Where Do We Start

Interest in understanding thought has a long and extensive history. Although there are many different approaches to this question, here we consentrate on the work of two groups: logicians and AI researchers. For simplicity we characterize these efforts as 1) the goals of logicians include describing what knowledge is and how we know that the reasoning we do when making jugements about our knowledge is 'correct'; and 2) the goals of AI researchers includes building computer applications that that can underdtand some aspect of the world and can use reasoning to make judgements about what it knows.

Logicians invented formal systems (syntax) and set theory (semantics). They simultaneously used these ideas to give a sound explaination of mathematical thinking. The group of AI researchers, (somtimes called neats) tried to use these ideas to build AI applictions that knew about the world and could do everyday thinking about the world. The result can be sumarized as: classical first order theories with set theoretic model theories capture what people (mathematcians or not) do when thinking about the world.

Not everyone agrees with this—objections are plentiful. Three forms of interlocking objections are common: some persons have serious philosophical disagreements with this view; others proved theorems in a particular formal system that are unexpected enough to cast doubt on this claim; and some proposed scenarios that don't seem to fit nicely into this format. The 'neats' generally propose a new 'logic' to addresses this objection.

Many of these objections are discussed detail in the sections below but we mention a few important ones here to illustrate their scope.

From logicians: (reasoning) intuitionism, first developed by L.E.J. Brouwer, that maintains that some classical reasoning principles are unreliable; (set theory) is vague, the continuum hypothesis is indpendent of ZF; Russell's paradox shows naive set theory is inconsitent; some mathmaticins believe that categories should replace sets in the explainations of mathematics; (first order) first order Peano arithmetic is not catagorical, Dedekind; arithmetic has many non-standard models, Skolem, the Lowenheim-Skolem theorem; ...

From AI reseachers: the frame problem and circumscription, John McCarthy; non-monotonitic logic, McDermett and Doyle; default logic, Reiter; model logic, Aristotle!! belief and knowledge, Montugue; possible worlds, Kripke; situation semantics, Barwise; nlp, Winograd (Shrdlu); (the scruffies) neural networks; the Declarative Proceedural contravercy ... psychology, neurobiology, ... , cognitive science

From philosophers: universals, objects independant of thinkers; ... ; nominalism, a view that abstract objects exist only as names or labels; finitism, which claims that infinite sets are not real.

All of these 'objections' make important observations about the problems encountered when trying to understand the world. My concern with their 'solutions' is that

The problems I am interested in need more than explainations. I believe the efforts fail to address my needs in two fundamentl ways.

Although these goals are well established and well thought out, they fall short in that they have not lead to either theories or programs that have anywhere near the capability of people to understand and reason.

In AI people use deep learning and statistical methods that display amazing engineering prowess (eg competing at jeaprody or driving 'autonomous' vehicles) and design 'cognative architectures' (eg SOAR or ACT-R) using ideas about 'how' people think.

Logicians, on the other hand, after the basic structure of formal systems was codified in the 1930s and 1940s have concentrated on extending the original theories using 'large' cardinals or proposing new formalisms to account for 'real' problems (eg model logic, relavence logic, paraconsistent logic, ...) Although the work in all these areas has been extensive and shows extreme technical competence I believe they miss the mark.

Our goal is to use computer centric technology build an agent that only communicates with the world with its sensors and affectors. That is, build an artifact that subsumes the original goals of both AI and logic. I believe this requires a shift in perspective that reinterprets the ideas and discussions of logicians in light of our current understanding of computers.

The current notions of logicians relating to formalism were largely developed before the existense of actual computers. The pioneer logicians: Frege, Cantor, Russell, Brouwer, Skolem, Hilbert, Godel, Wittgenstein, Kleene, Turing, ... lacked any knowledge of what an actual computer would be like. Our work starts from the premiss that we have real computers (with increasing capabilities) and that we ought to use our knowledge of computers to refocus the last hundred plus years of thinking about knowing using the insights of our current knowledge of computers.

We ask: in what sense (if any) can the solutions proposed by logicians to the question of how reasoning works be used to build an artifact that can think? More generally, can we interpret the ideas developed by logicians (ostensibly to understand reasoning) as a blueprint for actually constructing a computer system that can understand the world it inhabits and reason about its ongoing experiences.

These questions touch many of the philosophical questions that have been discussed over the last century and a half (or if you prefer ideas that originated over two millenia ago with the Greeks) and many recent ideas about how understanding can happen.

On the pessimistic side I believe that the current formulations of logic do not provide answers to the question of how to build a thinker. On the other hand the notions developed by logicians seem to me to have the germ of the answer and, for, me they carry conviction. I ask the question: how can we understand the results of logic in a way that provides operationsl guide (ie, as mentioned above, a blueprint) for building an artifact that can understand and reason.

On the optimistic side I believe that there is a reformulation of the work in logic that will facilitate building systems that can reason and understand and at the same time lead to a better understanding of the issues that have plagued logicians, philosophers and AI resarchers alike.

I have a proposal but before I start I want to paraphrase Kriesel, "If you attempt to address foundations you need to respect the fact that the ideas of your predessors are almost right." This has the corollary that people will almost certainly attempt to reformulate 'new' ideas as variations of the current orthodoxy. For this Kriesal expressed the idea that you needed to ask what notions are implicit in the 'new' notions themselves and guard against thinking about them in traditional terms. This requires a kind of 'suspension of belief' until the new ideas can stand on their own. The proposal presented here is widereaching and requires time and experiencing it before its power becomes clear. Also my expository capabilities are limited, so please give these ideas a chance.