Introduction (to this argument itself) and Argumentation.
This is the case for Cumulativism in the expression of Interconnectedness, Complexity and Technology, (ICT).
It's clear to me that if the Paradigms of Kuhn are supposed to be true, they have to be logically equivalent. I believe Kuhn states that one isn't able to choose rationally any Paradigm, you are more or less drawn into one by all sorts of strange reasons whether they be feelings, social connections or what. You have this Ptolemaic System. Is this supposed to be equivalent to Einstein's Theory of Relativity or Copernicus' Heliocentric Worldview? It's obvious they are not equivalent. It's also obvious the various worldviews hold different cognition based on different assumptions and observations. Let me add the technological development that has made extensions to our eyes, like the Hubble telescope.
It's therefore established that these K. Paradigms are "chosen" or chosen relatively closely temporally. In this, one first problem is to come up with something at all. Each of these are also building on assumptions of concepts, models - theories, and underlying, historical work whether this is mathematics, (naive) remarkable discoveries, development in technology such as telescopes, magnifying glass, general thinking of what reality should be, ie. conceptualisation and speculation. Maybe we get 2 or 3 "Paradigms" to choose from. As these Paradigms are considered, elaborate testing is going on, perhaps coming up with something.
Today, what are our options in choosing from paradigms? We have perhaps these 2 or 3 theories in quantum physics. I sense that scientists are well aware they may be wrong! This means competition is open. We can't certainly begin to doubt observations in space and come up with a different astronomical worldview. We have to say that technology nails something for us. Again I point to advances in other fields that are not actually considered by these scientists in this paradigm.
Conclusion: We have this giant landscape in science (2009) where advances happen all over. Scientists are connected by the internet to exchange agreements, thoughts, and differences of opinion. They are probably expecting new technology and checking for relevant work done elsewhere on Earth and ISS, all-other-wise. There are, I guess, numerous problems in science currently that are being investigated like the dualism of photons and what have you. Then, it's impossible to determine any single paradigm because everything is interconnected and is developed in unison everywhere. It's impossible to make an incision around particular efforts as a consequence. The "community" lives and dies together. Besides, as I see it, today, most disagreements are theoretical and thus not subject to empirical testing. How is Kuhn doing? I think he looks bleak!
Further: In the case of the Paradigm of Einstein's Relativity, shouldn't one acknowledge both Einstein and Riemann on it? As I've pointed out, it's impossible to make a "jump" in time and come up with our science, let's say, 500 years ago or 2500 years ago. This should be blatant and clear! I thereby come up with a second conclusion, that we are in effect "climbing a mountain, science-wise" or "scaling that Babel's tower, science-wise". I think I can say that we know that back in time, people have been more wrong or less objective than we are today, but this may have been necessary! It can't be said definitely, but the scope of the development through history lies there. A new theory of evolution, science-wise?
When I use the word "truth" in connection with paradigm, I mean of course that it's the concept of paradigm that's supposed to be true. I must be crazy if I say that the Ptolemaic worldview is supposed to represent truth, I mean of course, the paradigm.
One of my arguments here is that technology may be the whole engine of cognition and scientific progress. Does it matter to consider paradigms if the Ptolemaians have not had the chance, i.e. aids to see with, the corroboration of observations, to make the cognition that is required to become Copernicans (I may have left out some mathematics here and more). So you seem to have skipped the argument of the technological requirements of scientific progress. If it's technology that makes scientific happen, does it make sense to call it a paradigm? It's obvious that technology represents the inter-subjective.
Can you truly say that our future scientific progress doesn't have a broad inter-subjective, "objective", character in that everyone will recognise the right theory to believe in because it's technology that will decide those beliefs?
So all in all, I think it's better to see science as a whole doing gradual advances in the light of the development of "assumptions of concepts, models - theories, and underlying, historical work whether this is mathematics, (naive) remarkable discoveries, development in technology such as telescopes, magnifying glass, general thinking of what reality should be, i.e. conceptualisation and speculation". All science is broadly based therefore only the scientist-spearheads make the mistakes while cognition of the best alternative is inevitable.
I also note that scientists are well aware they may be wrong! Isn't this counter to Kuhn who is asserting that scientists are blind when they are in a paradigm and that they die with it. Because the scientists die (of old age and whatever) and are those who are driving the paradigms, new paradigms emerge. Is this the case today? I think not. I fail to see that Kuhn is happy with underlying, historical work in explaining his paradigms.
I try to establish cognition as a function of history, especially in the sense of technology with writing "we have to say that technology nails something for us." I believe it's clear that technology isn't subject to paradigms.
A thought strikes that is already implicit. Kuhn can really be accused of crudeness in creating the paradigms because he's ignoring those processes leading to the paradigms in sufficiently thorough terms. Call my assumption contextualism or what you want, but it's derived from "assumptions of concepts, models - theories, and underlying, historical work whether this is mathematics, (naive) remarkable discoveries, development in technology such as telescopes, magnifying glass, general thinking of what reality should be, ie. conceptualisation and speculation". As Kuhn fails to deal with these processes properly, his argument of paradigms is an illusion.
The concept of paradigm is wrong, ie. first question. The science that makes up these "paradigms" is historically false, too, but at that stage in history, that science is still very reasonable. The current science is, of course, the best we have. You know there may be troubles if I use the word "objective".
I say there's definitely cognition in science when the theories are being tested (I don't want to go through the whole HDM and otherwise here) and in the meanwhile that advances in other fields, especially the development of technology, come into play and seal the deal cognitively. You admit that Kuhn makes a point of "strange reasons", but I say that in my argument there are no such "strange reasons" (I don't account for crazy scientists).
I believe Kuhn makes the point that scientists in a paradigm are blind, have no cognition, of advances that competing scientists make. Again, I take it further with technology, it's the technology which is definitely cognitive, that decide the cases where scientific progress can be made.
When I write "paradigms are not true" I intend to say that Kuhn's invention or use of the concept of paradigm in his theory or description of the structure of scientific revolutions is wrong or mistaken or faulty or an illusion. There's no doubt that Kuhn is serious with his book, but this is obvious! Otherwise, I'll do exactly what you have written! Thanks!
Note: Some people may point out that some paradigms happen as a function of "accidents" or unforeseen events. I'm thinking of penicillin or whatever, but I want people to have in mind that these investigative people have been through education and what (Einstein is a Ph.d. when he comes up with the relativity theory, not that it is an accident) and are usually in the process of rigorous research. These people, like Sir Alexander Fleming, are extremely attuned to pick up remarkable events. I don't think any such possible situation is weakening my attack on "paradigms", Kuhn's book. This is so because they are building on that foundation of assumptions that is historically set. I don't deny there are excellent scientists, but they are a part of history, "standing on the shoulders of giants".
I will work on the history of science part. We'll see where it gets. One start may be to draw in as much people as possible into the relativity theory as an example and also make an analysis of assumptions that have proved crucial to Einstein's work.
My point with the technology is simply to emphasise this, it's a blatant truth that some people work on astronomy and some on the substance of glass, i.e. telescopes. In this way, discoveries, the work on theories, in a wide sense, happen in an almost impossibly identifiable manner. So many people are involved in any field of science and continuously so as one field doesn't stop the other in times of less progress.
Copernicus has had a library at his disposal and it leads me to the notion of corroboration of observances. What has been the Ptolemaians' opportunity to systematise and archive their observations? There may be other angles into it. Just this also: Claudius Ptolemaeus, 90 A.D. - 168 A.D. and Nicolaus Copernicus, 19 February 1473 A.D. - 24 May 1543 A.D. Equal pre-conditions?
Along with the point that science, and so technology, is being developed all the time in every field, I think when it comes to the readily applicable technology, it's inter-subjective. The cognitive value of the Hubble telescope is striking. This makes me think that as soon as technology is developed, from that very other field of science, i.e. electronics and what else, that is used in astronomy for example, can decide scientific disputes quite easily. Let's think of x-rays in the case of a broken leg or something thereof. It's bad to say it this way, but I'm in difficulty of finding an outstanding example. I can also point to advances in computing power to the fields of science that can have great use of that.
I have no wish to say there's no theory in technology and that as such, it's just one theory to another. Still, the efforts are obviously broad as theoreticians working with logic in computer-circuits have no idea what the user end is. Similarly, scientists in remote areas may unknowingly work toward a common goal. The other side is that relative transparency in science allows scientists to check for better equipment and "methods" in the interconnectedness. I have the sense that when technology (the host of theories that underlie it) is brought in, one has a clear idea of its utility. (I should perhaps be more cautious here, but I take it from the use of scientific instruments in satellites.) May it be possible to create a giant scientific map of theories in every field and then calculate their upper boundary of discovery? That sounds like some Devil's work. I'm not sure if that's possible to calculate. If you use MRI in some cognitive science, you say that the theory of the MRI limits the cognitive science's aspect in this case, to create theory that is useful? Not only that but this is supposed to be some sort of "self-validation"? I think I disagree (strongly). Let's think of chemistry. If we use some sort of device to analyse chemical compounds, that is a case of self-validation? Even if we agree that the device is calibrated to detect some compound, it's use is not given in determining the world. This should be clear.
There's no chance in identifying one paradigm that isn't affected by the development in the other fields, concrete or abstract. The actual "paradigm" is so fundamentally connected to both the history leading up to this and the contemporary efforts in other fields that it's useless to bother calling it paradigm. There's no explanatory force beyond this particular problem that has gotten stuck and that the other fields of science lack the ability to make it unstuck, progressing. I may be inaccurate with the phases of Kuhn's here. Please, bear with me. However, the point is made.
As progress happens in every field and is thus broad, it's impossible to say which advances in which field will prove crucial to any other field. The applicability of discoveries is not for certain. Yes, I'm definitely looking for a better or simply more comprehensive and interconnected, i.e. different, historiography of science if it's possible to acquire.
This should be said, I rely on the cognitivity of science being worked with and that scientists are able to see the futility or success of their own theory, work. As you have pointed out, back in the old days, this probably has taken a whole lot of time and that people have perished before some decisive event would happen.
I think a "paradigm" in Kuhn's sense is the emergence of an important theory of science that people at that time view as "true", "reliable" or whatever thereof and that it's being worked on and corroborated, perhaps, with the additions of ad-hoc sentences or corrections. The period of the dominance of this theory is this "paradigm".
With the word "cognition" I mean "that which one can grasp or understand with one's mind". It should be fairly common. As for the choice of theory to work with I guess I'm a kind of Popperian, that if the theory one scientist is working with gets bashed, nulled by the work of others, this one scientist is very much able to understand it and shift the efforts to some other theory. Equally I think the opposite is true too. All in all, scientists are able to recognise their own and others' failures or successes in working with theories.
What I'm thinking of when I say that technology is cognitive, is that the results of using this technology definitely are inter-subjective, like looking at some kind of imaging, spectrograph, the rest. That there's no doubt about the utility of this technology.
Let's assume some scientists are working on glass and optics and some other scientists are working on astronomy. Now, the scientists working on glass and optics come up with an improved telescope. The scientists working on astronomy are wondering about the features on the moon or something and use this improved telescope. If the scientists working on astronomy get new knowledge from this, are we then supposed to consider this invalid because "the developments this theory (on the substance of glass and optics, basically mathematics) allows on the "right" theory of the features of the moon and thus that this constitutes "some sort of self-validation"? I must say that this is false! Are we supposed to doubt the mathematics expressed through glass? Can we predict the use of advances in science applied to all of nature? Definitely not!
It's obvious that technology relies on theory, but sometimes it may be a lot more pragmatic than f.x. a theory in astronomy or cosmology. The point is still the interconnectedness in all of science, more or less! As such, these considerations may not be new, but I've yet to see anyone making a good case for it, ie. historiography of science, an actual work published digitally or at least in paper, (multi-volume) book.
Necessarily, my attack on Kuhn includes that scientific revolutions and paradigms are considered pop-culture. The truth is that advances in science are gradual and progressive. At least, the data collected is clearly cumulative and perhaps corrected. It should be exciting to see what levels on can achieve in micro- and macro-scopes in the sciences. My exposition, view of scientific historiography, consists of the three factors, Interconnectedness, Complexity and Technology (ICT). This will make the best explanation of the history of science and defeat Kuhn's theory of "Paradigms".
Concerning the status of paradigms through time, I have to admit that I'm wrong in equalling the paradigms regardless of time. Let me quote Kuhn from SSR, 3rd ed., chapter 9, p. 96: wrote:
Quote: "...After the pre-paradigm period the assimilation of all new theories and of almost all new sorts of phenomena has in fact demanded the destruction of a prior paradigm and a consequent conflict between competing schools of scientific thought..."
If I find more of these instances I'll quote them too.
The amount of data is in every matter considered independently of "paradigm" or phase of history of science you're in. If our perception of gravity changes significantly, it's no more gravity. It's something else. That is, it's the data that guide us in making appropriate concepts and descriptions. This may be seen as causal, but I think it represents something else. The word "gravitare" means to attract or so and it fits nicely the observation we have of seeing things fall to the ground. It sounds basic and I'll try to look for a better example or two.
From SSR 3rd ed. p. 96 about Normal science and cumulation:
Quote: "Normal research [as opposed to outside the specific paradigm], which is cumulative, owes its success to the ability of scientists regularly to select problems..."
I think Kuhn mentions a number of times that in his theory, Normal science is cumulative. This is opposed to my view that science is overall cumulative in the data gathering.
As such, if it's only "normal science" that is cumulative then it should be indeed possible to claim that "paradigms" are equal in standing because previous gathering of sense-data and speculation are obsolete in Kuhn's language. This is abruptly wrong in my opinion. One only needs to look to the steady progress of technology to get a clue of this. Not only that, but I've made it a main point that science very much interacts with technology. Technology is, as we all know, just a different expression of science that is worked out in other fields than where it's applied, typically in the scientific experiments in this regard and usually decisively so.
Are the data thrown out? No! In the experiments that are taken to support the Caloric-theory, there are inaccuracies. These inaccuracies lead to misinterpretations and to the faulty conclusion. I think, if we carry out the experiments today in the same way they have been then, we should get the same data as in the past. Obviously, we look at those data very differently now than back then. We are probably able to identify where they have gone wrong and how the set of data may be corrupt or at least inaccurate. At times, I find that Kuhn isn't separating between the generation of experimental data and the inferred theories thereof. Rather the correct view should be that all sorts of experiments generate a data bank of past experience. If the experiments have been carried out correctly in the past with that technology and accuracy of the time then it's just to repeat them and we get the same data over again. Past experiments are inter-subjective or objective within the boundary of what they have available at that time. We continually use this history to position ourselves for the future, not to repeat ourselves.
