It is evident that—from the very beginning—Hahnemann and his acolytes were immune to scientific evidence, which questioned their dogmatic system. In one of his major inquiries, The Logic of Scientific Discovery/Logik der Forschung, Sir Karl Popper argued that the scientific method relied on reproducibility and falsifiability . Popper also acknowledged the importance of theories but emphasized that theories must be challenged, because only this leads to their improvement and thus ultimately to scientific progress . From the perspective of scientific approach, homeopathy has four problems: (i) the assumptions underlying its theory lack plausibility and they violate fundamental laws of chemistry and physics, i.e. the law of mass action and the second law of thermodynamics. (ii) The theory is being immunized against scrutiny and falsification. (iii) Homeopathy has no explanatory power. (iv) Last but not least, homeopathic remedies are ineffective, if examined in adequately controlled clinical trials.
The principle of similarity is a dogma, which must be believed; there is neither rational nor empirical support to justify this assumption. Human physiology is understood in considerable detail. The same is true for the pathophysiology of many diseases. There is little rationale to support the assumption that diseases can be cured by interventions, which provoke the very same disease: it is, for instance, not logical to posit that diabetes mellitus can be cured by raising glucose levels or by inducing insulin resistance. The only situation where the assumption “like cures like” is valid, is immunization by vaccines; vaccination, however, is typically rejected by practitioners of homeopathy.
Hahnemann equated symptoms and diseases, hence removing the symptoms is equivalent to healing the disease (§6 and §7 of the Organon). It is obvious that this assumption is fundamentally flawed. The repertory of homeopathic drugs is based on a collection of observed/perceived symptoms, which are elicited by a given drug in volunteers. As outlined above, from the very beginning, homeopathic pathogenetic trials were not reproducible. More than 200 years after the seminal self-experiment with quinidine, the repertory was still judged to rely on poorly conducted trials . More recent studies are also unconvincing: the effects of ozone C30 (i.e. diluted 1060-fold) was most frequently equated to Haliaeetus leucocephalus sanguinaria, i.e. a remedy prepared from blood of the American bald eagle . It is worthwhile to quote the explanation of the authors verbatim:
“The HPT (= homeopathic pathogenetic trial) databases of Ozone and Haliaeetus leucocephalus sanguinaria share the theme of ‘upward’ or floating sensations, such as feeling light and free, feelings of elation and euphoria and dreams of being high up in the mountains” .
It is obvious that there has to be more than a pinch of mysticism to accept the fact that ingestion of blood of an eagle causes these feelings. It is also questionable, whether these feelings are relevant to the treatment of any disease. Finally, it is not logical that ozone should be uplifting like an eagle: ozone is heavier than air and therefore sinks. The homeopathic literature abounds in statements such as these. They may be poetic but they are meaningless from a scientific perspective.
During the 1930s, when homeopathy enjoyed political support by the Nazi regime in Germany for ideological reasons (see above), the Imperial Ministry of Health (Reichsgesundheitsamt) encouraged homeopathic pathogenetic trials. These were to be carried out in a blinded and placebo-controlled fashion. The publication of the results was apparently suppressed. Fritz Donner, a German physician and homeopath, however, provided a frank account on both the trials and the dangerous machinations in clinical medicine, where patients with ulcers, pernicious anemia, gonorrhea, hyperthyroidism etc. were treated with homeopathic remedies. Proponents of homeopaths were most prone to report amazing symptoms, when challenged with placebos in the homeopathic pathogenetic trials, and to ignore the lack of therapeutic effects in their patients ([32,33,34,35,36] and the report can also be accessed at https://www.kwakzalverij.nl/behandelwijzen/homeopathie/der-donner-bericht/). It is worth noting that the publication of this report was actively suppressed by the Association of German Homeopaths (Deutsche Zentralverein homöopathischer Ärzte).
The law of mass action governs all chemical reactions and hence also the action of drugs: drugs bind to targets and this binding reaction elicits a biological action. Metaphorically, one can choose to refer to this binding reaction as a transfer of information, as proponents of homeopathy like to do. Nevertheless, Avogadro’s number imposes a lower limit for chemical reactions. While Avogadro’s number was not known to Hahnemann, current homeopathy cannot ignore this problem as it cannot ignore the impurities, which are present in water or any other solvent. The vast majority of water molecules, which are ingested have been present for millennia. Fortunately, when ingested, these water molecules do not bear any memory of their past exposures. It defies logical thinking to posit that homeopathic water (or any other solvent) differs from any other water or solvent of equal purity. Homeopaths credit the vigorous shaking for imparting information from the solute to the solvent. The energy, which is provided by shaking and thus presumed to create ordered water molecules (or quantal entanglement), is trivial relative to entropy: water (and other solvent) molecules move rapidly and stochastically by Brownian motion and hydrogen bonds rearrange on the femtosecond to picosecond scale [17, 18]. Thus, the second law of thermodynamics precludes any conservation of order/information. A theory, which violates these fundamental laws of nature, requires substantially larger proof than resorting to quoting Hamlet in an pseudo-erudite fashion (There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy).
