Can you give an example of how one would conduct a placebo-contolled drug trial under a strictly Bayesian rubric? I cannot. While there are difficulties in a strict positivist framing of inquiry, the the quanification framework of Popper's falsificationism is remarkably elegant and clean. I have seen hybrid frameworks where a Bayesian prior has been added to account for knowledge aquired prior to an experiment (in the Popper falsification framework of rejecting a null in favor or an alternative hypothesis) but I have not seen one which altogether disgards this sort of test and enables drawing an applicable conclusion. Theories are great, but without an appropiate armory of machinery, they have no teeth.

Dear Karen, thank you for your question. I am no specialist in drug trial, i just try to argue on how to improve falsifiability without recourse to anarchism view of science (Feyerabend). For drug clinical trial, perhaps you will find this article in Nature,2006, useful as guide. It was written by Donald A. Berry (see http://www.nature.com/nrd/journal/v5/n1/abs/nrd1927.html). His email is [email protected].

Other than Bayesian acceptance of a theory, another alternative is perhaps SOC model of scientific discovery ( Soc means self organized criticality). But so far, i do not find any reference on this proposal. Best wishes

Victor- I think Barry is implmenting a Baysian methodology in the context of classical hypothesis testing context of reaching a conclusion involving a p value. This p value provides the determination to reject or fail to reject the null hypothesis. The framework of rejecting a null hypothesis is implicitly falsificationism. This is what I cull from the abstract. I will pull the full article tomorrow.

Jochen- I will think on this and respond tomorrow.

KG

Dear Victor Christianto:

You raise some interesting issues, but alas they touch upon a number of some of the most debated matters in the philosophy of science, the philosophy of probability, epistemology, and scientific methods. I would find it helpful if you could clarify certain comparisons and distinctions you seem to have made or not made that I find rather central.

For example, you set up something of a dichotomy between Popperian epistemology and Bayesian epistemology. But subjective interpretations of probability aren't limited to Bayesian, and the opposing approach to Bayesian analysis isn't really any philosophy of science per se but rather the frequentist philosophical interpretation of probability. This is not to say that Bayesian epistemology is compatible with Popperian philosophy of science. It is simply to point out that objective interpretations of probability and subjective interpretations are perhaps better contrasting epistemological approaches than comparing an extension of conditional probability from statistical inference to a formalized scientific epistemology over and against a rather specific, detailed, and singular philosophy of science.

Likewise, I find it a bit confusing to refer to Feyerabend's views as critical of Popper's, which of course it is, but seemingly gloss over how the same is just as incompatible (or nearly so) with Bayesian epistemology. On a related note, the primary opposition to Popper's philosophy of science comes from not from Bayesian epistemology but the Quine-Duhem thesis (although for a critical review on the appropriateness of this nomenclature, see Zammito's A Nice Derangement of Epistemes, pp. 17-25). For a brief but relatively comprehensive treatment on the changes to the philosophy of sciences originating around the beginning of the 20th century, see e.g., Hrheinberger's Historische Epistemologie (also, Zammito's text cited above is a good source, albeit ~200 pages longer). In general, it seems as if your presentation of Popper on the one hand and Bayesian epistemology on the other seems to miss the rather important differences between what each were intended for as well as the other, more directly comparable approaches to the philosophy of science and/or epistemology (including the philosophy of probability).

As for falsification, perhaps THE method for hypothesis testing is the ritualistic null hypothesis significance testing (NHST). This is the standard "reject the null, accept the alternative" (given some alpha level) used in the medical, psychological, social, and other sciences. I hate to rehash material I've already repeated here, but as I took some time to find a short but comprehensive set of resources, I will anyway:

"One wishes to know the probability that a biological or medical hypothesis, H, is true in view of the sadly incomplete facts of the world...But the statistical tests used in many sciences (though not much in chemistry or physics) do nothing to aid such judgments. The tests that were regularized or invented in the 1920s by the great statistician and geneticist Ronald A. Fisher (1890-1962) measure the probability that the facts you are examining will occur assuming that the hypothesis is true....The mistake here is known in statistical logic as “the fallacy of the transposed conditional.” If cholera is caused not by polluted drinking water but by bad air, then economically poor areas with rotting garbage and open sewers will have large amounts of cholera. They do. So cholera is caused by bad air. If cholera is caused by person-to-person contagion, then cholera cases will often be neighbors. They are. So cholera is caused by person-to-person contact. Thus Fisherian science."