Concerning the Ptolemy astronomy versus the Copernican astronomy. There are still these factors that may have contributed to the progress possible. One should have in mind that this is a period of 1300 years:
1. Increasing number of astronomers and people contributing to astronomy.
2. The formalisation of specific educational training of astronomers.
3. Increasing observation gathering incl. increasing documentation of observations, perhaps also more accurate.
4. The printing press is developed some 150 years ahead of Copernicus, further making his library of astronomy actual. There's also the development of writing equipment and the quality of paper itself.
There you have it. Has this been included in the account made by Kuhn? Not that I know of.
It says in "Logic of Discovery or Psychology of Research?" p. 17, Philosophy of Science - The Central Issues by M. Curd and J. A. Cover, "On some occasions, at least, tests are not requisite to the revolutions through which science advances. But that is not true of puzzles."
Kuhn makes a point in "Logic of Discovery or Psychology of Research?" implying that puzzle solving promotes science better than Popper's testing of hypotheses, but when Kuhn does this, he forgets that the actual astronomical observations can be tested against the explanation that best fits the picture of the set of observations. This is actually the case with the anomaly of Newton's system where the perihelion of Mercury has been out of line. The anomaly has been bothering astronomers all the time up to Einstein's Theory of Relativity. This is written on p. 85 of Donald Gillies' book, Philosophy of Science in the Twentieth Century.
This may be some of the reason why my criticism of Kuhn has been made possible. He has devoted himself in too great a degree to linguistic constructs and less to the objective facts concerning the actual scientific observations that in a sense represent Scientific Realism. This can partly explain his motivation to hold the Theory of Paradigms even if it's in fact been written appx. 8 years after 1. ed. of "The Structure".
Further: I've been reading Kuhn some more and I find this striking statement: Kuhn, SSR, p. x, Preface write: Quote: "Though subsequent events have somewhat relaxed those restrictions and have made possible simultaneous independent publication, this work remains an essay rather than the full-scale book my subject will ultimately demand." It's quite astonishing that the followers of Kuhn call his work definitive when he surely haven't bothered to finish it. This is written in February 1962 and Kuhn lives to 1996. It looks sloppy by Kuhn. I wonder how many excuses that are going to be made on the grounds that the book is unfinished. It makes me think of an analogy with the religious character of Jesus who can be said to be more holes than substance. At least, everyone can now see how the Complexity part falls into my pocket.
To make the distinction fully between Kuhn and myself and why my description has more use than Kuhn's, beside being true, is that with my theory of ICT it should be possible to determine the careful steps that lead to a successful theory in a complex picture of historiography of science rather than the very crude image given by Kuhn and his incomplete work, by his own words, of The Structure!
Preliminary notes follow.------------------------------
Kuhn, SSR, p. 4, writes:
Quote: "Nor does it make less consequential the particular constellation to which the group, at a given time, is in fact committed."
The sense of mine is here that Kuhn seems to incorporate this into his beginning paradigm of normal science where the alleged puzzle solving takes place in order to reveal anomalies to theory as science is developed. I like to draw a comparison to ancient Greek history and suggest that its scope certainly entails Einstein's work. What does this mean? I point out that one is dedicated to the best no matter what one's situation is. Therefore, I think, it's equally good to suggest that one is attacking the current theory as much as one is making confirmations to it. The message is that the observations are calling for the theory's future, whether one is "friendly" or "hostile" to it. It's my impression that Kuhn puts a great deal of theory-laden observations into his foundation of SSR, (clearly) to the extent that he blurs out the distinction between (experimental) observations and theory that's tested. As one knows, the theory is supposed to be defined in a way that makes testing possible, otherwise the experiment is useless or not an experiment at all. Does this mean that the ancient Greek have been committed to anything less than to the best of their ability? No, because they at that time needed more observations and the appropriate observations. Those, as we all know, haven't been achieved or developed, especially technically, before much later.
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Some further writings of various kind.
I've been reading the article, "Logic of Discovery or Psychology of Research?", before SSR has arrived from the bookstore. It's funny why Kuhn bothers to reiterate his puzzle solving and compare it against Popper's testing of hypothesis. It should be clear what Kuhn says before bothering to say that his view opposes Popper's.
It turns out that puzzle solving is formulated in ch. 4 of SSR. The very chapter is named "Normal Science as Puzzle-Solving".
Missing pieces in physics! Missing pieces in the other fields of science! So, the question is, are we in crisis in Particle Physics according to Kuhn? We have currently a situation akin to the one in Newtonian physics where the anomaly of the perihelion of Mercury is known.
This also comes together with our ability to make observations without being dependent on theory or without fusing our theories with our observations. I think we are just forced to carry on with scientific investigations regardless of what Kuhn's analysis tells us and, at the same time, without being blind while doing so.
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I just like to add, having learnt of Ian Hacking's "Interactive Kinds", that it may be just as an effective term to describe the history of science as my "Interconnectedness, Complexity and Technology (ICT)". Also, "interactive kinds" reinforces "natural kinds" beautifully!
Therefore, you may already now want to begin to read Ian Hacking and make your own Cumulativist version of it!
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I'm wondering about writing about the "paradigm" of the microscope to crush the notion of paradigm because the microscope (or the telescope) extends so beautifully from our natural observing capacity and through relatively plausible optics mechanisms. Eventually I hope this is to happen, the crushing of the notion of paradigm, nevertheless.
It can be worth noting the preceding history to the laboratory and why one has decided to use laboratories in the first place. Because Kuhn is explicitly unable or not willing to separate theory and necessary experiment apparatus for making the case of the theory. Thus, experiment apparatus is not some arbitrary "black magic" device, but maybe in the Kuhnian sense, charicaturely!
What other choice is there? There are indeed deep limitations to being a human being, thus we need the microscope, the LHC, the other particle accelerators, the SOHO satelite, the spectrometer and the rest!
It maybe unnecessary to say that this writing or outlining will be a total crash with "The Structure" even if his "Structure" in many senses is well told and expertly composed.
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(I write forthcoming on quotes from SSR until I've finished reading it.)
Case studies by ICT. (Upcoming!)------------------------------
The two cases I've decided on are "Einstein and the possible contestants" and "Lavoisier and the Caloric theory of heat". I may add more cases than this, but nominally these are the two cases I desire to investigate. I think these two cases also provide enough workload and they are also sufficient to provide credibility of ICT if the work is done properly. This is just a notice to interested readers and it is going to be removed as the case studies are played out.
By L. F. Olsnes-Lea (formerly Terje Lea)
Note: The guilt of not having finished this lies totally on Norway for obstructing the normal ways to academic performance in my life, rather choosing a despicable, lunatic strategy for seeking influence in suppressing my person, thus making very awful psychological impressions to people and without bothering that this takes place too!
You may want to take note of the word "stratagem", but please add a big deal of idiocy!
Note2: That this makes me look a bit like a fool must be clear, but Norway has chosen "dumb" as virtue for itself and it has forced me to detours and greater delays. File your complaints to Idiot-Norway, please!
----
Explicitly, the difference between Kuhn and myself in short:
Thomas Kuhn = "normal science", a special concept of his, p. 24.
Me, Lukas F. Olsnes-Lea = "only normal science",
- normal science is what I insist on and that I declare all science to be, and not a step outside research ethics either.
"The followers to Kuhn are therefore required to deliver this "scientific" voodoo film evidence to somewhere credible for evaluation BY ALL! Hah-hah-hah-hah."
The names for our plotting in finishing the ICT by one example against the SSR of T. Kuhn:
Ptolemyan (Ptolemy, ca. 90 - 168 CE) - Copernican (Copernicus, 1473 - 1543 CE) - Brahean (Brahe, 1546 - 1601 CE) - Galileoean (Galileo, 1564 - 1642 CE) - Keplerian (Kepler, 1571 - 1630 CE) - Newtonian (Newton, 1642 - 1727 CE) - Einsteinian (Einstein, 1879 - 1955 CE).
Despite some disagreements between the 3 above, with Galileo already being credibly more forceful then, decided by Copernicus(?, fraud on the internet?)/Newton! (Let me come back to this point.)
And not Krausses 1000s of religions either!
Then its for us to plot the names ourselves by time and number of observations graph, inside the x, y-axes of time and number and with a bit of "printing press"-time dot under the y-axis! The SSR (The Structure) seems ever smaller? Not comparable texts as theories by the 7 scientists above?
Note: This is one account for one data-set under MY standard (the bl**dy hardest, blog language) for Historiography of Science. Also, it is well known with us, the philosophers of science, that the data-set stretches all the way back to ancient China and one observation of Haley's Comet or whatever (need check of non-fake book not under corrupt Norway). The set is also, of course, being updated today and in the future as well, I think it's fair to say.
Note2: This comes in also after trying to identify the part where Thomas Kuhn describes this universal machine of science where he claims he can put anything in and get anything out in principle (requiring the text of a non-fake book not under corrupt Norway).
Retrying:
Despite some disagreements between the 3 above, with Galileo already being credibly more forceful then, decided by Newton, not entirely recalling the comparison of theories between them!
As I've been looking into the book, SSR/the Structure of Kuhn more, I'll make this short for the readers already now so that no "excess"/"waste of time" reading or effort is required:
The text is found on p. 76 and reads, "...that more than one theoretical construction can always be placed upon a given collection of data."
First, my point of view is that very few (understating 1, reasonably) such "constructions" can be achieved whatsoever if they are to be 1. incompatible and 2. differ significantly.
A formal note goes to the theories (with the data-sets) which are failures simply because they are theoretically too many and too insignificant to consider.
That is, these "constructions" will never differ in ways that are outside the best achievable theory (and data-set) and that the "constructions" will have little or no impact in the scientific World and much of it is probably made by "I-defy-you"-philosophers of science either way and look terribly artificial and desperate too.
This point is regarded as crucial in considering my opposition to Kuhn in providing the best Philosophy of Science, allowing me a much more refined account of History of Science by ICT. The rest of Kuhn's book (210 pages) is read in my light onto Kuhn by my interpretation of these "constructions", being a kind of general phrase for the science that Kuhn represents in this book and after.
If two lessons can be drawn from history of science, they are these: accuracy and added description. Not scientific revolutions, not cognitively new worlds!
The telescopes of history can be viewed in combination by the focusing telescope that's able to go from the view of the naked eye to the starry heavens and zooming in on a given bit of astronomical sky! Thereby you go from the weakest telescopes in history, meaning the earliest, to the most powerful telescopes in history, meaning the somewhat latest.
Please also see the improved historiography on astronomy in comparing this work of mine to Kuhn's SSR:
https://whatiswritten777.blogspot.no/2017/01/case-in-point-astronomy-against-kuhns.html
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Swinging stone in ancient Greece vs. pendulum in Renaissance Italy
Relating to Aristotle and Galileo by Kuhn and SSR, p. 118 - 125 and the difference of a swinging stone and the pendulum.
Aristotle: 384 BC - 322 BC, seeing a swinging stone, I guess, by chain or thread.
Galileo: 15 February 1564 - 8 January 1642, seeing the pendulum.
The difference between them: roughly 2000 yrs.
So, by Cumulativism, if we have 2000 years between 2 people and suppose a "revolution" as Galileo considers the pendulum I'd like people to think again because that's 2000 years of engineering history as well.
Let's list some factors for these 2000 years of engineering history:
* Measurements - https://en.wikipedia.org/wiki/History_of_measurement
* Accuracy and precision - https://en.wikipedia.org/wiki/Accuracy_and_precision
* Technological ability to manipulate objects (i.e., tools and more) - https://en.wikipedia.org/wiki/Technology - https://en.wikipedia.org/wiki/Tool - https://en.wikipedia.org/wiki/Renaissance (for "simple machines")
So it proceeds from the factors above that a "revolution" hardly can be noted over the course of 2000 entire years and with the advance of the factors above.
Orderly: https://en.wikipedia.org/wiki/Pendulum.
Aristotle: https://en.wikipedia.org/wiki/Aristotle
Galileo: https://en.wikipedia.org/wiki/Galileo_Galilei
Monday, 16 July 2018
Case in Point - Astronomy - Against Kuhn's Revolutions and Paradigms #1
First, some links,
https://en.wikipedia.org/wiki/Aristarchus_of_Samos Aristarchus of Samos, c. 310 - c. 230 BC
- The heliocentric view that has failed to take hold
https://en.wikipedia.org/wiki/Babylonian_astronomical_diaries Babylonian astronomical diaries
https://en.wikipedia.org/wiki/Ptolemy Ptolemy, c. 100 AD - c. 170 AD
- The geocentric worldview
https://en.wikipedia.org/wiki/Latin_translations_of_the_12th_century#List_of_translations
"- Ptolemy (2nd century A.D.)
Almagest: from Greek, Sicily c. 1160; Gerard of Cremona, from Arabic, Toledo 1175
Optica: Eugenius of Palermo, from Arabic, c. 1154"
https://en.wikipedia.org/wiki/Printing_press Printing press
"The printing press spread within several decades to over two hundred cities in a dozen European countries. By 1500, printing presses in operation throughout Western Europe had already produced more than twenty million volumes. In the 16th century, with presses spreading further afield, their output rose tenfold to an estimated 150 to 200 million copies. The operation of a press became so synonymous with the enterprise of printing that it lent its name to an entire new branch of media, the press."
https://en.wikipedia.org/wiki/Nicolaus_Copernicus Nicolaus Copernicus, 19 February 1473 - 24 May 1543 (AD)
- The heliocentric worldview (start)
- Growing archive/database of observations, library of astronomical data
https://en.wikipedia.org/wiki/Tycho_Brahe Tycho Brahe 14 December 1546 – 24 October 1601
- Growing archive/database of observations, library of astronomical data
- Wrongly posited the geo-heliocentric worldview, the Tychonic system
"Well known in his lifetime as an astronomer, astrologer and alchemist, he has been described as "the first competent mind in modern astronomy to feel ardently the passion for exact empirical facts." His observations were some five times more accurate than the best available observations at the time."
https://en.wikipedia.org/wiki/History_of_the_telescope History of the telescope
https://en.wikipedia.org/wiki/List_of_telescope_types List of telescope types
https://en.wikipedia.org/wiki/Observatory#Oldest_astronomical_observatories Astronomical observatories - oldest
A selection...
- Galileo's use: "Galileo Galilei, happening to be in Venice in about the month of May 1609, heard of the invention and constructed a version of his own."
