Archive for September, 2011

Stanley Rosen’s book Nihilism

Sep 14 2011 Published by under Uncategorized


Stanley Rosen’s Nihilism is a key book for understanding the nature of the Western Worldview. Both Heidegger and Nietzsche make Nihilism a center piece of their philosophies. Rosen pursues the nature of nihilism by contrasting the philosophies of Heidegger and Wittgenstein as Nihilistic opposites. Nihilism was originally coined as a term by Turgenev in Fathers and Sons, where it basically meant how youth who embraced science did not appreciate traditional norms any longer. From there the meaning of Nihilism morphed into a position that everything was meaningless and basically took the place of skepticism as the strawman to be discredited by philosophers. Nietzsche was the first one to attempt to show it was a central feature of the western worldview, and Heidegger took this up and specified that it was the essence of technology.

Once we begin to understand nihlism we can see that it is one of the core phenomena generated by the Western worldivew, and that it is itself the nihilistic opposite of Emergence. In order to understand this nihilistic and emergent duality of emergence and nihlism within the western worldview we must appropriate the meaning of nihilism, and it seems to me that Rosen has the best definition. Basically Nihilism when two antagonistic forces in society that produce a dynamic of conflict are recognized to be exactly the same thing. If you were caught up in the conflict and suddenly looked at the enemy and said “we confronted the enemy and we were them” then that would be a loss of meaning in your world. This is precisely what happens to Achilles in the Iliad when he realizes that the Greeks are no better than the Trojans when Agamemnon takes his war prize Briseis. He withdraws from the conflict, but then when his friend Patroclus is killed he goes into a berzerker state. Both of his reactions are themselves nihilistic. Thus the Iliad functions as a users manual for living in a Nihilistic worldview. It also tells us about the nature of emergence. And so this fundamental duality is at the core of our epic tradition and needs to be understood by those encompassed by the Western worldview. Stanley Rosen’s book on Nihilism clarified the philosophical meaning of this term so it can be a basic tool in our attempts to understand the Western worldview.


No responses yet

Quora answer: What is software architecture?

Sep 11 2011 Published by under Uncategorized

There are quite a few good books about Software Architecture. So I think the literature defines Software Architecture well. But what you are really asking about is where the Architect fits into the Software Development Team. With the change over from Agile and Scrum approaches to Software Development the architecture and requirements seems to be left out of account in most of the agile process models and so it seems that the architect role and requirements role have been eclipsed and we seem to think that architecture and requirements are no longer needed and systems can accrete, but of course this leads to Technological Debt. So what I would like to address is the agile at scale where the project is big enough to need the differentiation of requirements and architecture to produce a coherent product.

Now the problem seen with Architecture and Requirements is that they produce documents that are not executable, and thus get out of date, and are not kept up throughout development, and thus are seen as waste from a lean perspective. And as you say all developers have a view of the whole system they are working on in their heads, so why do we need architecture? I am going to try to address that question.

We should recognize that Design itself is applicable at all levels of System and Software development. Thus developers who do not consider themselves or are not considered “architects” are doing design when ever they create something new or different in software. We have software patterns, but the combination and adoption of the patterns is still a design task, even if we do not have to make up new patterns. Design is ubiquitous in development and no one has exclusive access to design within software development, and especially if we adopt agile methods, we should realize that everyone owns the design, and autocratic approaches that give design rights to one developer over others may be expedient but in the long run is harmful, because everyone on the team needs to share the architectural design of the product they are developing together. We know how to share implementation, but we are not as good at group self-organization of the architecture. But the self-organization of the team should reflect the self-organization of the architecture.

I would like to mention that I have just done my dissertation on Emergent Design and what I am going to say is based on that research See

The problem is with agile (scrum) type methods is that although they espouse self-organization of the team there is no real theory of self-organization upon which they are based. Therefore I would like to offer a model of self-organization upon which I will base my remarks.


See also

I have constructed a model of software process based on this model in my book Wild Software Meta-systems.

