and the complex expression of its ID indicate by themselves nothing beyond themselves. If an IF is adduced, then the ID can begin to take on meaning, at first by assigning tentative meanings to the ID's constituent terms and then testing the effects on the whole ID. But there is nothing unique about the interpretive framework that might be adduced, at least, nothing that can be distinguished at first. And so discussion is forced to take up the relations between interpretive frameworks that turn on the different senses of signs, the different directions they give to activity.
It may be useful to expand on the current description of agent's role. A complete specification of the agent is required to indicate the whole "agent system" that is conceived to be involved in the inquiry. In its fullest sense, the role of the "agent" incorporates the whole complex of activity that is embodied by the inquiry. As a result, the function of the agent includes not only the parts of all the "actors" but the full participation of the "audience" that is involved in the play of inquiry, even if all of these personifications are filled by the same substantive entity or community. In doing so, the agent function assimilates the role of the ordinary agent or the "active" agency of inquiry along with both its "passive" addressee and its "terminus ad quem", the point to which the whole play of inquiry is directed. In a very real sense, the ultimate addressee of any inquiry is the all-purpose agent's intended "state of information" (SOI), a fixed and certain belief that hopefully embodies knowledge. This is the "end toward which" it tends, the goal and the object of the whole inquiry.
It may be useful to expand on the current description of agent's role. A complete specification of the agent is required to indicate the whole "agent system" that is conceived to be involved in the inquiry. In its fullest sense, the role of the "agent" incorporates the whole complex of activity that is embodied by the inquiry. As a result, the function of the agent includes not only the parts of all the "actors" but the full participation of the "audience" that is involved in the play of inquiry, even if all of these personifications are filled by the same substantive entity or community. In doing so, the agent function assimilates the role of the ordinary agent or the "active" agency of inquiry along with both its "passive" addressee and its "terminus ad quem", the point to which the whole play of inquiry is directed. In a very real sense, the ultimate addressee of any inquiry is the all-purpose agent's intended "state of information" (SOI), a fixed and certain belief that hopefully embodies knowledge. This is the "end toward which" it tends, the goal and the object of the whole inquiry.
=====3.3.2.1. Digression on Signs=====
=====3.3.2.1. Digression on Signs=====
At this point, the discussion of inquiry makes contact with the pragmatic theory of signs. It appears that signs and inquiries have a lot in common. Signs and inquiries both act to affect the uncertainty that an agent has about an object. Moreover, taking these concepts in their positive senses, "good" signs and "good" inquiries always act to reduce that uncertainty.
At this point, the discussion of inquiry makes contact with the pragmatic theory of signs. It appears that signs and inquiries have a lot in common. Signs and inquiries both act to affect the uncertainty that an agent has about an object. Moreover, taking these concepts in their positive senses, "good" signs and "good" inquiries always act to reduce that uncertainty.
It is easy to imagine how one might have classified "signs", as embodied in the singular acts of observing a sign or receiving a signal, to be the simplest cases of "inquiries", incorporating arbitrarily complex protocols of sign-observations and symbol-manipulations, but the pragmatic theory of signs takes another tack. It analyzes inquiry into different kinds of logical proceedings that are called "arguments", classifies all arguments as being special forms of "symbols", and classifies all symbols as being special forms of "signs", namely, those that require the contribution of an interpretive agent in a significantly substantive way to constitute the resulting meaning of the sign.
It is easy to imagine how one might have classified "signs", as embodied in the singular acts of observing a sign or receiving a signal, to be the simplest cases of "inquiries", incorporating arbitrarily complex protocols of sign-observations and symbol-manipulations, but the pragmatic theory of signs takes another tack. It analyzes inquiry into different kinds of logical proceedings that are called "arguments", classifies all arguments as being special forms of "symbols", and classifies all symbols as being special forms of "signs", namely, those that require the contribution of an interpretive agent in a significantly substantive way to constitute the resulting meaning of the sign.