- Kepler's use: "The Keplerian telescope, invented by Johannes Kepler in 1611, is an improvement on Galileo's design. It uses a convex lens as the eyepiece instead of Galileo's concave one."
https://en.wikipedia.org/wiki/Galileo_Galilei Galileo Galilei, 15 February 1564 - 8 January 1642
- The heliocentric worldview (supported)
- Growing archive/database of observations, library of astronomical data
- Refracting telescope, Galilean telescope, supporting the heliocentric worldview
https://en.wikipedia.org/wiki/Johannes_Kepler Johannes Kepler, December 27, 1571 – November 15, 1630
- The heliocentric worldview (supported)
- Growing archive/database of observations, library of astronomical data
- Refracting telescope, Keplerian telescope, supporting the heliocentric worldview
https://en.wikipedia.org/wiki/Heliocentrism Heliocentrism
https://en.wikipedia.org/wiki/Binoculars Binoculars
https://en.wikipedia.org/wiki/Reflecting_telescope Reflecting telescope
https://en.wikipedia.org/wiki/Isaac_Newton Sir Isaac Newton FRS 25 December 1642 - 20 March 1726/27
- Growing archive/database of observations, library of astronomical data
- Reflecting telescope, Newtonian telescope (1668), supporting the heliocentric worldview
- Theory of gravity
https://en.wikipedia.org/wiki/Newtonian_telescope Newtonian telescope
- Newton's invention
"In late 1668 Isaac Newton built his first reflecting telescope. He chose an alloy (speculum metal) of tin and copper as the most suitable material for his objective mirror. He later devised means for shaping and grinding the mirror and may have been the first to use a pitch lap to polish the optical surface."
https://en.wikipedia.org/wiki/William_Herschel Frederick William Herschel KH, FRS 15 November 1738 – 25 August 1822
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
"During his career, he constructed more than four hundred telescopes. The largest and most famous of these was a reflecting telescope with a 49 1⁄2-inch-diameter (1.26 m) primary mirror and a 40-foot (12 m) focal length. Because of the poor reflectivity of the speculum mirrors of that day, Herschel eliminated the small diagonal mirror of a standard Newtonian reflector from his design and tilted his primary mirror so he could view the formed image directly."
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
https://en.wikipedia.org/wiki/Universe The Universe
"The earliest scientific models of the Universe were developed by ancient Greek and Indian philosophers and were geocentric, placing the Earth at the center of the Universe. Over the centuries, more precise astronomical observations led Nicolaus Copernicus (1473–1543) to develop the heliocentric model with the Sun at the center of the Solar System. In developing the law of universal gravitation, Sir Isaac Newton (NS: 1643–1727) built upon Copernicus's work as well as observations by Tycho Brahe (1546–1601) and Johannes Kepler's (1571–1630) laws of planetary motion. Further observational improvements led to the realization that our Solar System is located in the Milky Way galaxy and is one of many solar systems and galaxies. It is assumed that galaxies are distributed uniformly and the same in all directions, meaning that the Universe has neither an edge nor a center. Discoveries in the early 20th century have suggested that the Universe had a beginning and that it is expanding at an increasing rate."
https://en.wikipedia.org/wiki/Edwin_Hubble Edwin Powell Hubble November 20, 1889 – September 28, 1953
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
- "was an American astronomer who played a crucial role in establishing the field of extragalactic astronomy and is generally regarded as one of the most important observational cosmologists of the 20th century. Hubble is known for showing that the recessional velocity of a galaxy increases with its distance from the earth, implying the universe is expanding, known as "Hubble's law", although a preliminary version of this relation was proposed by Georges Lemaître two years earlier in a less prominent journal."
https://en.wikipedia.org/wiki/Harlow_Shapley Harlow Shapley November 2, 1885 – October 20, 1972
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
"He used RR Lyrae stars to correctly estimate the size of the Milky Way Galaxy and the sun's position within it by using parallax. In 1953 he proposed his "liquid water belt" theory, now known as the concept of a habitable zone."
https://en.wikipedia.org/wiki/Albert_Einstein Albert Einstein 14 March 1879 - 18 April 1955
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
- Theory of relativity
https://en.wikipedia.org/wiki/Satellite Satellite
"The world's first artificial satellite, the Sputnik 1, was launched by the Soviet Union in 1957. Since then, thousands of satellites have been launched into orbit around the Earth. Some satellites, notably space stations, have been launched in parts and assembled in orbit. Artificial satellites originate from more than 40 countries and have used the satellite launching capabilities of ten nations. About a thousand satellites are currently operational, whereas thousands of unused satellites and satellite fragments orbit the Earth as space debris. A few space probes have been placed into orbit around other bodies and become artificial satellites to the Moon, Mercury, Venus, Mars, Jupiter, Saturn, Vesta, Eros, Ceres, and the Sun."
https://en.wikipedia.org/wiki/Moon_landing Moon landing
"A Moon landing is the arrival of a spacecraft on the surface of the Moon. This includes both manned and unmanned (robotic) missions. The first human-made object to reach the surface of the Moon was the Soviet Union's Luna 2 mission, on 13 September 1959.
The United States' Apollo 11 was the first manned mission to land on the Moon, on 20 July 1969. There have been six manned U.S. landings (between 1969 and 1972) and numerous unmanned landings, with no soft landings happening from 22 August 1976 until 14 December 2013."
My claim is then that "bits and pieces" make the scientific day against Kuhn's "orderly" Paradigms and so on, that science takes place in a "Cumulativist" (ICT) way where science gets increasingly accurate and on Truth!
Additionally:
I've identified a mark of stupidity in history of science in that Galileo Galilei's superior has failed to commission/make the order for building, let's say, 10 Galilean telescopes when in fact his opponents and contemporaries alike have been in need of one!
This is remarkable because it shows that his contemporaries have not (to my knowledge) been interested to learn what Galileo Galilei has seen in his telescope!
Conclusion: the opponents of Galileo Galilei have not been driven by a (first-hand) thirst for knowledge!
History shows that there are quite some examples of this kind of behaviour, I think!
This also shows that Galileo Galilei has failed to teach people the way of the telescope and the calculations for his (famous) claim in support of Copernicus!
Kuhn also seems to forget that the Galilean telescope can be directed at a far-away tree or any other object. This is, of course, not a "new worldview", but enhanced sight!
From this text I intend to show that the title reveals the truth. Largely speaking "revolutions" is the
language of the tabloids!
https://en.wikipedia.org/wiki/Aristarchus_of_Samos Aristarchus of Samos, c. 310 - c. 230 BC
- The heliocentric view that has failed to take hold
https://en.wikipedia.org/wiki/Babylonian_astronomical_diaries Babylonian astronomical diaries
https://en.wikipedia.org/wiki/Ptolemy Ptolemy, c. 100 AD - c. 170 AD
- The geocentric worldview
https://en.wikipedia.org/wiki/Latin_translations_of_the_12th_century#List_of_translations
"- Ptolemy (2nd century A.D.)
Almagest: from Greek, Sicily c. 1160; Gerard of Cremona, from Arabic, Toledo 1175
Optica: Eugenius of Palermo, from Arabic, c. 1154"
https://en.wikipedia.org/wiki/Printing_press Printing press
"The printing press spread within several decades to over two hundred cities in a dozen European countries. By 1500, printing presses in operation throughout Western Europe had already produced more than twenty million volumes. In the 16th century, with presses spreading further afield, their output rose tenfold to an estimated 150 to 200 million copies. The operation of a press became so synonymous with the enterprise of printing that it lent its name to an entire new branch of media, the press."
https://en.wikipedia.org/wiki/Nicolaus_Copernicus Nicolaus Copernicus, 19 February 1473 - 24 May 1543 (AD)
- The heliocentric worldview (start)
- Growing archive/database of observations, library of astronomical data
https://en.wikipedia.org/wiki/Tycho_Brahe Tycho Brahe 14 December 1546 – 24 October 1601
- Growing archive/database of observations, library of astronomical data
- Wrongly posited the geo-heliocentric worldview, the Tychonic system
"Well known in his lifetime as an astronomer, astrologer and alchemist, he has been described as "the first competent mind in modern astronomy to feel ardently the passion for exact empirical facts." His observations were some five times more accurate than the best available observations at the time."
https://en.wikipedia.org/wiki/History_of_the_telescope History of the telescope
https://en.wikipedia.org/wiki/List_of_telescope_types List of telescope types
https://en.wikipedia.org/wiki/Observatory#Oldest_astronomical_observatories Astronomical observatories - oldest
A selection...
- 1577: Istanbul observatory of Taqi al-Din, Turkey
- 1580: Uraniborg, Denmark
- 1581: Stjerneborg, Denmark
- 1642: Panzano Observatory, Italy
- 1642: Round Tower, Denmark
- 1633: Leiden Observatory, Netherlands
- 1667: Paris Observatory, France
- 1675: Royal Greenwich Observatory, England
- 1695: Sukharev Tower, Russia
- 1711: Berlin Observatory, Germany
- 1724: Jantar Mantar, India
- Galileo's use: "Galileo Galilei, happening to be in Venice in about the month of May 1609, heard of the invention and constructed a version of his own."
- Kepler's use: "The Keplerian telescope, invented by Johannes Kepler in 1611, is an improvement on Galileo's design. It uses a convex lens as the eyepiece instead of Galileo's concave one."
https://en.wikipedia.org/wiki/Galileo_Galilei Galileo Galilei, 15 February 1564 - 8 January 1642
- The heliocentric worldview (supported)
- Growing archive/database of observations, library of astronomical data
- Refracting telescope, Galilean telescope, supporting the heliocentric worldview
https://en.wikipedia.org/wiki/Johannes_Kepler Johannes Kepler, December 27, 1571 – November 15, 1630
- The heliocentric worldview (supported)
- Growing archive/database of observations, library of astronomical data
- Refracting telescope, Keplerian telescope, supporting the heliocentric worldview
https://en.wikipedia.org/wiki/Heliocentrism Heliocentrism
https://en.wikipedia.org/wiki/Binoculars Binoculars
https://en.wikipedia.org/wiki/Reflecting_telescope Reflecting telescope
https://en.wikipedia.org/wiki/Isaac_Newton Sir Isaac Newton FRS 25 December 1642 - 20 March 1726/27
- Growing archive/database of observations, library of astronomical data
- Reflecting telescope, Newtonian telescope (1668), supporting the heliocentric worldview
- Theory of gravity
https://en.wikipedia.org/wiki/Newtonian_telescope Newtonian telescope
- Newton's invention
"In late 1668 Isaac Newton built his first reflecting telescope. He chose an alloy (speculum metal) of tin and copper as the most suitable material for his objective mirror. He later devised means for shaping and grinding the mirror and may have been the first to use a pitch lap to polish the optical surface."
https://en.wikipedia.org/wiki/William_Herschel Frederick William Herschel KH, FRS 15 November 1738 – 25 August 1822
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
"During his career, he constructed more than four hundred telescopes. The largest and most famous of these was a reflecting telescope with a 49 1⁄2-inch-diameter (1.26 m) primary mirror and a 40-foot (12 m) focal length. Because of the poor reflectivity of the speculum mirrors of that day, Herschel eliminated the small diagonal mirror of a standard Newtonian reflector from his design and tilted his primary mirror so he could view the formed image directly."
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
https://en.wikipedia.org/wiki/Universe The Universe
"The earliest scientific models of the Universe were developed by ancient Greek and Indian philosophers and were geocentric, placing the Earth at the center of the Universe. Over the centuries, more precise astronomical observations led Nicolaus Copernicus (1473–1543) to develop the heliocentric model with the Sun at the center of the Solar System. In developing the law of universal gravitation, Sir Isaac Newton (NS: 1643–1727) built upon Copernicus's work as well as observations by Tycho Brahe (1546–1601) and Johannes Kepler's (1571–1630) laws of planetary motion. Further observational improvements led to the realization that our Solar System is located in the Milky Way galaxy and is one of many solar systems and galaxies. It is assumed that galaxies are distributed uniformly and the same in all directions, meaning that the Universe has neither an edge nor a center. Discoveries in the early 20th century have suggested that the Universe had a beginning and that it is expanding at an increasing rate."
https://en.wikipedia.org/wiki/Edwin_Hubble Edwin Powell Hubble November 20, 1889 – September 28, 1953
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
- "was an American astronomer who played a crucial role in establishing the field of extragalactic astronomy and is generally regarded as one of the most important observational cosmologists of the 20th century. Hubble is known for showing that the recessional velocity of a galaxy increases with its distance from the earth, implying the universe is expanding, known as "Hubble's law", although a preliminary version of this relation was proposed by Georges Lemaître two years earlier in a less prominent journal."
https://en.wikipedia.org/wiki/Harlow_Shapley Harlow Shapley November 2, 1885 – October 20, 1972
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
"He used RR Lyrae stars to correctly estimate the size of the Milky Way Galaxy and the sun's position within it by using parallax. In 1953 he proposed his "liquid water belt" theory, now known as the concept of a habitable zone."
https://en.wikipedia.org/wiki/Albert_Einstein Albert Einstein 14 March 1879 - 18 April 1955
- Growing archive/database of observations, library of astronomical data
- All telescopes for this era!
- Library of theories (Theory of gravity, Kepler, Copernicus, Newton etc.)
- Theory of relativity
https://en.wikipedia.org/wiki/Satellite Satellite
"The world's first artificial satellite, the Sputnik 1, was launched by the Soviet Union in 1957. Since then, thousands of satellites have been launched into orbit around the Earth. Some satellites, notably space stations, have been launched in parts and assembled in orbit. Artificial satellites originate from more than 40 countries and have used the satellite launching capabilities of ten nations. About a thousand satellites are currently operational, whereas thousands of unused satellites and satellite fragments orbit the Earth as space debris. A few space probes have been placed into orbit around other bodies and become artificial satellites to the Moon, Mercury, Venus, Mars, Jupiter, Saturn, Vesta, Eros, Ceres, and the Sun."
https://en.wikipedia.org/wiki/Moon_landing Moon landing
"A Moon landing is the arrival of a spacecraft on the surface of the Moon. This includes both manned and unmanned (robotic) missions. The first human-made object to reach the surface of the Moon was the Soviet Union's Luna 2 mission, on 13 September 1959.
The United States' Apollo 11 was the first manned mission to land on the Moon, on 20 July 1969. There have been six manned U.S. landings (between 1969 and 1972) and numerous unmanned landings, with no soft landings happening from 22 August 1976 until 14 December 2013."
My claim is then that "bits and pieces" make the scientific day against Kuhn's "orderly" Paradigms and so on, that science takes place in a "Cumulativist" (ICT) way where science gets increasingly accurate and on Truth!
Additionally:
I've identified a mark of stupidity in history of science in that Galileo Galilei's superior has failed to commission/make the order for building, let's say, 10 Galilean telescopes when in fact his opponents and contemporaries alike have been in need of one!
This is remarkable because it shows that his contemporaries have not (to my knowledge) been interested to learn what Galileo Galilei has seen in his telescope!
Conclusion: the opponents of Galileo Galilei have not been driven by a (first-hand) thirst for knowledge!
History shows that there are quite some examples of this kind of behaviour, I think!
This also shows that Galileo Galilei has failed to teach people the way of the telescope and the calculations for his (famous) claim in support of Copernicus!