McCloskey, D. N., & Ziliak, S. T. (2009). The Unreasonable Ineffectiveness of Fisherian" Tests" in Biology, and Especially in Medicine. Biological Theory, 4(1), 44.

(http://stephentziliak.com/doc/Transposed%20conditionals%20in%20Biology%20and%20Medicine.pdf)

“In a recent article, Armstrong (2007) points out that, contrary to popular belief, “there is no empirical evidence supporting the use of statistical significance tests. Despite repeated calls for evidence, no one has shown that the applications of tests of statistical significance improve decision making or advance scientific knowledge” (p. 335). He is by no means alone in arguing this. Many prominent researchers have now for decades protested NHST, arguing that it often results in the publication of peer-reviewed and journal endorsed pseudo-science. Indeed, this history of criticism now extends back more than 90 years (e.g., Armstrong, 2007; Bakan, 1966, 1974; Berkson, 1938; Boring, 1919; Campbell, 1982; Carver, 1978, 1993; Cohen, 1990, 1994; Edwards, 1965; Falk, 1998; Fidler, Thomason, Cumming, Finch, & Leeman, 2004; Fisher, 1955, 1956; Gigerenzer, 1987, 1993, 2004; Gigerenzer et al., 1989; Gill, 1999; Granaas, 2002; Greenwald, 1975; Hubbard & Armstrong, 2006; Hubbard & Lindsay, 2008; Hubbard & Ryan, 2000; Jones & Tukey, 2000; Kirk, 1996, 2003; Lindsay, 1995; Lykken, 1968, 1991; Meehl, 1967, 1978, 1990; Nunnally, 1960; Rosnow & Rosenthal, 1989; Rozeboom, 1960; Schmidt, 1992, 1996; Schmidt & Hunter, 1997; Sedlmeier & Gigerenzer, 1989; Skinner, 1972; Thompson, 1996, 1999, 2002, 2006, 2007; Tukey, 1991)…It is certainly a “significant” problem for the social sciences that significance tests do not actually tell researchers what the overwhelming majority of them think they do (Bakan, 1966). Bakan thought that “everybody knows this” and that to say it out loud is to be like the child who pointed out that the emperor is wearing no clothes. He argues that if we pull out the strand of NHST much of the tapestry of psychology would fall apart. Indeed, NHST, Gerrig and Zimbardo (2002) state, is the “backbone of psychological research” (p. 46). So, instead of abandoning it, which could be very embarrassing, we make the adjustment of simply misinterpreting what it actually tells us, which is…not much.”

Lambdin, C. (2012). Significance tests as sorcery: Science is empirical—significance tests are not. Theory & Psychology, 22(1), 67-90.

(http://psychology.okstate.edu/faculty/jgrice/psyc5314/SignificanceSorceryLambdin2012.pdf)

"402 Citations Questioning the Indiscriminate Use of Null Hypothesis Significance Tests in Observational Studies"

(http://warnercnr.colostate.edu/~anderson/thompson1.html)

"The Null Ritual: What You Always Wanted to Know About Significance Testing but Were Afraid to Ask"

(http://www.sozialpsychologie.uni-frankfurt.de/wp-content/uploads/2010/09/GG_Null_20042.pdf)

Gigerenzer, G. (2004). Mindless statistics. The Journal of Socio-Economics, 33(5), 587-606.

(http://people.umass.edu/~bioep740/yr2009/topics/Gigerenzer-jSoc-Econ-1994.pdf)

At any rate, thanks for broaching the topic. I'm looking forward to others' input (particularly given the two experts who have already contributed and will, I hope, continue to).