=====3.3.2.2. Empirical Status of ID=====
=====3.3.2.2. Empirical Status of ID=====
Of all the descriptions of inquiry that live in memory and imagination, this ID is the one that comes forward in my own mind most frequently, having survived many tests of usefulness, both for its comprehensive coverage of established domains as well as for its fruitfulness in suggesting new avenues of exploration. It returns on a perennial basis at the outset of each new try at understanding inquiry. Perhaps it comes with the territory of inquiry or lies embedded in the equipment of thought itself. Perhaps it was designed to serve as a legend, a minimal set of instructions woven into the material basis of the mind's ability to map the world. Perhaps it is an archetyped script, an innate ID inscribed from the factory on an inobtrusive corner of the mind's otherwise blank state. Or perhaps it is only an ID fixe? But history is rife with comprehensive theories whose wealth of explanations was purchased at the price of inflating their descriptive economies to the point of indefeasibility. So this description continues to have the status of a hypothesis, or a summary of one, whose full account needs to be evaluated.
Of all the descriptions of inquiry that live in memory and imagination, this ID is the one that comes forward in my own mind most frequently, having survived many tests of usefulness, both for its comprehensive coverage of established domains as well as for its fruitfulness in suggesting new avenues of exploration. It returns on a perennial basis at the outset of each new try at understanding inquiry. Perhaps it comes with the territory of inquiry or lies embedded in the equipment of thought itself. Perhaps it was designed to serve as a legend, a minimal set of instructions woven into the material basis of the mind's ability to map the world. Perhaps it is an archetyped script, an innate ID inscribed from the factory on an inobtrusive corner of the mind's otherwise blank state. Or perhaps it is only an ID fixe? But history is rife with comprehensive theories whose wealth of explanations was purchased at the price of inflating their descriptive economies to the point of indefeasibility. So this description continues to have the status of a hypothesis, or a summary of one, whose full account needs to be evaluated.
After these preliminaries and others that might arise in the process have been satisfied, the synthetic mode of evaluation takes over. This stage of investigation requires a pause, to take stock of the accumulated theory of inquiry that has developed up that point, and a turn to the task of testing the theory in action, by constructing computational models that satify its fundamentals.
After these preliminaries and others that might arise in the process have been satisfied, the synthetic mode of evaluation takes over. This stage of investigation requires a pause, to take stock of the accumulated theory of inquiry that has developed up that point, and a turn to the task of testing the theory in action, by constructing computational models that satify its fundamentals.
====3.3.3. Expansion of Terms====
====3.3.3. Expansion of Terms====
In order to continue testing the aptness of the ID, its usefulness as a picture of inquiry, I need to expand its terms until they are clear enough to suggest computational models. Also, I need to develop my characterization and justification of the modeling methods chosen, and to say how their results are intended to be understood.
In order to continue testing the aptness of the ID, its usefulness as a picture of inquiry, I need to expand its terms until they are clear enough to suggest computational models. Also, I need to develop my characterization and justification of the modeling methods chosen, and to say how their results are intended to be understood.
One thread of this description that needs to be disentangled from its context has to with the class of "agents" I have in mind, the ways they are "analogous" to the human kind, and the aspects of their relation to the realm of "most people" that are relevant to empirical inquiry.
One thread of this description that needs to be disentangled from its context has to with the class of "agents" I have in mind, the ways they are "analogous" to the human kind, and the aspects of their relation to the realm of "most people" that are relevant to empirical inquiry.
=====3.3.3.1. Agency=====
=====3.3.3.1. Agency=====
As the word is used here, an "agent" is any kind of embodied activity. Thus, an electronic machine running a program is one sort of agent, but how it weighs in on the balance between a rock and a heart place of humane agency is another question.
As the word is used here, an "agent" is any kind of embodied activity. Thus, an electronic machine running a program is one sort of agent, but how it weighs in on the balance between a rock and a heart place of humane agency is another question.
=====3.3.3.2. Abstraction=====
=====3.3.3.2. Abstraction=====
An "abstract agent" refers to a general description or a functional specification of an agent, and allows that anything fitting the description or satisfying the specification will be recognized as an instance or model of that abstract description. The convenience of an abstraction, when it is apt, lies in our being able to reason about whole classes of entities from their stated properties alone. The usefulness of an abstraction, however, depends on our having identified the right list of properties for the purpose in mind.