So given that context let me begin by saying that self-organization can be seen in the nature of knots that are organized against themselves by their own self-interference. So we have a very precise model of self-organization in knot theory. Knot theory is a new discipline, and probably one if the youngest of the mathematical disciplines. The best work on this is that of Louis Kauffman whose work I follow. Particularly because he is interested and takes seriously the work of G. Spencer Brown in Laws of Form.

Self-organization is related to self-production which is Autopoiesis, and we are talking about teams that produce these complex systems in most cases so that means that we have reflexive autopoietic systems exhibiting this self-organization. Self-organization of the team, and the organization of the product developed by the team are two different but deeply related matters. What we need to understand better is how the alleopoietic organization of the product of the team reflects the self-organization of the team.

In other words we are arguing that requirements and design are intrinsic to the self-organization of the team, and that this is reflected in the requirements and architectural design of the product produced by the team. So let us consider what requirements and how they relate to functions. Requirements have to be developed in relation to a functional model of the system. This is because without the functional model you would not know whether the requirements set is complete, consistent, or clear or balanced, or fully describes the intended system. Requirements are ideally Godellian statements of the hypothetical emergent properties of the system that is desired. I like the statement that I read somewhere that the requirements carry the customer value of the system being developed, and allow us to keep our focus on that during the development process. But Requirements are un-ordered, they are axiomatic statements.

The physical and functional architecture are related to the Agent and Functional viewpoints on the realtime system which are partially ordered. But those partially ordered viewpoints ultimately have to yield embodiment in spacetime as eventdata computation that is fully ordered. Thus the relation of requirements, design, and implementation are determined by what Klir in Architecture of Systems Problem Solving, the methodological distinctions with respect to the ordering of variables in the system.

At the highest level we have unordered requirements, and then at the next level we have partially ordered functions and agents, then at the next leve we have either partial order with distance or linear order without distance which are duals of each other. Finally we have full order with distance which is the condition that is necessary for computation and full implementation. So when we say organized, there are different levels of order that we may be alluding to.

Now what is fascinating is that once we realize that the methodological distinctions orders determine the level of organization which is present in the system being developed and that there is a duality in this lattice between linear order without distance or partial order with distance. These two duals have the kind of duality that exists in the minimal methods. The minimal methods are the information order that is necessary to capture the relations between viewpoints. Since there are four viewpoints on a realtime system there are six different transformations between these viewpoints. Interestingly these more or less correspond to what exists as methods in UML and SysML. Functions were taboo in the original UML specification but this minimal method has been added back in with SysML. The only difference between object oriented and functional dataflow minimal methods is whether you are looking at data from the point of view of function or function from the point of view of data.

Now once we understand the minimal methods as bridges between the viewpoints on a real time design we can start thinking about this in both allopoietic and autopoietic ways in order to relate the self-organization of the team and the alleopoietic organization of the architecture of the system.

My own research led me to create the Integral Software Engineering Methodology (ISEM) which was a domain specific language to give a model based description of software architectural designs. Recently I gave a paper on how this might be updated to work at the Systems Design level based on the research in my dissertation. This paper can be seen at which is my resume page. But at the bottom you can see my CSER paper on the changes that I have made to my design language to make it easier to do Systems Design.

First I advocate using Domain Specific Languages to express design. You can see why in my critique of SysML:

The key idea that instead of diagrammatic visualization that we get in UML and SysML we should express designs in text like we express code. This way as text we can keep it like the code and even put it within the code as comments. It could act as constraints on the code structure and thus be part of the execution strategy when we build the code or even be the basis of code generation. The problem with UML and SysML is that they are semantically weak being composed of only relations.

So let us go back to the question at hand, which is how the self-organization of the team is related to the organization of the structure of the software. Architecture can be seen as a protocol for organizing team coordination over the structure of the product being built. In other words the team provides a reflexive social meta-system within which individual team members function together and coordinate their development work. But part of the information they have to convey to each other and preserve is about the internal structure of the application that they are building. Requirements and Architectural Design is part of the protocol for communicating about the structure of the program that is based on the self-organization of the team. In other words the team is producing an intersubjective synthesis. The production process is structured and that allows the product to be structured at the macro level. But this means there must be a protocol which will allow the team to develop different parts of the system without working against each other or stepping on each others work, such that the whole system works together when integrated, verified and validated.

