Difference between revisions of "La lógica del lenguaje clásico"

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La lógica clásica será discutida en este capítulo. En la primera parte se ilustrará el formalismo matemático y las reglas que lo componen. En la segunda parte, se dará un ejemplo clínico para evaluar su eficacia en la determinación de un diagnóstico.  

En conclusión, es evidente que una lógica clásica del lenguaje, que tiene un enfoque extremadamente dicotómico (o algo es blanco, o es negro), no puede describir los múltiples matices que tienen las situaciones clínicas reales.

Como pronto veremos, este artículo mostrará que la lógica clásica carece de la precisión necesaria, obligándonos a mejorarla con otro tipo de lenguajes lógicos.{{ArtBy|

==Introduction==

We parted ways in the previous chapter on the ‘[[The logic of medical language|Logic of Medical Language]]’ in an attempt to shift the attention from clinical symptom or sign to encrypted machine language for which, the arguments of Donald E Stanley, Daniel G Campos and Pat Croskerry are welcome but connected to time <math>t_n</math> as an information carrier (anticipation of the symptom) and to the message as a machine language and not as a non-verbal language).<ref>{{Cite book  

  }}</ref><br>Obviously, this does not preclude the validity of the clinical history built on a pseudo-formal verbal language by now well rooted in the clinical reality and which has already proved its diagnostic authority. The attempt to shift attention to a machine language and to the System provides nothing but an opportunity for the validation of Diagnostic Medical Science.

We are definitely aware that our Linux Sapiens is still perplexed about what has been anticipated and continues to wonder{{q4|... <!--11-->but... <!--12-->could the logic of Classical Language help us to solve poor Mary Poppins' dilemma?|<!--13-->a little patience, please}}

We cannot provide a conventional answer because science does not progress with assertions that are not justified by scientifically validated questions and reflections; and this is actually the reason why we will try to give voice to some thoughts, perplexities and doubts expressed on some basic topics brought into discussion in some scientific articles.

One of these fundamental topics is 'Craniofacial Biology'.

Let's start with a well known study by Townsend and Brook<ref name=":0">{{Cite book  

  }}</ref>: in this work the authors question the status quo of both fundamental and applied research in 'Craniofacial Biology' to extract clinical considerations and implications. One topic they covered was the "Interdisciplinary Approach", in which Geoffrey Sperber and his son Steven saw the strength of the exponential progress of 'Craniofacial Biology' in technological innovations such as gene sequencing, CT scanning, MRI imaging, scanning laser, image analysis, ultrasonography and spectroscopy<ref>{{Cite book  

Another topic of great interest for the implementation of 'Craniofacial Biology' is the awareness that biological systems are 'Complex Systems'<ref>{{Cite book  

  }}</ref> and that 'Epigenetics' plays a key role in craniofacial molecular biology. Researchers from Adelaide and Sydney provide a critical review in the field of epigenetics aimed, in fact, at the dental and craniofacial disciplines.<ref>{{Cite book  

  }}</ref> Phenomics, in particular, discussed by these authors (see [[wikipedia:Phenomics|Phenomics]])) is a general research field that involves the measurement of changes in the teeth and associated orofacial structures resulting from the interactions between genetic, epigenetic and environmental factors during development.<ref>{{Cite book  

  }}</ref> In this same context, the work of Irma Thesleff from Helsinki, Finland, should be highlighted. She explains in her work that there are a series of transient signalling centres in the dental epithelium that play important roles in the programme of tooth development.<ref>{{Cite book  

  }}</ref> Besides there are other works, by Peterkova R, Hovor akova M, Peterka M, Lesot H, providing a fascinating review of the processes that occur during dental development;<ref>{{Cite book  

  }}</ref> for the sake of completeness, let's not forget the works by Han J, Menicanin D, Gronthos S, and  Bartold PM., who review comprehensive documentation on stem cells, tissue engineering and periodontal regeneration.<ref>{{Cite book  

In this review, arguments could not be missing on genetic, epigenetic and environmental influences during morphogenesis that lead to variations in the number, size and shape of the tooth<ref>{{Cite book  

  }}</ref> and the influence of tongue pressure on growth and craniofacial function.<ref>{{Cite book  

  }}</ref>Townsend and Brook's extraordinary work too deserves a mention<ref name=":0" />, and the intrinsic content of what has been reported in it matches equally well with another commendable author: HC Slavkin.<ref>{{Cite book  

  }}</ref> Slavkin asserts that:

:"''The future is full of significant opportunities to improve the clinical outcomes of congenital and acquired craniofacial malformations. Clinicians play a key role as critical thinking and clinical audience substantially improve diagnostic accuracy and therefore clinical health outcomes''."

