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Reliability of WFM Data and Justified Inferences


 Abstract  WFMs can be observed like many other phenomena and their study is a scientific endeavor well in the scope of common and established science. We may not be able to unravel everything about the true fabric of the world. But our scientific endeavours should be aimed to finding the most empirically adequate theories. WFM footage provides sufficiently reliable data to take this phenomenon very seriously and motivate a thorough scientific study, which includes further data gathering. The presented WFM data is sufficiently reliable because (a) they are gathered without sensationalizing intent, (b) their sources are socially and technically very diverse, (c) lack of personal gain for the originator providing them, (d) they cannot easily be fabricated due to technical reasons, (e) many captures are accidental and only later pointed out, (f) they show a high variation of flight characteristics, (g) different equipment results in different video characteristics of the footage, (h) no good explanation of the data is available.


I have an extensive academic background in philosophy of science. Therefore, I start this chapter with some general remarks about what science entails that I deem crucial for the discussion of WFMs as a scientific phenomenon worth investigating.

On Truth, Proof, Falsification and Justified Beliefs

        What makes a hypothesis good or a field of study worth doing is by no means easily answered. A significant part of the most cited works in the academic branch of philosophy of science deals with these questions implicitly or explicitly. The result of my PhD thesis is that, briefly summarized, the scientist's community's body of background assumptions, including the theories they hold, and the pragmatic needs of society guide what we accept to talk about in science.

        Some different general frameworks of how to understand scientific practice evolved out of the discussions in philosophy of science. Realism is the idea that good science, in particular our best theories in physics, describes the actual reality of the world (or comes very close to that). Anti-realists are more prudent in this regard and believe that the vast history of once valid and now overthrown theories (e.g. Newtonian mechanics) teach us that even widely accepted theories could be inferior to new and crucially different approaches. Therefore, strictly speaking, we cannot consider theories as true or theoretical objects of our theories as describing reality. They are rather the best available descriptions.

        Some widely cited modern classics of the field help to further sharpen the view. Kuhn (1962) describes that scientific practice is historically and socially partitioned into paradigms. A paradigm is a group of closely related theories, methods, questions and even vocabulary that make up the more or less complete activity of a scientific field or subfield. Quantum physics, psychoanalysis or the theory of evolution are examples of paradigms. Kuhn stresses that working in accordance with a paradigm, as everyday scientist almost always do, is more like solving riddles with a well-defined repertoire of solving tools (e.g. carbon-14 dating), than any higher quest of finding truth. According to Kuhn, the majority of scientists is unable to adapt to very new, but crucially important novelties whenever they stand in conflict with important parts of the paradigm the feel obligated to. They usually ignore these novelties, but when the incommensurability of empirical findings with the standards of the paradigm gets too extreme, then a paradigm shift occurs along a long process. Kepler and Galieo's heliocentrism, Einstein's general relativity or Darwin's theory of evolution serve as examples of major paradigm shifts, which usually come with a lot of social pain for the representatives of the old paradigm.

        Anti-realistic philosophers like van Fraassen (1980) implicitly stress the classical idea that we cannot be certain that our empirical measurements really reveal everything there is to the world. Descartes (1641) speculates that a world ruled by an almighty demon, who wants to trick us, could by no good reason be ruled out. Kant (1787) describes our mind as being crucially predetermined for a specific way of perceiving the outside world. Modern computers show us vividly how humans are generally restricted to a certain level of maximum complexity for the expression of our thoughts and theories. On this background of pragmatism, van Fraassen introduced the notion of empirical adequateness to describe the criteria for good scientific theories. A theory is empirically adequate, if it explains or predicts a phenomenon, as we are able to perceive it, and it must, in addition to some other pragmatic criteria, be expressible with the humanly available cognitive resources. Note that this does not exclude the use of technically highly advanced measurement devices—if there is dark matter to detect with highly sophisticated technical detectors, then this fact does not have any implications on the question whether Descarte's demon created this phenomenon as part of the illustion. It is rather the case that we can form more or less empirically adequate theories of all of the scientifically accessible world via material causal interactions, but this does not entail whether this causal material interactions are everything there is to the world.