If we see requirements and architectural design as this communication protocol that holds the macro synthesis together then it is possible to see how architecture and requirements are nothing different from the value stream of the team by which the emergent properties sought are projected into Being. If one is doing software within some predetermined framework then the framework is giving the order to the whole application that the various team members are contributing to. But if the application has a unique structure that needs more than the framework then we will need an architecture that is designed to give a macro structure to coordinate work.

No responses yet

Quora answer: What is a narrative?

Sep 11 2011 Published by under Uncategorized


As a person who does not understand narrative very well intrinsically I have become fascinated with the topic through a personal deficiency.

One thing that I can understand is that narratives are inversions of maps. In other words narratives are to time what maps are to space.

So as we can say the map is not the territory we can also say that the narrative is not the temporality.

We can consider the fractal nature of time. It is flowing at all scales.

An excellent example of a narrative map is at

A good example of a map narrative is “Everything Sings: Maps for a Narrative Atlas” by Denis Wood

The relation of Map to Narrative is a spacetime interval. This means there is a phase space between time and space within the interval, such that from some points of view the map is bigger and the narrative smaller, and from other points of view the narrative is bigger and the map smaller.

So you would think that if I can understand maps and diagrams I would by a simple transform be able to understand narratives. But it really does not work that way. I can understand narratives of works of art that I do structural analysis of, but I cannot invent a narrative myself. I manage to tell stories in daily life but I cannot make up one. I found this out when I tried to write an Epic See

My problem is that to me all possible paths are the same, and I don’t know how to choose between them. This is nihilistic of course. But what are we to do . . .

No responses yet

Quora answer: What are some cool, unique story-lines?

Sep 11 2011 Published by under Uncategorized

No one for a long time has written a book that encapsulates the worldview. Dreyfus gives some examples from history like the Anead, lliad/Odyssey, Dante’s inferno, Brothers Karamazov, or Moby Dick. He has a new book about that called the Shining Ones.

I have a fundamental handicap that I cannot understand how to produce a narrative, even though the narative is merely the inverse of the map. So although I know the structure of the Worldview, I have not figured out how to turn that in to a Novel. I started writing and Epic Poem of the last adventure of Odysseus ( in order to attempt to produce a story that reflected my knowledge. I agree with Heidegger that Poetry and Thinking are intertwined but allow you to get at different kinds of depth. I tend to attempt to write poetry rather than narratives myself. But unless the worldivew is posited as a narrative then it is not possible to absorb it easily for others entrapped in that worldview.

So lets invent something. First I would like to posit the premise that Male and Female differ in that Males are oriented toward Space and Females toward time. And so the spacetime interval appears in human relations between genders. Now smith said that genders are a kind of a kind, but if you think about it we can see that in terms of category theory that the genders are actually modifications. Thus there are arrows, functors, natural transformations, modifications and fluctuations as the first five levels of N-Category theory. So one thing to think about is how the various relations between people, say a couple or a family or a group are conditioned by the various N-Categories with gender falling at the modification level.

Now the way that genders relate to the worldivew is in terms of the initiation ceremonies. It turns out that Apollo and Artimis are the masters of initiation for the two sexes, with boys becoming wolves and girls becoming bears. Now it turn out that boys and girls experience the meta-levels of Being in different orders in the initiation ceremonies, but the initiation ceremonies are complementary. See my Jung reading group presentation at and

It turns out that these sequences in the initiation ceremonies are the same as the sequences through life that the different sexes follow.

The story of Ariadne maps out the female initiation ceremony. Perseus maps out the male initiation ceremony more or less. Goux has described Oedipus as a failed hero who has aborted the initiation process.

So I think there is a story in that. But how to turn it into a narrative I am not sure. I can map it, but cannot temporize it properly into a narrative.

No responses yet

Quora answer: How has monotheism affected a civilizations’ ability to progress in science?