Dear Dr. Wilhem:

Regarding your (in my opinion correct) criticism that Lambdin does not sufficiently define "due to chance" (or chance), and in particular does not define it so that it may be properly distinguished from probability: I had overlooked this, as I am so used to thinking of "due to chance" and "probability" in terms of NHST where "due to chance" is defined in terms of a failure to meet some alpha level (or p-value, the term Lambdin does). The logic of NHST is to assume that, given some probability distribution (usually approximately normal), there is some outcome that is sufficiently far from the expected value that we can assert it isn't "due to chance". I think Lambdin is expecting the reader to be familiar with the ways in which standard hypothesis testing methods are defined in terms of "chance" as outcomes that are less probable than some alpha level and are thus not distinct from probability but are defined by some interval within a probability distribution.

That said, I agree with your remarks, and thanks to your remarks I feel it necessary to add something to what I said. I was thoroughly indoctrinated to accept NHST, and have been required to teach it for years. I sometimes unconsciously assume, unfortunately, a stance against the kind of understanding of NHST I had years ago and my students have had- i.e., a limited understanding both of its underlying logic, its criticisms and defenses against these, and in general the kind of nuanced understanding of both the philosophy of probability and the logic of statistical inference. While this is in general appropriate when I deal with students, it isn't here. So I would welcome links and/or references to comprehensive defenses of NHST, as I have spent far too long trying to break the death-grip of its ritualistic use to concentrate on the counters to those arguments I use to challenge complacency.

Dear Karen, Jochen, and Andrew. Thank you so much for all your answers. I need some time to digest all your deep comments, before making further remarks.

Allow me to say that i just got that idea of Bayesian acceptance of a theory yesterday, and then a quick search at bing.com reveals that only a few people brought this topic before, therefore i think it would be interesting to compare it vis a vis Popperian falsifiability, which some scientists have objection to. One of my reasoning to propose Bayesian epistemology is because Falsifiability is merely a general concept, while bayesian probability has strict definition.

Now i got another idea: provided that Bayesian epistemology is worth to consider, then perhaps we can extend it further to become Dempster-Shafer epistemology. That is because Dempster-Shafer theory is a generalization of Bayesian probability, see this article http://www.glennshafer.com/assets/downloads/articles/article48.pdf. So what do you think? Thanks and best wishes

Dear all, one more question: i just read a new book by Prof. Florentin Smarandache where he extends Bayesia. Rule to become Neutrosophic Bayesian rule ( see page 70-71 in this attached book). Then does it mean we can introduce indeterminacy to Bayesian acceptance?

In this perspective, then each theory has its own indeterminacy, therefore it cannot be fully accepted. 

Book Introduction to Neutrosophic Measure, Neutrosophic Integral,...

Dear Jochen, yes you are right, a theory cannot be fully accepted.

In Bayesian sense, for example, the sun rises each morning, and it has been so for many thousand years, so the probability of the sun will rise again tomorrow is very close to 1, although it cannot be 1. Therefore even in that case, it cannot be fully accepted. Best wishes

Dear Victor,

I entirely agree with Jochen and Andrew criticisms saying that Popperian philosophy and probabilistic theory are not directly compatible. In order to go further, I will show that the opposition between the more general Popperian deductivism, for which falsificationism is only a part, and the Baconian inductivism, is in fact the important dichotomy.

For Popper, who considers induction as inconsistent, the only way to scientific methodology is not to prove a hypothesis but only to show that we have the possibility to falsify it. This way of reasoning from a hypothesis to the facts implied by it, will lead to as much theories as there are hypotheses to verify, and will restrict scientific research to a task of validation. However, as Hume, he defines induction in an incorrect way, as a generalization from specific observations. In this case it is true that such a generalization may always be refuted by a new observation.