Kuhn also seems to forget that the Galilean telescope can be directed at a far-away tree or any other object. This is, of course, not a "new worldview", but enhanced sight!
From this text I intend to show that the title reveals the truth. Largely speaking "revolutions" is the
language of the tabloids!
Case in Point - Early Physics by The Pendulum - Against Kuhn's Revolutions and Paradigms #2
Case in Point #2: Swinging stone in ancient Greece vs. pendulum in Renaissance Italy
Relating to Aristotle and Galileo by Kuhn and SSR, p. 118 - 125 and the difference of a swinging stone and the pendulum.
Aristotle: 384 BC - 322 BC, seeing a swinging stone, I guess, by chain or thread.
Galileo: 15 February 1564 - 8 January 1642, seeing the pendulum.
The difference between them: roughly 2000 yrs.
So, by Cumulativism, if we have 2000 years between 2 people and suppose a "revolution" as Galileo considers the pendulum I'd like people to think again because that's 2000 years of engineering history as well.
Let's list some factors for these 2000 years of engineering history:
* Measurements - https://en.wikipedia.org/wiki/History_of_measurement
* Accuracy and precision - https://en.wikipedia.org/wiki/Accuracy_and_precision
* Technological ability to manipulate objects (i.e., tools and more) - https://en.wikipedia.org/wiki/Technology - https://en.wikipedia.org/wiki/Tool - https://en.wikipedia.org/wiki/Renaissance (for "simple machines")
So it proceeds from the factors above that a "revolution" hardly can be noted over the course of 2000 entire years and with the advance of the factors above.
Orderly: https://en.wikipedia.org/wiki/Pendulum.
For comparison, one can note that difference in weaponry as well, in telling a story of engineering:
https://en.wikipedia.org/wiki/History_of_weapons
https://en.wikipedia.org/wiki/Dardanelles_Gun
History of metalworking:
http://www.hackingtheuniverse.com/science/history-of-science-and-technology/genarticles/timeline-of-metalworking
Aristotle: https://en.wikipedia.org/wiki/Aristotle
Galileo: https://en.wikipedia.org/wiki/Galileo_Galilei
"Thus the press/media reports an ongoing revolution by transition from a swinging stone to a pendulum for 2000 years."
Future Cumulativism (ICT) accounts of history of science:
I'd like to speak out against "paranoia" about the pharmaceutical industry and the medicines.
Generally, for the history of science (and psychiatry), I find that the market is served, that there is real progress and so forth.
I agree that Big Pharma can be greedy, but that there has been and there is real progress in terms of medicines to the benefit of all patients even if science continues to be abused for the sake of evil, that is, the malpractice of (some) physicians and others.
Relating to Aristotle and Galileo by Kuhn and SSR, p. 118 - 125 and the difference of a swinging stone and the pendulum.
Aristotle: 384 BC - 322 BC, seeing a swinging stone, I guess, by chain or thread.
Galileo: 15 February 1564 - 8 January 1642, seeing the pendulum.
The difference between them: roughly 2000 yrs.
So, by Cumulativism, if we have 2000 years between 2 people and suppose a "revolution" as Galileo considers the pendulum I'd like people to think again because that's 2000 years of engineering history as well.
Let's list some factors for these 2000 years of engineering history:
* Measurements - https://en.wikipedia.org/wiki/History_of_measurement
* Accuracy and precision - https://en.wikipedia.org/wiki/Accuracy_and_precision
* Technological ability to manipulate objects (i.e., tools and more) - https://en.wikipedia.org/wiki/Technology - https://en.wikipedia.org/wiki/Tool - https://en.wikipedia.org/wiki/Renaissance (for "simple machines")
So it proceeds from the factors above that a "revolution" hardly can be noted over the course of 2000 entire years and with the advance of the factors above.
Orderly: https://en.wikipedia.org/wiki/Pendulum.
For comparison, one can note that difference in weaponry as well, in telling a story of engineering:
https://en.wikipedia.org/wiki/History_of_weapons
https://en.wikipedia.org/wiki/Dardanelles_Gun
History of metalworking:
http://www.hackingtheuniverse.com/science/history-of-science-and-technology/genarticles/timeline-of-metalworking
Aristotle: https://en.wikipedia.org/wiki/Aristotle
Galileo: https://en.wikipedia.org/wiki/Galileo_Galilei
"Thus the press/media reports an ongoing revolution by transition from a swinging stone to a pendulum for 2000 years."
Future Cumulativism (ICT) accounts of history of science:
I'd like to speak out against "paranoia" about the pharmaceutical industry and the medicines.
Generally, for the history of science (and psychiatry), I find that the market is served, that there is real progress and so forth.
I agree that Big Pharma can be greedy, but that there has been and there is real progress in terms of medicines to the benefit of all patients even if science continues to be abused for the sake of evil, that is, the malpractice of (some) physicians and others.
Friday, 14 December 2012
The Free Will Theorem and Quants - Complexity
In considering "The Free Will Theorem Lectures" with Princeton University (and the John Locke Lectures?), I have made this addition:
(Various!Posted by Leonardo F. Olsnes-Lea 2011-07-05 03:30:40)
I think it requires complexity of heavier bodies of matter for free will to obtain.
The Free Will Theorem is presented by John Conway and Simon Kochen and the Wikipedia page has a criticism of them as a part of presenting The Free Will Theorem.
The url to it is this: http://en.wikipedia.org/wiki/Free_will_theorem.
Fx. a stream of photons of visible light can only do that much when speeding away from the Sun. There is no evidence that the stream of photons can change anything in particular, let's say direction, compensating for some gravity. See Einstein's relativity for gravity effects on photons.
Also, complexity should also be required for the decision for choosing between pleasure and relaxation and exercise and feeding and hunt. Although, these properties are only present with animals and ourselves, the humans.
So unless a bigger body is chosen and the choices are somehow explicated, I think "undetermined" is too weak for giving any plausibility to it or credibility for that matter.
I think, though, that the Dr. Dick Bierman experiments of Holland show that "monades" are likely to obtain in a fundamental way, in line with The Free Will Theorem by John Conway and Simon Kochen, rather than an unknown mechanism that may be impossible to find. This is a warning to future experimenters (the physicists).
The conclusion must be that a bigger system is effectuating the free will existing everywhere whether you call it God or some strange uknown super entity of the Universe / Multiverse or whatever.
Note: originally posted as http://blog.t-lea.net/#post232
Note2: you can also read about this on Static Display... on Facebook, it's an open group of mine.
Note3: THIS IS A BLOG and doesn't intend to live up to any Chicago Manual of Style or the very hard standards on supporting or relating material, also as I remain virtually without feedback from other people!
(Various!Posted by Leonardo F. Olsnes-Lea 2011-07-05 03:30:40)
I think it requires complexity of heavier bodies of matter for free will to obtain.
The Free Will Theorem is presented by John Conway and Simon Kochen and the Wikipedia page has a criticism of them as a part of presenting The Free Will Theorem.
The url to it is this: http://en.wikipedia.org/wiki/Free_will_theorem.
Fx. a stream of photons of visible light can only do that much when speeding away from the Sun. There is no evidence that the stream of photons can change anything in particular, let's say direction, compensating for some gravity. See Einstein's relativity for gravity effects on photons.
Also, complexity should also be required for the decision for choosing between pleasure and relaxation and exercise and feeding and hunt. Although, these properties are only present with animals and ourselves, the humans.
So unless a bigger body is chosen and the choices are somehow explicated, I think "undetermined" is too weak for giving any plausibility to it or credibility for that matter.
I think, though, that the Dr. Dick Bierman experiments of Holland show that "monades" are likely to obtain in a fundamental way, in line with The Free Will Theorem by John Conway and Simon Kochen, rather than an unknown mechanism that may be impossible to find. This is a warning to future experimenters (the physicists).
The conclusion must be that a bigger system is effectuating the free will existing everywhere whether you call it God or some strange uknown super entity of the Universe / Multiverse or whatever.
Note: originally posted as http://blog.t-lea.net/#post232
Note2: you can also read about this on Static Display... on Facebook, it's an open group of mine.
Note3: THIS IS A BLOG and doesn't intend to live up to any Chicago Manual of Style or the very hard standards on supporting or relating material, also as I remain virtually without feedback from other people!
Sunday, 9 December 2012
The Modern Corpus of Philosophy of Law - Here Defined!
I see from the Jurisprudence article on Wikipedia, that people may want some words on Philosophy of Law from me. These are:
1. There should be no holes in a good system of legal practice/legislation system!
2. The laws are absolute and they can't be reasonably dodged. This point is supported by point 1.
3. (if nec.) The laws are complete and describe only objective circumstances (pertaining to HDM and quality of evidence) and most certainly only real life.
4. Legislation is on TOP. The courts are nr. 2 and the Police are nr. 3. There are various security concerns to this. I think the Police need clear rules/procedures as they do their work. I think the Judges only need to set a precedent if the Legislative Assembly (National Parliament) feigns its duties. So I want/hold a theory for a sharp and pro-active Legislative Body and "Judges only to the rescue", acting secondarily so to speak! Good?
Just in case of interest, I find Antonin Scalia's Originalist position compatible with a "Legislationist" position. Thus I pay respect to forming laws "in the spirit of the Book of Laws (fx. Norges Lover)". Or when you sit there writing, that you are "in a spirit of the Law". This should be the beginning bricks for foundation! (Not having read a book, but generally (very) interested for a long time (I'm 35).
You should note my point on Godel (Goedel) in Phil. Notes. I'm hard and I know it. There will be no excuses if the future is properly cared for!!!
The header of it says: Opinions on Gödel's Theorems of Incompleteness and Possibly Tarski and link is (one of them): http://whatiswritten777.blogspot.com/2011/08/philosophical-notes-of-intellectual.html.
Also take note on the meditative state for making laws. Legislation happens at most meditative state, down to the Judges (by the heat of the Trial and direct Justice down further to Police under fire, so to speak! Thus, this comes natural!
You can get good lessons from Court TV (Nancy Grace) and various interviews from your or U.S. American Supreme Court Members by 60 Minutes. General media awareness isn't so bad either...
I must add that Europe can do well with its own Courts reporting (by example of Nancy Grace) and Justice section on CNN U.S. American edition and a Situation Room type of Legal Practice reporting (in media where there is "interest"). I welcome a more aware and active Legal Practice reporting in Europe. Also in the Pan-European sense (to close some holes for these "U.S. Americans" if not the "Colombians"...
I believe it has been Clarence Thomas who has uttered the words on an interview with CBS 60 Minutes that "you _need_ legislation to make verdicts". Consequently, I have the "Legislationist" position from him, but I'm uncertain if it is he who says the words or somebody else because a fair amount of time has passed since then.
When I write "Absolutist", I mean of course that there should be (normativity) little or no room for "interpretation". Burglary is thus burglary and rape, even for the sexist or crazy, is still the rape. The victim can never be the burglar oneself and the victim can't either be the rapist oneself. Some people are blind to this, they fail to make proper distinctions of words or situations or whatever. I also think that today's systems across the world seeks brevity of law as description of law on a rather unfounded basis. Therefore, I can imagine a more complete description to go with the law as it's delivered from the Legislative Assembly. Fx. in case it's needed, a better description can be given as a secondary compilation to the laws by corresponding documents to the collection of laws where these are needed. A law concerning The Protection of Private Information as fx. one's private address can be given a better description until it reaches a level of descriptive completeness, possibly adding 1, 2 or 3 pages.
Even if we speak of filming for the press, there is still no valid objection to having this filmed by Court's Archiving Services! Thus, Courts would have the pressure to do the job right and appeals could become much more clear. Corruption could also get rooted out much faster and idiot judges would never be allowed. But corruption to the archiving system makes every problem return again! I say, attack! (Because the world really looks retarded!)
So under the "Issues from the Internet", under the header of "What are your philosophical positions?" you can now add on me, Philosophy of Law: Absolutist, Legislationist and Originalist. Just for the update.
A hard list of modern notions to (every) Philosophy of Law, I introduce to you:
1. I've made a novel move in terms of describing the real and hard criminal nature of "monkey business", in conjunction with mSomatism!
2. I've suggested a national assembly approved official commentary that is to support the courts and reduce the amounts of precedents, so also as to diminish their mistaken authority throughout the World, even if they have served us to some good extent in the past! Germany is explicitly on the move in this respect.
3. I've described the definitive relations between the national assembly, the courts, and the police forces, so as to make the lines of duty more clear and to reduce any illusion of "self-made-policies" in that auto-generated sense. This is really /the/ policies killer, withholding the far more serious "police instructions", fx.!
4. I've made Objective Ethics including the crucial 4 methods of lie-detection to be used, potentially, at the same time, inside the police "interrogation room"/"questioning room". These are, of course, (f)MRI, "a swim hat of sensors", voice-stress analyzer, mimicry, including eye-dialation, and polygraph-testing, the reaction of body to nervousness in exuding sweat, essentially.
5. I have, together with others, suggested to film all cases in the courts so as to heavily reduce poor judge performance in the long run and to definitely place the possibilities for democratic control well within the proper hands of democratic care-takers! So that the court-archives will take on the most definite character and leave no doubt how the case has run. Some set-ups may even contain one or more of these 4 methods above.
This should speak well for me in demolishing any legal Hilbert's program! (Hilbert for insiders.)
Good?
1. There should be no holes in a good system of legal practice/legislation system!
2. The laws are absolute and they can't be reasonably dodged. This point is supported by point 1.
3. (if nec.) The laws are complete and describe only objective circumstances (pertaining to HDM and quality of evidence) and most certainly only real life.
4. Legislation is on TOP. The courts are nr. 2 and the Police are nr. 3. There are various security concerns to this. I think the Police need clear rules/procedures as they do their work. I think the Judges only need to set a precedent if the Legislative Assembly (National Parliament) feigns its duties. So I want/hold a theory for a sharp and pro-active Legislative Body and "Judges only to the rescue", acting secondarily so to speak! Good?
Just in case of interest, I find Antonin Scalia's Originalist position compatible with a "Legislationist" position. Thus I pay respect to forming laws "in the spirit of the Book of Laws (fx. Norges Lover)". Or when you sit there writing, that you are "in a spirit of the Law". This should be the beginning bricks for foundation! (Not having read a book, but generally (very) interested for a long time (I'm 35).
You should note my point on Godel (Goedel) in Phil. Notes. I'm hard and I know it. There will be no excuses if the future is properly cared for!!!
The header of it says: Opinions on Gödel's Theorems of Incompleteness and Possibly Tarski and link is (one of them): http://whatiswritten777.blogspot.com/2011/08/philosophical-notes-of-intellectual.html.
Also take note on the meditative state for making laws. Legislation happens at most meditative state, down to the Judges (by the heat of the Trial and direct Justice down further to Police under fire, so to speak! Thus, this comes natural!