Sep 11 2011 Published by under Uncategorized

This is actually a complicated question to answer because so many things are being assumed in the question and the first anonymous response which I take to be the questioners further explanation. However, the question itself does beg for an answer. Is Monotheism a precursor for Modern Science and our progress in it which has changed the world so much? This core question is pretty significant if it were true, that monotheism was a prerequisite. Personally I don’t think this is so. And my evidence for that is that China discovered everything that was available in the Renaissance a thousand years earlier and then forgot them again and again. The real key to progress (or regress, as it may be) is not forgetting and adding various inventions on to each other to produce new inventions. This is something that Indo-Europeans managed to do, and I think the concept of Being, unique to them, has something to do with their success in this regard. I think Being is a precursor. In other words I don’t think it is the semitic contribution of monotheism that is as important. However, there is no doubt that it played a role by supplying through synthesis the idea of the Supreme Being when Monotheism and Ontology are conflated. But these are the contributions of the two nomadic tribes in the Middle East. But there are also the contributions of Egypt and Mesopotamia, which we are just now starting to appreciate, because it had been lost for so long. All of these factors contributed to the foundations of Science through the production of a meta-worldview, which we now live in as the world wide dominant worldview which is quickly supplanting all the others. It could be argued that Science would not be what it is if it did not have to struggle against Christianity. And it is certainly true that Reason defines itself against the superstition of religion. But the fact is that Reason existed in Plato’s academy which lasted for a long time, and through Euclid’s elements persisted to become the core of the educational system in the West. In Euclid’s elements we get a condensation of the knowledge of Being and its relation to rationality. But it took a long time for rationality to show the kind of results in science that would allow it to pull free of religious superstition. But on the other hand, rationality itself fully developed in a Polytheistic society. One could argue that Christianity merely delayed the rise of Scientific culture though the intensification of superstition after the Roman era. The seeds were sown by the take over of the world by Alexander which seeded Athenian Greek culture across the known world. But Romans were not interested in theory, but only practical applications, and when Rome fell apart after adopting Christianity, then the dark ages and general european collapse ensued until the Renaissance when there was a rediscovery of the Classical past in which Reason was given pride of place within a polytheistic context. Thus one could argue that Reason is the child of Polytheism and that it was only with the re-introduction of polytheistic elements during the Renaissance that that Reason could gain a foothold again, as something other than a support to religious superstition. However, it is way more complicated than that, because polytheistic societies like Greece and Egypt, were in fact really monotheistic at core, which we see in Plato and Aristotle where they talk about God and the gods. It was assumed in those societies that there was a Godhead, and that all the gods were merely manifestations of that godhead. So it is not even true that Egypt and Greece were completely polytheistic because they understood well that there was one god behind the various manifestations of that reality behind the appearances of the gods. And so we could make a case for the fact that Greece and Egypt were monotheistic in a sense similar to that of the Semites up until the second destruction of the temple. After that second destruction Judaism purified its Monotheism and that is when radical monotheism with one god and no others entered the scene. But before then it was always assumed that beyond polytheism there was a deeper monotheism. Same is true in Hinduism. Polytheism is itself not pure, but a kind of Monotheism that allows differentiation into gods who manifest the powers of the hidden single Godhead (Brahman) behind all the phenomena of its manifestation in the world as separate powers and attributes which explains why the world is such a mess, where evil came from etc.

So I think this is a question that could have several competing answers and it would be hard to disentangle what the true precedents are for science. Monotheism in this deeper sense can be one of them, but it is not clearly the case.


No responses yet

Quora answer: How long does it take to write the first draft of a book?

Sep 11 2011 Published by under Uncategorized





I wrote the first draft of my dissertation Emergent Design at in six weeks. Then it took ten or eleven months to rework it so that the english was acceptable with my wife as my editor. We argued over every sentence. After I was done I did a diff between the original draft and the final passed dissertation, there were a few words that went untouched, like I noticed that the phrase “In other words, . . . ” on one page remained untouched throughout the editing process. Not sure how those words were spared.


No responses yet

Quora answer: What does it take to be a prolific writer?