{{q4|... <!--35-->I understand the progress of Science described by the authors but I don't understand the change of thought|<!--36-->I'll give you a practical example}}

In the chapter "[[Introduction]]" we  posed certain questions on the subject of malocclusion but in this context we simulate the dentist's logic of medical language when faced with the clinical case presented in the "Introduction chapter" with its diagnostic and therapeutic conclusions.

The patient has a posterior unilateral crossbite and an anterior openbite.<ref>

}}</ref> The crossbite is another disturbing element of the normal occlusion<ref>{{cita libro

}}</ref> for which it is compulsorily treated together with the openbite.<ref>{{cita libro

}}</ref> This type of reasoning means that the model (masticatory system) is 'normalized to occlusion'; and read in reverse, it means that the occlusal discrepancy is the cause of malocclusion, hence, a disease of the Masticatory System, and therefore an intervention to restore the physiological masticatory function is justifiable. (Figure 1a).

This example is Classical Logic Language, as we are going to explain in detail, but now a doubt arises:

:At the time when orthodontic and orthognathics axioms were constructing protocols confirmed by the International Scientific Community, were they aware of the information we discussed in the introduction to this chapter?

Certainly not because time '''<math>t_n</math> is the bearer of information''' but despite this cognitive limit we proceed with a very questionable Classical Language Logic for the safety of the citizen.{{q2|... <!--46-->this statement seems a bit risky!|<!--47-->sure, but the logical sequence has already been anticipated}}

If the same case were interpreted with a mindset that followed a 'System's language logic' (it will be discussed in the appropriate chapter), the conclusions would be surprising.

If we observe the electrophysiological responses performed on the patient with malocclusion in figures 1b, 1c and 1d (with the explanation made directly in the caption to simplify the discussion), we shall notice that these data can make us think about anything except a 'Malocclusion' and, therefore, the axioms of type orthodontic and orthognathics 'cause/effect' leave a conceptual void.<gallery widths="350" heights="282" perrow="2" mode="slideshow">

File:Occlusal Centric view in open and cross bite patient.jpg|'''Figure 1a:''' Patient with malocclusion, open bite and right posterior crossbite who in rehabilitation terms must be treated with orthodontic therapy and / or orthognathic surgery

File:Bilateral Electric Transcranial Stimulation.jpg|'''<!--52-->Figure 1b:''' <!--53-->Motor evoked potential from electrical transcranial stimulation of the trigeminal roots.Note the structural symmetry calculated by the peak-to-peak amplitude on the left and right masseters (traces upper and lower respectively)

File:Jaw Jerk .jpg|'''<!--54-->Figure 1c:''' <!--55-->Mandibular reflex evoked or jaw jerk by percussion of the chin through a triggered neurological hammer. Note the functional symmetry calculated by the peak-to-peak amplitude on the left and right masseters (traces upper and lower respectively)

File:Mechanic Silent Period.jpg|'''<!--56-->Figure 1d:''' <!--57-->Mechanical silent period evoked by percussion of the chin through a triggered neurological hammer. Note the functional symmetry calculated on the integral area of the right and left masseters (traces upper and lower respectively).

{{q4|<!--58-->Let me better understand what Classical Language Logic has to do with it|<!--59-->We will do it following the clinical case of our Mary Poppins}}

==Mathematical formalism==

In this chapter, we will reconsider the clinical case of the unfortunate Mary Poppins suffering from Orofacial Pain for more than 10 years to which her dentist diagnosed a 'Temporomandibular Disorders' (TMDs) or rather Orofacial Pain from TMDs. To better understand why the exact diagnostic formulation remains complex with a Logic of Classical Language, we should understand the concept on which the philosophy of classical language is based with a brief introduction to the topic.

