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== Abstract ==
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The text deals with the logic of probabilistic language applied to the medical field, highlighting how uncertainty is an intrinsic part of scientific practice. Through probabilistic and statistical concepts, efforts are made to manage and understand the uncertainties associated with medical theory and practice.
The role of probability in the relationship between theory and observation is emphasized, distinguishing between subjective uncertainty and randomness. Subjective uncertainty concerns individuals' state of knowledge and belief, while randomness refers to the lack of a certain connection between cause and effect.
In the medical approach, the importance of understanding and distinguishing between subjective and objective probability is discussed. Subjective probability reflects individual belief, while objective probability is based on data and empirical evidence.
The concept of probabilistic-causal analysis is then further explored, which seeks to quantify the relationship between events and random processes in clinical diagnosis. A detailed exposition is presented on how conditional probabilities can be interpreted and how causal relevance partitioning can be used to formulate a differential diagnosis.
Finally, the theme of interdisciplinarity in scientific research is addressed, highlighting the importance of an interdisciplinary approach to tackling complex problems. Fuzzy logic is also mentioned as a possible tool for managing uncertainty in medical contexts.


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| autore2 = Riccardo Azzali
| autore2 = Riccardo Azzali
| autore3 = Flavio Frisardi
| autore3 = Flavio Frisardi
}}
}}Every scientific idea—whether in medicine, architecture, engineering, chemistry, or any other field—when implemented, is prone to small errors and uncertainties. Mathematics, through the lens of probability theory and statistical inference, aids in precisely managing and thereby mitigating these uncertainties. It must always be considered that in all practical scenarios, "the outcomes also depend on many other external factors to the theory," be they initial and environmental conditions, experimental errors, or others.


== Abstract ==
The uncertainties surrounding these factors render the theory-observation relationship probabilistic. In medical practice, two types of uncertainty predominantly impact diagnoses: subjective uncertainty and causality.<ref>{{Cite book | autore = Vázquez-Delgado E | autore2 = Cascos-Romero J | autore3 = Gay-Escoda C | titolo = Myofascial pain associated with trigger points: a literature review. Part 2: Differential diagnosis and treatment | url = http://www.medicinaoral.com/pubmed/medoralv15_i4_pe639.pdf | volume = | opera = Med Oral Patol Oral Cir Bucal | anno = 2007 | editore = | città = | ISBN = | PMID = 20173729 | PMCID = | DOI = 10.4317/medoral.15.e639 | oaf = <!-- any value --> | LCCN = | OCLC = }}</ref><ref>{{Cite book | autore = Thoppay J | autore2 = Desai B | titolo = Oral burning: local and systemic connection for a patient-centric approach | url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6459460/ | volume = | opera = EPMA J | anno = 2019 | editore = | città = | ISBN = | PMID = 30984309 | PMCID = PMC6459460 | DOI = 10.1007/s13167-018-0157-3 | oaf = <!-- any value --> | LCCN = | OCLC = }}</ref> Therefore, in this context, it becomes crucial to differentiate between these two uncertainties and to demonstrate that the concept of probability assumes different meanings in these contexts. We will endeavor to elucidate these concepts by connecting each critical step to the clinical approach that has been documented in previous chapters, particularly focusing on the dental and neurological domains in vying for diagnostic supremacy for our dear Mary Poppins.
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==Subjective Uncertainty and Causality==
Let's imagine asking Mary Poppins which of the two medical colleagues—the dentist or the neurologist—is correct.
 
The question would generate a kind of agitation based on internal uncertainty; therefore, the notions of certainty and uncertainty refer to the subjective epistemic states of human beings, and not to states of the external world, because there is no certainty or uncertainty in that world. In this sense, as we have mentioned, there are an inner world and an external world that both do not adhere to canons of uncertainty, but rather to probability.
 