Sep 11 2011 Published by under Uncategorized

I am a prolific writer. Prolific does not necessarily mean a good writer, as my wife keeps reminding me. But there is a certain point when one begins to be able to just set down and start writing. Taking that stream of consciousness and making it into something worth reading is then a lot of work, which I do not do except for things that are published. So I have a lot of very doubtful writings on my web sites and what is available (over 10,000 pages) is just the tip of the iceburg of what exists off line or in manuscript form. Writing is my way of thinking things through. I learned to write working papers in college, and never stopped. I also learned to do diagrams as the basis of my thinking. When you combine that with a lot of reading, almost ten years sitting in the British Museum reading everything in Philosophy and myriad other subjects I could get my hands on, and almost every book that existed was available there, then eventually you think you might have something to say.

I know, I know that is all illusory. But it keeps me going, now writing answers on Quora, as an advertisement of my more serious works available on my web sites. I tried going to conferences but that did not work, so here I am slaving away answering questions on Quora in hopes that someone out there will find Special Systems and Emergent Meta-systems interesting.

At a certain point I became fluent in my writing. And after that all I had to do was sit down and start writing. As I write I discover things that I did not know before, and that gives me the elevated interest and really fascination or thrill of discovery that leads me to read on in the myriad subjects of my interest, which is fairly wide. I will never forget after I received approval for my Ph.D. in England which took about nine years, all my Advisor had to say was, now you have a general education. In other words he was saying, you are just beginning, and you now have the basis for going further and doing your own research on your own. One thing leads to another and after a while you have read a lot of pages and written a lot of pages in response to what you have read. And years have gone by. Some parts of life you missed out on, myriad parties I suppose. But on the other hand when all is said and done, a little knowledge goes a long way. My favorite book along these lines as I have mentioned previously is Knowledge Painfully Acquired by Lo Chin Shun.

There is someone who spent their whole life thinking very deeply, who came to a conclusion after myriad avenues explored, and set his conclusions down succinctly as a guide to others. Being prolific but not being a very good writer has many disadvantages, one of which is that your work does not get read even if it deserves to be read. So my advice is to learn your lessons well, and then strive to become prolific after becoming proficient. Those who become prolific prior to becoming proficient are doomed to fail even if their ideas are very good.

However, failure in terms of getting attention should not be counted as overall failure. The actual reward is in the discovery process itself. The thrill of the chase in to a territory never visited by anyone else, not mapped out, and with no beaten tracks. It may be rare in the earth, but in the landscape of ideas there are still many continents left to discover, and there the local inhabitants do not mind.

No responses yet

Quora Answer: Do Continental philosophers resent their lack of mathematical ability?

Sep 11 2011 Published by under Uncategorized

This is a silly question. This is the kind of Question that we should not answer. If we were to not answer questions like this then perhaps questions would improve here on Quora, where there are many silly questions and the only reason that quora is worth reading is the fact that good people who know something take time to answer these silly questions.

But since I don’t want my complaint about this silly question, whose author cannot be serious about, I will offer an answer myself, even though it is against my better judgement.

First of all Continental Philosophy is just the Western tradition carrying on. It is Analytic Philosophy in England and the USA following suit which branches off into Realistic Empiricism, Language Critique, and Language Games, mostly specialized argument for arguments sake.

Since Math is the basis of all philosophy, Continental Philosophers are at home in it as any western intellectual and their work is meant to deepen our knowledge of science, just as analytical philosophers do. Neither specialize in Mathematics, because Philosophy is more fundamental than mathematics in many ways. Plato said that mathematics was a pre-requisite for learning about philosophy, and Continental Philosophers take that just as seriously today. First of all we must realize that education in Europe is superior to education here in the USA. So they know more math on average than equivalent philosophy students in the USA. So the whole premise of the question is just silly. And is a joke, and thus we should not take such questions seriously. When we say this we are denigrating Europeans in general when in fact their standards are higher than ours in many cases, and their students certainly know more than ours at given levels of education. Their Ph.D. degrees are more valuable than those in the USA because they have higher standards of scholarship in many cases.

So now to the serious answers that have been made to this question. Mention is made of Badiou’s interest in Set Theory as the basis of Being, and Deleuze’s use of Calculus as a reference in his philosophy. Of these the case made by Badiou is the most interesting. However, it is Deleuze’s philosophy which is deeper of the two, which would be the case whether or not he used Calculus as a grounding for some of his ideas. Badiou’s idea is interesting because of its extremity. But also because his argument centers on Cohen’s Forcing argument within set theory. Badiou makes a clever generalization of Cohen’s argument. I made a lot of progress in my dissertation research by showing why Badiou’s argument is incomplete. Let me mention just one way.