===Propositions===

Classical logic is based on propositions. It is often said that a proposition is a sentence that asks whether the proposition is true or false. Indeed, a proposition in mathematics is usually either true or false, but this is obviously a little too vague to be a definition. It can be taken, at best, as a warning: if a sentence, expressed in common language, makes no sense to ask whether it is true or false, it will not be a proposition but something else.

It can be argued whether or not common language sentences are propositions as in many cases it is not often evident if a certain statement is true or false.

''Fortunately, mathematical propositions, if well expressed, do not show such ambiguities’.''

Simpler propositions can be combined with each other to form new, more complex propositions. This occurs with the help of operators called ''logical operators'' and quantifying connectives which can be reduced to the following<ref><!--68-->For the sake of simplicity of exposition and reading, we will deal in this chapter with the ''symbol of belonging'', the ''symbol of consequence'' and the "''such that''" as if they were quantifiers and connectives of propositions in classical logic.<br><!--69-->Strictly speaking, within classical logic they should not be treated as such, but even if we do, this does not absolutely change the meaning of the speech and no inconsistencies of any kind are created.</ref>:

#''Conjunction'', which is indicated by the symbol <math>\land</math>  (and):

#''Disjunction'', which is indicated by the symbol <math>\lor</math> (or):

#''Negation'', which is indicated by the symbol <math>\urcorner</math>  (not):

#''Implication'', which is indicated by the symbol <math>\Rightarrow</math> (if ... then):

#''Consequence'', which is indicated by the symbol <math>\vdash</math> (is a partition of..):

#''Universal quantifier'', which is indicated by the symbol <math>\forall</math> (for all):

#''Demonstration'', which is indicated by the symbol <math>\mid</math> (such that): and

#''Membership'', which is indicated by the symbol <math>\in</math> (is an element of) or by the symbol <math>\not\in</math> (is not an element of):

===Demonstration by absurdity===

Furthermore, in classical logic there is a principle called the <u>excluded third</u> which declares that a sentence that cannot be false must be taken as true since there is no third possibility.

Suppose we need to prove that the proposition <math>p</math> is true. The procedure consists in showing that the assumption that <math>p</math> is false leads to a logical contradiction. Thus the proposition <math>p</math> cannot be false, and therefore, according to the law of the excluded third, it must be true. This method of demonstration is called ''demonstration by absurdity''<ref>{{Cite book  

===Predicates===

What we have briefly described so far is the logic of propositions. A proposition asserts something about specific mathematical objects such as: '2 is greater than 1, so 1 is less than 2' or 'a square has no 5 sides then a square is not a pentagon'. Many times, however, the mathematical statements concern not the single object, but generic objects of a set such as: '''<math>X</math>'' are taller than 2 meters' where ''<math>X</math>'' denotes a generic group (for example all volleyball players). In this case we speak of predicates.

Intuitively, a predicate is a sentence concerning a group of elements (which in our medical case will be the patients) and which states something about them.{{q4|<!--99-->Then poor Mary Poppins is a TMD patient or she is not!|<!--100-->let's see what Classical Language Logic tells us}}

In addition to the confirmations derived from the logic of medical language discussed in the previous chapter, the dentist colleague acquires other instrumental data that allow him to confirm his diagnosis. The latter tests concern the analysis of the axiographic traces by using a customized functional paraocclusal clutch which allow the visualization and quantification of the condylar traces in masticatory functions. As can be seen from Figure 4 the flattening of the condylar traces on the right side both in the mediotrusive masticatory kinetics (green colour) and the opening and protrusion cycles (gray colour) confirm the anatomical and functional flattening of the right TMJ in the dynamics chewing. In addition to the axiography, the colleague performs a surface electromyography on the masseters (Fig. 6) asking the patient to exert  the maximum of his muscles force. This type of electromyographic analysis is called "EMG Interferential Pattern" due to the high frequency content of the spikes that undergo phase interference. In fact, Figure 6 shows an asymmetry in the recruitment of the motor units of the right masseter (upper trace) compared to those of the left masseter (lower trace).<ref>{{cite book