Axiomatized logic structures, instincts, the aesthetic, and you – notes from a lecture

29th June, 2008

Below are my lecture notes from the beginning of my talk to MICA’s Summer MFA in Studio Art, and Graduate Art Education students.

The second half of the talk featured various artworks of mine that can be found by looking under the artworks category on this blog or clicking the projects tab in the upper right corner of this page:

Lecture Notes:

Charles S. Peirce (1839-1914):

Nature is a far vaster and less clearly arranged repertory of facts than a census report; and if men had not come to it with special aptitudes for guessing right, it may well be doubted whether in the ten or twenty thousand years that they may have existed their greatest mind would have attained the amount of knowledge which is actually possessed by the lowest idiot.

Both man and animal come to this world with two classes of ideas which adapt them to their environment.

In the first place, they all have from birth some notions, however crude and concrete, of force, matter, space, and time; and, in the next place, they have some notion of what sort of objects their fellow-beings are, and of how they will act on given occasions.

Our innate mechanical ideas are so nearly correct that they needed but slight correction. The other physical sciences are the results of inquiry based on guesses suggested by the ideas of mechanics.

The moral sciences are equally developed out of our instinctive ideas about human nature.

Man has thus far not attained to any knowledge that is not in a wide sense either mechanical or anthropological in its nature, and it may be reasonably presumed that he never will.” pp 214-215 Philosophical Writings of Peirce, edited by Justus Buchler.

We come into the world with instincts for mechanics, or natural law, and anthropologic interactions, so says C.S. Peirce.

An example of Mechanical instincts is at the top of the post.

An example of Anthropologic Instincts:
My four month old niece is suddenly able to focus her eyes. My sister says that one of the ways infants learn about things like eating solid food is by watching other people eat solid food – obviously infants don’t consult books about such things, their instincts provide the necessary knowledge via an impetus to interact and observe.

Intellectual Constructions, a third mode of interaction, increasingly significant since the industrial revolution.

An example: Einstein’s Simultaneity (1905):

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Jean Piaget (1896-1980) from Genetic Epistemology:

…if this redefinition of the possibility of events to be simultaneous at great distances from each other went against the grain of our logic, there would have been a considerable crisis within physics. We would have had to accept one of two possibilities: either the physical world is not rational, or else human reason is impotent – incapable of grasping external reality. Well, in fact nothing of this sort happened. There was no such upheaval.

Why in fact was it not a crisis?

It was not a crisis because simultaneity is not a primitive notion: It is not a primitive concept, and it is not even a primitive perception.

…our experimental findings have shown that human beings do not perceive simultaneity with any precision.

If we look at two objects moving at different speeds, and they stop at the same time, we do not have an adequate perception that they stopped at the same time.

Similarly, when children do not have a very exact idea of what simultaneity is, they do not conceive of it independently of the speed at which objects are traveling.

Simultaneity, then, is not a primitive intuition; it is an intellectual construction.

Godel’s (Kurt Godel, 1906-1978) Incompleteness Theorem (1931): There are limits to formalisation:

Axioms are statements that can be taken as true without proof.

Theories can be taken as true if they don’t violate any of the axioms upon which they are built.

Some theories can be true without proof.

“This sentence is not provable.” is true but not provable in the theory.

An axiomatized logic structure is a structure based on axioms.

Intellectual constructions use specialized, axiomatized linguistic structures (like calculus, or other systems of calculation guided by the symbolic manipulation of expressions, like Boolean algebra, the axiomatized logic upon which modern computers are based) to formalize specific ideas. Their development is fundamentally different than knowledge developed from our mechanical and anthropologic instincts.

What does logic formalize?

Any axiomatic system contains the undemonstrable propositions or the axioms, at the outset, from which the other propositions can be demonstrated, and also the undefinable, fundamental notions on the basis of which the other notions can be defined.

What lies underneath the undemonstrable axioms and the undefinable notions?

A feeling may lead to a thought, which may connect to a belief, which may lead to judgment/decision. A belief is an organization of thoughts, a logical system, possibly an axiomatised logical system.

The root of thought is feeling.

If our thoughts develop from feelings and if our feelings are an index of interactions with our environment the resulting logic has a physical connection to the world as our feet have a relationship to the ground.

The necessity for considering feeling itself as well as considering axiomatised logical systems, since it is from human feeling and thought that logical systems develop and maintain an intuitive quality.

Summary:

We have primitive instincts for natural law and learning from each other by observation and interaction. Neither of these requires a formalized logic system nor a specialized linguistic structure. Both of these seem innate and similar to instincts observable in other animals.

We have an environment increasingly embedded with physical instantiations of axiomatized logical structures (the computer, [and, by extension, the internet] a Boolean algebra machine, is an example). To which we respond intuitively – as we do to any physical structure we encounter.

Feeling > thought > belief > judgment/decision (logical structure, possibly axiomatized logical structure).

Godel’s theorum demonstrates that our axiomatized logical systems are fundamentally different than our intuitive understandings of natural law and learning by observing and imitating each other.

Axiomatized logical systems require specialized linguistic structures and fundamental concepts based on knowledge derived from specialized linguistic structures, i.e, intellectual constructions for which we often seem to have no clear intuitive understanding.

two excerpts from this post:

I’ve been doing some work in a small room with a sliding glass door that opens to the rear of my father’s house. I’ve been leaving this door unlocked, and a moment ago I tried to slide it open and found that the movement of the door was impeded by a small piece of stone that had found its way into the track on the floor. As soon as I tried to open the door it stopped at that lower corner, and I immediately knew that something was blocking its’ way, and where the blockage was, I could feel it. A matter of seconds later the track was clear and here I am.

My instincts – based on observable natural law, and observing the behaviors of others, permit me to make relatively quick inferences in a variety of situations.

Our intellectual constructions do not, in my experience, and in general, respond successfully to quick inferences. They are more complex and require knowledge that is often not immediately available. Often the required knowledge under the surface isn’t itself stable.

When I was trying to open the door I could feel and observe where the obstruction was, and I could infer how to remove it, quickly.

When my friend tells me my blog suddenly doesn’t appear when he points his browser to it, and when I take an look and have the same experience, and that experience doesn’t provide enough information for me to even guess what’s wrong, I consult my host’s tech support, then read a few documents, then look at a few message boards, then try, then fail, then try again, etc.

What I observe in both cases (door/blog) is that I have an impulse to make a quick inference based on the available information, to act on that information, to observe the result, refine my actions, minimize error, achieve the result, etc. I have an impulse to engage in classic negative feedback.

With the blog (an intellectual construction within a network of intellectual constructions) the necessary information is far from anything resembling a surface.

With the door, all of the necessary information was right in front of me, literally, the entire time, and my instincts lead me to the right conclusion right away.

I think that a major challenge we face is how to function within an environment for which we have increasingly insufficient, and often difficult to locate information within a psychological domain in which our instincts are prompting us to use what is immediately available to make quick inferences to solve the problem.

Our mechanical and anthropologic instincts and interactions are all based on information that is an intuitive, common, aspect of our interactions with the elements of our environment. I characterize the nature of these intuitive interactions as real-time proof.

It is by triangulating our actions within the intuitive and intellectually constructed that we come to understand our experience.

I am interested in observing how axiomatized logical structures and intuitive understandings function together, and how different environments may affect the degrees to which one mode may be more prevalent than another at a given moment.

I wonder it is possible to manage, or exert influence over these interactions in such a way as to increase knowledge holistically within this general environment.

The aesthetic experience, to me, is a point of balance between the instinctual and the intellectually constructed.

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