Definition and Tense

In philosophy we have the seemingly innocent concept of reference. To what do you allude to (the word 'allude', itself being a concept). But when we talk about a reference we must first consider what a definition is because we tend to refer to things as being defined when in reality they are anything but. 

For example, I see an ant. I refer to that object as an ant. I step on that object and obliterate it to the point where its constituent components no longer exist yet what can be said about my reference to that ant. What about any modifications to its environment that ant may have made. It did exist at some point in time, even if that point in time does nothing more than define my relationship to that ant (IE the ant no longer existed in its ant type form AFTER it interfaced with me). 

Consider Abraham Lincoln. Is this a hard reference to a well defined object or a loose reference to something that no longer exists? So the concept of tense is central to the concept of a reference and the concept of a reference is strongly tied to the definition of an object. 

Consider a hard reference something to the effect "I saw Abraham Lincoln remove his hat' versus a soft reference like "Abraham Lincoln's mother passed away today". 

Since Abraham Lincoln no longer exists we must rely on the definition of what an Abraham Lincoln was in order to understand what we actually have a reference to. In other words the reference may refer to something which exists in one of two tenses; exists, or does not currently exist. There are many other dimensions we must consider like 'is in my present space', which we can examine later but for now let's limit ourselves to separating references into one of two groups; currently exists and currently does not exist. We can group a bunch of these attribute like things together later and refer to these things in a context but for now let's keep things simple. 

So in the simple case where we have a hard reference to a well defined object (I saw Abraham Lincoln remove his hat today) we can now think about the difficulty in actually defining an object and face head-on the fact that in all such cases we must ultimately limit our concept of a definition in some significant ways. 

The statement 'Abraham Lincoln was a human' is pretty much accepted fact. The exact definition of a human MUST be abstract. Not all humans are identical therefore our definition of a human must be based on physical attributes (like organs, etc) clipped at some level, which themselves are abstract concepts predicated on other abstract concepts like atoms. Think of the concept of a hand. Is there an absolute limit on the size (small or large) of a hand? Must it be operational? Must it be attached to a human? Must it be part of a biological organism? Do monkeys have hands? If all things must ultimately be composed of some atomic entity can we measure all things using this unit of measure? Can we say this love is stronger than that love because it contains more atoms? How many atoms does it take to make a love and in what configuration? 

Regardless of how we go about this defining business (since absolutely defining something is technically impossible) what this definition must ultimately reconcile is what we accept as historical facts (effects) about this entity, regardless of entity tense. One might argue that once a reference no longer refers to a physical object it MUST reference the set of effects (we will call these 'accepted facts') this entity caused, however, one could also argue the set of effects this entity has accumulated over time must also be considered even when evaluating existing entities. Put another way you (and every other entity in the universe) are simply defined as the set of things you have affected even if the only thing you effected was yourself. References to you are either direct or indirect and refer to this set of facts. 

So basically all references are weak and all objects are loosely defined. Such are the concerns of true AI.

Percival and Such

Perhaps the reason we never hear from anyone after they leave this world (if as Percival believes we still exist) is because it is so insignificant in the grand scheme of things that it isn't even worth a passing thought.

Understand the Answer. Hell it Took Me 30 Years to Understand the Question!

My hobbies over the years have been mathmatical logic, the attempt to model thought and deterministic programming. Obviously this has brought me to many odd places like feedback robotics, natural language parsing, symbolic logic, the ontology of time, etc., so it is not surprising over the years I have run across the halting problem and Godels refutation of Peano's axioms, to name just a few of the philosophical conundrums confounding modern day philosophers.

I finally had some free time this past week so I returned to a topic that has always eluded me; namely why is the halting problem such a big deal. I liken it to Godel's proof because they both rely on the use of Cantor's Diagonal to formally construct their proofs. Cantor's Diagonal is a way to formally introduce the concept of infinity into an equation. He was an evil man :-)

I guess one of my problems with understanding the actual question (or problem) is that being brought up as a computer programmer I always had to take into consideration the resources at hand when developing algorithms so I rarely had the luxury of assuming unlimited (or infinite) resources in any application I would develop. When I would study a problem in classic mathematical logic it became clear many proofs that a system was inconsistent would rely on the introduction into the equations of the notion of infinity and this always confused me. After all, nothing is infinite in real-life so how do we allow it into our every day equations like it is some real quantity rather than some abstract notion? It almost makes one glad Cantor ended up institutionalized.

So this past week it finally dawned on me the halting problem (much like Godel's proof) is simply the result of allowing infinity into the equation. While it is derived from Hilbert's Entscheidungsproblem it is basically the problem of recursively allowing the output of an operation to be used as the input. It really has little to do with recursive function theory or set theory and more to do with ignoring the very real constraints we experience in every day life (like time, clipping, etc).