Immunization against falsifiability
The literature on homeopathy is rife with immunization strategies: because of the unique nature of homeopathy, its essence cannot be captured by a randomized clinical trial. This is a priori not true. Randomized trials can obviously be designed to address essentially all questions in clinical medicine including those raised by homeopathy: a patient’s symptoms can be catalogued by a homeopath and the appropriate medication selected based on the resulting diagnosis. The patient can then be randomly assigned to the appropriate homeopathic remedy or to a placebo. When adequately powered (i.e. with a sufficiently large sample of patients), the beneficial effect of the homeopathic treatment ought to be evident. Because this has not been the case, patient-practitioner remedy (PPR) entanglement (see above) has been invoked . Additional immunization strategies can also be found: in a trial, where placebo was—surprisingly—superior to the homeopathic remedy in treating pain associated with rheumatoid arthritis, the authors shifted the focus from the lack of efficacy to raising the issue of cost-effectiveness by stating : “Instead of trying to disentangle ‘genuine’ effects of homeopathy from the placebo response, we suggest that a more directly relevant research question is whether it is cost-effective to complement conventional therapy in patients requesting homeopathy. It seems more important to define, if homeopathists can genuinely control patients’ symptoms and less relevant to have concerns about whether this is due to a ‘genuine’ effect or to influencing the placebo response”.
Homeopathic theory claims that the homeopathic remedy may initially lead to an aggravation of symptoms, which is not always seen and which is followed by a slow, but steady recovery. Aggravation serves as a convenient immunization strategy, which precludes any falsification of the treatment hypothesis: its occurrence proves the efficacy of the homeopathic remedy, but its absence is also acceptable; however, when examined in published placebo-controlled trials, aggravations are as likely to occur in patients receiving placebo as in those who were administered the homeopathic remedy . In fact, aggravation and slow but steady recovery is the natural course of many diseases. In clinical trials conducted according to the principles of evidence-based medicine any aggravation must be recorded as an adverse event regardless of whether it can be linked to the treatment intervention or not.
Proponents eschew questions on reproducibility. The individualized approach to the patient and the remedy a priori provides a convenient excuse to neglect reproducibility; however, homeopathic research has also ventured into experimental studies. One of the most prominent examples is the claim that progressive dilutions of antibodies directed against IgE enhance their capacity to degranulate basophil leucocytes in human blood . The statistical flaws of this study were exposed in a highly debated on-site visit . Most importantly, an independent study failed to reproduce the original findings: regardless of whether it was succussed or not, anti-IgE diluted below 1: 100 did not cause any appreciable degranulation of basophils . It is evident that the later publication did not receive as much media coverage as the original paper by Benveniste et al. .
Lack of explanatory power
Theories, which make testable predictions, can be falsified; they can be abandoned or improved. It is evident that this drives the progress in scientific medicine: the theory of the four humours (imbalance in/dyscrasia of αἷμα/blood, χολή/yellow bile, φλέγμα/mucus and µέλαινα χολή/black bile as an explanation of disease) and the resulting dogmas of Galen of Pergamo were received, unquestioned/unquestionable knowledge for some 1500 years; however, this dogmatic view was discredited by William Harvey, when he described the circulation of blood based on experimental evidence . In the past 350+ years, progress in scientific medicine has been amazing. In §1 and §8 of the Organon, Hahnemann ridiculed hypothesis-driven research and the approach of correlating clinical symptoms of diseases with pathological changes; however, it is remarkable that, in the past two centuries, homeopathy did not make any contribution to our current understanding of human physiology or pathophysiology: there is not a single disease entity, which can be explained by homeopathy. This is not surprising, because homeopathy does not make any testable predictions.
It has to be acknowledged, though, that homeopathy can be credited for spurring the development of blinded, placebo-controlled trials , of randomization and double-blinding and meticulous documentation thereof [14, 15], but this was largely an unintended consequence. Similarly, Hahnemann’s criticism of the remedies, which were administered in his day, was justified; there was little evidence to support their use, many interventions were not only ineffective but also harmful. Hence, homeopathy can also be credited for stimulating the scientific approach to pharmacotherapy .
