Day forty-two -- axiomatic domain, theory and system.
From Tienzen Gong: There are zillion facts and truths in the world. Yet, the only truths that I am interested in here are "theory based" truths. Now, we have settled that what Occam's razor is all about. We must, then, discuss what a theory is.
Every theory is domain bounded. What is a domain? Domain encompasses a system. Then, what is a system? We can go on with this kind of word game for quite a while. Seemingly, you all always have your ideas about words. So, let me define my words. If yours is different from my definition, then, you keep yours, and I keep mine. There is no point of doing the "war of words".
The only domain that I am interested in is the axiomatic domain. Every axiomatic domain's boundary is marked by some axioms. Different axioms will encircle different domains. The contradictory axioms are simply enclosing different domains, such as the different geometries from the different parallel axioms. The structure of inside the domain is defined by "definitions." For example, Windows and Apple are two different domains. How their hard disc is formatted is by their definitions. Thus, with some "arbitrary" axioms and some "arbitrary" definitions, we get one domain. And, there is no right or wrong issue for those axioms and definitions but an issue of good or bad. A bad domain is, often, useless.
With a domain (having boundary and internal structure), some members come alive and roam in the domain. From the interactions of those members, some laws can be found by induction. And, some theorems can be found by deduction. Now, we have a baby as follow,
1. some axioms
2. some definitions
For theorems, they must be provable with deduction. For laws, they must be verifiable with tests. Of course, both law and theorem are domain bounded, or sub-domain bounded. Yet, there is one additional baby in every domain, and it transcends the birth process of both deduction and induction. It comes alive as Godly ordained, and it is called "Principle." Principle is deemed to be true in the entire domain.
Now, this domain becomes a system. In a system, many more phenomena arise. From these phenomena, someone can come up a hypothesis. From hypothesis, it comes a theory. From a theory, it comes a prediction. From a prediction, it comes test plans. From test plan, it comes test result. With the test result, the "hypothesis" is either verified or disproved.
Question -- from "sangi39" -- Yours is also wrong, the sequence is:
2. Initial Observation
3. Hypothesis based on Initial Observation
4. The Design of a Test and Methodology to Enquire the Validity of Hypothesis
5. Carrying Out the Test
6. Collection and Analysis of Results
7. Conclusions Regarding Results and Relation to Hypothesis (do they support the hypothesis or not?)
8. Analysis of Test and Methodology
9. Reassign Hypothesis
10. Redefine Test and Methodology
11. Carry out Test
12. .... etc.
A theory is not formed directly after the formation of the hypothesis until enough iterations of the above sequence have been carried out to end up with accurate predictions. Thus your example only works for a final iteration, i.e. that a hypothesis becomes a theory once it can actually predict specific results which occurs after a number of hypothesis>test iterations.
Answer -- The interplay between a theory and its final test (the final iteration) is the only beef for the issue. However many warm up tests were done, the final test issues the verdict of either a verification or a disprove for a theory. Many theories are still "waiting" the vindication from a final test.
After a theory is verified, the repeat of the test has two names, calibration and production. After the Top quark was verified in 1995, the repeated runs are Top quark production, no longer tests. With that production, we are trying to analyze the top quark decaying pathways. With this analysis, we are trying to form a new hypothesis for a new theory. The cycle of,
Hypothesis -> Theory -> Prediction -> Test -> Verification -> Production -> New hypothesis
is called epistemology telescoping. This is it.
PreBabel is a system with hypotheses, theory, laws, theorems and thus is testable.
Hypothesis : every language can be ciphered with a closed set of root words.
Theorem 1: every language can be ciphered with the same closed set of root words.
1. Law 1: Encoding with a closed set of root words, any arbitrary vocabulary type language will be organized into a logically linked linear chain.
2. Law 2: When every natural language is encoded with a universal set of root words, a true Universal Language emerges.
1. Prediction 1: from law 1, the PB (language x) can be easier learned than to learn language x.
2. Prediction 2: from law 2, a true auto-translation machine for the world's languages can be built.
That is it.
Note: Any test which does not test against a "hypothesis" is a meaningless test, a phony and bogus test.
PreBabel is the true universal language, it is available at