        Due to our cognitive limitations, a highly complex world of empirical phenomena and also the danger of overconfidences, which make us irrational and biased, Popper (1935/1959) stresses that we should not focus so much on validating theories that we deem good, but rather on them being falsifiable. He describes that political doctrines and some scientific ways to frame theories, for instance psychoanalysis, make them inherently impossible to rebut, because they do not imply predictive claims that can easily be shown to be false by empirical experiments. Popper was impressed by Einstein's presentation of general relativity that was very welcoming to skepticism unless proper experiments failed to falsify it. Popper concluded that science should be very open to even the most imaginative hypotheses, if they can be falsified by empirical experiments, and we should put a lot more effort into always discussing falsifiable theories, and conducting proper experiments aiming for falsification.

        Feyerabend (1975) criticizes scientists' common biases more radical than Kuhn does. He describes scientists, and in particular the philosophers of science, who suggest ideas to distinguish between good and bad science, as heavily overvaluing their methods and findings as necessarily best rational explanations. Feyerabend writes that new ideas are very unfairly evaluated in the light of the established theories. More specific, one cannot compare a very new and creative theory with weak empirical support with an established and competing theory on which's corroboration a myriad of scientists already worked for decades. He describes that new theories, even the ones that are now very established, such as heliocentrism, were historically defended by irrational and social strategies in their early phases (e.g. Galileo writing in Italian and not in Latin), rather than by reference to an Eureka moment connected to an experiment with undoubtedly disruptive impact.

        What can we make of these classical ideas? I suggest the following. Words like truth or proof are very inaccurate, when it comes to sciences. There are several layers of problems for the claim that a good scientific theory is true or proven:
  1. The world is something, but we can only observe what causally interacts with us. There is no way of knowing about Descarte's demon, gods or even alternate universes or the like without any material causal interaction.

  2. Even what we are able to empirically observe is, regarding a scientific investigation, restricted to what we are able to express linguistically. There might be many empirically superior theories or models that are too complex to understand for a human mind.

  3. Not even the empirically most adequate theories are automatically the most accepted ones, because psychological fallacies, dogmatism and paradigms can be in the way of an open comparison of ideas.

        A good pragmatic approach for a philosophical framework for science is Bayesianism. Bayesianism evaluates theories by assigning them degrees of justified belief between 0 and 1 using the standard calculus of probability theory. These degrees of justified belief change over the course of time due to new empirical findings and ideas. A new experiment or even some accidentally retrieved information can raise or lower a theory's degree of justified believability. The most crucial aspect of Bayesianism is that these degrees only very rarely reach the values 0 or 1, meaning that in almost every scientific context we cannot say with absolute certainty that a claim is true or wrong. The actual scientific effort is devoted to deciding whether a candidate theory is empirically more adequate than its competitors, and not whether it is true in any deep metaphysical sense. Science is a very grey area of constantly updated evaluations of ideas and the best we can do is providing best explanations without any unjustified dogmatic baggage.

        Furthermore, science as a whole is a vastly complex intellectual game without any simple rules or checking routines. Physics, archaeology, social sciences, psychology and other fields have vastly different methods and standards and usually only the very bright scientists are able to introduce something new and useful. Even worse, only the very brightest among the scientists are able to detect a colleagues revolutionary idea. The reason for this is that doing good science is really hard and demands a specific set of rare talents and creativity.

Uncontrolled Environments and Non-Repeatable Observations

        Judged by several discussions I had in academic contexts many people with the status of a professional scientist tend to dismiss phenomena like WFM, but also UFO sightings, poltergeists and the like by claiming that scientific investigations must be repeatable and happen in controlled environments. These are surely very ideal circumstances and what they have in mind here are the experiments how they are usually conducted in laboratories for physics, chemistry or biology. Particle accelerator's serve as an example for how much effort scientific groups put into creating these circumstances. However, this reason for dismissal is beside the point and here is why.

        Scientific phenomena occur in extremely different environments and the majority of scientific branches cannot control the environment of observation or repeat any of their observations. Economists (in particular macroeconomists), for instance, can only investigate one complex world and have to derive their conclusions from these sparse observatory sources. Psychologists cannot control all the variables of their subjects. Even astronomers cannot check the behavior of black holes or galaxies in any controlled way. The crucial point I want to make is this: the phenomena, the causally accessible part of the world, our cognitive abilities and technical circumstances determine how we have to approach observations. These approaches are often not epistemically ideal and barely any field except physics of small and medium scale reaches ideal circumstance. With observations we need the same approach as with theories: we need to make the best of what we have at hand. Gathering data in a new scientific context is a hard task, too. The crucial criterion for a theorie to be scientific is whether there is any possible form of observation at all to measure the empirical variables of the theory.