I do not mean to say that time, resource constraints, etc are the only problems as Russell's Paradox demonstrates it is really more infinity based, or the belief that any system can handle unrestrained totality. In reality systems are constrained and I believe we are best served by constructing systems with input constraints in mind. In so doing we can reduce the unpredictable to predictable within reason.

FrankenGov

There are those who believe the less government in our lives the better, and I tend to agree, however, I am not a believer in eradication of the government. I believe government is a necessary evil, but must be controlled. Many would argue government is a Faustian bargain at best, ultimately becoming so large it overtakes its master and turns the tables so now the citizen supports the government and not the other way around. It is a valid concern but it is my belief this state of affairs is more a result of human corruption then of something inherent in the concept of a government. A government should exist to serve its citizens; nothing more, nothing less. It is a concept brought to realization by a collection of humans. It does not think for itself; it is not FrankenGov. 

There is a difference between government size and number of government services provided. Government size is the set of resources the government consumes while "number of government services" speaks to how many useful services the government provides to its citizens. They are not directly related and should not be. 

The IRS is a perfect example. At one point in time it was probably a laborious task to process all the tax forms from the citizens each year. These days one would think computers could replace nearly all the IRS workers, but alas, the IRS never seems to reduce head count. Without knowing all the details, from the outside looking in, one might consider this a bit odd. If, however, we could reduce the IRS head count by say 70% then this would be a good thing for almost everyone except the IRS employees who were laid off (and possibly some politicians). That's fine. The needs of the many should outweigh the needs of the few. 

Another example, might be when the Environmental Protection Agency (EPA) falls down (as it did with VW in 2015). I am sure the EPA's explanation might be along the lines that they are over worked and under paid. We can look at this as emblematic of all the other government agencies. So what do we do? The way I see it, we have 3 options; we can eradicate the agency, we can throw money at the agency, or we can figure out what's broken in the agency, fix it and optimize it. To be colloquial "we could run it like a business". This last option seems like the only sane option available to us. 

I suspect the problem we have with our government is one of apathy, and once that sets in corruption is sure to follow. Almost any American if asked the question is government too big would answer yes. We all know it yet no one seems interested in fixing it. It is this apathetic status quo mentality that I believe is at the root of the problem. Put simply, there is no impartial oversight for most government organizations. I don't see anything good coming from this. 

One way to correct this is to develop indices which chart how similar operations in the public sector perform and use that to develop performance metrics for each government organization. It is not acceptable to ask the individual government organizations to develop these indices. This must be done by a disconnected third party. It is crucial to keep corruption out of this process. 

So perhaps the solution is to simply make government agencies accountable and monitor their performance as any business owner would do. 

I Am A Recovering Libertarian

Just as all political debates inevitably end with someone making a Hitler comparison, all debates with libertarians sooner or later involve the claim that taxation is theft [whistlinginthewind.org].

The problem with most libertarian arguments is that it assumes we have only rights but no responsibilities.

Libertarians make the mistake of thinking of people as isolated individuals isolated from the rest of the world. For some reason they have difficulty understanding that wealth is not created in isolation, it is as much a product of society as it is the individual. They act as though, I and I alone earned my wage and therefore it belongs to no one else. They want some entity to enforce their theory of ownership but they don't want the entity. In reality, we are hugely dependent on others and society. 

One may make the case that society is at best a Faustian contract but it is nonetheless a contract. In this light, taxes are not theft. They are a social contract. 

The United States are exactly that. A collection of states, voluntarily united. This point can not be overstated. Becoming a member of this society required a great deal of work. States had to apply to voluntarily become a member of this union. They did so because when people become wealthy and powerful they typically do not place nice so they wanted justice. They also were under constant attack from hostile forces (Indians, Mexicans, etc.) so they needed protection and they needed infrastructure to improve commerce. To make the case that they did not need the government to do these things is to ignore reality. If they could have accomplished these things by themselves they would have. Since they didn't the assumption is they were not able to. 

When you complain you don't want the government now that all the Indians have been killed off and the roads have been built and the judiciary is in place it doesn't make you morally superior; it makes you an ingrate.

The belief that it would be just great if we had no government assumes we have no examples of such a place when in reality we have many. Mogadishu Somalia (to take one example) has been without any form of government for years. It is rated one of the least safe places on the planet. 

So the next time you want to make the case of how much better we would be without government consider the literacy rate and life expectancy in Mogadishu. 

Idiomatic Conceptualization and Contextual Concepts

This is a bit more detailed discussion of what I mean when I say idiomatic conceptualization and how that relates to contextual concepts.

First, I believe the proper approach to natural language processing (NLP) and information derivation is to NOT parse language as linguistic entities which have a direct correlation to an object and which may be logically manipulated, but rather to interpret language constructs as recognizable patterns which are translatable to contextual concepts.