An "abstract agent" refers to a general description or a functional specification of an agent, and allows that anything fitting the description or satisfying the specification will be recognized as an instance or model of that abstract description. The convenience of an abstraction, when it is apt, lies in our being able to reason about whole classes of entities from their stated properties alone. The usefulness of an abstraction, however, depends on our having identified the right list of properties for the purpose in mind.
=====3.3.3.3. Analogy=====
=====3.3.3.3. Analogy=====
The models of an abstract description are all "analogues" of each other, since they all share the properties that have been identified as being relevant to a particular discussion. In the pragmatic theory of signs, an "icon" is any sign or symbolic entity that accomplishes its reference to its object by virtue of sharing one or more properties with it. Whenever a person builds a model of a phenomenon or process, whether fashioned in concrete materials or expressed in abstract calculi, the usefulness of the simulation is determined by the structural and functional properties that it has in common with its object.
The models of an abstract description are all "analogues" of each other, since they all share the properties that have been identified as being relevant to a particular discussion. In the pragmatic theory of signs, an "icon" is any sign or symbolic entity that accomplishes its reference to its object by virtue of sharing one or more properties with it. Whenever a person builds a model of a phenomenon or process, whether fashioned in concrete materials or expressed in abstract calculi, the usefulness of the simulation is determined by the structural and functional properties that it has in common with its object.
=====3.3.3.4. Accuracy=====
=====3.3.3.4. Accuracy=====
The number and kinds of properties that a model is required to share with its object phenomenon can vary to a vast degree. Sometimes the only thing that matters is that the numbers generated at the end of a computation are the same, more or less, as the numbers that result from certain observations and measurements made on the phenomenon. These are usually called "numerical models" since they do little more than translate a quantitative mathematical model into a calculational form.
The number and kinds of properties that a model is required to share with its object phenomenon can vary to a vast degree. Sometimes the only thing that matters is that the numbers generated at the end of a computation are the same, more or less, as the numbers that result from certain observations and measurements made on the phenomenon. These are usually called "numerical models" since they do little more than translate a quantitative mathematical model into a calculational form.
=====3.3.3.5. Authenticity=====
=====3.3.3.5. Authenticity=====
But there are times when the purpose of imitation is more sincere, and it cannot be satisfied with a flattering image or an inactive reduction of the original performance. If the intent of the model is fully authentic, and the aim of simulation is not to mock up a mere appearance but means to achieve a genuine result through the emulation of an actual performance, then the modeler must embody both more substantial and more instrumental properties of the target agency in order to reproduce the intended faculty.
But there are times when the purpose of imitation is more sincere, and it cannot be satisfied with a flattering image or an inactive reduction of the original performance. If the intent of the model is fully authentic, and the aim of simulation is not to mock up a mere appearance but means to achieve a genuine result through the emulation of an actual performance, then the modeler must embody both more substantial and more instrumental properties of the target agency in order to reproduce the intended faculty.
The synthetic method employed in this project involves a reliance on computational models of abstractly specified agents. This practice implicitly extends the concept of an "agent" to include both human and machine forms of "agency", both concretely instantiated and abstractly formulated. This requires me to say how I understand the relations between these materially diverse categories of existence.
The synthetic method employed in this project involves a reliance on computational models of abstractly specified agents. This practice implicitly extends the concept of an "agent" to include both human and machine forms of "agency", both concretely instantiated and abstractly formulated. This requires me to say how I understand the relations between these materially diverse categories of existence.
====3.3.4. Anchoring Terms in Phenomena====
====3.3.4. Anchoring Terms in Phenomena====
To develop the ID of inquiry and articulate its terms in relation to actual experience, I need to pursue the phenomenology of the doubtful situation that initiates inquiry, and of its opposite pole, the condition of certainty that terminates inquiry. A couple of questions arise in this pursuit. How do the local poles that lie within an agent's finite compass of certainty line up with the global poles of information that pervade an encompassing field of inquiry? What are the modes of access that a finite agent has to information, certainty, knowledge, and belief?
