Get your own Free Home Pageby Eldon E. New
A) The Merger of Logic, Mathematics and Philosophy seems to have started with a hint from Leibnitz: "Combinatorics treats of calculus in general, of genral signs or characters ( such as A, B, C, where any one could be taken for another at will), and of the various laws of arrangements and transitions, or of formulas in general." [1]
The laws of logic themselves became the target of analysis by mathematics. Then mathematics became formalized though logic and philosophy until tools were created to analyze math itself, and eventually formalize it.
"Liebnitz enlarged the margins of the Aristotelian system, and two enturies later so did English logicians George Boole, Augustus de Morgan, and John Venn."..."It is modern logic that is the real stuff, and the real stuff is allmost entirely the creation of Gottlob Frege..." [2]
Hilbert got a systematic approach started in 1900 when he presented a set of problem for mathematics to solve in the future.
Bertrand Russell attempted to show that every statement could be written in the form of "predicate calculus" so that it could be proved or disproved.
Goedel showed that there would besome statements that could never be proved. Turing invented the computer to work on this problem, but he couldn't reveal the military secret. Von Neumann may have invented the idea of the "stored program", or he may have gotten it from Turing.
Now there are two major developments that seem to breath new life int Russells "Principia Mathematica" idea. One is the development of a speakable human language called Lojban or LogLan for "Logical Language".
Kent Kemish sent this from an introductory brochure about Lojban:
"Lojban was originally designed for the purpose of supporting research on a concept known as the Sapir-Whorf hypothesis: "the structure of a language constrains the thinking of people using that language". Lojban allows the full expressive capability of a natural language, but differs in structure from other languages in major ways. This allows its use as a test vehicle for scientists studying the relationships between language, thought, and culture. " [3]
Another development is the Semantic Web being developed on top of the World Wide Web. Tim Berners-Lee mentions something about the Semantic Web being "Turing complete" I believe, in some web page. The developers of the Semantic Web are aware of the historical predecessors of the Web, but they know that they cannot forsee all the implications. [4]
Some of the implications are B) and C) below:
B) Consilience of the sciences is dissolving the old boundaries between diciplines that Buckminster Fuller complained about
Edward O. Wilson has written about the convergence of the sciences in his book "Consilience : The Unity of Knowledge"
"After listening to me natter for a while about my lofty goal of classifying all the ants of Alabama, he handed me a copy of Ernst Mayr's 1942 Systematics and the Origin of Species. Read it, he said, if you want to become a real biologist."
"The thin volume in the plain blue cover was one of the New Synthesis works, uniting the nineteenth-century Darwinian theory of evolution and modern genetics. By giving a theoretical structure to natural history, it vastly expanded the Linnaean enterprise. A tumbler fell somewhere in my mind, and a door opened to a new world. I was enthralled, couldn't stop thinking about the implications evolution has for classification and for the rest of biology. And for philosophy. And for just about everything. Static pattern slid into fluid process. My thoughts, embryonically those of a modern biologist, traveled along a chain of causal events, from mutations that alter genes to evolution that multiplies species, to species that assemble into faunas and floras. Scale expanded, and turned continuous. By inwardly manipulating time and space, I found I could climb the steps in biological organization from microscopic particles in cells to the forests that clothe mountain slopes. A new enthusiasm surged through me. The animals and plants I loved so dearly reentered the stage as lead players in a grand drama. Natural history was validated as a real science."
"I had experienced the Ionian Enchantment. That recently coined expression I borrow from the physicist and historian Gerald Holton. It means a belief in the unity of the sciences--a conviction, far deeper than a mere working proposition, that the world is orderly and can be explained by a small number of natural laws. Its roots go back to Thales of Miletus, in Ionia, in the sixth century B.C. The legendary philosopher was considered by Aristotle two centuries later to be the founder of the physical sciences. He is of course remembered more concretely for his belief that all matter consists ultimately of water. Although the notion is often cited as an example of how far astray early Greek speculation could wander, its real significance is the metaphysics it expressed about the material basis of the world and the unity of nature. " [5]
C) Thechnological Convergence
The result of these convergences that we will be most affected by are three areas that David Easley has suggested:
1) Information Technology
2) Bio-technology
3) Nanotechnology
Information Technology has resulted in the computer I am typing this on and the web I may post it on. But the advance of these technologies is advancing at an accellerating rate and will take on new meanings soon.
Advances in bio-technology affects medicine and the recent collaboration between government and industry has allowed massive amounts of data about the Human Genome Project to be made available over the internet.
From the "International Human Genome Research Institute":
"The international genome consortium published a series of scientific papers in Feb. 15, 2001, issue of NATURE magazine. The analysis described in the papers reveal, for the first time, surprising new details about how the human genome is organized and how it evolved. For example, the genome only contains 30,000 to 40,000 genes, far fewer than the 100,000 estimate used for most of the last decade. The analysis also reveals information about the evolution of humans, the surprising observation that some human genes appear to have come directly from bacteria and information about the mutation rate in males verses females." [6]
Nanotechnology is another area that will have interesting effects.
From a paper by Swinton Roof:
"Most of us have some familiarity with micro-technology and its breathtaking changes in our world. Nano-technology in comparison promises a truly awesome next step for mankind... Nano-technology proposes an engineering based upon molecular machinery capable of self-replication and controlled by either molecular or electronic information systems. In other words, a technology of minute, invisible machines programmable by humans and capable of independant action and reproduction. Eric Drexler calls nano-machines, 'Engines of Creation' in his excellent book by that name. No one seemed prepared to accept the unbelievable meteoric storm of the computer-age, but I feel that nano-technology promises to truly come like 'a thief in the night'!" [7]
Semantic Integration from Cycorp webpage: In the above diagram [see link below], information stored in a database or on the web is made available to the inference engine as virtual assertions. These sets of virtual assertions are managed by heuristic level (HL) modules. For example, the inference engine "broadcasts" a query on the bus. An HL module recognizes that the request asks for an assertion which maps into its virtual knowledge space. The HL module intercepts the request, communicates with the database, web site or other knowledge source, and returns bindings to the inference engine. Inference then continues, combining information from multiple sources. http://www.cyc.com/products2.html#kb
[1] "The Advent of the Algorithm", by David Berlinski, pg 19
[2] "The Advent of the Algorithm", pg 48
[3] more about Lojban or Loglan at this website: Lojban
[4] "Semantic Web Road map" by Tim Berners-Lee .Design Issues
[5] "Consilience : The Unity of Knowledge" by Edward O. Wilson Consilience
[6]International Human Genome Research Institute First Analysis of Human Geome Sequence, Feb 15, 2001 Genome Sequence
[7] Toward an Understanding of Nano-Technology written in E-Prime Text by Swinton Roof
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