Inquiry Into Inquiry

Pragmatic Truth • Discussion 25

Posted on July 15, 2024 by Jon Awbrey

Re: Pragmatic Truth • (1) • (2)
Re: OEIS Wiki | Correspondence Theory Of Truth
Re: FB | Inquiry Driven Systems • Richard Saunders

RS:: Given that “facts are basically combinations of objects together with their properties or relations; so the fact that Fido barks is the combination of an object (i.e., Fido) with one of Fido’s properties (that he barks)”, if the object and the property are real, then the correspondence theory of truth seems adequate for most purposes. But the question remains, what is “real”? I like Phillip Dick’s suggestion that reality is what remains when you stop believing in it.

Dear Richard,

Let me clear up a few things about that section of the Correspondence Theory article you quote above. The style of it tells me other Wikipedians probably had a bigger hand in it than I did — for my part I most likely took it as a thumbnail sketch of the conventional view, a sop to the two‑headed dogma of analytic philosoppy, if you will.

Pragmatic treatments of truth begin from a decidedly different standpoint and make a radical departure from correspondence accounts. But there is nothing new about the pragmatic view, as we can see from the way Kant and even the Ancients had already criticized correspondence theories.

Resources

cc: FB | Inquiry Driven Systems • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Posted in Aristotle, C.S. Peirce, Coherence, Concordance, Congruence, Consensus, Convergence, Correspondence, Dewey, Fixation of Belief, Information, Inquiry, John Dewey, Kant, Logic, Logic of Science, Method, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Semiotics, Sign Relations, Triadic Relations, Truth, Truth Theory, William James | Tagged Aristotle, C.S. Peirce, Coherence, Concordance, Congruence, Consensus, Convergence, Correspondence, Dewey, Fixation of Belief, Information, Inquiry, John Dewey, Kant, Logic, Logic of Science, Method, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Semiotics, Sign Relations, Triadic Relations, Truth, Truth Theory, William James | 4 Comments

Pragmatic Truth • 4

Posted on July 13, 2024 by Jon Awbrey

Truth Theories

Theories of truth may be described according to several dimensions of description affecting the character of the predicate “true”. The truth predicates used in different theories may be classified according to the number of things which have to be taken into account in order to evaluate the truth of a sign, counting the sign itself as the first thing. The number of dimensions is sometimes called the arity or adicity of the truth predicate.

A truth predicate is monadic if it applies to its main subject, typically a concrete representation or its abstract content, independently of reference to anything else. In that case one may think of a truth bearer as being true in and of itself.
A truth predicate is dyadic if it applies to its main subject only in reference to something else, a second subject. Most commonly, the ancillary subject is either an object, an interpreter, or a language to which the representation bears a specified relation.
A truth predicate is triadic if it applies to its main subject only in reference to a second and a third subject. For example, in a pragmatic theory of truth one has to specify both the object of the sign and either its interpreter or another sign called its interpretant. In that case, one says the sign is true “of” its object “to” its interpreting agent or sign.

There are practical considerations we need to keep in mind when contemplating such radically simple schemes of classification. Real‑world practice seldom presents us with pure cases and ideal types. There are many settings where it is useful to speak of a truth theory as “almost” $k$ -adic or to say it “would be” $k$ -adic if certain details are abstracted away and neglected in a particular context of discussion. That said, given the generic division of truth predicates according to their dimensionality, further species may be differentiated within each genus according to a number of more refined features.

The truth predicate in a correspondence theory of truth tells of a relation between representations and objective states of affairs and is therefore expressed by a dyadic predicate. In general terms, one says a representation is true of an objective situation, more briefly, a sign is true of an object. The nature of the correspondence may vary from theory to theory in this family. The correspondence can be fairly arbitrary or it can take on the character of an analogy, an icon, or a morphism, where a representation is rendered true of its object by the existence of corresponding elements and a similar structure.

Resources

cc: FB | Inquiry Driven Systems • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Pragmatic Truth • 3

Posted on July 12, 2024 by Jon Awbrey

Truth Predicates

An inquiry into the character of truth generally begins with the idea of an informative, meaningful, or significant element, the goodness of whose information, meaning, or significance may be put in question and needs to be evaluated. Depending on context, the element may be called an artefact, expression, image, impression, lyric, mark, performance, picture, sentence, sign, string, symbol, text, thought, token, utterance, word, work, and so on. However that may be, one has the task of judging whether the bearers of information, meaning, or significance are indeed truth‑bearers or not. That judgment is typically expressed in the form of a specific truth predicate, whose positive application to a sign, or so on, asserts the truth of the sign.