Badiou says Set Theory is Being. The one thing I can identify with in this idea is that Set Theory is based on axioms and the axioms are fragmented as shown by Cohen’s argument and so that generally shows that Being is fragmented which is a position I have held for a long time, which is contra to the Idea that Badiou criticizes of Deleuze that Being is Univocal despite its embrace of heterogeneity. Identity and difference are the two sides of one aspect of Being. There are three others: Reality, Truth and Presence with their anti-aspects. Deleuze squarely stays within the perview of ontology by claiming that Being is Difference but has a de-totalized totality (to borrow a phrase from Sartre) that is univocal and thus conferring unity of a sort to Being. What Badiou is missing is that there are many claimants to the throne of being the basis for Mathematics and Set Theory is only one of them. We have to consider the others, like Category Theory for instance, or Mereology, etc. But beyond this there is another deeper problem. Sets have a dual, which are Masses. Masses appear in our language as non-count nouns as opposed to count nouns. Non-count nouns are things like furniture or grass, we say as piece of furniture or a blade of grass, i.e. we have to have a counter to refer to a part of the mass. Masses cannot be counted unless there is a counting term. Now from a Category Theory point of view the anti-set you get when you reverse the arrows are also just sets. So something more than merely reversing the arrows of the category Set is needed, and I call this an inverse dual. Dual would just be reversing the arrows, but also some properties have to be inverted as well. For instance the emergent part of the set is the particular within the set not the set itself. On the other hand for Masses the emergent part is the whole mass and not the instances that make up the mass and exist within its vocabulary. But more importantly Sets have Syllogistic Logic while Masses have Pervasion Logics like that developed by G. Spencer-Brown in Laws of Form which was clarified by N. Hellerstein in Diamond and Delta Logics. So when Badiou goes on to describe Worlds in terms of Logic, we can be sure that he is talking about syllogistic logic which is the only one we know here in the West. But pervasion logics were the more prevalent in India and China. And so although I have not read the second volume of his study yet, I will bet that he does not deal with Pervasion Logics just like he did not deal with Masses. So this is a major flaw in his attribution to Set theory of all the trappings of Being itself, because there are obviously masses with Being as well as particulars that can be placed in Sets. So it is clear that Badiou is wrong, in general, but the fact that he uses higher set theory as the basis for his analysis really does raise the bar on theories of Being, because there is a sense in which what he says is true. That is Set Theory has some key characteristics that are of necessity the same as those of Being like perdurence. But of course this perdurence is bought at a price and that price is the fact that it occurs in a void, where there are no particulars yet in the sets but the sets are pure projections with the null set and empty set acting as marked and unmarked signs. The appearance of the first particular he calls the Ultra One. Prior to this are two principles: The Event, and the Multiple. These prior grounds of the Set as empty projection are prior to One arising, so the Multiple comes before One and Many. It is what Badiou calls true heterogeneity and difference (unlike that of Deleuze) without reference to the One either as totality or unity.

What I learned from Badiou’s use of Cohen’s forcing briefly is that a transcendental is the same across an entire immanence and that is why it is an invisible, because it is something that does not set up a difference within the immanence. Forcing does outside the immanence and forces a transcendental on it to see if there is a difference generated. It there is no difference generated then it is the same transcendental, if there is a different difference generated then it is not the same transcendental. This may be a wrong interpretation but this is what I got out of what he was saying generalizing on Cohen’s work and seeing ontological significance in it. It has long been assumed that transcendentals are infinite. But in Cantor’s theory we can only really tell the difference between the countable and uncountable (real number) infinitudes. What is strange is that cardinal infinities are not at set distances from each other beyond aleph. This I think shocked Cantor and others once they got use to there being different infinities. We are used to numbers being about the same distance from each other in normal math. When suddenly we don’t know the distance between them then we really don’t know what it means when we count to higher infinities. It more or less makes the exercise fruitles.