        When it comes to WFMs, it is unreasonable to completely dismiss the phenomenon by reference to the need of better data. The case for the existence of WFMs, as presented on this web page, is not on the level of a Nobel prize winning empirical revelation. Instead, my aim is to show that sufficiently solid evidence is available to consider the existence of WFMs as well corroborated. To say it in Bayesian terms, I want to increase the former degree of justified belief in WFM from P(WFM)=0.01 to an updated P(WFM)>0.5. If I accomplish my goal, then we need to search for good explanations of WFMs.

Trust

        Trust plays an important role in scientific discussions. Not every participant of a discussion can repeat the crucial observations. Scientists trust each other and their institutions to appropriately describe and conduct experiments and observations. Honest and detailed reporting belongs among the most central goals of a scientific education (and are often not intact in non-scientific social environments). When observations happen in uncontrolled environments, then a high degree of trust in the observing institutions, technology and participants is necessary to put the actual weight of playing the role of evidence in a major scientific discussion on the data.

        Regarding WFM footage that someone uploads (anonymously) to YouTube, the prima facie level of trust that we are willing to give in the reliability of the data is low. Furthermore, in the context of sensationalized alleged UFO videos, white orbs were already discussed (see introduction) and are part of the collective knowledge about alleged UFOs.

        However, on the other hand, it is deeply unscientific, but nevertheless surprisingly common among scientists, to dismiss every video as hoaxed that documents a scientifically undocumented new phenomenon. For a scientific treatment of WFM, the central part of the discussion is how likely they are hoaxed. This is not a project of only natural sciences (i.e. What are WFMs?), this is rather a project of journalistic investigation (i.e. Do these WFM videos point to something new with a sufficiently high degree of certainty?). For this quest, we need to investigate how reliable the data is. The claim that I defend is that they are sufficiently reliable to accept the existence of WFMs with a very high degree of certainty.

Why these WFM Videos are Reliable Data

        This is a list of reasons why these videos are sufficiently reliable for the described goal:

(a) Unsensational: Hoaxes (in particular UFO related ones) are usually designed to optimize its sensational effect. The hoaxer aims to fool many people or to sell his footage very profitable. WFM videos do in most cases not fulfill this criterion. What they show is by many viewers quickly explained away as light reflections or insects. Only a more detailed analysis reveals that this explanations are not valid. One of the rare cases that can be identified as a WFM hoax shows an alleged WFM causing a fighter jet to malfunction and crash (ref: Ukraine case), which is a highly sensational incident.

(b) Evidence Pluralism: An important factor for trust in observations is that many independent witnesses observe one and the same phenomenon from different perspectives and under different circumstances. WFM footage is a very good example for exactly that: a phenomenon is captured by different and socially unrelated individuals (see (b.1) below), under different weather conditions and with different technical equipment in a relatively stable way. It makes a crucial difference whether we have only very few socially not independent video sources for WFMs or such a diverse group of sources.

(b.1) Socially Pluralistic Sources: The originators have very diverse backgrounds. They speak different languages (e.g. English, Russian, French, Spanish, Czech), they live in different countries, their political interests differ, they have different attitudes towards religion. A few of them have a specific interest in UFO related topics, but most of them do not. The only commonalities among a majority of them is a comparatively high interest in technology and, if the gender is revealed, they are all male. Furthermore, most of the WFM footage are from areas in Europe and Northern America, but this fact is easily explained by the strong positive influence of wealth on the proliferation of high-end hobbyist drones. (b.2) describes how I got this information about the originators.

(b.2) Background Check on Sources Possible: YouTube users have openly accessible profiles, which include lists of uploaded videos, liked videos, subscribed-to channels and written comments. In many cases these profiles help to find more information about a person's interests and, implicitly, its background, because most originators of YouTube videos are also heavily active viewers on YouTube. Even if the originator uses an alias, a many years long history of YouTube activities is very revealing regarding his/her interests and psychological traits. This helps to substantiate argument (b.1).

