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[[File:Spasmo_emimasticatorio_JJ.jpg|alt=|left|250x250px]]

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In this chapter, we will discuss the logic of language coupled with mathematical probability. 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, so other enrichments are being sought for our language.  

<translate>In this chapter, we will discuss the logic of language coupled with mathematical probability</translate>. <translate>We have seen that [[The logic of classical language|classical logic]] alone is insufficient to determine accurate diagnoses</translate>; <translate>hence, a conceptual and formal overview is given on why probability can be very useful</translate>. <translate>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</translate>.  

 

<translate>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, so other enrichments are being sought for our language</translate>.  

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==Probabilistic language logic in medicine==

==<translate>Probabilistic language logic in medicine</translate>==

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 to 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.  

<translate>Every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties</translate>. <translate>Mathematics - through probability theory and statistical inference - helps to precisely control and thereby contain these uncertainties</translate>. <translate>It always has to 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</translate>.  

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  

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

  | autore = Vázquez-Delgado E

  | autore = Vázquez-Delgado E

  | autore2 = Cascos-Romero J

  | autore2 = Cascos-Romero J

  }}</ref>

  }}</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.  

<translate>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</translate>.  

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 dear Mary Poppins.

<translate>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 dear Mary Poppins</translate>.

==Subjective uncertainty and casuality==

==<translate>Subjective uncertainty and casuality</translate>==

Let us imagine asking Mary Poppins which of the two medical colleagues — the dentist or the neurologist — is right.  

<translate>Let us imagine asking Mary Poppins which of the two medical colleagues — the dentist or the neurologist — is right</translate>.  

The question would create a kind of agitation based on inner uncertainty; therefore, the notions of certainty and uncertainty refer to 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 a world outside ourselves that both do not respond to canons of uncertainty, yet of probability.  

<translate>The question would create a kind of agitation based on inner uncertainty; therefore, the notions of certainty and uncertainty refer to 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 a world outside ourselves that both do not respond to canons of uncertainty, yet of probability.</translate>

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 because "uncertainty" is a subjective, epistemic state below the threshold of knowledge and belief; hence the term.  

<translate>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 because "uncertainty" is a subjective, epistemic state below the threshold of knowledge and belief; hence the term</translate>.  

====Subjective uncertainty====

====<translate>Subjective uncertainty</translate>====

Without a doubt the term ‘subjective’ scares many, especially those who intend to practice science by pursuing the healthy ideal of ‘objectivity’, as this term is perceived by common sense. It is, therefore, appropriate to make some clarifications on the use of this term in this context:   

<translate>Without a doubt the term ‘subjective’ scares many, especially those who intend to practice science by pursuing the healthy ideal of ‘objectivity’, as this term is perceived by common sense. It is, therefore, appropriate to make some clarifications on the use of this term in this context</translate>:   

*‘Subjective’ indicates that the probability assessment depends on the information status of the individual who performs it.

*‘<translate>Subjective</translate>’ <translate>indicates that the probability assessment depends on the information status of the individual who performs it</translate>.

*‘Subjective’ does not mean arbitrary.

*‘<translate>Subjective</translate>’ <translate>does not mean arbitrary</translate>.

The so-called ‘objectivity’, as perceived by those outside scientific research, is defined when a community of rational beings shares the same state of information. But even in this case, one should speak more properly of ‘intersubjectivity’ (i.e. the sharing, by a group, of subjective opinions).  

<translate>The so-called ‘objectivity’, as perceived by those outside scientific research, is defined when a community of rational beings shares the same state of information. But even in this case, one should speak more properly of ‘intersubjectivity’ (i.e. the sharing, by a group, of subjective opinions). </translate>

In clinical cases — precisely because patients rarely possess advanced notions of medicine — subjective uncertainty must be considered. Living with uncertainty requires us to use a probabilistic approach.

<translate>In clinical cases — precisely because patients rarely possess advanced notions of medicine — subjective uncertainty must be considered. Living with uncertainty requires us to use a probabilistic approach</translate>.

======Casuality======

======<translate>Casuality</translate>======

The casuality 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 adverse problems in determining a diagnosis.  

<translate>The casuality 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 adverse problems in determining a diagnosis.</translate>

In a clinical case a phenomenon <math>A(x)</math> (such as for example 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> it's 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.

<translate>In a clinical case a phenomenon <math>A(x)</math> (such as for example a malocclusion, a crossbite, an openbite, etc ...) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration)</translate>; <translate>when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> it's 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</translate>.

{{q2|We are moving from a deterministic condition to a stochastic one.|}}

{{q2|<translate>We are moving from a deterministic condition to a stochastic one</translate>.|}}

==Subjective and objective probability==

==<translate>Subjective and objective probability</translate>==

In this chapter, some topics already treated in the fantastic book by Kazem Sadegh-Zadeh<ref>{{cita libro

In this chapter, some topics already treated in the fantastic book by Kazem Sadegh-Zadeh<ref>{{cita libro