You can get good lessons from Court TV (Nancy Grace) and various interviews from your or U.S. American Supreme Court Members by 60 Minutes. General media awareness isn't so bad either...
I must add that Europe can do well with its own Courts reporting (by example of Nancy Grace) and Justice section on CNN U.S. American edition and a Situation Room type of Legal Practice reporting (in media where there is "interest"). I welcome a more aware and active Legal Practice reporting in Europe. Also in the Pan-European sense (to close some holes for these "U.S. Americans" if not the "Colombians"...
I believe it has been Clarence Thomas who has uttered the words on an interview with CBS 60 Minutes that "you _need_ legislation to make verdicts". Consequently, I have the "Legislationist" position from him, but I'm uncertain if it is he who says the words or somebody else because a fair amount of time has passed since then.
When I write "Absolutist", I mean of course that there should be (normativity) little or no room for "interpretation". Burglary is thus burglary and rape, even for the sexist or crazy, is still the rape. The victim can never be the burglar oneself and the victim can't either be the rapist oneself. Some people are blind to this, they fail to make proper distinctions of words or situations or whatever. I also think that today's systems across the world seeks brevity of law as description of law on a rather unfounded basis. Therefore, I can imagine a more complete description to go with the law as it's delivered from the Legislative Assembly. Fx. in case it's needed, a better description can be given as a secondary compilation to the laws by corresponding documents to the collection of laws where these are needed. A law concerning The Protection of Private Information as fx. one's private address can be given a better description until it reaches a level of descriptive completeness, possibly adding 1, 2 or 3 pages.
Even if we speak of filming for the press, there is still no valid objection to having this filmed by Court's Archiving Services! Thus, Courts would have the pressure to do the job right and appeals could become much more clear. Corruption could also get rooted out much faster and idiot judges would never be allowed. But corruption to the archiving system makes every problem return again! I say, attack! (Because the world really looks retarded!)
So under the "Issues from the Internet", under the header of "What are your philosophical positions?" you can now add on me, Philosophy of Law: Absolutist, Legislationist and Originalist. Just for the update.
A hard list of modern notions to (every) Philosophy of Law, I introduce to you:
1. I've made a novel move in terms of describing the real and hard criminal nature of "monkey business", in conjunction with mSomatism!
2. I've suggested a national assembly approved official commentary that is to support the courts and reduce the amounts of precedents, so also as to diminish their mistaken authority throughout the World, even if they have served us to some good extent in the past! Germany is explicitly on the move in this respect.
3. I've described the definitive relations between the national assembly, the courts, and the police forces, so as to make the lines of duty more clear and to reduce any illusion of "self-made-policies" in that auto-generated sense. This is really /the/ policies killer, withholding the far more serious "police instructions", fx.!
4. I've made Objective Ethics including the crucial 4 methods of lie-detection to be used, potentially, at the same time, inside the police "interrogation room"/"questioning room". These are, of course, (f)MRI, "a swim hat of sensors", voice-stress analyzer, mimicry, including eye-dialation, and polygraph-testing, the reaction of body to nervousness in exuding sweat, essentially.
5. I have, together with others, suggested to film all cases in the courts so as to heavily reduce poor judge performance in the long run and to definitely place the possibilities for democratic control well within the proper hands of democratic care-takers! So that the court-archives will take on the most definite character and leave no doubt how the case has run. Some set-ups may even contain one or more of these 4 methods above.
This should speak well for me in demolishing any legal Hilbert's program! (Hilbert for insiders.)
Good?
Tuesday, 20 November 2012
On Metaphysics of Time
[by Terje Lea 12.
July 2011, time 08:42 by Facebook data only.]
[This begins with a drawing, crude and principal, but useful.]
[This begins with a drawing, crude and principal, but useful.]
The time moves along the y/z-axis while your view is positioned at origo or along a somewhat objective history x where the x-line (with no value as such) represents the threshold between past and future and thereby is the resultgiving x-plane on how the spherical waves entwine and create history and thereby giving you a certain historical view. This exposition of time can also be seen as a kind of psychometry (please associate this with telemetry). Make the most of your time!
I can deduce consistency and coherency from Descartes' Meditations and if you have consistency and coherency, you also have continuity, the flow of time!
This is primarily made to describe the ongoing passage of time in relation to agents (people) and their ideas.
This view here can be referred to as Block time or Eternalism, yet I think it's too radical to deduct our psychological experience of closeness of the present and what it represents. In my view, it's implicit that you should maximise the use of your experience through time so that the scope of future becomes as wide as possible.
We can surely say that the past of time has generated the course for the present moment and equally surely we can say the future lies in the scope of the present even though the future consists in only one course, becoming both the present and the past. Therefore, it's not irrelevant what has taken place in the past and the future has to come out of what is our present moment! We can look at everything in our present moment and conclude with certainty that a number of things must have led up to this. At least, this must be the nature of reality, otherwise we wouldn't be alive in exactly this scope of reality as it is. I think this supports block theory of time. This may be plain and is thus probably more pedagogical than informative. My view, however, is now more deeply explained and should be impossible to retreat from unless I trash the whole block theory of time.
McTaggart is wrong in presenting his A and B bands/tracks dichotomy. I believe the origin of time historically has its roots in the seasons, the Sun and possibly the life span of human kind by every single person. The clock is thus determined by the 24 hrs cycle of the Sun (on Earth), essentially giving the time when the Sun is highest through the day. Later, one has divided the Earth into 24 time zones with few exceptions. McTaggart comes out weak in his academic life of presenting time as he does. Let me guess he has lived an incredibly relaxed life with few necessary daily routines. This is from the reason that everyone, historically, has their primary activities during the day and catches the sleep during the night. This is undeniable if one goes back to the medieval times, at least. It is eventually the objective time, given by the Sun and the passing of years, historically, that triumphs the notion of time whether you sense time in this way or that or have funny thoughts about time.
Just let me clarify:
Time is, of course, a physical requirement, being at least, 1 of 4 dimensions. This is not the question. The question is how we as human beings have come to know time, both as concept and our cognition of it. Historically, I believe one has addressed "a day's worth of work", but the revolve of the Earth making the days has been essential of this formation. I believe the timing of motion is quite recent (1400 CE or so, just as a guess, especially in referring to the feather and stone experiment in testing gravity and at the same time having the perception of time in this regard). One can perhaps check out the invention of the first time-taking pieces or clocks on Wikipedia.
Clearly then, there's no questioning of time as such, but it's worth noting that we all live under the sun and it remains our compass of time until then! This may change if we settle in a new star system, but this is not some time soon, I can predict.
In responding to Charles Taylor, Metaphysics, 4th ed., this fleeting moment, referring in particular to The Elusive Present, pp. 85-87, of the present can only float in one direction, forward!
Time is also stuck to the time-track. 1980/01/01 CE will always be 1980/01/01 CE even if you consider it as 1980 CE + 13,7 x 10^9 CE years. This will always yield present time point, X CE + 13,7 x 10^9 CE where 13,7 x 10^9 CE is the most precise scientific estimate of the universe relevant to time and X is current date by year or date. I can write it like this: X + S being the X years from 0 CE and the scientific estimate from 0 CE to the beginning of the universe according to the Big Bang theory and scientific community's consensus.
The time of relativity/absurdism is slashed in the Metaphysical sense of Time theory.
This is also meant as an indicium for free will and the rationalist's approach, only in this regard.
Note. Don't pay too much attention to "rationalist's approach". It's simply put this way for suggesting the special place consciousness may have in regarding events of time and especially the consciousness of other "agents" in this perspective.
©Terje Lea, 2001-2010 with 25.03.2010, 26.03.2010, 12.04.2010, 19.04.2010, 27.04.2010 and 28.04.2010. A little comment has been added, 20.05.2010, to the word "psychometry".
Back to front page.
My mentioning of Block Time Theory and Eternalism may require a definition of them that are uniquely suitable for my Time theory. It's questioned whether time stops when or if (/this/) human kind is no more and if another human kind (equivalent) arises elsewhere in the Universe and whether this /new/ human kind discovers or not that another human kind has lived (us) in the Universe... This is all theory and my time theory may not exactly fit the two concepts that are mentioned by my time theory, thus requiring this adjustment of them, not the other way around, that I change my description of my time theory!!! This is merely a notice...
Note: First written to Facebook, 9 March at 05:43 (CET?)
Note: First written to Facebook, 9 March at 05:43 (CET?)
Regarding time as moving forward, that I write under my Time of Metaphysics, I have now added "steadily moving forward within a very small fraction of change, possibly, yet to determine, each year for our Sun time, in being Earth years from this Sun time"!
Note: Written to Facebook 1. March at 00:48 (CET?).
Note: Written to Facebook 1. March at 00:48 (CET?).
Also, it is plain that the Elusive Present is not so elusive as we always "stand in it" to say it with Heraclitus... Time flows itself, but we float with it as well..
After some "thoughts" it may be that my exact launching of the Time.html of 2001 and the Time theory of metaphysics lies at 21. Jan. 2001, some eleven years ago!
Note: a notice made to Facebook 24. February at 22:08.
Note: a notice made to Facebook 24. February at 22:08.
Some more notice on 13,7 Bn years of age by Universe:
Upon writing 13,7 Bn years as the age of the Universe, I now declare my own value to be 14,5627426 Bn years instead of, let's say, 16,7 or 16,4 Bn years. The foundation for this lies in...
24 February at 21:37
the Hubble constant (H) that is H = (15 - 25) km/s per Million light years ... Not only this, but...
24 February at 21:39
...I happen to have a book on Physics, "Rom, Stoff, Tid, 3FY by Øgrim, Ormestad, Lunde and 2 others written in 1991 and published by Cappelen! This book has a (standard) Astrophysics chapter that contains the above information. Probably all other World GCSE students share this with me so I'm not anything unique, but the above number of 14,5... ! Good?
24 February at 21:43
The book itself defines the scope of valid numbers by the above constant to appx. 12 - 20 Billion years! But you can calculate the exact numbers yourself...
24 February at 21:45
I'll give you some basic formula: t (time) = d (distance) / (div. on) v (speed) = d / H d = 1 / H = so and so, put in for constant scope!
24 February at 22:00
...or your favourite estimate...!
24 February at 22:00
In this book there are also two other notes based on estimated "life" spans of the Universe: 1. Theories on stars' life and development gives a closer scope of 15 plus/minus 3 Bn years. 2. Studies of radioactive materials in meteorites gives us the same as above...
24 February at 22:03
So the scientific consensus doesn't lie at 16,7 but rather at something like 15! (Shame on you, you t*rd scientists!)
24 February at 22:04
Or I'll make it 14,7 + some as my 2nd favourite...!
24 February at 22:36 · Like
Again to Facebook as noted.
Upon writing 13,7 Bn years as the age of the Universe, I now declare my own value to be 14,5627426 Bn years instead of, let's say, 16,7 or 16,4 Bn years. The foundation for this lies in...
24 February at 21:37
the Hubble constant (H) that is H = (15 - 25) km/s per Million light years ... Not only this, but...
24 February at 21:39
...I happen to have a book on Physics, "Rom, Stoff, Tid, 3FY by Øgrim, Ormestad, Lunde and 2 others written in 1991 and published by Cappelen! This book has a (standard) Astrophysics chapter that contains the above information. Probably all other World GCSE students share this with me so I'm not anything unique, but the above number of 14,5... ! Good?
24 February at 21:43
The book itself defines the scope of valid numbers by the above constant to appx. 12 - 20 Billion years! But you can calculate the exact numbers yourself...
24 February at 21:45
I'll give you some basic formula: t (time) = d (distance) / (div. on) v (speed) = d / H d = 1 / H = so and so, put in for constant scope!
24 February at 22:00
...or your favourite estimate...!
24 February at 22:00
In this book there are also two other notes based on estimated "life" spans of the Universe: 1. Theories on stars' life and development gives a closer scope of 15 plus/minus 3 Bn years. 2. Studies of radioactive materials in meteorites gives us the same as above...
24 February at 22:03
So the scientific consensus doesn't lie at 16,7 but rather at something like 15! (Shame on you, you t*rd scientists!)
24 February at 22:04
Or I'll make it 14,7 + some as my 2nd favourite...!
24 February at 22:36 · Like
Again to Facebook as noted.
(Transferred from Whatiswritten777.)
Sunday, 30 September 2012
Ethics, Ethical Objectivity - Objection to Arguments of Companions in Guilt
To begin with, I believe in ethical, moral objectivity. I
believe there's no particular problem in proving this/make a good case for
it.
1. That the ethical system is flawless in the sense that there is no obvious allowance of moral wrongdoing in it.
2. "...ethical claims are objective if it is possible for agents who make them to do so correctly or incorrectly. Objectivity in this sense implies the possibility of moral error.(3)" That is to say that moral mistakes exist, not that moral errors are committed ethically.
3. "...ethical claims are objective if they are 'answerable to substantial [ethical] facts and properties in the world that exist independently of the contingent practice of making those claims and the relevant attitudes of those who make them' (p. 6)(1).(4)"
4. "...ethical claims are objective if reasonable agents competent with the concepts that constitute them would converge in 'favorable circumstances of rational inquiry' (p. 7)(2).(5)" That is to say, in my opinion, that there are objective moral duties in relation to the object in question.
From the book review of (1)(2)Hallvard Lillehammer's Companions in Guilt: Arguments for Ethical Objectivity written by (3)(4)(5)Terence Cuneo in the journal Mind Volume 118, Number 470, April 2009, ISSN 0026-4423.
It's also worth mentioning the book of Paul Bloomfield's Moral Reality, OUP, 2004 that the review mentions.
I see the description of an Ethical Objective system as an (mathematical) intersection of the above 4 points. The Ethical Objective system should thus satisfy the most strict and strongest requirements for such a system. It's worth noting that it should be humanly possible to fit into it with a least one member, one human being, and that it should live up to general requirements of plausibility and reasonability.
One more thing: I think it should be noted that "reasonable agents" mean people who are able to separate right from wrong and are basically in agreement with the actual system of ethics in question. If the case is otherwise, they fall into a different group and are not relevant to the system that is being discussed. This may limit the number of people who can adhere to that system quite severely, but that is the nature of the current diversity of humanity.
I've made some additions to the book review and as such the whole is more a new argument than a factual instance that I like to address.
The framework for every Ethical Objective System can be as extensive as every legal framework as I see it, without imposing particular problems.