Considered within the broadest horizon, there is little reason to imagine the process of judging a work, which leads to a predication of false or true, is necessarily amenable to formalization, and that task may always remain what is commonly called a judgment call. But there are many well-circumscribed domains where it is useful to consider disciplined forms of evaluation and the observation of those limits allows for the institution of what is called a method of judging truth and falsity.

One of the first questions to be asked in this setting concerns the relationship between the significant performance and its reflective critique. If one expresses oneself in a particular fashion, and someone says “that’s true”, is there anything useful at all to be said in general terms about the relationship between those two acts? For instance, does the critique add value to the expression criticized, does it say something significant in its own right, or is it but an insubstantial echo of the original sign?

Resources

cc: FB | Inquiry Driven Systems • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Pragmatic Truth • 2

Posted on July 10, 2024 by Jon Awbrey

Truth as the Good of Logic

Pragmatic theories of truth enter on a stage set by the philosophies of former ages, with special reference to the Ancient Greeks, the Scholastics, and Immanuel Kant. Recalling a few elements of that background can provide valuable insight into the play of ideas as they have developed up through our time. Because pragmatic ideas about truth are often confused with a number of quite distinct notions it is useful say a few words about those other theories and to highlight the points of significant contrast.

In one classical formulation, truth is defined as the good of logic, where logic is classed as a normative science, in other words, an inquiry into a good or value which seeks to arrive at knowledge of it and the means to achieve it. In that view, truth cannot be discussed to much effect outside the context of inquiry, knowledge, and logic, all very broadly conceived.

Resources

cc: FB | Inquiry Driven Systems • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Pragmatic Truth • 1

Posted on July 8, 2024 by Jon Awbrey

Questions about the pragmatic conception of truth have broken out in several quarters, asking in effect, “What conceptions of truth arise most naturally from and are best suited to pragmatic ways of thinking?” My best thoughts on that score were written out quite a few years ago, in an article I originally wrote for Wikipedia. I haven’t dared look at what’s become of it on that site — linked below is my current fork on another wiki.

Pragmatic Theory Of Truth

It begins as follows …

Pragmatic theory of truth refers to those accounts, definitions, and theories of the concept truth distinguishing the philosophies of pragmatism and pragmaticism. The conception of truth in question varies along lines reflecting the influence of several thinkers, initially and notably, Charles Sanders Peirce, William James, and John Dewey, but a number of common features can be identified.

The most characteristic features are (1) a reliance on the pragmatic maxim as a means of clarifying the meanings of difficult concepts, truth in particular, and (2) an emphasis on the fact that the product variously branded as belief, certainty, knowledge, or truth is the result of a process, namely, inquiry.

Et sic deinceps …

Resources

cc: FB | Inquiry Driven Systems • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Constraints and Indications • 2

Posted on July 4, 2024 by Jon Awbrey

Re: Constraints and Indications • 1
Re: Ontolog Forum • Joseph Simpson

Coping with collaboration, communication, context, integration, interoperability, perspective, purpose, and the reality of the information dimension demands a transition from conceptual environments bounded by dyadic relations to those informed by triadic relations, especially the variety of triadic sign relations employed by pragmatic semiotics.

Along the lines of my first post on this topic I am presently concerned with the logical and mathematical requirements of dealing with constraints but when it comes to the constraints involved in communicating across cultural and disciplinary barriers I could recommend a paper Susan Awbrey and I wrote for a conference devoted to those very issues.

Conference Presentation

Awbrey, S.M., and Awbrey, J.L. (1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA. Online.

Published Paper

Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284. Abstract. Online.