If a transcendence is an infinity, and then we try to go to the next higher infinity level to get a higher transcendence, if that movement does not make a difference within our immanence then really we have the same transcendence as we started with. As we expand the Universe of coverage by transcendences then we are forcing certain properties on the immanent realm that is being immersed in the larger space. If this forcing does not produce a difference within the immanent range then there is no difference that makes a difference by the introduction of the new transcendence, and really all we have is the old transcendence in a new guise.

This is my understanding. I stand ready to be corrected. If I got anywhere close to the right answer I am happy because this is one of the most esoteric ideas I have run into. But it allows us to know that the Continuum Hypothesis is independent of the ZF axioms, which means the fragmentation is real between the ZFC axioms.

For me this was important for my research into Schemas Theory because after formulating General Schemas Theory I thought I had to then formulate a worlds theory in order to know its context. General Schemas Theory gives the context of Systems Theory, or the theories of the other schemas. But what I realized is that I did not have to give the context of General Schemas Theory if the world theory did not produce any difference at the level of schemas. For instance we produce General Schemas Theory so we do not disturb the meanings of lower level Schemas like facet, monad, pattern, form, system, meta-system or domain, etc. If the world theory we introduced affected the structure of Schemas Theory, or if Schemas Theory produced a difference in systems theory then we would think it was an anomaly and would try another approach toward producing a theory that was truly general.

Once I realized that any World theory I created would not change general schemas theory, I stopped trying to find a context for Schemas theory. It saves us from needless foundational searches such as I was engaged in. It does not matter which world we are in if it does not change our schemas, and it does not matter which schmatization we have if it does not change the various schemas that are covered by the generic schematization. This turns out to be a good test of generality of a theory. We don’t want ad hoc changes by introducing a new level of transcendental.

This turns out to be an important metaphysical consideration. And we should give Badiou credit for understanding that there was a metaphysical equivalent to forcing.

Mathematics is odd. Analysis banned infintesimals, and this gave rise to non-standard analysis. Yet Mathematics accepted Cantor’s paradise. And we justify our Idealist aspirations by the fact that we can understand infinities as processes, even if we cannot understand them in terms of Pure Being, as a frozen fully present reality. There is something strange going on here, which also implicates the split between intuitionist or constructionist mathematics and traditional mathematics that subscribes to excluded middle. The mathematical universe is not symmetrical. For instance we only have topology and geometry as mass maths while almost all of the rest of our math is set based, and that is why we might be fooled into thinking that Set Theory is all we need to ground mathematics. Husserl developed his entire phenomenology in order to answer the question “What is a number?”. When we see the complexity of consciousness seen from a Phenomenological perspective it is amazing that we can do math at all.

I have shown in other writings that there are various forms of math associated with the Meta-levels of Being.

Pure Being = Calculus
Process Being = Probability
Hyper Being = Fuzzy Possibilities
Wild Being = Chaotic Propensities
Ultra Being = Singularities in Catastrophe Theory (Rene Thom).

But when we look at mathematics what we see is that it is really all Present-At-Hand or inscribed in Pure Being. Even Probability theory is described in terms of functions. So I have hypothesized not only that there are mathematical forms at each meta-level of Being, but also that these should be split, perhaps asymmetrically between Set-based and Mass-based Categories. However the current asymmetry strikes me as being too great.

Fundamentally I think that Constructivism and Intuitionism is more correct than Traditional Excluded Middle mathematical argumentation because it is precisely the excluded middle that bans non-duality.

I am putting my money on Surreal Numbers as the more basic kind of mathematics based on Game Theory. From it you get all the kinds of numbers that otherwise have to be constructed based on the limitations of each earlier kind of number. Surreal numbers gives us all the various kinds of numbers, along with both Infinities and Infintessimals. But unfortunately it is meta-systemic and thus the numbers have holes in them, and you can calculate with the holes. It as the void prior to the arising of the progressive bisection of the number, and then there is the emptiness between the braches of the number tree where a specific number is approximated by the up and down arrows that represent the moves of the game within the field of all possible moves.

