Dynamics of inquiry

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Every mind which passes from doubt to belief must have ideas which follow after one another in time. Every mind which reasons must have ideas which not only follow after others but are caused by them. Every mind which is capable of logical criticism of its inferences, must be aware of this determination of its ideas by previous ideas. (Peirce, "On Time and Thought", CE 3, 68–69.)

All through the 1860s the young Charles Peirce was busy establishing a conceptual base-camp and a technical supply line for the intellectual adventures of a lifetime. Taking the long view of this activity and trying to choose the best titles for the story, it all seems to have something to do with the dynamics of inquiry. This broad subject area has a part that is given by nature and a part that is ruled by nurture. On first approach, it is possible to see a question of articulation and a question of explanation:


 * What is needed to articulate the workings of the active form of representation that is known as conscious experience?


 * What is needed to account for the workings of the reflective discipline of inquiry that is known as science?

The pursuit of answers to these questions finds them to be so entangled with each other that it's ultimately impossible to comprehend them apart from each other, but for the sake of exposition it's convenient to organize our study of Peirce's assault on the summa by following first the trails of thought that led him to develop a theory of signs, one that has come to be known as 'semiotic', and tracking next the ways of thinking that led him to develop a theory of inquiry, one that would be up to the task of saying 'how science works'.

Opportune points of departure for exploring the dynamics of representation, such as led to Peirce's theories of inference and information, inquiry and signs, are those that he took for his own springboards. Perhaps the most significant influences radiate from points on parallel lines of inquiry in Aristotle's work, points where the intellectual forerunner focused on many of the same issues and even came to strikingly similar conclusions, at least about the best ways to begin. Staying within the bounds of what will give us a more solid basis for understanding Peirce, it serves to consider the following loci in Aristotle:


 * The basic terminology of psychology, in On the Soul.


 * The founding description of sign relations, in On Interpretation;


 * The differentiation of the genus of reasoning into three species of inference that are commonly translated into English as abduction, deduction, and induction, in the Prior Analytics.

In addition to the three elements of inference, that Peirce would assay to be irreducible, Aristotle analyzed several types of compound inference, most importantly the type known as 'reasoning by analogy' or 'reasoning from example', employing for the latter description the Greek word 'paradeigma', from which we get our word 'paradigm'.

Inquiry is a form of reasoning process, in effect, a particular way of conducting thought, and thus it can be said to institute a specialized manner, style, or turn of thinking. Philosophers of the school that is commonly called 'pragmatic' hold that all thought takes place in signs, where 'sign' is the word they use for the broadest conceivable variety of characters, expressions, formulas, messages, signals, texts, and so on up the line, that might be imagined. Even intellectual concepts and mental ideas are held to be a special class of signs, corresponding to internal states of the thinking agent that both issue in and result from the interpretation of external signs.

The subsumption of inquiry within reasoning in general and the inclusion of thinking within the class of sign processes allows us to approach the subject of inquiry from two different perspectives:


 * The syllogistic approach treats inquiry as a species of logical process, and is limited to those of its aspects that can be related to the most basic laws of inference.


 * The sign-theoretic approach views inquiry as a genus of semiosis, an activity taking place within the more general setting of sign relations and sign processes.

The distinction between signs denoting and objects denoted is critical to the discussion of Peirce's theory of signs. Wherever needed in the rest of this article, therefore, in order to mark this distinction a little more emphatically than usual, double quotation marks placed around a given sign, for example, a string of zero or more characters, will be used to create a new sign that denotes the given sign as its object.

Semeiotic : Peirce's theory of signs
Peirce referred to his general study of signs, based on the concept of a triadic sign relation, as semeiotic or semiotic, either of which terms are currently used in both singular of plural forms. Peirce began writing on semeiotic in the 1860s, around the time that he devised his system of three categories. He eventually defined semiosis as an "action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs". (Houser 1998: 411, written 1907). This triadic relation grounds the semeiotic.

In order to understand what a sign is we need to understand what a sign relation is, for signhood is a way of being in relation, not a way of being in itself. In order to understand what a sign relation is we need to understand what a triadic relation is, for the role of a sign is constituted as one among three, where roles in general are distinct even when the things that fill them are not. In order to understand what a triadic relation is we need to understand what a relation is, and here there are traditionally two ways of understanding what a relation is, both of which are necessary if not sufficient to complete understanding, namely, the way of extension and the way of intension. To these traditional approximations, Peirce adds a third way, the way of information, that integrates the other two approaches in a unified whole.

Sign relations

 * Main article : Sign relation

With that hasty map of relations and relatives sketched above, we may now trek into the terrain of sign relations, the main subject matter of Peirce's semeiotic, or theory of signs.

Types of signs
Peirce proposes several typologies and definitions of the signs. More than 76 definitions of what a sign is have been collected throughout Peirce's work. Some canonical typologies can nonetheless be observed, one crucial one being the distinction between "icons", "indices" and "symbols" (CP 2.228, CP 2.229 and CP 5.473). This typology emphasizes the different ways in which the representamen (or its ground) addresses or refers to its object, through a particular mobilisation of an interpretant (but Peirce proposes also other typologies based on other criteria).