Resources

cc: FB | Inquiry Driven Systems • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Posted in Adaptive Systems, Artificial Intelligence, Ashby, C.S. Peirce, Constraint, Control, Cybernetics, Determination, Error-Controlled Regulation, Feedback, Indication, Indicator Functions, Information, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intentionality, Learning Theory, Semiotic Information, Semiotics, Systems Theory, Uncertainty | Tagged Adaptive Systems, Artificial Intelligence, Ashby, C.S. Peirce, Constraint, Control, Cybernetics, Determination, Error-Controlled Regulation, Feedback, Indication, Indicator Functions, Information, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intentionality, Learning Theory, Semiotic Information, Semiotics, Systems Theory, Uncertainty | Leave a comment

Constraints and Indications • 1

Posted on July 2, 2024 by Jon Awbrey

Re: Peirce List • Kaina Stoicheia and the Symbol Grounding Problem
Re: Jerry Chandler • Christophe Menant • Jon Awbrey • Christophe Menant

The system‑theoretic concept of constraint is one that unifies a manifold of other notions — definition, determination, habit, information, law, predicate, regularity, and so on. Indeed, it is often the best way to understand the entire complex of concepts.

Entwined with the concept of constraint is the concept of information, the power signs bear to reduce uncertainty and advance inquiry. Asking what consequences those ideas have for Peirce’s theory of triadic sign relations led me some years ago to the thoughts recorded on the following page.

Pragmatic Semiotic Information

Here I am thinking of the concept of constraint that constitutes one of the fundamental ideas of classical cybernetics and mathematical systems theory.

For example, here is how W. Ross Ashby introduces the concept of constraint in his Introduction to Cybernetics (1956).

A most important concept, with which we shall be much concerned later, is that of constraint. It is a relation between two sets, and occurs when the variety that exists under one condition is less than the variety that exists under another. Thus, the variety of the human sexes is 1 bit; if a certain school takes only boys, the variety in the sexes within the school is zero; so as 0 is less than 1, constraint exists. (1964 ed., p. 127).

At its simplest, then, constraint is an aspect of the subset relation.

The objective of an agent, organism, or similar regulator is to keep within its viable region, a particular subset of its possible state space. That is the constraint of primary interest to the agent.

Reference

Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.

Resources

cc: FB | Inquiry Driven Systems • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Theme One Program • Jets and Sharks 3

Posted on June 23, 2024 by Jon Awbrey

Re: Theme One Program • Jets and Sharks • (1) • (2)

Example 5. Jets and Sharks (cont.)

Given a representation of the Jets and Sharks universe in computer memory, we naturally want to see if the memory serves to supply the facts a well-constructed data base should.

In their PDP Handbook presentation of the Jets and Sharks example, McClelland and Rumelhart suggest several exercises for the reader to explore the performance of their neural pool memory model on the tasks of retrieval and generalization (Exercise 2.1).

Using cactus graphs or minimal negations to implement pools of mutually inhibitory neurons lends itself to neural architectures on a substantially different foundation from the garden variety connectionist models. At a high level of abstraction, however, there is enough homology between the two orders to compare their performance on many of the same tasks. With that in mind, I tried Theme One on a number of examples like the ones suggested by McClelland and Rumelhart.

What follows is a brief discussion of two examples as given in the original User Guide. Next time I’ll fill in more details about the examples and discuss their bearing on the larger issues at hand.

With a query on the name “ken” we obtain the following output, giving all the features associated with Ken.

$\text{Jets and Sharks} \stackrel{_\bullet}{} \text{Query 1}$

With a query on the two features “college” and “sharks” we obtain the following outline of all features satisfying those constraints.

$\text{Jets and Sharks} \stackrel{_\bullet}{} \text{Query 2}$

From this we discover all college Sharks are 30‑something and married. Further, we have a complete listing of their names broken down by occupation.

References

McClelland, J.L. (2015), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, 2nd ed. (draft), Stanford Parallel Distributed Processing Lab. Online, Section 2.3, Figure 2.1.
McClelland, J.L., and Rumelhart, D.E. (1988), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, MIT Press, Cambridge, MA. “Figure 1. Characteristics of a number of individuals belonging to two gangs, the Jets and the Sharks”, p. 39, from McClelland (1981).
McClelland, J.L. (1981), “Retrieving General and Specific Knowledge From Stored Knowledge of Specifics”, Proceedings of the Third Annual Conference of the Cognitive Science Society, Berkeley, CA.

