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We have seen that [[The logic of classical language|classical logic]] alone is insufficient to determine accurate diagnoses; hence, a conceptual and formal overview is given on why probability can be very useful. Providing illustrations of instances of clinical cases, we will see how the logic of probabilistic language is able to provide us a differential diagnosis in a ‘good enough’ way.  

We have seen that [[The logic of classical language|classical logic]] alone is insufficient to determine accurate diagnoses; hence, a conceptual and formal overview is given on why probability can be very useful. Providing illustrations of instances of clinical cases, we will see how the logic of probabilistic language is able to provide us a differential diagnosis in a ‘good enough’ way.  

The conclusion is that it is possible to demonstrate that even with the addition of probabilistic reasoning alone, it is not possible to determine exact diagnoses, and, so, other enrichments are being sought for our language.  {{ArtBy|

The conclusion is that it is possible to demonstrate that even with the addition of probabilistic reasoning alone, it is not possible to determine exact diagnoses, and, so, other enrichments are being sought for our language.   

 

{{ArtBy|

| autore = Gianni Frisardi

| autore = Gianni Frisardi

| autore2 = Riccardo Azzali

| autore2 = Riccardo Azzali

Every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties. Mathematics—through probability theory and statistical inference—helps precisely control and thereby contain these uncertainties. It must always be considered that in all practical cases, ‘the outcomes also depend on many other factors external to the theory’, whether they be initial and environmental conditions, experimental errors, or something else.  

Every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties. Mathematics—through probability theory and statistical inference—helps precisely control and thereby contain these uncertainties. It must always be considered that in all practical cases, ‘the outcomes also depend on many other factors external to the theory’, whether they be initial and environmental conditions, experimental errors, or something else.  

All the uncertainties about these factors make the theory–observation relationship a probabilistic one. In the medical approach, there are two types of uncertainty that weigh the most on diagnoses: subjective uncertainty and casuality.<ref>Eduardo Vázquez-Delgado, Jordi Cascos-Romero, Cosme Gay-Escoda. [https://pubmed.ncbi.nlm.nih.gov/20173729/ Myofascial pain associated to trigger points: a literature review. Part 2: differential diagnosis and treatment.] Med Oral Patol Oral Cir Bucal. 2010 Jul 1;15(4):e639-43. doi: 10.4317/medoral.15.e639.</ref><ref>Jaisri Thoppay, Bhavik Desai. [https://pubmed.ncbi.nlm.nih.gov/30984309/ Oral burning: local and systemic connection for a patient-centric approach.]EPMA J. 2019 Jan 14;10(1):1-11. doi: 10.1007/s13167-018-0157-3</ref>

All the uncertainties about these factors make the theory–observation relationship a probabilistic one. In the medical approach, there are two types of uncertainty that weigh the most on diagnoses: subjective uncertainty and casuality.<ref>{{Cite book

| autore = Vázquez-Delgado E

| autore2 = Cascos-Romero J

| autore3 = Gay-Escoda C

| titolo = Myofascial pain associated to trigger points: a literature review. Part 2: differential diagnosis and treatment

| url = http://www.medicinaoral.com/pubmed/medoralv15_i4_pe639.pdf

| opera = Med Oral Patol Oral Cir Bucal

| DOI = 10.4317/medoral.15.e639

}}</ref><ref>{{Cite book

| autore = Thoppay J

| autore2 = Desai B

| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6459460/

| opera = EPMA J

| anno = 2019

| DOI = 10.1007/s13167-018-0157-3

}}</ref>

It becomes essential, therefore, in this scenario to distinguish between these two uncertainties and to show that the concept of probability has different meanings in these two contexts. We will try to expose these concepts by linking each crucial step to the clinical approach that has been reported in the previous chapters and in particular the approach in the dental and neurological context in contending for the primacy of the diagnosis for our sympathetic Mary Poppins.

