Homunculomorphisms • 2

Re: John BaezThe Internal Model Principle

There’s a far-ranging discussion that takes off from this point, touching on links among analogical reasoning, arrows and functors, cybernetic images, iconic versus symbolic representations, mental models, systems simulations, etc., and just how categorically or contingently those functions are necessary to intelligent agency, all of which questions have enjoyed large and partly overlapping literatures for a long time now.

It is one question whether a regulator has “knowledge” of the object system and another question whether that knowledge is embodied in the more specific form of a “model”.  At this point we encounter a variety of meanings for the word “model”.  In my experience the meanings divide into two broad classes, “logical models” and “analogical models”.

  • Logical modeling involves a relation between a theory and anything that satisfies the theory, in practice either the original domain of phenomena the theory is created to describe or a formal object we construct to satisfy the theory.
  • Analogical modeling involves a relation between any two things that have similar properties or structures or that satisfy the same theory.

It is possible that a regulator has knowledge, competence, or a capacity for performance that exists in the form of a theory or other data structures without necessarily having either type of model on hand.

There is little doubt that models of either sort are extremely useful when we can get them but there are reasons for thinking that the mirror of nature does not go all the way down to the most primitive structures of adaptive functioning.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
Posted in Analogy, Ashby, Automata, Control Systems, Cybernetics, Homunculi, Homunculomorphisms, Iconicity, Information Theory, Inquiry, Inquiry Driven Systems, Intentionality, Internal Models, Logic, Logic of Science, Mathematics, Mental Models, Model Theory, Optimal Control, Peirce, Semiotics, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Homunculomorphisms • 1

Re: John BaezThe Internal Model Principle

Ashby’s book was my own first introduction to cybernetics and I recently returned to his discussion of regulation games in connection with some issues in Peirce’s theory of inquiry.

In that context it appears that the formula \rho \subset [\psi^{-1}(G)]\phi would have to be saying that the Regulator’s good moves are a subset given by applying the portion of the game matrix with goal values in its body to the Disturber’s input.

Excursion

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
Posted in Ashby, Automata, Category Theory, Control, Control Systems, Control Theory, Cybernetics, Homunculi, Homunculomorphisms, Information, Information Theory, Inquiry, Inquiry Driven Systems, Intentionality, Internal Models, Logic of Science, Mathematics, Mental Models, Optimal Control, Peirce, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Problems In Philosophy • 5

Re: Michael HarrisAre Your Colleagues Zombies?

What makes a zombie a legitimate object of philosophical inquiry is its absence of consciousness.  And today’s question is whether mathematical research requires consciousness, or whether it could just as well be left to zombies.

There are many things that could be discussed in this connection, but coming from a perspective informed by Peirce on the nature of inquiry and the whole tradition augured by Freud and Jung on the nature of the unconscious makes for a slightly shifted view of things compared, say, to the pet puzzles of analytic philosophy and the varieties of cognitive psychology that repress any thought of affects, emotions, and unconscious dynamics.

There is almost always in the back of my mind a question about how the species of mathematical inquiry fits within the genus of inquiry writ large.

That raises a question about the nature of inquiry.  Do machines or zombies — unsouled creatures — inquire or question at all?  Is awareness or consciousness necessary to inquiry?  Inquiry in general?  Mathematical inquiry as a special case?

One of the ideas we get from Peirce is that inquiry begins with the irritation of doubt and ends with the fixation of belief.  This splices nicely into the frames of our zombie flick for a couple of reasons:

  • It harks back to Aristotle’s idea that the cognitive is derivative of the affective.
  • It reminds me of what my high school biology texts always enumerated as a distinctive feature of living things, their irritability.
Posted in Aristotle, Automata, Automated Research Tools, Automation, Cognition, Computation, Consciousness, Freud, Inquiry, Inquiry Driven Systems, Intentionality, Mathematics, Mechanization, Michael Harris, Peirce, Philosophy, Philosophy of Mathematics, Philosophy of Mind, Plato, Psychology, Routinization, Socrates, Sophist, Turing Test | Tagged , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Problems In Philosophy • 4

Re: R.J. Lipton and K.W. ReganDid Euclid Really Mean ‘Random’?

These are the forms of time,
which imitates eternity and
revolves according to a law
of number.

Plato • Timaeus • 38 A
Benjamin Jowett (trans.)

It is clear from Aristotle and places in Plato that the good of reasoning from fair samples and freely chosen examples was bound up with notions of probability, which in the Greek idiom meant likeness, likelihood, and likely stories, the question being how much the passing image could tell us of the original idea.

Posted in Aristotle, Computation, Computer Science, Euclid, Genericity, Geometry, Iconicity, Likelihood, Likely Story, Likeness, Mathematics, Number Theory, Philosophy, Philosophy of Mathematics, Plato, Probability, Socrates | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Problems In Philosophy • 3

Re: R.D. Mounce

Making reality our friend is necessary to survival and finding good descriptions of reality is the better part of doing that, so I don’t imagine we have any less interest in truth than the Ancients.  From what I remember of him, Plato had specific objections to specific styles of art, poetry, or their interpretation, and hardly painted art in general with a broad brush.  Indeed, there is a Pythagorean tradition that reads The Republic as a metaphorical treatise on musical theory, applied no doubt to achieving harmony in society.  Truth in fiction and myth is a matter of interpretation, and come to think of it, that’s not essentially different from truth in more literal forms of expression.

Posted in Aesthetics, Computation, Computer Science, Ethics, Heap Problem, Logic, Mathematics, Model Theory, Normative Science, Paradox, Peirce, Philosophy, Pragmatism, Problem Solving, Proof Theory, Sorites | Tagged , , , , , , , , , , , , , , , | Leave a comment

Problems In Philosophy • 2

Re: R.J. Lipton and K.W. ReganYou Think We Have Problems

One classical tradition views logic as a normative science, the one whose object is truth.  This puts it on a par with ethics, whose object is justice or morality in action, and aesthetics, whose object is beauty or the admirable in itself.

The pragmatic spin on this line of thinking views logic, ethics, and aesthetics as a concentric series of normative sciences, each a subdiscipline of the next.  Logic tells us how we ought to conduct our reasoning in order to achieve the goals of reasoning in general.  Thus logic is a special application of ethics.  Ethics tells us how we ought to conduct our activities in general in order to achieve the good appropriate to each enterprise.  What makes the difference between a normative science and a prescriptive dogma is whether this telling is based on actual inquiry into the relationship of conduct to result, or not.

Here’s a bit more I wrote on this a long time ago in a galaxy not far away —

Logic, Ethics, Aesthetics

Posted in Aesthetics, Computation, Computer Science, Ethics, Heap Problem, Logic, Mathematics, Model Theory, Normative Science, Paradox, Peirce, Philosophy, Pragmatism, Problem Solving, Proof Theory, Sorites | Tagged , , , , , , , , , , , , , , , | 3 Comments

Problems In Philosophy • 1

Re: R.J. Lipton and K.W. ReganYou Think We Have Problems

I used to think about the heap problem a lot when I was programming and I decided the heap quits being a heap as soon as you remove one grain because then it becomes two heaps.

The Pascal sorting of the sorites played on moves between heaps and stacks, but I’ve forgotten the details of that epiphany.  The whole-systems point is clear enough though — the system as a whole makes a discrete transition from one state of organization to another.

Posted in Computation, Computer Science, Heap Problem, Paradox, Philosophy, Sorites | Tagged , , , , , | Leave a comment