To develop the ID of inquiry and articulate its terms in relation to actual experience, I need to pursue the phenomenology of the doubtful situation that initiates inquiry, and of its opposite pole, the condition of certainty that terminates inquiry. A couple of questions arise in this pursuit. How do the local poles that lie within an agent's finite compass of certainty line up with the global poles of information that pervade an encompassing field of inquiry? What are the modes of access that a finite agent has to information, certainty, knowledge, and belief?
Unless the very use of language will forever prejudice the question, I believe I can defer judgment on the existence of absolute poles for the field of inquiry. Therefore, the task is now to ask how the relative poles of an agent's local compass are related to the superrelative poles of a global field of inquiry.
Unless the very use of language will forever prejudice the question, I believe I can defer judgment on the existence of absolute poles for the field of inquiry. Therefore, the task is now to ask how the relative poles of an agent's local compass are related to the superrelative poles of a global field of inquiry.
=====3.3.4.1. A Mistaken ID=====
=====3.3.4.1. A Mistaken ID=====
=====3.3.4.2. Phenomenology of Doubt=====
=====3.3.4.2. Phenomenology of Doubt=====
=====3.3.4.3. Modalities of Knowledge=====
=====3.3.4.3. Modalities of Knowledge=====
This subsection enumerates several kinds of representation or "knowledge" that I shall speak of agents having of a concept or its objects.
This subsection enumerates several kinds of representation or "knowledge" that I shall speak of agents having of a concept or its objects.
====3.3.5. Sets, Systems, and Substantive Agents====
====3.3.5. Sets, Systems, and Substantive Agents====
This project is heavily invested in the discussion of various mathematical objects and the ways that these objects can be said to be represented in minds and other media. Depending on the context of discussion and application, the same objects may be described from slightly different perspectives, most frequently in the alternative guises of sets, systems, or systematic agents.
This project is heavily invested in the discussion of various mathematical objects and the ways that these objects can be said to be represented in minds and other media. Depending on the context of discussion and application, the same objects may be described from slightly different perspectives, most frequently in the alternative guises of sets, systems, or systematic agents.
Intention = the state of holding something held in mind, the state or its object?
Intention = the state of holding something held in mind, the state or its object?
====3.3.6. Interpretive Systems====
====3.3.6. Interpretive Systems====
This account of inquiry is intended to have a ...
This account of inquiry is intended to have a ...
This implies, quite literally, that a complete account of a thinking process could be represented a relational data base with exactly three columns, at each moment of the process listing the object, sign, and interpretant involved in that moment's transition.
This implies, quite literally, that a complete account of a thinking process could be represented a relational data base with exactly three columns, at each moment of the process listing the object, sign, and interpretant involved in that moment's transition.
=====3.3.6.1. Syntactic Systems=====
=====3.3.6.1. Syntactic Systems=====
A notion of acceptability, or candidate potential for meaning, a dichotomy of meaningful versus meaningless expressions decidable on formal grounds alone. Implemented by means of programs called parsers.
A notion of acceptability, or candidate potential for meaning, a dichotomy of meaningful versus meaningless expressions decidable on formal grounds alone. Implemented by means of programs called parsers.
=====3.3.6.2. Semantic Systems=====
=====3.3.6.2. Semantic Systems=====
A notion of meaning or sense, or equivalence and distinction of meaning, a partition of expressions into semantic equivalence classes.
A notion of meaning or sense, or equivalence and distinction of meaning, a partition of expressions into semantic equivalence classes.
Propositions that comment on the proceedings are not for that reason out of order but may be entirely fitting and dutiful. If so, they ought to receive due consideration as items on the agenda and enjoy a proper place in the order of actions executed.
Propositions that comment on the proceedings are not for that reason out of order but may be entirely fitting and dutiful. If so, they ought to receive due consideration as items on the agenda and enjoy a proper place in the order of actions executed.
=====3.3.6.3. Pragmatic Systems=====
=====3.3.6.3. Pragmatic Systems=====
A notion of clarity, or quality of representation in a a semantic equivalence class.
A notion of clarity, or quality of representation in a a semantic equivalence class.
Practical bearing: under experienced conditions, actions lead to further experiences.
Practical bearing: under experienced conditions, actions lead to further experiences.
