Changes

<translate>The dentist believes that Mary Poppins' claim (that she does not have TMD under these premises) is a contradiction so the main claim is true</translate>.

<translate>The dentist believes that Mary Poppins' claim (that she does not have TMD under these premises) is a contradiction so the main claim is true</translate>.

===Neurophysiological proposition===

===<translate>Neurophysiological proposition</translate>===

Let us imagine that the neurologist disagrees with the conclusion <math>(1)</math> and asserts that Mary Poppins is not affected by TMDs or that at least it is not the main cause of Orofacial Pain but that she is affected by a neuromotor Orofacial Pain (_nOP), therefore that she does not belong to the group of 'normal patients' but is to be considered a 'non-specific patient' (uncommon in the specialist context).

<translate>Let us imagine that the neurologist disagrees with the conclusion</translate> <math>(1)</math> <translate>and</translate> <translate>asserts that Mary Poppins is not affected by TMDs or that at least it is not the main cause of Orofacial Pain, but that, rather, she is affected by a neuromotor Orofacial Pain</translate> (_nOP), <translate>therefore that she does not belong to the group of 'normal patients' but is to be considered a 'non-specific patient' (uncommon in the specialist context)</translate>.

Obviously this dialectic would last indefinitely because both would defend their scientific-clinical context but let us see what happens in the logic of predicates.

<translate>Obviously, this dialectic would last indefinitely because both would defend their scientific-clinical context; but let us see what happens in the logic of predicates</translate>.

The neurologist's statement would be like this:

<translate>The neurologist's statement would be like</translate>:

<math>\{a \not\in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \and A( a)\rightarrow \urcorner B(a) \}</math>.                                       <math>(3)</math>

<math>\{a \not\in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \and A( a)\rightarrow \urcorner B(a) \}</math>. <math>(3)</math>

The assumption <math>(3)</math> means that every patient who is TMJ CT positive has TMDs but even though Mary Poppins is TMJ CT positive, she does not have TMDs.

"<math>(3)</math>" <translate>means that every patient who is TMJ CT positive has TMDs but even though Mary Poppins is TMJ CT positive, she does not have TMDs</translate>.

In order to prove that this proposition is true, we must use the <u>demonstration by absurdity</u> mentioned above. If its denial creates a contradiction, surely the neurologist's proposition will be true:

<translate>In order to prove that this proposition is true, we must use once again the above mentioned</translate> <u><translate>demonstration by absurdity</translate></u>. <translate>If its denial creates a contradiction, surely the neurologist's proposition will be true</translate>:

<math>\urcorner\{a \not\in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \and A( a)\rightarrow \urcorner B(a) \}</math>.                               <math>(4)</math>

<math>\urcorner\{a \not\in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \and A( a)\rightarrow \urcorner B(a) \}</math>. <math>(4)</math>

{{q4|<translate>then the dentist triumphs</translate>!|<translate>don't take it for granted</translate>}}

 

{{q4|then the dentist triumphs!|it's not for sure}}

===Compatibility and incompatibility of the statements===

===Compatibility and incompatibility of the statements===