But for Bacon, induction has another meaning more thorough. For the previous meaning, he clearly said: “For the induction which proceeds by simple enumeration is childish; its conclusions are precarious and exposed to peril from a contradictory instance; and it generally decides on too small a number of facts, and on those only which are at hand.” (The new Organon, 1620, Book 1, CV). The second meaning, which had been used by Galileo, Descartes and Newton, is defined by Bacon as: “The other derives from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried.” (The new Organon, 1620, Book 1, XIX). For him the axioms are not “self-evident and necessary truths”, as the Webster’s Dictionary said, but are drawn from experience. They are not everlasting as new experiences may lead to new axioms. They are principles inferred by experience. The way Newton found his laws, not from hypotheses but by induction in the Baconian meaning, is a perfect example of this way of reasoning. Nowadays this Baconian induction leads to the mechanistic theory applied as well in natural sciences , as in biological sciences or in social sciences (see for example: Franck ed., 2002, The explanatory power of models, or Craver and Bechtel, 2006, Mechanisms, in The philosophy of science: an Encyclopedia, p. 469-479).

Looking forward for your comments on this point.

Dear Daniel, thank you for your answer. I think that both deduction and induction are both required for a proper scientific method. The question is how. Best wishes

Dear Victor,

I don’t think that deduction and induction are both required for a proper scientific method. As Sir Harold Jeffreys said in his Theory of probability (1939): “Running through the whole is the tendency to claim that scientific method can be reduced in some way to deductive logic, which is he most fundamental fallacy of all: it can be done only by rejecting its chief nature, induction.” This induction is not, as I previously said, a generalisation from particular instances, but “consists in discovering a system’s principle from a study of its properties, by way of experiment and observation”, as Franck said in his 2002 book. So that it appears to be clearly conceived as the inverse procedure which is followed in deduction, and this last procedure has to be abandoned as a method of scientific explanation, if we use induction.

Daniel, you are right that some people rejected induction as a form of logic, for instance  Peter Medawar and Karl Popper. See http://www.ssr.org/sites/ssr.org/files/uploads/attachments/node/16/rothchild_scimethod.pdf

But i still think that both approaches are required. For instance, when you study some lietaratures in order to form a hypothesis, you use deduction. But when you use statistics, and infer conclusion from a set of given data, then you use induction. At least that is what i learned from a lecture of research methodology. Of course, one can argue which form of logic is better. Best wishes

Jochen, you may be right that even in forming hypothesis, a scientist can use induction too. What i meant with deduction is logical conclusion derived from past findings/theories. For instance, if we believe a theory which says that serotonin has relation to juvenile delinquency (youth crimes), then one can hypothesize that certain food types  can trigger serotonin activity therefore they may affect anger behavior (related to juvenile delinquency). Then one can begin designing certain experiment to validate or invalidate that hypothesis, that is by inductive reasoning. But perhaps i can make mistakes here. 

So what do you think? Thanks

Dear Jochen, yes perhaps there is misinterpretation here. If you want simple definitions of deduction vs. induction, please check: http://www.ssr.org/sites/ssr.org/files/uploads/attachments/node/16/rothchild_scimethod.pdf.

For example, induction is generalization from particular observation/data using statistical inference. For example, if you conduct polling or survey, then you always take certain sample, but then you try to make conclusion for the entire population. This is called statistical inference, and it is determined by method of and size of sampling. But if you use logical reasoning from a general theory to derive a particular hypothesis, that is called deductive reasoning. From what i learned several years ago, the textbooks also explain like that. Best wishes

Dear Jochen, dear Victor,

I think that the main difference between deduction and induction may be the following: deduction consists in deducing consequences from principles taken as given; induction consists of the deduction of principles from the study of their consequences. So that induction can be seen as the exact opposite of deduction. We can say that the modern sciences, at the time of Bacon, were born from the abandonment of deduction as a method of explanation, in favor of induction. Unfortunately later, with the empiricist tradition put forward by Hume or Mill and developed by Popper, deduction became again the main method for explanation, as they considered induction only as a generalisation from particular instances. Only recently a renewal of interest in classical induction appears. Once the functional architecture is known (by induction) then it can guide (by deduction) the empirical investigation of the mechanism which generate the observed properties. See for more details Franck, 2002, The explanatory power of models.

Thanks Daniel. best wishes

Dear All, thank you so much for all your answers. Allow me to upload here a summary of our discussion. best wishes

Dear All, here allow me to share a file discussing Popperian falsifiability on cosmology. best wishes