The further work to the Ethical Objectivity is this. The obstacle one meets is concerning depth. I think the human cognition decides the depth of the ethical system's reach, absolutely and objectively, of the Ethical Objectivity discussed. If the human being can't have knowledge about a deeper fact of nature then one can't also say that the human being can commit any mistakes in that relation. It's therefore of no use to point to a phenomenon that lies outside the normal or possible human cognition because a sufficient ethically objective system isn't constructed at all to take care of those phenomena's ethical content. No matter what, the ethically objective system will therefore relate to our common life-world, the life-world that one can actually say something objective about. It's therefore the case that all hypothetical micro- and macro-phenomena are outside the domain that actually can have some influence on the human being's ethical and moral life. It's therefore not decisive to have absolute knowledge to have an efficient ethical objective system as long as one does one's duties for the best in this actual effective ethical objective system in what concerns information and possibilities. In that kind of view, one can plausibly say that doctors in ancient history may have been acting ethically objective in some cases, if not all, of course, despite a very limited knowledge about the human body. It's clear that science will form an outer frame for our life-worlds wherein this Ethical Objective System functions as in the question of preventive measures concerning Global Climate Changes and also about our limitations in size of total world population that should or can exist without collapsing into chaos and extinction of being examples of conscious beings capable of knowledge, possibly effecting one's own salvation.
Consequently, let's look at abortion again. What if two parties agree on the fact that guilt may not apply for abortion because there are factors that speak strongly for and against as well as the indeterminate status of the fetus to be removed, both on brain function and emotional function(1) when the procedure is carried out? Thus, abortion for these two parties remains a private, informed and "esoteric" decision, yet respected by either party in companionship without guilt!
Hypothetically speaking, it's plausible to say that being a human without an ethical system in the 21st century and aligning oneself with the ancient humans and humanoids like the Cro-Magnons, seems just crazy! It's laying such a waste to a whole heritage, legacy of philosophical civility! The ancient humans before civilization can be said to be driven by evolutionary, biological instincts! Nihilism, relativism or other destructive ethical approaches are historically insensitive, possibly rationally insensitive, absurd or out of touch.
As much as Paul Bloomfield makes the argument of having and maintaining good physical health, I'd like to add the following:
It should be possible to determine Integrity, Mental Health and Physical Health by keeping one's ethics. People may fool themselves, but I think that the most sensitive factor of these three, being Integrity, is very much affected by both bad attitude/mindset and bad actions, altogether being bad morals and possibly bad ethics.
Through the arsenal of diagnostics like various lie-detectors, (f)MRI-scans, interviews, somatic examinations and what have you it should be possible to make good judgment on the status of these 3 factors, Integrity, Mental Health and Physical Health. Any reasonable doubt can therefore be removed for what kind of companion one is socialising with. Any person with substantial deviation in either Integrity, Mental Health and Physical Health from the characteristics that are condoned by exactly this Ethical Objectivity can thus be excluded from the desirable group of people that comply with Ethical Objectivity. The days of the Arguments of Companions in Guilt are consequently numbered!
It should be a fundamental belief that morality/ethics is to respect rationality in others, also the potential of such in others, eg. children. This doesn't capture ecology very well, but I can think of it as intelligent/rational to allow nature and animals alike a natural life (for various reasons) incl. agricultural/aquacultural. Thus, as this is a facet of being rational as a person, every person should respect people with ecological views and the ecological view therefore becomes the only ethical view in this respect, a general starting point.
Rationality in this sense is nothing mysterious. It's just the capacity to score well/great on IQ-tests, having a fine, intelligent flow of thoughts and doing a good or great working performance, whatever this may be, being in the stream so to speak!
Although I've written about rationality above I like to write the following to make it perfectly clear. There are (at least) two kinds of Rationality that it's fair to speak of. One is the rationality according to function, being the way you apply your mind to whatever problems, practical or intellectual. The other one is rationality as in being of good mental health, being well-developed. It should be clear that rationality is the top premise of this Ethically Objective system that I ascribe and develop from a Neo-Kantian position.
This is a writing for removing any religious notion to the word Rationality and thus the system of Rationality may seem reasonable to everyone. I'm in doubt whether I. Kant has meant any religiousness at all with his "kingdom of ideas". People have interpreted it this way, but I can't see that there's a single factual instance of this in his text. Quite the opposite, I think he thinks that the common person is able to make clever thoughts, to take part in the "kingdom of ideas". I find this a much more charitable reading of him and it makes him look better too!
Repugnance and appeal to emotions/feelings/aestheticism are not any good way to get there even though I support every argument that makes a good foundation for Ethical Objectivity.
It should be noted that people of good moral attitude and behaviour seem better able to create and maintain, by keeping the duties, social relationships both in symmetric and asymmetric terms.
I'm with Dr. Sam Harris when he argue by objectivity of flourishing and happiness, potentially by and in everyone, on TED Talks that some/all moral questions or some/all outside spectrums of some/all moral spectrums can be answered by science. Now, I don't know if this is consensus within a group of scientists and philosophers alike and if this is documented by scientific articles. He does mention psychology and neuro-science as two (obvious) angles to answer this scientifically. It must be admitted by myself, whether or not Dr. Sam Harris agrees, however, that flourishing and happiness are still normative, unscientific, ethical objectives. One can indeed be relatively poor and still be generally happy and one can work too much and thus flourish beyond one's happiness. It's also a question to what ends we are supposed to be flourishing and happy. Where does this flourishing and happiness lead to if there's no destination in sight? Isn't then life only a matter of taste and artistry in life? What about doing extreme sports and other activities where one does risk one's own life? The question is not so much a matter of this risk-taking person's life, but this person's social connections, possibly causing grief in these people by the risk-taking. Thus, it's yet to see to what extent one can fully argue that the objectives of flourishing and happiness can be scientific. Indeed, this scientific notion has implicitly some kind of normative destiny to it that Dr. Sam Harris is in debt to answer.
It's admirable of Dr. Sam Harris of denoting this "scientific", given the normative objectives, and at the same time quenching the lunatics who promote death and destruction. It's certainly worth a thorough scientific study of what underlying causes there are for people's misfortunes when it's so commonly known that most or all people like to be happy, flourishing or both.
(1)Remark concerning abortion by The Royal College of Obstetricians and Gynaecologists (RCOG):
By The Royal College of Obstetricians and Gynaecologists (RCOG),
"Fetal Awareness - Review of Research and Recommendations for Practice".
From this link:
http://www.rcog.org.uk/fetal-awareness-review-research-and-recommendations-practice
Fetal Awareness
* The fetus cannot feel pain before 24 weeks because the connections in the fetal brain are not fully formed
* Evidence examined by the Working Party showed that the fetus, while in the chemical environment of the womb, is in a state of induced sleep and is unconscious
* The Working Party concluded that because the 24 week-old fetus has no awareness nor can it feel pain, the use of analgesia is of no benefit
* More research is needed into the short and long-term effects of the use of fetal analgesia post-24 weeks.
The full report: http://www.rcog.org.uk/files/rcog-corp/RCOGFetalAwarenessWPR0610.pdf
Article, this particular webpage, is published: 25/06/2010 (summary and more).
Game over! You lose, relativists and subjectivists! I'd say there is no objection by the subjectivists and relativists that can overcome Ethical Objectivity (now)! I've been meditating this for quite a while and I'm now at peace by the preceding sentences. There is simply no chance to refute Ethical Objectivity anymore.
The argument is not finished by these words and remains to be made a paper of academic quality, if not a book.
By Terje Lea / Leonardo F. Olsnes-Lea, 2009 - 2010, 2012 - and still ongoing.
By Terje Lea, 11th November, 2009, 9th December, 2009, 11th December, 2009, 6th March, 2010, 24th March, 2010, 26th March, 2010, 12th April, 2010, 22nd April, 2010, 25th April, 2010, 26th April, 2010, 4th May, 2010, 10th May, 2010, 9th June, 2010, 28th June, 2010 and 24th October, 2010. Minor change of title, 18.11.2010. Now controlled under my new name, Leonardo F. Olsnes-Lea.
1. That the ethical system is flawless in the sense that there is no obvious allowance of moral wrongdoing in it.
2. "...ethical claims are objective if it is possible for agents who make them to do so correctly or incorrectly. Objectivity in this sense implies the possibility of moral error.(3)" That is to say that moral mistakes exist, not that moral errors are committed ethically.
3. "...ethical claims are objective if they are 'answerable to substantial [ethical] facts and properties in the world that exist independently of the contingent practice of making those claims and the relevant attitudes of those who make them' (p. 6)(1).(4)"
4. "...ethical claims are objective if reasonable agents competent with the concepts that constitute them would converge in 'favorable circumstances of rational inquiry' (p. 7)(2).(5)" That is to say, in my opinion, that there are objective moral duties in relation to the object in question.
From the book review of (1)(2)Hallvard Lillehammer's Companions in Guilt: Arguments for Ethical Objectivity written by (3)(4)(5)Terence Cuneo in the journal Mind Volume 118, Number 470, April 2009, ISSN 0026-4423.
It's also worth mentioning the book of Paul Bloomfield's Moral Reality, OUP, 2004 that the review mentions.
I see the description of an Ethical Objective system as an (mathematical) intersection of the above 4 points. The Ethical Objective system should thus satisfy the most strict and strongest requirements for such a system. It's worth noting that it should be humanly possible to fit into it with a least one member, one human being, and that it should live up to general requirements of plausibility and reasonability.
One more thing: I think it should be noted that "reasonable agents" mean people who are able to separate right from wrong and are basically in agreement with the actual system of ethics in question. If the case is otherwise, they fall into a different group and are not relevant to the system that is being discussed. This may limit the number of people who can adhere to that system quite severely, but that is the nature of the current diversity of humanity.
I've made some additions to the book review and as such the whole is more a new argument than a factual instance that I like to address.
The framework for every Ethical Objective System can be as extensive as every legal framework as I see it, without imposing particular problems.
The further work to the Ethical Objectivity is this. The obstacle one meets is concerning depth. I think the human cognition decides the depth of the ethical system's reach, absolutely and objectively, of the Ethical Objectivity discussed. If the human being can't have knowledge about a deeper fact of nature then one can't also say that the human being can commit any mistakes in that relation. It's therefore of no use to point to a phenomenon that lies outside the normal or possible human cognition because a sufficient ethically objective system isn't constructed at all to take care of those phenomena's ethical content. No matter what, the ethically objective system will therefore relate to our common life-world, the life-world that one can actually say something objective about. It's therefore the case that all hypothetical micro- and macro-phenomena are outside the domain that actually can have some influence on the human being's ethical and moral life. It's therefore not decisive to have absolute knowledge to have an efficient ethical objective system as long as one does one's duties for the best in this actual effective ethical objective system in what concerns information and possibilities. In that kind of view, one can plausibly say that doctors in ancient history may have been acting ethically objective in some cases, if not all, of course, despite a very limited knowledge about the human body. It's clear that science will form an outer frame for our life-worlds wherein this Ethical Objective System functions as in the question of preventive measures concerning Global Climate Changes and also about our limitations in size of total world population that should or can exist without collapsing into chaos and extinction of being examples of conscious beings capable of knowledge, possibly effecting one's own salvation.
Consequently, let's look at abortion again. What if two parties agree on the fact that guilt may not apply for abortion because there are factors that speak strongly for and against as well as the indeterminate status of the fetus to be removed, both on brain function and emotional function(1) when the procedure is carried out? Thus, abortion for these two parties remains a private, informed and "esoteric" decision, yet respected by either party in companionship without guilt!
Hypothetically speaking, it's plausible to say that being a human without an ethical system in the 21st century and aligning oneself with the ancient humans and humanoids like the Cro-Magnons, seems just crazy! It's laying such a waste to a whole heritage, legacy of philosophical civility! The ancient humans before civilization can be said to be driven by evolutionary, biological instincts! Nihilism, relativism or other destructive ethical approaches are historically insensitive, possibly rationally insensitive, absurd or out of touch.
As much as Paul Bloomfield makes the argument of having and maintaining good physical health, I'd like to add the following:
It should be possible to determine Integrity, Mental Health and Physical Health by keeping one's ethics. People may fool themselves, but I think that the most sensitive factor of these three, being Integrity, is very much affected by both bad attitude/mindset and bad actions, altogether being bad morals and possibly bad ethics.
Through the arsenal of diagnostics like various lie-detectors, (f)MRI-scans, interviews, somatic examinations and what have you it should be possible to make good judgment on the status of these 3 factors, Integrity, Mental Health and Physical Health. Any reasonable doubt can therefore be removed for what kind of companion one is socialising with. Any person with substantial deviation in either Integrity, Mental Health and Physical Health from the characteristics that are condoned by exactly this Ethical Objectivity can thus be excluded from the desirable group of people that comply with Ethical Objectivity. The days of the Arguments of Companions in Guilt are consequently numbered!
It should be a fundamental belief that morality/ethics is to respect rationality in others, also the potential of such in others, eg. children. This doesn't capture ecology very well, but I can think of it as intelligent/rational to allow nature and animals alike a natural life (for various reasons) incl. agricultural/aquacultural. Thus, as this is a facet of being rational as a person, every person should respect people with ecological views and the ecological view therefore becomes the only ethical view in this respect, a general starting point.
Rationality in this sense is nothing mysterious. It's just the capacity to score well/great on IQ-tests, having a fine, intelligent flow of thoughts and doing a good or great working performance, whatever this may be, being in the stream so to speak!
Although I've written about rationality above I like to write the following to make it perfectly clear. There are (at least) two kinds of Rationality that it's fair to speak of. One is the rationality according to function, being the way you apply your mind to whatever problems, practical or intellectual. The other one is rationality as in being of good mental health, being well-developed. It should be clear that rationality is the top premise of this Ethically Objective system that I ascribe and develop from a Neo-Kantian position.
This is a writing for removing any religious notion to the word Rationality and thus the system of Rationality may seem reasonable to everyone. I'm in doubt whether I. Kant has meant any religiousness at all with his "kingdom of ideas". People have interpreted it this way, but I can't see that there's a single factual instance of this in his text. Quite the opposite, I think he thinks that the common person is able to make clever thoughts, to take part in the "kingdom of ideas". I find this a much more charitable reading of him and it makes him look better too!
Repugnance and appeal to emotions/feelings/aestheticism are not any good way to get there even though I support every argument that makes a good foundation for Ethical Objectivity.
It should be noted that people of good moral attitude and behaviour seem better able to create and maintain, by keeping the duties, social relationships both in symmetric and asymmetric terms.
I'm with Dr. Sam Harris when he argue by objectivity of flourishing and happiness, potentially by and in everyone, on TED Talks that some/all moral questions or some/all outside spectrums of some/all moral spectrums can be answered by science. Now, I don't know if this is consensus within a group of scientists and philosophers alike and if this is documented by scientific articles. He does mention psychology and neuro-science as two (obvious) angles to answer this scientifically. It must be admitted by myself, whether or not Dr. Sam Harris agrees, however, that flourishing and happiness are still normative, unscientific, ethical objectives. One can indeed be relatively poor and still be generally happy and one can work too much and thus flourish beyond one's happiness. It's also a question to what ends we are supposed to be flourishing and happy. Where does this flourishing and happiness lead to if there's no destination in sight? Isn't then life only a matter of taste and artistry in life? What about doing extreme sports and other activities where one does risk one's own life? The question is not so much a matter of this risk-taking person's life, but this person's social connections, possibly causing grief in these people by the risk-taking. Thus, it's yet to see to what extent one can fully argue that the objectives of flourishing and happiness can be scientific. Indeed, this scientific notion has implicitly some kind of normative destiny to it that Dr. Sam Harris is in debt to answer.