These recognizable patterns, also known as idioms do not correlate directly to an object, that is, there is no 1:1 mapping from idiom to concept and no philosophical manipulation of idioms as each idiom is atomic unto itself, however, an idiom does provide enough information to the system to combine with context and stored knowledge to produce one or more concepts. It should be noted that these concepts are unique to the interpreting system and not universal among systems, though several systems may agree upon concept interpretation and encoding. To understand this better, think of the concept of the color red. It is not only based on context and environment, but consider how a color blind person stores this information internally versus a person who is not color blind. Do not discount this example as one of faulty input, it is the fact that two different systems may perceive the same sequence of events and derive entirely different information from this activity.

Words do not map to objects and idioms do not map to objects. There is no such thing as the word apple directly referring to an apple, or any word directly referring to any object. Certain idioms may include the concept of an apple but the word apple is not an idiom. To refer to an apple one is not referencing an unchanging object in undefined space for an infinite amount of time, but rather a concept at a certain place at a certain time with a certain atrophy and certain interactions with its environment, and in the case of the concept of an apple, that is really not very valuable information by itself as the apple is typically a part of a larger environment, which in reality may have very little to do with the fact that an apple is contained within it.

I mean this is not the way we think. It is an exercise in futility to just think 'unchanging apple (or anything) in a vacuum forever' because that is a meaningless concept; there is no value there. It is a philosophical contrivance, not a real thought with meaning and purpose. It is not worthy of being parsed or stored.

There is also no such thing as a universal concept or universal truth that is valid for an infinite amount of time. There are no absolutes. There are concepts in contexts which are unique to a given system at a given time; nothing more and nothing less. Systems exist in perceived environments which is nothing more than a collection of contextual concepts.

The set of stored concepts represent the knowledge of the system. The derivation of truth from these concepts may be thought of as the beliefs of the system. Given identical inputs, different systems may produce different belief function outputs. The same system may produce different belief function outputs at different times. There is no such thing as universal truth; truth is an agreed upon belief between one or more systems. Predictions may be made and information may be deduced but the only eternity is the present.

My Philosophical Inspirations

So due to the fact that I have had 3 wives and 4 sons to support, coupled with the desire to work in industry rather than academia, I have had to put my true passion of thinking machines on a back burner for nearly 25 years now, but since I am nearing retirement and limited financial stability I will begin to research this subject more frequently in the years until I pass.

This post is more a collection of authors who have influenced my thinking on this subject so if someone were to read some of my writings on this subject in the future, they will have a better understanding of where I am coming from and what/who has influenced my thinking in this area.

I guess the first book, which I basically stumbled upon over 30 years ago in the FAU library which got me started was by Russell and Whitehead and I believe it was called 'Mathematical Logic'.  From there I read a paper by, I believe David Robinson on the 'Theory of Resolution' (since Prolog was en vogue at the time for these sorts of things though my work at the time was done in LISP) and another by Putnam and Davis which I can't recall the name of, but each of these were too technical for me to understand and so I moved on to Alonzo Church and Lambda Calculus.

I then took a formal logic class with which I was extremely dissatisfied (Perch Charts and such) so from there I read 'Many Valued Logic' by Nicholas Rescher and then I advanced to different writings by Frege (more centering on his discssions of concepts rather than his formal mathematical work) and many texts on set and group theory. I revisited Russell, and I did some basic research on modal (especially temporal) logic which brought me to A.N. Prior and indirectly to Kripe's work regarding modal logic (the information if I recall was scant at best as was Prior's) and then I read Wittgenstein. Perhaps no one author has had a more profound influence on me than Wittgenstein, though McTaggart's Paradox and related writings by Q. Smith, Oaklander, etc fascinated me as I had not given the concept of time that much thought when considering formal systems and thinking machines. One last thing, is that since my mentor at the time was Marty Solomon from FAU and he was developing a system called Peirce based on the American philosopher, I also have been influenced (especially on the topic of concepts) by him also.

That pretty much sums it up. I mean I have read a bunch on formal math (Pascal, Euler, Galois, etc) and formal systems (Aristotle, Augustine, Mills, Turing) when needed but my true passion has always been on the intersection between philosophy, reality and mathematical logic and now that I am moving on to my system of contextual concepts (from my system of idiomatic conceptualization) I will lean heavily on Wittgenstein, Frege and anyone else I happen to uncover.

So to sum it up, I am a believer that reality is a very personal (Wittgenstein), difficult to share experience which will lend itself to a fuzzy (Frege) exchange at best, when an attempt to formalize that exchange (Church) is made. I believe a great starting point is many valued truth (Rescher) and modal systems (Krupke/Prior). So now, if you were to read my writings you would know where they are coming from. These authors and their works represent my foundational base and my philosophical inspirations.