====3.3.7. Inquiry Driven Systems====
====3.3.7. Inquiry Driven Systems====
=====3.3.7.1. A Definition of Inquiry=====
=====3.3.7.1. A Definition of Inquiry=====
John Dewey's lifetime of reflection on the nature and nurture of inquiry has tendered a definition of inquiry that remains unmatched in its clarity of depiction and its comprehension of the subject.
John Dewey's lifetime of reflection on the nature and nurture of inquiry has tendered a definition of inquiry that remains unmatched in its clarity of depiction and its comprehension of the subject.
This definition of inquiry is abstracted from the conduct and reflection of living agents who carry on inquiry, deploying it to convert their situations, as they experience them, from a condition of uncertainty to a character of unity. With living agents, intelligent enough to fall into question, this transformation serves as a preparation for action. For an agent to engage in competent action, it relies on a power to resolve two kinds of uncertainties, those about the predicates of a current situation and those about the prerequisites of a desired situation.
This definition of inquiry is abstracted from the conduct and reflection of living agents who carry on inquiry, deploying it to convert their situations, as they experience them, from a condition of uncertainty to a character of unity. With living agents, intelligent enough to fall into question, this transformation serves as a preparation for action. For an agent to engage in competent action, it relies on a power to resolve two kinds of uncertainties, those about the predicates of a current situation and those about the prerequisites of a desired situation.
=====3.3.7.2. The Faculty of Inquiry=====
=====3.3.7.2. The Faculty of Inquiry=====
It is conventional to assume that inquiring agents have a specialized faculty of inquiry that allows them to carry out the transformations required by the process. But even this simple postulate is not free from objection, and it should not be granted without a grain or two of critical reflection.
It is conventional to assume that inquiring agents have a specialized faculty of inquiry that allows them to carry out the transformations required by the process. But even this simple postulate is not free from objection, and it should not be granted without a grain or two of critical reflection.
The next order of business is to analyze the structure and function of this faculty of inquiry with the aim of devising a program of inquiry.
The next order of business is to analyze the structure and function of this faculty of inquiry with the aim of devising a program of inquiry.
=====3.3.7.3. A Definition of Determination=====
=====3.3.7.3. A Definition of Determination=====
=====3.3.7.4. A Definition of Definition=====
=====3.3.7.4. A Definition of Definition=====
===3.4. Organization of the Project : A Way Through Inquiry===
===3.4. Organization of the Project : A Way Through Inquiry===
====3.4.1. The Problem : Inquiry Found as an Object of Study====
====3.4.1. The Problem : Inquiry Found as an Object of Study====
This project takes as its object the nature of inquiry, and contemplates its nurture in the computer medium.
This project takes as its object the nature of inquiry, and contemplates its nurture in the computer medium.
====3.4.2. The Method : Inquiry Found as a Means of Study====
====3.4.2. The Method : Inquiry Found as a Means of Study====
The subject is inquiry, and inquiry, too, is the method of approach. Can inquiry into inquiry be a valid form of inquiry, or is it only a vicious circle, a vacuous self-reference? The reader has a right to question whether this self-described project can possibly be taken seriously, or whether inquiry into inquiry is a mere form of words, a vapid prototype outlining an impossible bootstrap. Worse yet, it is not just the faculty of inquiry whose self-application can be called into question. It can be doubted whether it makes sense to apply any function at all to itself, or whether the very idea of self-application is itself vain, devoid of any consistent meaning or purpose.
The subject is inquiry, and inquiry, too, is the method of approach. Can inquiry into inquiry be a valid form of inquiry, or is it only a vicious circle, a vacuous self-reference? The reader has a right to question whether this self-described project can possibly be taken seriously, or whether inquiry into inquiry is a mere form of words, a vapid prototype outlining an impossible bootstrap. Worse yet, it is not just the faculty of inquiry whose self-application can be called into question. It can be doubted whether it makes sense to apply any function at all to itself, or whether the very idea of self-application is itself vain, devoid of any consistent meaning or purpose.