It's admirable of Dr. Sam Harris of denoting this "scientific", given the normative objectives, and at the same time quenching the lunatics who promote death and destruction. It's certainly worth a thorough scientific study of what underlying causes there are for people's misfortunes when it's so commonly known that most or all people like to be happy, flourishing or both.
(1)Remark concerning abortion by The Royal College of Obstetricians and Gynaecologists (RCOG):
By The Royal College of Obstetricians and Gynaecologists (RCOG),
"Fetal Awareness - Review of Research and Recommendations for Practice".
From this link:
http://www.rcog.org.uk/fetal-awareness-review-research-and-recommendations-practice
Fetal Awareness
* The fetus cannot feel pain before 24 weeks because the connections in the fetal brain are not fully formed
* Evidence examined by the Working Party showed that the fetus, while in the chemical environment of the womb, is in a state of induced sleep and is unconscious
* The Working Party concluded that because the 24 week-old fetus has no awareness nor can it feel pain, the use of analgesia is of no benefit
* More research is needed into the short and long-term effects of the use of fetal analgesia post-24 weeks.
The full report: http://www.rcog.org.uk/files/rcog-corp/RCOGFetalAwarenessWPR0610.pdf
Article, this particular webpage, is published: 25/06/2010 (summary and more).
Game over! You lose, relativists and subjectivists! I'd say there is no objection by the subjectivists and relativists that can overcome Ethical Objectivity (now)! I've been meditating this for quite a while and I'm now at peace by the preceding sentences. There is simply no chance to refute Ethical Objectivity anymore.
The argument is not finished by these words and remains to be made a paper of academic quality, if not a book.
By Terje Lea / Leonardo F. Olsnes-Lea, 2009 - 2010, 2012 - and still ongoing.
By Terje Lea, 11th November, 2009, 9th December, 2009, 11th December, 2009, 6th March, 2010, 24th March, 2010, 26th March, 2010, 12th April, 2010, 22nd April, 2010, 25th April, 2010, 26th April, 2010, 4th May, 2010, 10th May, 2010, 9th June, 2010, 28th June, 2010 and 24th October, 2010. Minor change of title, 18.11.2010. Now controlled under my new name, Leonardo F. Olsnes-Lea.
Friday, 21 September 2012
Over Animal Ethics and to PETA Too - This time it is the pigs...
Over PETA again and domestic animals, being a part of the animal ethics and applied ethics
This time it is over the pigs. The suggestion is one of multi-modal-approach, that the covers/shelters to wind and rain out on the grass fields must be in place, or at least is in place normatively as by recommendation and that one arranges for the animals to have special birth-bins with half-concrete (but enough still) and half-grass mat as with the cows and oxes formerly explained. Ordinary bins as with the cows and oxes (although they are called "stalls") should also be arranged for, but pigs are less complicated because they are not milked! Then the rest is up to you. Some even play music for the animals. This also concerns food and so on. Cleanliness level should be as high as vet standards demand and general animal standards outside this is also (largely/sufficiently) described by vet standards! Good luck to you, the farmers, the agronomists!
Note: For whatever the shelters, the bins, the stalls, animals do not walk about sharp edges very well and get easily cut up! This is also a notice, but probably already well into the vet's recommendations!
Note2: Just published to Facebook as message under profile and note also. Today, 2012-09-21 CEST.
This time it is over the pigs. The suggestion is one of multi-modal-approach, that the covers/shelters to wind and rain out on the grass fields must be in place, or at least is in place normatively as by recommendation and that one arranges for the animals to have special birth-bins with half-concrete (but enough still) and half-grass mat as with the cows and oxes formerly explained. Ordinary bins as with the cows and oxes (although they are called "stalls") should also be arranged for, but pigs are less complicated because they are not milked! Then the rest is up to you. Some even play music for the animals. This also concerns food and so on. Cleanliness level should be as high as vet standards demand and general animal standards outside this is also (largely/sufficiently) described by vet standards! Good luck to you, the farmers, the agronomists!
Note: For whatever the shelters, the bins, the stalls, animals do not walk about sharp edges very well and get easily cut up! This is also a notice, but probably already well into the vet's recommendations!
Note2: Just published to Facebook as message under profile and note also. Today, 2012-09-21 CEST.
Tuesday, 11 September 2012
A Part of Gödel's Paper on the Two Incompleteness Theorems
First, here you have some in German, as I aim for Section 3 and 4 to complement
the work by M. Hirzel given freely elsewhere on the Internet. So German now and
English later:
[Section] 3.
Wir ziehen nun aus Satz VI weitere Folgerungen und geben zu diesem Zweck folgende Definition:
Eine Relation (Klasse) heißt arithmetisch, wenn sie sich allein mittels der Begriffe +, . [Addition und Multiplikation, bezogen auf natürliche Zahlen, (x), = definieren l Zahlen beziehen dürfen Entsprechend wird der Begriff "arithmetischer Satz" definiert. Insbesondere sind z.B. Die Relationen "größer" und "kongruent nach einem Modul" arithmetisch, denn as gilt: x > y ~(Ez) [y = x + z]
Wir beweisen den Satz in der Gestalt: Jede Relation der Form x0 = j (x1 ... xn) wo j rekursiv ist, ist arithmetisch, und wenden vollständige Induktion nach der Stufe von j an. j habe die s-te Stufe (s > 1). Dann gilt entweder:
was möglich ist, da je zwei der Zahlen 1 + (i + 1) l! (i = 0, 1, ... k – 1) relativ prim sind. Denn eine in zwei von diesen Zahlen enthaltene Primzahl müßte auch in der Differenz (i1 – i2) l! und daher wegen |i1 - i2| < l in l! enthalten sein, was unmöglich ist. Das Zahlenpaar n, l! leistet dann das Verlangte.
Wir leiten schließlich noch folgendes Resultat hier:
Satz IX: In allen in Satz VI genannten formalen Systemen (53) gibt es unentscheidbare Probleme des engeren Funktionenkalküls54 (d. h. Formeln des engeren Funktionenkalküls, für die weder Allgemeingültigkeit noch Existenz eines Gegenbeispiels beweisbar ist)55.
Ferner bilden wir die Sätze:
die Voraussetzung der v-Widerspruchsfreiheit ersetzen durch die folgende: Die Aussage "x ist widerspruchsvoll" ist nicht x-beweisbar.
Notes:49 Die Null wird hier und im folgenden immer mit zu den natarlichen
On formally undecidable propositions of Principia Mathematica and related systems I.
(German: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I.)
Kurt Gödel, Wien
[Section] 3.
Wir ziehen nun aus Satz VI weitere Folgerungen und geben zu diesem Zweck folgende Definition:
Eine Relation (Klasse) heißt arithmetisch, wenn sie sich allein mittels der Begriffe +, . [Addition und Multiplikation, bezogen auf natürliche Zahlen, (x), = definieren l Zahlen beziehen dürfen Entsprechend wird der Begriff "arithmetischer Satz" definiert. Insbesondere sind z.B. Die Relationen "größer" und "kongruent nach einem Modul" arithmetisch, denn as gilt: x > y ~(Ez) [y = x + z]
x º y (mod n) ~(Ez) [(x
= y + z & n) Ú (y = x + z & n)] Es gilt der
Satz VII: Jede
rekursive Relation ist arithmetisch.
Wir beweisen den Satz in der Gestalt: Jede Relation der Form x0 = j (x1 ... xn) wo j rekursiv ist, ist arithmetisch, und wenden vollständige Induktion nach der Stufe von j an. j habe die s-te Stufe (s > 1). Dann gilt entweder:
1. j (x1 ...
xn) = r [c1 (x1 … xn), c2 (x1 … xn),
… cm (x1 … xn)]5 (wo r und sämtliche ci kleinere Stufe haben als s) oder:
2. j (0, x2
... xn) = y (x2 … xn)
j (k + 1, x2 ... xn) = m [k, j (k, x2 … xn),
x2 … xn]
(wo y, m niedrigere Stufe
als s haben).
Im ersten Falle
gilt:
x0 =
j (x1 … xn) ~(E y1 … ym) [R (x0,
x1 … xn) & S1(y1, x1
… xn) & ... & Sm(ym x1 … xn)]
wo R bzw. Si die
nach induktiver Annahme existierenden mit x0 = r (y1 … ym) bzw. y = ci(x1 ... xn)
äquivalenten arithmetischen Relationen sind. Daher ist x0 = j (x1 … xn) in diesem Fall arithmetisch.
Im zweiten Fall
wenden wir folgendes Verfahren an: Man kann die Relation x0 = (x1 …
xn) mit Hilfe des
Begriffes „Folge von Zahlen“ (f)52
folgendermaßen ausdrücken:
x0 = j (x1 … xn)
~(E f) {f0 = y (x2 … xn) & (k) [k <
x1 Þ fk+1 = (k, fk,
x2 … xn)] & x0 = fx1}
Wenn S (y, x2 … xn) bzw. T (z, x1
… xn + 1) die nach
induktiver Annahme existierenden mit y = (x2 … xn)
bzw. z = (x1 … xn + 1)
äquivalenten arithmetische Relationen sind, gilt daher:
x0 = j (x1 … xn)
~(E f) {S (f0 = (x2
… xn) & (k) [k < x1 Þ T (fk+1, k, fk, x2
… xn)] & x0 = fx1}
Nun ersetzen wir den Begriff “Folge von Zahlen” durch
“Paar von Zahlen”, indem wir dem
Zahlenpaar n, d die Zahlenfolge f(n, d) (fk(n,
d) = [n]1 + (k + 1) d) zuordnen, wobei [n]p den
kleinsten nicht negativen Rest von n
modulo p bedeutet.
Es gilt
dann der
Hilfssatz
1: Ist f eine beliebige Folge natürlicher Zahlen und k eine
beliebige natiirliche Zahl, so gibt es
ein Paar von natürlichen Zahlen n, d, so daß f(n, d) und f in
den ersten k Gliedern
übereinstimmen.
Beweis:
Sei l die größte der Zahlen k, f0, f1, … fk
- 1. Man bestimme n so, daß:
n º fi [mod (1 + (i + 1) l!)] für i = 0, 1, ... k - 1
was möglich ist, da je zwei der Zahlen 1 + (i + 1) l! (i = 0, 1, ... k – 1) relativ prim sind. Denn eine in zwei von diesen Zahlen enthaltene Primzahl müßte auch in der Differenz (i1 – i2) l! und daher wegen |i1 - i2| < l in l! enthalten sein, was unmöglich ist. Das Zahlenpaar n, l! leistet dann das Verlangte.
Da die
Relation x = [n]p durch:
x º n (mod p) & x < p
definiert
und daher arithmetisch ist, so ist auch die folgendermaßen definierte Relation
P (x0, xl … xn):
P (x0
... xn) º
(E n,
d) {S[([n]d + 1, x2 ... xn)
& (k) [k < x1 Þ T ([n]1 + d (k + 2),
k, [n]1 + d (k + 1), (x2 … xn)] & x0 = [n]1
+ d (x1 + 1)}
arithmetisch,
welche nach (17) und Hilfssatz 1 mit: x0 = j (x1 … xn) äquivalent ist (es kommt bei der Folge f in (17) nur auf ihren
Verlauf bis zum x1 + 1-ten Glied an). Damit ist Satz VII bewiesen.
Gemäß
Satz VII gibt es zu jedem Problem der Form (x)F(x) (F rekursiv) ein
äquivalentes arithmetisches Problem und
da der ganze Beweis von Satz VII sich (für jedes spezielle F) innerhalb
des
Systems P formalisieren läßt, ist diese Äquivalenz in P beweisbar. Daher gilt:
Satz
VIII: In jedem der in Satz VI genannten formalen Systeme53
gibt es unentscheidbare arithmetische Sätze.
Dasselbe
gilt (nach der Bemerkung auf Seite 190) für das Axiomensystem der Mengenlehre
und dessen Erweiterungen durch v-widerspruchsfreie rekursive
Klassen von Axiomen.
Wir leiten schließlich noch folgendes Resultat hier:
Satz IX: In allen in Satz VI genannten formalen Systemen (53) gibt es unentscheidbare Probleme des engeren Funktionenkalküls54 (d. h. Formeln des engeren Funktionenkalküls, für die weder Allgemeingültigkeit noch Existenz eines Gegenbeispiels beweisbar ist)55.
Dies
beruht auf:
Satz X:
Jedes Problem der Form (x)F(x) (F rekursiv) läßt sich zurückführen auf die
Frage nach der Erfüllbarkeit einer
Formel des engeren Funktionenkalküls (d.h. zu jedem rekursiven F kann man eine Formel des engeren Funktionenkalküls
angeben deren Erfüllbarkeit mit der Richtigkeit von (x)F(x) äquivalent ist).
Zum
engeren Funktionenkalkül (e. F.) rechnen wir diejenigen Formeln, welche sich
aus den Grundzeichen: ~, Ú, (x), =; x, y ... (Individuenvariable)
F (x), G (x, y), H (x, y, z)... (Eigenschafts-
und Relationsvariable) aufbauen56,
wobei (x) und = sich nur auf Individuen beziehen dürfen. Wir fügen zu diesen Zeichen noch eine dritte Art
von Variablen j (x), w (x, y), c (x, y, z) etc.
hinzu, die Gegenstandsfunktionen
vertreten (d. h. j (x), w (x, y) etc.) bezeichnen eindeutige Funktionen, deren Argumente und Werte Individuen sind57. Eine Formel, die außer den zuerst
angeführten Zeichen des e. F. noch Variable dritter Art j ( (x), w (x, y) ... etc.)
enthält, soll eine Formel im weiteren Sinne (i. w. S.) heißen58. Die Begriffe "erfüllbar",
"allgemeingültig" übertragen sich ohneweiters auf Formeln i. w. S.
und es gilt der Satz, daß man zu jeder Formel i. w. S. A eine gewöhnliche
Formel des e. F. B angeben kann, so daß
die Erfüllbarkeit von A mit der von B äquivalent ist. B erhält man aus A, indem man die in A vorkommenden Variablen
dritter Art j (x), w (x, y) ... durch Ausdrücke der
Form: (i, z) F (z, x), (i, z) G (z, x, y) ... ersetzt, die "beschreibenden" Funktionen im
Sinne der PM. I * 14 auflöst und die so
erhaltene Formel mit einem Ausdruck logisch multipliziert59,
der besagt, daß sämtliche an Stelle der j, w .. gesetzte F, G .. hinsichtlich der ersten Leerstelle genau eindeutig
sind.