It becomes essential, therefore, in this scenario to distinguish between these two uncertainties and to show that the concept of probability has different meanings in these two contexts. We will try to expose these concepts by linking each crucial step to the clinical approach that has been reported in the previous chapters and in particular the approach in the dental and neurological context in contending for the primacy of the diagnosis for our sympathetic Mary Poppins.

==Subjective and objective probability==

==Subjective and objective probability==

In this chapter, some topics already treated in the fantastic 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|volume=|opera=|anno=2012|editore=Springer|città=Dordrecht|ISBN=978-94-007-2259-0|LCCN=|DOI=10.1007/978-94-007-2260-6|OCLC=}}.</ref> which tackles the problem of the logic of medical language are taken up again and we reshape their content by referring them to our clinical case of Mary Poppins for an understanding more in keeping with dental contexts.

In this chapter, some topics already treated in the fantastic 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

|volume=

|opera=

|anno=2012

|editore=Springer

|città=Dordrecht

|ISBN=978-94-007-2259-0

|LCCN=

|DOI=10.1007/978-94-007-2260-6

|OCLC=

}}.</ref> which tackles the problem of the logic of medical language are taken up again and we reshape their content by referring them to our clinical case of Mary Poppins for an understanding more in keeping with dental contexts.

Random and subjectively uncertain events are said to be probable and consequently, casuality and uncertainty are treated as qualitative, comparative or quantitative probabilities.

Random and subjectively uncertain events are said to be probable and consequently, casuality and uncertainty are treated as qualitative, comparative or quantitative probabilities.

==Probabilistic-causal analysis==

==Probabilistic-causal analysis==

From these premises it is clear that the clinical diagnosis is made using the so-called hypothetical-deductive method referred to as DN<ref name=":1">Sahotra Sarkar. [https://pubmed.ncbi.nlm.nih.gov/26386529/ Nagel on Reduction]. Stud Hist Philos Sci. 2015 Oct;53:43-56.doi: 10.1016/j.shpsa.2015.05.006. Epub 2015 Jun 29.</ref> ([https://it.wikipedia.org/wiki/Modello_nomologico-deduttivo modello nomologico-deduttivo]). But this is not realistic since the medical knowledge used in clinical decision-making hardly contains causal deterministic laws to allow causal explanations and, hence, to formulate clinical diagnoses among other things in the specialist context. Let us try to analyse again the case of our Mary Poppins, this time trying a probabilistic-causal approach.

From these premises it is clear that the clinical diagnosis is made using the so-called hypothetical-deductive method referred to as DN<ref name=":1">{{Cite book

| autore = Sarkar S

| url = https://pubmed.ncbi.nlm.nih.gov/26386529/

| opera = Stud Hist Philos Sci

| anno = 2015

| DOI = 10.1016/j.shpsa.2015.05.006  

}}</ref> ([https://en.wikipedia.org/wiki/Deductive-nomological_model deductive-nomological model]<ref>''DN model of scientific explanation'', also known as ''Hempel's model'', the ''Hempel–Oppenheim model'', the ''Popper–Hempel model'', or the ''covering law model''</ref>). But this is not realistic since the medical knowledge used in clinical decision-making hardly contains causal deterministic laws to allow causal explanations and, hence, to formulate clinical diagnoses among other things in the specialist context. Let us try to analyse again the case of our Mary Poppins, this time trying a probabilistic-causal approach.

Let us consider a number <math>n</math> of individuals including people who report Orofacial Pain who generally have bone degeneration of the Temporomandibular Joint. However, there may also be other apparently unrelated causes. We must mathematically translate the 'relevance' that these causal uncertainties have in determining a diagnosis.

Let us consider a number <math>n</math> of individuals including people who report Orofacial Pain who generally have bone degeneration of the Temporomandibular Joint. However, there may also be other apparently unrelated causes. We must mathematically translate the 'relevance' that these causal uncertainties have in determining a diagnosis.