=====3.4.2.1. Conditions for the Possibility of Inquiry into Inquiry=====
=====3.4.2.1. Conditions for the Possibility of Inquiry into Inquiry=====
If inquiry into inquiry is to be found a sensible project, and not just a question that begs itself, a blank application to which nothing signs "nothing" as an empty formality, as arrogantly suspect as the proverbial agency that proposes to investigate its own improprieties, then I must examine the conditions for its possibility. But inquiry begins when one is uncertain about something, and it is clearly possible to be doubtful about the nature of inquiry, as I am for certain in setting out on this investigation.
If inquiry into inquiry is to be found a sensible project, and not just a question that begs itself, a blank application to which nothing signs "nothing" as an empty formality, as arrogantly suspect as the proverbial agency that proposes to investigate its own improprieties, then I must examine the conditions for its possibility. But inquiry begins when one is uncertain about something, and it is clearly possible to be doubtful about the nature of inquiry, as I am for certain in setting out on this investigation.
If inquiry into inquiry is possible, and if all one knows about inquiry is that it begins with doubt and ends with belief, then doubt about doubt is possible, and one can actually be uncertain about the nature of uncertainty itself.
If inquiry into inquiry is possible, and if all one knows about inquiry is that it begins with doubt and ends with belief, then doubt about doubt is possible, and one can actually be uncertain about the nature of uncertainty itself.
=====3.4.2.2. Conditions for the Success of Inquiry into Inquiry=====
=====3.4.2.2. Conditions for the Success of Inquiry into Inquiry=====
For inquiry into inquiry to succeed it is only asked that one be able to use an ability before one has settled exactly how that ability is able to succeed, but this is clearly something that human beings do all the time. What it demands is a facility for carrying out the conceptual analysis of initially vague terms.
For inquiry into inquiry to succeed it is only asked that one be able to use an ability before one has settled exactly how that ability is able to succeed, but this is clearly something that human beings do all the time. What it demands is a facility for carrying out the conceptual analysis of initially vague terms.
In viewing computer simulations as empirical hypotheses, however, an important qualification should be appreciated. Notice that these models can be modal or normative hypotheses, not necessarily descriptive ones. As such, they are especially useful in research enterprises where the goal is to extend a human capacity, not merely to describe its current level of functioning. And yet, because the extension is based on a principle of similarity with the original function, it can also have a measure of descriptive utility.
In viewing computer simulations as empirical hypotheses, however, an important qualification should be appreciated. Notice that these models can be modal or normative hypotheses, not necessarily descriptive ones. As such, they are especially useful in research enterprises where the goal is to extend a human capacity, not merely to describe its current level of functioning. And yet, because the extension is based on a principle of similarity with the original function, it can also have a measure of descriptive utility.
====3.4.3. The Criterion : Inquiry in Search of a Sensible End====
====3.4.3. The Criterion : Inquiry in Search of a Sensible End====
Inquiry comes to rest when the irritation of uncertainty that set it in motion is reduced to zero, that is, to a level of relative insignificance.
Inquiry comes to rest when the irritation of uncertainty that set it in motion is reduced to zero, that is, to a level of relative insignificance.
=====3.4.3.1. The Irritation of Doubt, and The Scratch Test=====
=====3.4.3.1. The Irritation of Doubt, and The Scratch Test=====
The first draft of this termination criterion is an idealized formulation, prescribing the sole end of inquiry to be relief from the irritation of doubt. But it treats the complex situation of inquiry as though each investigation is pursued in isolation from every other condition of the inquiring agent, and it operates under the doubtful assumption that every inquiry is eventually carried to completion. As a criterion for the end, goal, bounds, or purpose of inquiry there remains the need for a pragmatic definition, a touchstone that can serve in a hard-knocks test to mark each question's field of operation and to limit the term of its continuation. To do all this, the fundamental principle needs a few amendments (enabling provisos or stipulations) to make it useful in actual practice.
The first draft of this termination criterion is an idealized formulation, prescribing the sole end of inquiry to be relief from the irritation of doubt. But it treats the complex situation of inquiry as though each investigation is pursued in isolation from every other condition of the inquiring agent, and it operates under the doubtful assumption that every inquiry is eventually carried to completion. As a criterion for the end, goal, bounds, or purpose of inquiry there remains the need for a pragmatic definition, a touchstone that can serve in a hard-knocks test to mark each question's field of operation and to limit the term of its continuation. To do all this, the fundamental principle needs a few amendments (enabling provisos or stipulations) to make it useful in actual practice.