(b.3) Technically Diverse Equipment: WFMs were videoed using various technical equipment. Good footage is available from different drone models, including DJI Inspire 1, the DJI Phantom 3 series, the DJI Phantom 4 series, the DJI Mavic series, YUNeeC Q500, and a GoPro HERO3 Black mounted on a Finwing Sabre. The most important difference between different drone models regarding the reliability of WFM footage are the different camera sensors. This is th piece of hardware that translates incoming light into digital information. As table 1 shows, these different drone models use a variety of different sensors. In addition to the results from the technical analyses (see chapter on analyses methodoligies) this further corroborates that WFM footage is not the results of a very odd technical bug, but rather genuine videos of flying objects.

ModelCamera SensorCamera Lens
DJI Phantom 4 Pro V2.0Sony Exmor R 1"
effective pixels: 20M
84° FOV, 8.8 mm (35 mm format equiv.) f/2.8-f/11, auto focus at 1 m - to ∞
DJI Mavic Pro1/2.3" CMOS
effective pixels: 12.35M
84° FOV, 28 mm (35 mm format equiv.) f/2.8 shooting range 0.5 m to ∞
DJI Mavic Air1/2.3" CMOS
effective pixels: 12M
85° FOV, 24 mm (35 mm format equiv.) f/2.8 shooting range 0.5 m to ∞
DJI Phantom 4 Pro(+) / Advanced(+)1" CMOS
effective pixels: 20 M
84° FOV, 8.8 mm (35 mm format equiv.) f/2.8-f/11, auto focus at 1 m - to ∞
DJI Phantom 41/2.3" CMOS
effective pixels: 12M
94° FOV, 20 mm (35 mm format equiv.) f/2.8
DJI Phantom 3 Pro / 4K / Advanced Sony Exmor R 1/2.3"
effective pixels: 12.4 M
94° FOV, 20 mm (35 mm format equiv.) f/2.8 focus at ∞
DJI Phantom 3 SE 1/2.3" CMOS
effective pixels: 12M
94° FOV, 20 mm (35 mm format equiv.) f/2.8 focus at ∞
DJI Phantom 3Panasonic Smart FSI 1/2.3"
effective pixels: 12M
94° FOV, 20 mm (35 mm format equiv.) f/2.8 focus at ∞
GoPro HERO3 BlackSony Exmor R 1/2.3" (IMX117)
effective pixels: 12M
170° FOV
DJI Inspire 1Sony Exmor 1/2.3"
effective pixels: 12.4M
94° FOV, 20mm (35mm format equiv.) f/2.8 focus at ∞)
Tab 1. Optical sensors and lenses as precisely described as published by the producers or via manual disassemble. Producers often reveal this information only sparsely. Sources: Bold information is hyperlinked to a source, all other information is gathered from respective product manuals.

(b.3.1) Different Camera Sensors Show Different Smear Effects: As table 1 shows, DJI uses a variety of camera sensors for different models. Pro versions of a model series are more expensive and are advertised as being more capable. The choice of a camera sensor is both an important factor for cost and for imaging quality. Sony is regarded as a leading producer of camera sensors. Therefore, DJI advertises their drones with Sony Exmor R sensors prominently (see, for instance, the October 2018 retail presentation of the Phantom 4 Pro V2.0 and of the cheaper Phantom 4 Advanced). Sony's Exmor R sensors use back-illumination technology that leads to nearly twofold sensitivity and low noise. Shutter times of digital camera sensors are crucially determined by a sufficient amount of light reaching the sensor to capture a full frame. Therefore, genuine WFM footage from Sony Exmor R sensors should show weaker effects of insufficient shutter times, if all other hardware components are capable of processing the sensor's digital information quickly enough. Since DJI describes the minimum bound of the electronic shutter times for all of their models at ⅛ms (=8000fps) this problem should not occur. In our exemplary cases of WFM footage, find can identify the expected effect exactly: the smear effect of WFM footage from Sony Exmor R sensors is signicantly shorter than in other examples produced with cheaper camera sensors. The following closeup views of the footage (figures 1 and 2) substantiate this.