Wir
zeigen nun, daß es zu jedem Problem der Form (x)F(x) (F rekursiv) ein
äquivalentes betreffend die
Erfüllbarkeit einer Formel i.w.S. Gibt, woraus nach der eben gemachten
Bemerkung Satz X folgt.
Da F
rekursiv ist, gibt es eine rekursive Funktion F (x), so daß F(x) ~[F (x) = 0], und für F gibt es eine Reihe von Funktionen F1, F2 ... Fn, so daß: Fn = F, F1 (x) = x + 1 und für jedes Fk (1 < k ≦ n)
entweder:
1. (x2,
... xm) [Fk (0, x2 ... xm) = Fp (x2 ... xm)]
(18)
(x, x2
... xm) {Fk [F1 (x), x2
... xm] = Fq [x, Fk (x, x2 ... xm), x2
... xm]}
p, q < k
oder:
r < k, iʋ < k (für ʋ = l, 2 ... s)
oder:
3. (x1 ... xm)
[Fk (x1 ... xm)] = F1 (F1 ... F1 (0))] (20)
Ferner bilden wir die Sätze:
(x) F1 (x) = 0 & (x, y)
[F1 (x) = F1 (y) Þ x = y] (21)
(x)
[Fn (x) = 0] (22)
Wir
ersetzen nun in allen Formeln (18), (19), (20) (für k = 2, 3 . . . n) und in
(21) (22) die Funktionen i durch
Funktionsvariable i, die Zahl 0 durch eine sonst nicht vorkommende
Individuenvariable 0 und bilden die Konjunktion C sämtlicher so erhaltener
Formeln.
Die
Formel (E x0) C hat dann die verlangte Eigenschaft, d. b.
1. Wenn (x) [ (x) = 0] gilt, ist (E x0) C erfüllbar, denn die Funktionen F1, F2 ... Fn ergeben dann offenbar in (E x0) C für 1,
2 ... n eingesetzt einen richtigen Satz.
2. Wenn (E x0) C erfüllbar ist, gilt (x) [F (x) = 0].
Beweis: Seien Ψ1,
Ψ2 ... Ψn die
nach Voraussetzung existierenden Funktionen, welche in (E x0) C für φ1, φ2 ... φn eingesetzt einen richtigen Satz liefern. Ihr
Individuenbereich sei Á. Wegen der Richtigkeit von (E x0)
C für die Funktionen Ψi
gibt es ein Individuum a (aus Á), so daß sämtliche Formeln (18) bis
(22) bei Ersetzung der Fi durch Ψi und von 0 durch a in richtige Sätze (18') bis (22') übergehen. Wir bilden nun die kleinste
Teilklasse von Á, welche a enthält und gegen die Operation Ψ1
(x) abgeschlossen ist. Diese Teilklasse
(Á) hat die Eigenschaft, daß jede der Funktionen Ψi, auf Elemente
aus Á angewendet wieder Elemente aus Á ergibt. Denn für Ψ1 gilt dies
nach Definition von Á und wegen (18'), (19'), (20') überträgt sich diese Eigenschaft von Ψi mit niedrigerem Index auf solche mit höherem. Die Funktionen, welche
aus Ψi durch Beschränkung
auf den Individuenbereich Á entstehen, nennen wir Ψi'. Auch für diese Funktion
gelten sämtliche Formeln (18) bis (22)
(bei der Ersetzung von 0 durch a und Fi durch Ψi').
Wegen der Richtigkeit
von (21) für Ψ1' und a
kann man die Individuen aus Á eineindeutig auf die natürlichen Zahlen
abbilden u. zw. so, daß a in 0 und
die Funktion Ψ1' in die Nachfolgerfunktion F1 übergeht.
Durch diese Abbildung gehen aber sämtliche Funktionen Ψi' in die Funktionen Fi über und wegen der Richtigkeit von (22)
für Ψnʹ und a gilt (x) [Fn (x) = 0], oder (x) [F (x) = 0], was
zu beweisen war61.
Da man die Überlegungen, welche zu Satz X führen, (für jedes spezielle F)
auch innerhalb des Systems P durchführen kann, so ist die Äquivalenz zwischen
einem Satz der Form (x) F (x) (F rekursiv) und der Erfüllbarkeit der entsprechenden
Formel des e. F. in P beweisbar und daher folgt aus der Unentscheidbarkeit des
einen die des anderen, womit Satz IX bewiesen ist.[61]
[Section] 4.
Aus den Ergebnissen von Abschnitt 2 folgt Bin merkwürdiges Resultat, bezüglich
eines Widerspruchslosigkeitsbeweises des Systems P (und seiner Erweiterungen),
das durch folgenden Satz ausgesprochen wird:
Satz XI: Sei x eine beliebige
rekursive widerspruchsfreie[62] Klasse von
Formeln, dann gilt: Die Satzformel,
welche besagt, daß x widerspruchsfrei
ist, ist nicht x-beweisbar;
insbesondere ist die Widerspruchsfreiheit von P in P unbeweisbar[63],
vorausgesetzt, daß P widerspruchsfrei ist (im entgegengesetzten Fall ist natürlich
jede Aussage beweisbar).
Der Beweis ist
(in Umrissen skizziert) der folgende: Sei x
eine beliebige für die folgenden Betrachtungen ein für allemal gewählte
rekursive Klasse von Formeln (im
einfachsten Falle die leere Klasse). Zum
Beweise der Tatsache, daß 17 Gen r nicht
x-beweisbar ist[64], wurde,
wie aus 1. Seite 189 hervorgeht, nur die
Widerspruchsfreiheit von x benutzt,
d, h. es gilt:
Wid (x) Þ Bewx (17 Gen r) (23)
d. h. nach (6·1):
Wid (x) Þ (x) x
Bx (17 Gen r)
Nach (13) ist
17 Gen r = S b (p (19 / Z(p))) und daher:
Wid (x) Þ (x) x Bx S b (p
(19 / p Z(p)))
d. h. nach (8·1):
Wid (x) Þ (x) Q (x, p) (24)
Wir stellen nun folgendes fest: Sämtliche
in Abschnitt 266 und Abschnitt 4 bisher
definierte Begriffe (bzw. bewiesene Behauptungen) sind auch in P ausdrückbar
(bzw. beweisbar). Denn es wurden überall nur die gewöhnlichen Definitions- und
Beweismethoden der klassischen Mathematik verwendet, wie sie im System P
formalisiert sind. Insbesondere ist z (wie jede rekursive Klasse) in P
definierbar. Seit w die Satzformel, durch welche in P Wid (x)
ausgedrückt wird. Die Relation Q (x, y) wird gemäß (8·1), (9), (10) durch das Relationszeichen
q ausgedrückt, folglich Q (x,
p) durch r [ da nach (12) r = S b (q (19 / Z(p))] und der
Satz (x) Q (x, p) durch 17 Gen r.
Wegen (24) ist
also w Imp (17 Gen r) in P beweisbar67 (um so mehr x-beweisbar). Wäre
nun v x-beweisbar, so wäre auch 17 Gen r x-beweisbar
und daraus würde nach (23) folgen, daß x nicht widerspruchsfrei ist.
Es sei bemerkt,
daß auch dieser Beweis konstruktiv ist, d. h. er gestattet, falls ein Beweis aus x für w vorgelegt ist, einen Widerspruch aus x effektiv herzuleiten. Der ganze Beweis
für Satz XI läßt sich wörtlieh auch auf
das Axiomensystem der Mengenlehre M und der klassischen Mathematik68 A übertragen und liefert auch hier das
Resultat: Es gibt keinen Widerspruchslosigkeitsbeweis für M bzw. A, der
innerhalb von M bzw. A formalisiert werden könnte, vorausgesetzt daß M bzw. A
widerspruchsfrei ist. Es sei ausdrücklich bemerkt, daß Satz XI (und die entsprechenden
Resultate über M, A) in keinem Widerspruch
zum Hilbertschen formalistischen Standpunkt stehen. Denn dieser setzt nur die
Existenz eines mit finiten Mitteln geführten Widerspruchsfreiheitsbeweises
voraus und es wäre denkbar, daß es finite Beweise gibt, die sich in P (bzw. M,
A) nicht darstellen lassen.
Da für jede
widerspruchsfreie Klasse x, v nicht x-beweisbar ist, so gibt es
schon immer dann (aus x) unentscheidbare Sätze (nämlich w), wenn Neg (w) nicht x-beweisbar ist; m. a. W. man kann in Satz VI
die Voraussetzung der v-Widerspruchsfreiheit ersetzen durch die folgende: Die Aussage "x ist widerspruchsvoll" ist nicht x-beweisbar.
(Man beachte, daß
es widerspruchsfreie x gibt, für die diese Aussage x-beweisbar ist.)
Wir haben uns in
dieser Arbeit im wesentlichen auf das System P beschränkt und die
Anwendungen auf andere Systeme nur
angedeutet. In voller Allgemeinheit werden die Resultate in einer demnächst erscheinenden Fortsetzung
ausgesprochen und bewiesen werden. In dieser Arbeit wird auch der nur skizzenhaft geführte Beweis von
Satz XI ausführlich dargestellt werden.
(Eingelangt: 17. XI.
1930.)
___________
Temporary
note: The szmbol, Á, has been used incorrectly in the above text
and I am to replace it with something like ʒ´, Ҙ´, or
Ӡ´, whereof the last is probably the best. - Olsnes-Lea, the provider for this!
Notes:49 Die Null wird hier und im folgenden immer mit zu den natarlichen
Zahlen gerechnet.
50 Das Definiens eines solchen Begriffes muß sich
also allein mittels der
angeführten Zeichen, Variablen für
natürliche Zahlen x, y, . . . und den Zeiehen
0, 1 aufbauen (Funktions- und
Mengenvariable dürfen nicht vorkommen). (In den
Präfixen darf statt x natürlich auch jede
andere Zahlvariable stehen.)
51 Es
brauchen natürlich nicht alle x1 . . . xn in den ci tatsächlich vorzukommen
[vgl. das Beispiel in Fußnote 27].
52 f
bedeutet hier eine Variable, deren Wertbereich die Folgen natürl. Zahlen sind.
Mit fk wird das k + 1-te Glied einer Folge f bezeichnet (mit f0 das erste).
53 Das sind diejenigen v-widerspruchsfreien
Systeme, welche aus P durch Hinzufügung einer rekursiv definierbaren Klasse von
Axiomen entstehen.
54 Vgl. Hilbert-Ackermann, Grundzüge der
theoretischen Logik.
Im System P sind unter Formeln des engeren
Funktionenkalküls diejenigen zu verstehen, welche aus den Formeln des engeren
Funktionenkalküls der PM durch die auf S.176 angedeutete Ersetzung der
Relationen durch Klassen höheren Typs entstehen.
55 In meiner Arbeit: Die Vollständigkeit der
Axiome des logischen Funktionenkalküls, Monatsh. f. Math. u. Phys. XXXVII, 2, habe ich gezeigt, daß jede Formel
des engeren Funktionenkalküls entweder als allgemeingültig nachweisbar ist oder ein Gegenbeispiel
existiert; die Existenz dieses Gegenbeispiels ist aber nach Satz IX nicht
immer nachweisbar (in den angeführten
formalen Systemen).
56 D. Hilbert and W. Ackermann rechnen in dem eben
zitierten Buch das Zeichen = nicht zum
engeren Funktionenkalkül. Es gibt aber zu jeder Formel, in der das
Zeichen = vorkommt, eine solche ohne
dieses Zeichen, die mit der ursprünglichen gleichzeitig erfüllbar ist (vgl. die
in Fußnote 55) zitierte
Arbeit).
57 Und zwar soll der Definitionsbereich immer der
ganze Individuenbereich sein.
58 Variable dritter Art dürfen
dabei an allen Leerstellen für Individuenvariable stehen, z.B.: y = (x),
F(x, (y)), G [(x, (y)), x] : usw.
59 D.h. die Konjunktion bildet.
60 Ái (i = l .. s) vertreten irgend welche Komplexe der Variablen x1, x2 ... xm, z. B.: x1 x3 x2.
61 Aus Satz X folgt z. B., daß das Fermatsche und das Goldbachsche Problem 1ösbar wären, wenn man das Entscheidungsproblem des e. F. gelöst hätte.
62 Satz IX gilt natürlich auch für das Axiomensystem der Mengenlehre und dessen Erweiterungen durch rekursiv definierbare w-widerspruchsfreie Klassen von Axiomen, da es ja auch in diesen Systemen unentscheidbare Sätze der Form (x) F (x) (F rekursiv) gibt.
66 Von der Definition für "rekursiv" auf Seite 179 bis zum
Beweis von Satz VI inkl.60 Ái (i = l .. s) vertreten irgend welche Komplexe der Variablen x1, x2 ... xm, z. B.: x1 x3 x2.
61 Aus Satz X folgt z. B., daß das Fermatsche und das Goldbachsche Problem 1ösbar wären, wenn man das Entscheidungsproblem des e. F. gelöst hätte.
62 Satz IX gilt natürlich auch für das Axiomensystem der Mengenlehre und dessen Erweiterungen durch rekursiv definierbare w-widerspruchsfreie Klassen von Axiomen, da es ja auch in diesen Systemen unentscheidbare Sätze der Form (x) F (x) (F rekursiv) gibt.
63 x ist widerspruchsfrei
(abgekürzt als Wid (x)) wird folgendermaßen definiert: Wid (x) ≡ (E x) [Form (x) & Bewx (x)].
64 Dies folgt, wenn man
für x die leere Klasse von Formeln einsetzt.
65 r hängt natürlich (ebenso wie p) von x ab.
67 Daß aus (23) auf die Riehtigkeit von v Imp (17 Gen r)
geschlossen werden kann, beruht einfach darauf, daß der unentscheidbare Satz 17
Gen r, wie gleich zu Anfang bemerkt, seine eigene Unbeweisbarkeit
behauptet.
68 Vgl. J. v. Neumann, Zur Hilbertschen Beweistheorie, Math. Zeitschr.
26, 1927.
The rest is coming (section 3 and 4), wholly translated! Notes are now in.
Hirzel's paper: Hirzel, Martin, 2000, On formally undecidable propositions of Principia Mathematica and related systems I., successful, I think.
I am no novice and I hold credits, respects, as achievements, the Fitch
presentation of Gödel's Ontological Argument, now damn clear, and for resetting
the above mentioned paper totally new and toward completeness myself, countering
this paper and envisioning a new angle toward investigations to completeness
instead, introducing the two levels of axioms and logical results as basis for
this! Cheers!
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