Lack of efficacy in clinical trials
Proponents of homeopathy brush aside arguments about lack of plausibility, reproducibility, falsifiability and explanatory power by stating that “whoever heals, is right”; however, when designed with relevant primary and secondary outcomes and adequately powered, homeopathic trials fail to provide any evidence for a therapeutic action, which goes beyond that seen in the placebo group [37, 45]. In fact, it appears that it is the homeopathic consultation, i.e. the interaction with the physician, rather than the homeopathic remedy, which provides a beneficial effect . There are obviously numerous homeopathy trials, which report beneficial effects. These suffer from various methodological flaws. It has to be stressed that conventional scientific medicine is not immune to flawed studies. Flaws and bias can be exposed by studying individual studies, but they can also be revealed by meta-analytic approaches: Shang et al. carried out a meta-analysis of 110 homoeopathy trials and 110 matched conventional-medicine trials . Matching was done for disorders and outcome measures. Many more conventional medicine than homeopathic trials have been deposited in the databases. Hence, the authors selected the matched conventional medicine trials by a randomized approach. The effect size, which was reported in each individual study, was converted into an odds ratio (i.e., the probability that the verum was superior to placebo) to allow for intertrial comparison. This exercise revealed the expected inverse correlation between study size (i.e., size of the patient population) and the normalized effect size (i.e., the odds ratio in favour of the verum); in other words: large studies reported smaller beneficial effects. This is a well-known finding, which has been seen in many meta-analyses. It is consistent with regression to the mean; however, the interesting finding of Shang et al. was the fact that in homeopathic trials the mean regressed to an odds ratio of 0.88 with a 95% confidence interval of 0.65–1.19; this is not statistically different from 1 (an odds ratio of 1 indicates that there is no difference between verum and placebo). In contrast, for the matched conventional medicines trials, the odds ratio was 0.58 with a 95% confidence interval of 0.39–0.85 (and thus significantly different from 1 indicating that the conventional medicine had an effect, which was superior to placebo). Based on this meta-analysis, the authors concluded that homeopathic trials fail to show any effect, which goes beyond that provided by placebo treatment.
The study of Shang et al.  published by a leading medical journal and a leading team of experts in meta-analysis, was obviously anathema to the homeopathic community and therefore heavily criticized (see e.g. . and the rebuttal of the criticism ). An accompanying editorial in The Lancet pronounced the end of homeopathy, argued against “further investment in research to perpetuate the homoeopathy versus allopathy debate” and recommended that physicians be honest to their patients “about homoeopathy’s lack of benefit” ; however, the continuous popularity of homeopathy and the homeopathic industry still form an effective coalition to support lobbying for relaxed regulations of homeopathic remedies and for resource allocations, i.e. payments by sickness funds in various countries. These pressures have also resulted in enhanced scrutiny. Two large scale efforts, by the Australian National Health and Medical Research Council (NHMRC) in 2015  and by the European Academies’ Science Advisory Council (EASAC, an association formed by the national science academies of the EU Member States) , were conducted to review the claims that homeopathic treatments are efficacious. Both panels concluded that none of the many studies, which had been published provided any evidence for an effect that went beyond that of a placebo.
The Australian NHMRC considered systematic reviews, published between 1997 and 2013, which compared homeopathy to placebo or other treatments. A total of 57 systematic reviews including 176 individual studies were identified, which matched the (predefined) search criteria of the panel. In addition, information was submitted to the NHRMC panel by homeopathic interest groups and the public. The NHMRC panel of researchers assessed the quality of each individual study and found that homeopathic treatment was either not better than placebo, or the studies showing superiority of homeopathy were of poor quality. Considering the body of evidence, the NHMRC panel concluded that “… there are no health conditions for which there is reliable evidence that homeopathy is effective” . Similarly, it is worthwhile to cite the recommendations made by the European Academies’ Science Advisory Council (EASAC) :
There should be consistent regulatory requirements to demonstrate efficacy, safety and quality of all products for human and veterinary medicine, to be based on verifiable and objective evidence, commensurate with the nature of the claims being made. In the absence of this evidence, a product should be neither approvable nor registrable by national regulatory agencies for the designation of a medicinal product.
Evidence-based public health systems should not reimburse homeopathic products and practices unless they are demonstrated to be efficacious and safe by rigorous testing.
The composition of homeopathic remedies should be labelled in a similar way to other health products available: that is, there should be an accurate, clear and simple description of the ingredients and their amounts present in the formulation.
Advertising and marketing of homeopathic products and services must conform to established standards of accuracy and clarity. Promotional claims for efficacy, safety and quality should not be made without demonstrable and reproducible evidence.
It will be interesting to see if these recommendations will have repercussions for regulatory authorities. The US Federal Drug Administration (FDA) has recently signalled that homeopathic drugs will come under closer scrutiny .