Plato says that all who enter his academy should know geometry. Mathematics is the bar that is placed at the entry that must be passed to get to the real work of understanding the Platonic Forms. And there is no greater example of the representable Forms than all the various categories of mathematics discovered in the last century which has been a renaissance for mathematics. Who would have thought that we could finally prove that we had come to the end of the sporadic groups. Who would have thought we would have come up with not just category theory but n-category theory, or topoi, or discovered that the fourth dimension had no stable topology (Donaldson). The list goes on and on as the new mathematical categories have overwhelmed us as if we were caught in an avalanche of representable intelligibles. But what progress have we made on the representable intelligibles? Not really very much. Analytical Philosophy spent much of its time trying to prove that philosophy itself was just a bunch of mistakes following the language philosophers and Wittgenstein. My favorite of the lot was Schlick who sponsored Wittgenstein as the spokesman for the Vienna movement (Notice this was on the Continent.) Frege (who also lived on the Continent, and) who criticized Husserl’s early phenomenology and who changed his position based on Frege’s critique of his dissertation. Yet Husserl is forgotten by the Analytical Philosophers. Funny how Analytical Philosophers have such a bad memory. They cannot seem to remember anyone after Frege who lived on the Continent except Wittgenstein. Then suddenly everyone from then on lived in England or the USA. Meanwhile back in Europe, Europeans carried on Philosophy as they always had remembering Hegel, Kierkegaard, Nietzsche, and all those in the Phenomenological Tradition after Husserl, like Heidegger, Merleau-Ponty, Sartre, Deleuze, Derrida, Lacan etc. Continental Philosophers are just plain old Philosophers, while Analytic Philosophers are actually the ones with the resentament. First of all their arguments are isolated among themselves and have no bearing on Philosophy (Continental Philosophers are superstars in their own land compared to American or British philosophers, mainly because what continental Philosophers have to say are normally relevant to what is going on within society, culture, contemporary events, politics, etc.) And as I have shown in other posts Analytical Philosophy is dying while Continental Philosophy is thriving even if philosophers in general are not doing so well of late. So if you are in a field where you have to send out letters to students that say there is no chance you will ever get a job if you do a Ph.D. in Philosophy, which is irrelevant to contemporary society or culture, and which is being mentioned less and less in books, then that is the real case for resentment. Especially if you know that your continental friends are better educated and their Ph.D. programs are more rigorous than those in the USA. Do we sense in the animosity of the Analytical Philosophers some chagrin at being part of a dying field while Continental Philosophy has been adopted as the saviors of English Departments, giving them something worth while to talk about finally. And there are just so many more English students and departments than there are those in philosophy. And the whole sale adoption of Continental Philosophy by English Departments as their basis for the criticism of literature of all kinds, means that there is an unstoppable expansion under way for Continental Philosophy. They do not tell their students that they will not be able to get jobs as English majors. They tell them that they can write books and become famous authors and make lots of money or get a cushy job in any number of schools, colleges and universities that all teach English, even as a Second Language. In other words Continental Philosophy is taking over the world and becoming a dominant paradigm for looking at our own society, culture, literature, media, politics, psychoanalysis, psychotherapy, etc. Analytic Philosophy the child of McCarthyism is fading away slowly but surely, because they have nothing interesting to say beyond their own clique. The only really interesting Analytic Philosophers are those who study or take as their starting point Continental Philosophy like Dreyfus and Taylor.

Since Philosophers here in America are less educated than their Continental counterparts, and that includes in math, I think the resentment runs in the other direction. Of course, there are a few Analytical Philosophers whose work actually is about Philosophy of Math or Philosophy of Science and we presume that they know their stuff. But if there subjects of study are not math and science it is an odd thing to presume that that they know more math than their Continental Counter parts who actually know some math and science from their schooling. Just look at the ranking of kids with respect to math and science in Europe or even Asia in relation to America. We cannot fall behind like we have for years on end and expect to keep our place as the preeminent source of education within the Western world for third world societies.

I know, says one teaparty republican to another, we can solve the problem by cutting more from education. Global corporations shall solve the problem by getting their scientists and engineers from societies that believe in education and invest in it.


No responses yet

Shelfari: Book reviews on your book blog