 * An icon is a sign that denotes its objects by virtue of a quality that it shares with them. The sign is perceived as resembling or imitating the object it refers to (e.g. fork on a sign by the road indicating a rest stop). In other words, an icon thus "resembles" to its object. It shares a character or an aspect with it, which allows for it to be interpreted as a sign even if the object does not exist. It signifies essentially on the basis of its "ground".


 * An index is a sign that denotes its objects by virtue of an existential connection that it has with them. For an index to signify, the relation to the object is crucial. The representamen is directly connected in some way (physically or casually) to the object it denotes (e.g. smoke coming from a building is an index of fire). Hence, an index refers to the object because it is really affected or modified by it, and thus may stand as a trace of the existence of the object.


 * A symbol is a sign that denotes its objects solely by virtue of the fact that it is interpreted to do so. The representamen does not resemble the object signified but is fundamentally conventional, so that the signifying relationship must be learned and agreed upon (e.g. the word "cat"). A symbol thus denotes, primarily, by virtue of its interpretant.  Its action (semeiosis) is ruled by a convention, a more or less systematic set of associations that guarantees its interpretation, independently of any resemblance or any material relation with its object.

Note that these definitions are specific to Peirce's theory of signs and are not exactly equivalent to general uses of the notion of "icon", "symbol" or "index".

Theory of inquiry

 * Main article : Inquiry


 * Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy:

Do not block the way of inquiry.
 * Although it is better to be methodical in our investigations, and to consider the economics of research, yet there is no positive sin against logic in trying any theory which may come into our heads, so long as it is adopted in such a sense as to permit the investigation to go on unimpeded and undiscouraged. On the other hand, to set up a philosophy which barricades the road of further advance toward the truth is the one unpardonable offence in reasoning, as it is also the one to which metaphysicians have in all ages shown themselves the most addicted.  (Peirce, "F.R.L." (c. 1899), CP 1.135–136.)

Peirce extracted the pragmatic model or theory of inquiry from its raw materials in classical logic and refined it in parallel with the early development of symbolic logic to address problems about the nature of scientific reasoning. Borrowing a brace of concepts from Aristotle, Peirce examined three fundamental modes of reasoning that play a role in inquiry, processes that are currently known as abductive, deductive, and inductive inference.

In the roughest terms, abduction is what we use to generate a likely hypothesis or an initial diagnosis in response to a phenomenon of interest or a problem of concern, while deduction is used to clarify, to derive, and to explicate the relevant consequences of the selected hypothesis, and induction is used to test the sum of the predictions against the sum of the data.

These three processes typically operate in a cyclic fashion, systematically operating to reduce the uncertainties and the difficulties that initiated the inquiry in question, and in this way, to the extent that inquiry is successful, leading to an increase in the knowledge or skills, in other words, an augmentation in the competence or performance, of the agent or community engaged in the inquiry.

In the pragmatic way of thinking every thing has a purpose, and the purpose of any thing is the first thing that we should try to note about it. The purpose of inquiry is to reduce doubt and lead to a state of belief, which a person in that state will usually call knowledge or certainty. It needs to be appreciated that the three kinds of inference, insofar as they contribute to the end of inquiry, describe a cycle that can be understood only as a whole, and none of the three makes complete sense in isolation from the others.

For instance, the purpose of abduction is to generate guesses of a kind that deduction can explicate and that induction can evaluate. This places a mild but meaningful constraint on the production of hypotheses, since it is not just any wild guess at explanation that submits itself to reason and bows out when defeated in a match with reality. In a similar fashion, each of the other types of inference realizes its purpose only in accord with its proper role in the whole cycle of inquiry. No matter how much it may be necessary to study these processes in abstraction from each other, the integrity of inquiry places strong limitations on the effective modularity of its principal components.

If we then think to inquire, "What sort of constraint, exactly, does pragmatic thinking place on our guesses?", we have asked the question that is generally recognized as the problem of "giving a rule to abduction". Peirce's way of answering it is given in terms of the so-called pragmatic maxim, and this in turn gives us a clue as to the central role of abductive reasoning in Peirce's pragmatic philosophy.

Logic of information

 * Main article : Logic of information

Let us now return to the information. The information of a term is the measure of its superfluous comprehension. That is to say that the proper office of the comprehension is to determine the extension of the term. For instance, you and I are men because we possess those attributes &mdash; having two legs, being rational, &tc. &mdash; which make up the comprehension of man. Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead. (C.S. Peirce, "The Logic of Science, or, Induction and Hypothesis" (1866), CE 1, 467.)

Source materials
C.S. Peirce, &ldquo;On Time and Thought&rdquo;, MS 215, 8 March 1873.