Fig 1. Footage with very reliable estimates of travel speed and filmed with DJI Phantom 4 drones (not advertised as using Sony Exmor R sensors). Closeup view on last frame with visible WFM.
Top left: DJI Phantom 4 Pro, 1289km/h. Top right: Very likely DJI Phantom 4 Pro, 1424.8km/h.
Bottom left: DJI Phantom 4 Advanced, 2600km/h. Bottom right: DJI Phantom 4 Standard, 842.9km/h.
(click on images for case details)




Fig 2. Footage with very reliable estimates of travel speed and filmed with DJI drones that are specifically advertised as using Sony Exmor R sensors. Closeup view on last frame with visible WFM.
Top left: DJI Phantom 3 Pro, 5625km/h. Top right: DJI Phantom 3 Advanced, 4871.5km/h.
Mid left: DJI Phantom 3 4K, 1638km/h. Mid right: DJI Inspire 1, 7215.3km/h
Bottom: DJI Phantom 3 4K, 4806km/h
(click on images for case details) Double check speeds, estimates seem too fast


(c) No Personal Gain: Except for possibly enjoying the reactions of a fabricated hoax, there is not much gain in uploading WFM footage. As pointed out in (a), the lack of sensationality of WFM footage make it unattractive as a hoax project. The majority of uploads have only very few views and are not advertised by the originators. The related YouTube channels are often very tiny regarding the viewership and they are clearly not profitable. The method described in (b.2) leads to the conclusion that the majority of channels are hobbyist projects without professional intentions. The originators of the here presented WFM videos do not gain any money and a relevant amount of prestige from their upload. Rather the opposite seems to be the case. A user claiming I have had death threats because of this video! (6BUA6zdbgEE) describes this.

(d) Technical Incapability: There is a list of features that support the claim of WFM videos not being fabricated, most importantly the smear effect due to the camera's insufficient shutter times, the changes of the objects' sizes, compression artefacts and non-linear trajectories. A very capable video effect expert is able produce all these effects artificially with only little effort. However, non-experts would not be able to produce these effects without an in-depth study of the phenomenon as it is presented on this web page for—to my knowledge—the first time. If all the 4- and 5-star cases would be hoaxes, then they could not all look so convincing by exemplifying the mentioned properties according to my analysis results of WFM footage (see conclusions).

(d.1) No Easy Software Solution to Create Hoaxed WFM Footage: Having read hundreds of YouTube comments under WFM related videos, no commentator pointed to any easy way of hoaxing such footage (e.g. with a common software tool). Due to (b.1) and (c), the only way these footages are all hoaxes is that people get some easy technical aid for it. But if this aid is accessible that easily, skeptical commentators are able to find it as easily, too, and they would point it out. But this is not the case.

(e) WFM not Pointed Out: In some cases, the originator just uploaded a drone video without any comment of a WFM to occur. In these cases, other viewers later pointed the occurrence of a WFM out. This indicates that the originator might have not even been aware of the WFM, which increases the reliability of the WFM footage. 9P2A8m7RgnA is such a case. Figure 3 below shows accidental WFMs in compilation videos about destinations. Figure 4 shows a possible WFM captured by a bird watcher (filed as MUFON case). Figure 5 shows a possible WFM captured by someone claiming to film airplanes' contrials. I do not claim that we can be certain that all of these cases are genuine, i.e. not hoaxed. But I do claim that skeptics cannot make the argument that, if WFMs exist, then why do they only occur in drone footage? The drone footage provides better data about WFMs' flight behavior and corroborates other sightings (e.g. in the context of crop circles or as shown in figures 4 and 5).


(click images to start/stop animation)

Fig 3. Likely cases of WFMs in drone footage with no indication to showcase WFM specifically. The videos are titled Exploring Germany 4k - Beautiful Destinations (left) and Stunning aerial drone footage over GERMANY + AUSTRIA - 4k (right). View the original video for full size.


(f) Variations in WFM Cases: WFMs are white, fast and seemingly steered, but there are still high variations among the WFM cases. Their trajectory is straight or almost straight (e.g. 6BUA6zdbgEE, mgrI0MHZQQc, 9P2A8m7RgnA, O9R1wMq0VOI), along a curve with big radius (e.g. lnIUh2bPxu0, JJpSYozvasc) or with sudden maneuvers (e.g. 4KeZ7Pzbd9U). In some cases, we see the WFM approaching from a far distance, and sometimes only in a few frames shooting through the image. Their measured speed reaches from a few hundred km/h (e.g. P-iFx3VIiQ0, _p_inSwZcPQ) to several times the speed of sound (e.g. dNrtU1z_5EQ, 9P2A8m7RgnA). They most often keep a constant flight altitude, but in some cases they change their altitude significantly (e.g. d3ajks8OHCo, 9QZvy_SJT8E).