=====3.4.3.2. Enabling Provision 1 : The Scenes and Context of Inquiry=====
=====3.4.3.2. Enabling Provision 1 : The Scenes and Context of Inquiry=====
In a realistic setting, equilibrium with respect to a dimension of inquiry is reached when the issue raises a negligible effect in the contest of competing demands for attention. This need not mean that the question is stilled forever, but only that the net effects of its nettling causes have fallen for a spell under the threshold of other concerns. In sum, the issue of an issue may settle itself below the level of a noise that no longer annoys. The agent of inquiry becomes tolerant or habituated to anything less than the mean irritation it knows, and learns to ignore as making no sense many a nuisance that sinks beneath the main and the norm and the mundane sensation of its usual suspicions.
In a realistic setting, equilibrium with respect to a dimension of inquiry is reached when the issue raises a negligible effect in the contest of competing demands for attention. This need not mean that the question is stilled forever, but only that the net effects of its nettling causes have fallen for a spell under the threshold of other concerns. In sum, the issue of an issue may settle itself below the level of a noise that no longer annoys. The agent of inquiry becomes tolerant or habituated to anything less than the mean irritation it knows, and learns to ignore as making no sense many a nuisance that sinks beneath the main and the norm and the mundane sensation of its usual suspicions.
=====3.4.3.3. Enabling Provision 2 : The Stages and Content of Inquiry=====
=====3.4.3.3. Enabling Provision 2 : The Stages and Content of Inquiry=====
The progress of inquiry is closely analogous to that of interpretation, a process of increasing determination that concentrates and precipitates gradients of richer and deeper meaning around the seeds provided by initially meaningless symbols. Indeed, "inquiry", or "thinking" in the best sense of the word, has been described as "a term denoting the various ways in which things acquire significance" (Dewey 1910, 38).
The progress of inquiry is closely analogous to that of interpretation, a process of increasing determination that concentrates and precipitates gradients of richer and deeper meaning around the seeds provided by initially meaningless symbols. Indeed, "inquiry", or "thinking" in the best sense of the word, has been described as "a term denoting the various ways in which things acquire significance" (Dewey 1910, 38).
It is not a requirement of successful interpretation to ever achieve a level of perfectly determinate objects. Interpreters may settle for a satisfactory power of resolution, just enough to distill the ambiguities blocking specific actions, seeking only to develop their pictures of a situation into clear choices for the success or failure of their active goals. What matters is lighting on a level of concrete meaning that is particulate enough to support discrete actions, injecting elements of determination into the categories of imperative that interpreters must negotiate if their contemplated decisions are to become consequential. In the mean time, if not in the end, interpreters are content to grasp any shade of determination that is solid enough to act on.
It is not a requirement of successful interpretation to ever achieve a level of perfectly determinate objects. Interpreters may settle for a satisfactory power of resolution, just enough to distill the ambiguities blocking specific actions, seeking only to develop their pictures of a situation into clear choices for the success or failure of their active goals. What matters is lighting on a level of concrete meaning that is particulate enough to support discrete actions, injecting elements of determination into the categories of imperative that interpreters must negotiate if their contemplated decisions are to become consequential. In the mean time, if not in the end, interpreters are content to grasp any shade of determination that is solid enough to act on.
===3.5. Objectives of the Project : Inquiry All the Way===
===3.5. Objectives of the Project : Inquiry All the Way===
This project has two objectives, one substantial and one instrumental.
This project has two objectives, one substantial and one instrumental.
====3.5.1. Substantial Objective====
====3.5.1. Substantial Objective====
The substantive aim is to undertake a comparative and developmental study of formal systems. This effort involves the following subprojects.
The substantive aim is to undertake a comparative and developmental study of formal systems. This effort involves the following subprojects.