Mary Poppins may be subjectively certain or uncertain as to whether she is suffering from TMDs or a neuropathic or neuromuscular form of OP. This is because "uncertainty" is a subjective, epistemic state below the threshold of knowledge and belief; hence the term.
====Subjective Uncertainty====
Without a doubt, the term ‘subjective’ alarms many, especially those who aim to practice science by pursuing the noble ideal of ‘objectivity,’ as this term is perceived by common sense. Therefore, it is appropriate to make some clarifications on the use of this term in this context:
 
‘Subjective’ indicates that the probability assessment depends on the information status of the individual who performs it.


The document delves into the probabilistic language in medicine, underlining how inherent uncertainties in scientific practice can be addressed using probabilistic and statistical tools. The distinction between subjective uncertainty, which pertains to individual knowledge and beliefs, and randomness, which involves unpredictability in events, is emphasized. Through various probabilistic methods, the text aims to offer a framework for understanding and managing these uncertainties in medical theories and practices.
‘Objective’ does not mean arbitrary.


== Introduction ==
The so-called ‘objectivity,’ as perceived by those outside scientific research, is achieved when a community of rational beings shares the same state of information. But even in this case, one should more properly speak of ‘intersubjectivity’ (i.e., the sharing of subjective opinions by a group).
The introductory section sets the stage for discussing the integration of probabilistic approaches into the medical field. It highlights the challenges and necessities of managing uncertainties inherent in medical diagnosis and treatment. Probabilistic methods are presented as essential tools for bridging the theoretical knowledge of medicine with practical clinical observations, thereby enhancing decision-making processes.


== The Role of Probability in Medical Practice ==
In clinical cases—precisely because patients rarely possess advanced notions of medicine—subjective uncertainty must be considered. Living with uncertainty requires us to adopt a probabilistic approach.
This segment discusses the pivotal role that probability plays in linking medical theories to clinical observations. It explains the concepts of subjective and objective probabilities, which are crucial for understanding and managing uncertainties in medical practice. Subjective probability is associated with individual beliefs and knowledge, whereas objective probability is grounded in empirical evidence and data. The application of these probabilistic models is shown to be vital for informed clinical decision-making.
======Causality ======
Causality indicates the lack of a certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most challenging problems in determining a diagnosis.


== Understanding Uncertainty in Clinical Settings ==
In a clinical case, a phenomenon <math>A(x)</math> (such as a malocclusion, a crossbite, an openbite, etc.) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration); when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> is not always true (but it is most of the time), we will say that the relation <math>A(x) \rightarrow B(x)</math> is not always true but it is probable.{{q2|<!--30-->We are moving from a deterministic condition to a stochastic one.|}}
Here, the focus shifts to the complexities of dealing with uncertainty in clinical environments. The section outlines how probabilistic reasoning helps clinicians manage both subjective uncertainties, which are tied to individual perceptions, and objective uncertainties, which relate to measurable factors. Examples from various medical scenarios illustrate how probabilistic thinking enhances diagnostic accuracy and treatment efficacy.
==Subjective and Objective Probability==
In this chapter, we revisit some topics previously discussed in the insightful book by Kazem Sadegh-Zadeh<ref>{{cita libro
|autore=Sadegh-Zadeh Kazem
|titolo=Handbook of Analytic Philosophy of Medicine
|url=https://link.springer.com/book/10.1007/978-94-007-2260-6
|anno=2012
|editore=Springer
|città=Dordrecht
|ISBN=978-94-007-2259-0
|DOI=10.1007/978-94-007-2260-6
}}</ref>, which tackles the problem of the logic of medical language. We adapt their content to our clinical case of Mary Poppins, aiming to keep our understanding more relevant to dental contexts.


== Probabilistic-Causal Analysis in Diagnostics ==
Events that are both random and subjectively uncertain are considered probable; therefore, causality and uncertainty are approached as qualitative, comparative, or quantitative probabilities.
Probabilistic-causal analysis is explored in detail, showing how it helps quantify relationships between different medical events and outcomes. This approach uses conditional probabilities and causal relevance partitioning to refine the accuracy of differential diagnoses. This methodological advancement aids clinicians in making more precise diagnostic and treatment decisions, reducing the potential for errors and improving patient outcomes.