Every mind which passes from doubt to belief must have ideas which follow after one another in time. Every mind which reasons must have ideas which not only follow after others but are caused by them. Every mind which is capable of logical criticism of its inferences, must be aware of this determination of its ideas by previous ideas. But is it pre-supposed in the conception of a logical mind, that the temporal succession in its ideas is continuous, and not by discrete steps? A continuum such as we suppose time and space to be, is defined as something any part of which itself has parts of the same kind. So that the point of time or the point of space is nothing but the ideal limit towards which we approach, but which we can never reach in dividing time or space; and consequently nothing is true of a point which is not true of a space or a time. A discrete quantum, on the other hand, has ultimate parts which differ from any other part of the quantum in their absolute separation from one another. If the succession of images in the mind is by discrete steps, time for that mind will be made up of indivisible instants. Any one idea will be absolutely distinguished from every other idea by its being present only in the passing moment. And the same idea can not exist in two different moments, however similar the ideas felt in the two different moments may, for the sake of argument, be allowed to be. Now an idea exists only so far as the mind thinks it; and only when it is present to the mind. An idea therefore has no characters or qualities but what the mind thinks of it at the time when it is present to the mind. It follows from this that if the succession of time were by separate steps, no idea could resemble another; for these ideas if they are distinct, are present to the mind at different times. Therefore at no time when one is present to the mind, is the other present. Consequently the mind never compares them nor thinks them to be alike; and consequently they are not alike;  since they are only what they are thought to be at the time when they are present. It may be objected that though the mind does not directly think them to be alike; yet it may think together reproductions of them, and thus think them to be alike. This would be a valid objection were it not necessary, in the first place, in order that one idea should be the representative of another, that it should resemble that idea, which it could only do by means of some representation of it again, and so on to infinity; the link which is to bind the first two together which are to be pronounced alike, never being found. In short the resemblance of ideas implies that some two ideas are to be thought together which are present to the mind at different times. And this never can be, if instants are separated from one another by absolute steps. This conception is therefore to be abandoned, and it must be acknowledged to be already presupposed in the conception of a logical mind that the flow of time should be continuous. Let us consider then how we are to conceive what is present to the mind. We are accustomed to say that nothing is present but a fleeting instant, a point of time. But this is a wrong view of the matter because a point differs in no respect from a space of time, except that it is the ideal limit which, in the division of time, we never reach. It can not therefore be that it differs from an interval of time in this respect that what is present is only in a fleeting instant, and does not occupy a whole interval of time, unless what is present be an ideal something which can never be reached, and not something real. The true conception is, that ideas which succeed one another during an interval of time, become present to the mind through the successive presence of the ideas which occupy the parts of that time. So that the ideas which are present in each of these parts are more immediately present, or rather less mediately present than those of the whole time. And this division may be carried to any extent. But you never reach an idea which is quite immediately present to the mind, and is not made present by the ideas which occupy the parts of the time that it occupies. Accordingly, it takes time for ideas to be present to the mind. They are present during a time. And they are present by means of the presence of the ideas which are in the parts of that time. Nothing is therefore present to the mind in an instant, but only during a time. The events of a day are less mediately present to the mind than the events of a year; the events of a second less mediately present than the events of a day. (C.S. Peirce, CE 3, pp. 68–70).

Charles Sanders Peirce, MS 215, 1873, [&ldquo;On Time and Thought&rdquo;], pp. 68–71 in Writings of Charles S. Peirce : A Chronological Edition, Volume 3, 1872–1878, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.

Focal nodes

 * Inquiry Live
 * Logic Live

Peer nodes

 * Dynamics of Inquiry @ InterSciWiki
 * Dynamics of Inquiry @ MyWikiBiz
 * Dynamics of Inquiry @ Subject Wikis
 * Dynamics of Inquiry @ Wikiversity
 * Dynamics of Inquiry @ Wikiversity Beta

Logical operators

 * Exclusive disjunction
 * Logical conjunction
 * Logical disjunction
 * Logical equality


 * Logical implication
 * Logical NAND
 * Logical NNOR
 * Negation

Related topics

 * Ampheck
 * Boolean domain
 * Boolean function
 * Boolean-valued function
 * Differential logic


 * Logical graph
 * Minimal negation operator
 * Multigrade operator
 * Parametric operator
 * Peirce's law


 * Propositional calculus
 * Sole sufficient operator
 * Truth table
 * Universe of discourse
 * Zeroth order logic

Relational concepts

 * Continuous predicate
 * Hypostatic abstraction
 * Logic of relatives
 * Logical matrix


 * Relation
 * Relation composition
 * Relation construction
 * Relation reduction


 * Relation theory
 * Relative term
 * Sign relation
 * Triadic relation

Information, Inquiry

 * Inquiry
 * Dynamics of inquiry


 * Semeiotic
 * Logic of information


 * Descriptive science
 * Normative science


 * Pragmatic maxim
 * Truth theory

Related articles

 * Semiotic Information
 * Futures Of Logical Graphs
 * Propositional Equation Reasoning Systems


 * Differential Logic : Introduction
 * Differential Propositional Calculus
 * Differential Logic and Dynamic Systems


 * Introduction to Inquiry Driven Systems
 * Prospects for Inquiry Driven Systems
 * Inquiry Driven Systems : Inquiry Into Inquiry

Document history
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 * Dynamics of Inquiry, InterSciWiki
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