=====3.5.1.1. Objective 1a : The Propositions as Types Analogy=====
=====3.5.1.1. Objective 1a : The Propositions as Types Analogy=====
First, I investigate a correspondence that exists between two kinds of formal systems, called applicational calculi (AC's) and propositional calculi (PC's). This relationship is known as the "propositions as types" analogy, or PAT isomorphism. It has applications to the checking of type declarations in programming languages (AC's) and to the annotation of proofs in logical systems (PC's).
First, I investigate a correspondence that exists between two kinds of formal systems, called applicational calculi (AC's) and propositional calculi (PC's). This relationship is known as the "propositions as types" analogy, or PAT isomorphism. It has applications to the checking of type declarations in programming languages (AC's) and to the annotation of proofs in logical systems (PC's).
=====3.5.1.2. Objective 1b : The Styles of Proof Development=====
=====3.5.1.2. Objective 1b : The Styles of Proof Development=====
Second, I explore a variety of ways that proofs may be developed in different species of propositional calculus. The major dimension of interest is the contrast between classical and intuitionistic proof systems, but there are interesting questions also about the relationship of different proof styles among equivalent axiom systems.
Second, I explore a variety of ways that proofs may be developed in different species of propositional calculus. The major dimension of interest is the contrast between classical and intuitionistic proof systems, but there are interesting questions also about the relationship of different proof styles among equivalent axiom systems.
=====3.5.1.3. Objective 1c : The Analysis of Interpreters, or A Problem with Authority=====
=====3.5.1.3. Objective 1c : The Analysis of Interpreters, or A Problem with Authority=====
Finally, I advance an ulterior purpose for taking up the "comparative anatomy" and "developmental biology" of formal systems. Axiom systems and their associated proof styles can be taken as prototypes and precursors of a larger class of meaning-bearing calculi, called "interpretive systems". When it is convenient to describe systems in a substantive vein, the agents that implement interpretive systems are called "interpreters". With dynamic systems the agent is a local representative of the system that travels through succeeding points of its state space, but with formal systems the agent is regarded as a person or machine that executes the moves of the calculus according to its protocol of rules. It is one of the overarching goals of this project to seek a merger of these two perspectives, the dynamic and the formal.
Finally, I advance an ulterior purpose for taking up the "comparative anatomy" and "developmental biology" of formal systems. Axiom systems and their associated proof styles can be taken as prototypes and precursors of a larger class of meaning-bearing calculi, called "interpretive systems". When it is convenient to describe systems in a substantive vein, the agents that implement interpretive systems are called "interpreters". With dynamic systems the agent is a local representative of the system that travels through succeeding points of its state space, but with formal systems the agent is regarded as a person or machine that executes the moves of the calculus according to its protocol of rules. It is one of the overarching goals of this project to seek a merger of these two perspectives, the dynamic and the formal.
====3.5.2. Instrumental Objective====
====3.5.2. Instrumental Objective====
The instrumental goal is to provide software support for the design and analysis of complex formal systems, for example, programming languages and theorem provers, just to indicate the cases of ultimate interest. But first, a lot more work needs to be done understanding the functional and logical aspects of much simpler calculi.
The instrumental goal is to provide software support for the design and analysis of complex formal systems, for example, programming languages and theorem provers, just to indicate the cases of ultimate interest. But first, a lot more work needs to be done understanding the functional and logical aspects of much simpler calculi.
====3.5.3. Coordination of Objectives====
====3.5.3. Coordination of Objectives====
These two efforts are intended to complement and support each other. The software implementation is an obvious way to catalyze the task of building theories about formal systems. Conversely, the best way of designing programs for any problem area is to build on a knowledge of structure in that domain. Discovering lawful relationships between applicational and propositional aspects of formal systems is one more source of structural constraints, information that can be exploited to improve the capabilities of software tools for the task.
These two efforts are intended to complement and support each other. The software implementation is an obvious way to catalyze the task of building theories about formal systems. Conversely, the best way of designing programs for any problem area is to build on a knowledge of structure in that domain. Discovering lawful relationships between applicational and propositional aspects of formal systems is one more source of structural constraints, information that can be exploited to improve the capabilities of software tools for the task.
====3.5.4. Recapitulation — Da Capo, Al Segno====
====3.5.4. Recapitulation — Da Capo, Al Segno====
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