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\"An award-winning mathematician shows how we prove what's true, and what to do when we can't. How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods-logical, empirical, intuitive, and more-to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth. As mathematician Adam Kucharski shows, however, there is far more to proof than axioms, theories, and laws: when demonstrating that a new medical treatment works, persuading a jury of someone's guilt, or deciding whether you trust a self-driving car, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty-and never more so than when existing methods fail. Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof-and, just as importantly, of how to go forward when supposed facts falter\"-- Provided by publisher.

Theories occupy different positions in the scientific circle of enquiry as they vary in scope, abstraction, and complexity. Mid-range theories play a crucial bridging role between raw empirical observations and all-encompassing grand-theoretical schemes. A shift of perspective from ‘theories’ as products to ‘theorising’ as a process can enable empirical researchers to capitalise on the two-way relationships between empirical data and different levels of theory and contribute to the advancement of knowledge. This can be facilitated by embracing theoretically informative (in addition to merely theoretically informed) research, developing mechanism-based explanations, and broadening the repertoire of grand-theoretical orientations.

First, I discuss the older \"theory-centered\" and the more recent semantic conception of scientific theories. I argue that these two perspectives are nothing more than terminological variants of one another. I then offer a new theory-centered view of scientific theories. I argue that this new view captures the insights had by each of these earlier views, that it's closer to how scientists think about their own theories, and that it better accommodates the phenomenon of inconsistent scientific theories.

Background Theories provide a synthesizing architecture for implementation science. The underuse, superficial use, and misuse of theories pose a substantial scientific challenge for implementation science and may relate to challenges in selecting from the many theories in the field. Implementation scientists may benefit from guidance for selecting a theory for a specific study or project. Understanding how implementation scientists select theories will help inform efforts to develop such guidance. Our objective was to identify which theories implementation scientists use, how they use theories, and the criteria used to select theories. Methods We identified initial lists of uses and criteria for selecting implementation theories based on seminal articles and an iterative consensus process. We incorporated these lists into a self-administered survey for completion by self-identified implementation scientists. We recruited potential respondents at the 8th Annual Conference on the Science of Dissemination and Implementation in Health and via several international email lists. We used frequencies and percentages to report results. Results Two hundred twenty-three implementation scientists from 12 countries responded to the survey. They reported using more than 100 different theories spanning several disciplines. Respondents reported using theories primarily to identify implementation determinants, inform data collection, enhance conceptual clarity, and guide implementation planning. Of the 19 criteria presented in the survey, the criteria used by the most respondents to select theory included analytic level (58%), logical consistency/plausibility (56%), empirical support (53%), and description of a change process (54%). The criteria used by the fewest respondents included fecundity (10%), uniqueness (12%), and falsifiability (15%). Conclusions Implementation scientists use a large number of criteria to select theories, but there is little consensus on which are most important. Our results suggest that the selection of implementation theories is often haphazard or driven by convenience or prior exposure. Variation in approaches to selecting theory warn against prescriptive guidance for theory selection. Instead, implementation scientists may benefit from considering the criteria that we propose in this paper and using them to justify their theory selection. Future research should seek to refine the criteria for theory selection to promote more consistent and appropriate use of theory in implementation science.

Background A proliferation of theories, models, and frameworks (TMFs) have been developed in the implementation science field to facilitate the implementation process. The basic features of these TMFs have been identified by several reviews. However, systematic appraisals on the quality of these TMFs are inadequate. To fill this gap, this study aimed to assess the usability, applicability, and testability of the current TMFs in a structured way. Methods A scoping review method was employed. Electronic databases were searched to locate English and Chinese articles published between January 2000 and April 2022. Search terms were specific to implementation science. Additionally, hand searches were administered to identify articles from related reviews. Purpose and characteristics such as the type of TMF, analytical level, and observation unit were extracted. Structured appraisal criteria were adapted from Birken et al.’s Theory Comparison and Selection Tool (T-CaST) to conduct an in-depth analysis of the TMFs’ usability, applicability, and testability. Results A total of 143 TMFs were included in this analysis. Among them, the most common purpose was to identify barriers and facilitators. Most TMFs applied the descriptive method to summarize the included constructs or the prescriptive method to propose courses of implementation actions. TMFs were mainly mid-range theories built on existing conceptual frameworks or demonstrated grand theories. The usability of the TMFs needs to be improved in terms of the provision of conceptually matched strategies to barriers and facilitators and instructions on the TMFs usage. Regarding the applicability, little attention was paid to the constructs of macro-level context, stages of scale-up and sustainability, and implementation outcomes like feasibility, cost, and penetration. Also, fewer TMFs could propose recommended research and measurement methods to apply the TMFs. Lastly, explicit hypotheses or propositions were lacking in most of the TMFs, and empirical evidence was lacking to support the claimed mechanisms between framework elements in testability. Conclusions Common limitations were found in the usability, application, and testability of the current TMFs. The findings of this review could provide insights for developers of TMFs for future theoretical advancements.

[...]good theory must make sense, or at least acknowledge its contradictions. (The general consensus is that these studies did not establish the presence of extrasensory perception in college students, but the prevalence of overly flexible statistics; Bem defends the statistics as sound.) The work flouted well-supported ideas about physics and causality. Because the researchers required their results to be consistent with a broad theoretical framework, they probed deeper and discovered that their finding stemmed from a loose fibre-optic cable.

We start with a methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schrödinger (and reviews of D’Agostino). Following Helmholtz, Hertz established the “Bild conception” for scientific theories. Here, “Bild” (“picture”) carries the meaning “model” (mathematical). The main aim of natural sciences is construction of the causal theoretical models (CTMs) of natural phenomena. Hertz claimed that a CTM cannot be designed solely on the basis of observational data; it typically contains hidden quantities. Experimental data can be described by an observational model (OM), often based on the price of acausality. CTM-OM interrelation can be tricky. Schrödinger used the Bild concept to create a CTM for quantum mechanics (QM), and QM was treated as OM. We follow him and suggest a special CTM for QM, so-called prequantum classical statistical field theory (PCSFT). QM can be considered as a PCSFT image, but not as straightforward as in Bell’s model with hidden variables. The common interpretation of the violation of the Bell inequality is criticized from the perspective of the two-level structuring of scientific theories. Such critical analysis of von Neumann and Bell no-go theorems for hidden variables was performed already by De Broglie (and Lochak) in the 1970s. The Bild approach is applied to the two-level CTM-OM modeling of Brownian motion: the overdamped regime corresponds to OM. In classical mechanics, CTM=OM; on the one hand, this is very convenient; on the other hand, this exceptional coincidence blurred the general CTM-OM structuring of scientific theories. We briefly discuss ontic–epistemic structuring of scientific theories (Primas–Atmanspacher) and its relation to the Bild concept. Interestingly, Atmanspacher as well as Hertz claim that even classical physical theories should be presented on the basic of two-level structuring.

Science plays a central role in propelling social progress and evolution as it serves as a source of knowledge that catalysts innovation and fosters critical thinking. In this essay, the author expounds some reflections that aim to elucidate the nature of scientific knowledge and the limits of what we can comprehend about the physical world. Historically, one of the key questions in the philosophy of science has been whether or not we can truly comprehend everything about the physical world. This enquiry delves into the very essence of scientific knowledge. While scientific discovery is typically the result of planned causal research, historical exceptions to this rule exist. In our pursuit of knowledge, it is essential to differentiate between ‘truth’ and ‘reality’. Ultimately, the historical perspective highlights the importance of ongoing critical reflection and debate within the philosophical theory of human knowledge.