== Interdisciplinarity and Managing Uncertainty ==
To clarify this concept, let's use the example of Mary Poppins. A doctor, after hearing her symptoms, could state that:
The importance of an interdisciplinary approach in addressing complex medical challenges is highlighted in this section. It argues for integrating insights from various scientific disciplines to enhance the understanding and treatment of complex diseases. Furthermore, the section introduces fuzzy logic as a valuable tool for handling the inherent vagueness and ambiguity in medical contexts, offering a more nuanced approach to patient care.
# Mary Poppins is probably suffering from TMDs (qualitative term).
#Mary Poppins is more likely to have TMDs than neuropathic OP (comparative term: the number of diagnosed cases of TMDs vs. neuropathic OP).
#The probability that Mary Poppins has TMDs is 0.15 (quantitative term, relative to the population).
=== Subjective Probability===
In contexts of human subjective uncertainty, probabilistic, qualitative, comparative, and/or quantitative data can be interpreted by clinicians as measures of subjective uncertainty, to make 'states of conviction' numerically representable.


== Fuzzy Logic and Its Application in Medicine ==
For instance, stating "the probability that Mary Poppins is affected by TMDs is 0.15 of the cases" is akin to saying "with a 15% degree of belief, I think that Mary Poppins is affected by TMDs"; indicating that the degree of conviction corresponds to the degree of subjective probability.
An in-depth exploration of fuzzy logic and its application within the medical field is provided. This segment describes how fuzzy logic can be used to address the uncertainties and imprecise nature of many medical conditions, facilitating better diagnostic and treatment methodologies. Examples include its use in diagnostic algorithms and treatment decision processes, where traditional binary logic fails to capture the subtleties of human health conditions.
===Objective Probability===
Conversely, events and random processes cannot be accurately described by deterministic processes in the form 'if A then B'. Statistics are utilized to quantify the frequency of the association between A and B, representing their relationship as a degree of probability, which introduces the concept of objective probability.


== Future Directions in Medical Methodology ==
Amid the increasing acknowledgment of the role of probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become an integral part of medical language, methodology, and epistemology. Unfortunately, the distinction between subjective and objective probability is not always clearly made in medicine, as is the case in other disciplines too. Nevertheless, the vital contribution of probability theory in medicine, especially in concepts of probability in etiology, epidemiology, diagnostics, and therapy, lies in its aid in understanding and representing biological causality.
The document discusses the evolving landscape of medical research and practice, advocating for a dynamic adaptation of medical methodologies to incorporate probabilistic logic and interdisciplinary insights. This section envisions a future where medical practices are continuously updated and refined in response to advancements in scientific research, ensuring that patient care remains at the forefront of technological and methodological innovations.


== Conclusion ==
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In conclusion, the text "The Logic of Probabilistic Language in Medicine" presents a robust argument for the necessity of integrating probabilistic models and interdisciplinary approaches in medical practice. It calls for a paradigm shift in how medical professionals handle uncertainty, with a move towards more nuanced and adaptable methodologies that can lead to better patient outcomes. The document envisions a future where the fusion of probabilistic reasoning, advanced technology, and collaborative scientific efforts results in a new era of precision in diagnostics and personalized patient care.
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== [[Strategic dental topics for authors to subscribe an article]] ==
== [[Strategic dental topics for authors to subscribe an article]] ==
Probabilistic Language, Medical Field, Uncertainty Management, Subjective Uncertainty, Randomness in Medicine, Objective Probability, Clinical Decision-Making, Probabilistic-Causal Analysis, Differential Diagnosis, Interdisciplinary Approach, Fuzzy Logic, Medical Diagnostics, Treatment Efficacy, Precision Medicine, Personalized Patient Care</blockquote>
Probabilistic Language, Medical Field, Uncertainty Management, Subjective Uncertainty, Randomness in Medicine, Objective Probability, Clinical Decision-Making, Probabilistic-Causal Analysis, Differential Diagnosis, Interdisciplinary Approach, Fuzzy Logic, Medical Diagnostics, Treatment Efficacy, Precision Medicine, Personalized Patient Care</blockquote>
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