Resources

cc: FB | Theme One Program • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | 3 Comments

Theme One Program • Jets and Sharks 2

Posted on June 22, 2024 by Jon Awbrey

Example 5. Jets and Sharks (cont.)

As we saw last time, Theme One reads the text file shown below and constructs a cactus graph data structure in computer memory. The cactus graph represents a single logical formula in propositional calculus and that proposition embodies the logical constraints defining the Jets and Sharks data base.

$\text{Jets and Sharks} \stackrel{_\bullet}{} \text{Log File}$

Our cactus graph incorporates a vocabulary of 41 logical terms, each of which represents a boolean variable, so the proposition in question, call it $``q",$ is a boolean function of the form $q : \mathbb{B}^{41} \to \mathbb{B}.$ Given $2^{41} = 2,199,023,255,552$ we know a truth table for $q$ takes over two trillion rows and a venn diagram for $q$ takes the same number of cells. Topping it off, there are $2^{2^{41}}$ boolean functions of the form $f : \mathbb{B}^{41} \to \mathbb{B}$ and $q$ is just one of them.

Measures of strategy are clearly needed to negotiate patches of cacti like those.

References

McClelland, J.L. (2015), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, 2nd ed. (draft), Stanford Parallel Distributed Processing Lab. Online, Section 2.3, Figure 2.1.
McClelland, J.L., and Rumelhart, D.E. (1988), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, MIT Press, Cambridge, MA. “Figure 1. Characteristics of a number of individuals belonging to two gangs, the Jets and the Sharks”, p. 39, from McClelland (1981).
McClelland, J.L. (1981), “Retrieving General and Specific Knowledge From Stored Knowledge of Specifics”, Proceedings of the Third Annual Conference of the Cognitive Science Society, Berkeley, CA.

Resources

cc: FB | Theme One Program • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Theme One Program • Jets and Sharks 1

Posted on June 20, 2024 by Jon Awbrey

It is easy to spend a long time on the rudiments of learning and logic before getting down to practical applications — but I think we’ve circled square one long enough to expand our scope and see what the category of programs envisioned in Theme One can do with more substantial examples and exercises.

During the development of the Theme One program I tested successive implementations of its Reasoning Module or Logical Modeler on appropriate examples of logical problems current in the literature of the day. The PDP Handbook of McClelland and Rumelhart set one of the wittiest gems ever to whet one’s app‑titude so I could hardly help but take it on. The following text is a light revision of the way I set it up in the program’s User Guide.

Example 5. Jets and Sharks

The propositional calculus based on the minimal negation operator can be interpreted in a way resembling the logic of activation states and competition constraints in one class of neural network models. One way to do this is to interpret the blank or unmarked state as the resting state of a neural pool, the bound or marked state as its activated state, and to represent a mutually inhibitory pool of neurons $A, B, C$ by the proposition $\texttt{(} A \texttt{,} B \texttt{,} C \texttt{)}.$ The manner of representation may be illustrated by transcribing a well-known example from the parallel distributed processing literature (McClelland and Rumelhart 1988) and working through a couple of the associated exercises as translated into logical graphs.

Displayed below is the text expression of a traversal string which Theme One parses into a cactus graph data structure in computer memory. The cactus graph represents a single logical formula in propositional calculus and this proposition embodies all the logical constraints defining the Jets and Sharks data base.

$\text{Jets and Sharks} \stackrel{_\bullet}{} \text{Log File}$

References

McClelland, J.L. (2015), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, 2nd ed. (draft), Stanford Parallel Distributed Processing Lab. Online, Section 2.3, Figure 2.1.
McClelland, J.L., and Rumelhart, D.E. (1988), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, MIT Press, Cambridge, MA. “Figure 1. Characteristics of a number of individuals belonging to two gangs, the Jets and the Sharks”, p. 39, from McClelland (1981).
McClelland, J.L. (1981), “Retrieving General and Specific Knowledge From Stored Knowledge of Specifics”, Proceedings of the Third Annual Conference of the Cognitive Science Society, Berkeley, CA.

Resources

cc: FB | Theme One Program • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

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Truth Theories

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Truth Predicates

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Truth as the Good of Logic

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Example 5. Jets and Sharks (cont.)

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Example 5. Jets and Sharks (cont.)

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Example 5. Jets and Sharks

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