(g) Technical Details: Some technical details further corroborate the genuity of the footage as showing actually flying objects. Most importantly, different hardware behaves differently when filming WFMs at high speed. For instance, the DJI's Phantom 3 Pro, 4K and Advanced drone models consistently show less smear effects (due to a shorter effective shutter time of the Sony EXMOR camera sensors, see table 1) than its successor models DJI Phantom 4 and DJI Mavic.—Examplary cases for Phantom 3 Pro, 4K and Advanced footage are 6BUA6zdbgEE, O9R1wMq0VOI and VjW_QyXtyHA. Examplary cases for Phantom 4 footage are lnIUh2bPxu0, mgrI0MHZQQc and 4KeZ7Pzbd9U. Examplary cases for Mavic footage are JJpSYozvasc and (likely) adRsfMwpnQk.

(h) No Mundane Explanation: As discussed on the case pages more thoroughly, mundane explanations, such as light reflections, animals, secret human-made vehicles or common weather phenomena are unlikely the cause of what can be seen in the data. The chapter on explanatory hypotheses details this conclusion of mine. Most of the videos are uploaded without any originator's comment that indicates any explanation of the data. The only exception is the umbrella term unidentified flying object, often with an additional emphasis that this is meant as an umbrella term and does not necessarily include stronger claims (e.g. extraterrestrial visitors). This gives further reliability to the footage, because hoaxes are designed to fulfill presupposed criteria for an then strongly supported explanation.


(click images to start/stop animation)
Fig 4. Possible WFM in footage from someone:on my balcony I just recorded the birds flying around. (MUFON case description #85017, openly available video upload)


(click images to start/stop animation)
(click here for fullscreen image)
Fig 5. A possible WFM in a video that was intended to film the contrails of planes. (00:25-00:27)


FAQ

        I am frequently addressed with the following questions when discussing WFMs. I articulate the answers to them that seem most fitting to me.


Why then have WFM never been studied?

        As described above, I experienced that most scientists select the phenomena they want to investigate further according to certain, often very pragmatic characteristics. An important criterion for phenomenon selection is that scientists can find answers that fit neatly into a lot of very basic background assumptions in which they already belief. WFMs do not fulfill this criterion.

        Furthermore, high-definition drone videos are only available for a mass market for a few years now. As the example of filming a golf ball in flight exemplifies (see the chapter on analysis methodology), only very modern digital camera sensors are capable of capturing good WFM footage. Possibly military or intelligence owned data on WFMs might not be published.


Don't we need better data for this being a scientifically acceptable study?

        Great scientific discoveries often need decades to emerge from a first glimpse into a full-fleshed and well-corroborated theory. The existence of gravitational waves, for instance, took roughly hundred years, thousands of scientists and many hundreds of millions of $, €, £, ¥, and CHF to become established from Einstein's (or Poincaré's) first suggestion to LIGO's confirming measurements.

        The first important step for such a development in the case of WFM is phenomenon acceptance: there is something deeply puzzling and we should invest some effort into getting better data about it. In this regard, WFMs are more like Sprites or Northern Lights; these are undeniably there and we need to theorize around them to find adequate scientific answers for this phenomenon much further down the road. The aspect of being seemingly intentionally steered make the WFM phenomenon both theoretically very hard to tackle, but also very motivating. It could be a new natural phenomenon that neatly fits into the current body of knowledge about nature or it could be a door opener to a major paradigm shift.

References

Descartes, R. (1641). Meditationes de prima philosophia, in qua Dei existentia et animae immortalitas demonstratur. Michel Soly (Paris).

Feyerabend, P. (1975). Against Method. New Left Books (London).

van Fraassen, B. (1980). The Scientific Image. Oxford University Press (Oxford).

Kant, I. (1787). Critik der reinen Vernunft. 2nd edition, Hartknoch (Riga).

Kuhn, T. (1962). The Structure of Scientific Revolutions. University of Chicago Press (Chicago).

Popper, K. (1959). The Logic of Scientific Discovery. Hutchinson (London). First published in German (1935): Logik der Forschung. Springer (Vienna).



 
 
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