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Difference between revisions of "The logic of the classical language"
The logic of the classical language (view source)
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[[File:Occlusal Centric view in open and cross bite patient.jpg|left|200x200px]] | |||
This chapter explores the complexities of medical language, particularly within the context of diagnosis and treatment of Temporomandibular Disorders (TMD) and Orofacial Pain (OP). Medical language often leads to misunderstandings due to its hybrid nature, blending everyday language with specialized terms, which can be interpreted differently across medical disciplines. This is exemplified in the clinical case of Mary Poppins, who has suffered from OP for over a decade, with conflicting diagnoses from a dentist and a neurologist. The dentist diagnosed her with TMD based on clinical tests like axiography, electromyography (EMG), and radiographic imaging, while the neurologist attributed her pain to a neuromotor disorder (nOP). | |||
The chapter examines how classical logic language, used in traditional medical diagnostics, supports the dentist's diagnosis, focusing on the compatibility of evidence like condylar remodeling and masticatory muscle activity. However, the chapter also highlights the limitations of this approach, showing that new electrophysiological data could challenge the dentist’s assumptions and open the door to different interpretations of OP’s origins. | |||
In light of this, the chapter introduces the concept of "system logic language," which moves beyond cause-and-effect models to consider the masticatory system as a complex, dynamic entity. This perspective encourages a more nuanced understanding of patient conditions, recognizing that symptoms may not always align neatly with classical diagnostic frameworks. By analyzing Mary Poppins' case through both classical and system logic, the chapter calls for a reevaluation of medical language and diagnostic approaches, proposing a shift toward probabilistic and interdisciplinary methods for more accurate diagnoses. | |||
Ultimately, this chapter suggests that a deeper understanding of medical language and logic can improve clinical decision-making, reduce diagnostic errors, and foster a more comprehensive approach to patient care. | |||
==Introduction to the Logic of Medical Language== | ==Introduction to the Logic of Medical Language== | ||
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Among these critical topics is "'''Craniofacial Biology'''". | Among these critical topics is "'''Craniofacial Biology'''". | ||
=== '''Craniofacial Biology''' === | ==='''Craniofacial Biology'''=== | ||
We begin with an influential study by Townsend and Brook, | We begin with an influential study by Townsend and Brook, | ||
<ref name=":0">{{Cite book | <ref name=":0">{{Cite book | ||
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---- | ---- | ||
{{q2|So, how does the classic language logic connect to this context? |The contrast with the "system language logic" highlights the interpretive limits of traditional approaches to malocclusion. This suggests that orthodontic models of cause/effect might need a critical review in light of new electrophysiological evidence.}} | {{q2|So, how does the classic language logic connect to this context? |The contrast with the "system language logic" highlights the interpretive limits of traditional approaches to malocclusion. This suggests that orthodontic models of cause/effect might need a critical review in light of new electrophysiological evidence.}} | ||
==Mathematical Formalism== | == Mathematical Formalism== | ||
In this chapter, we will revisit the clinical case of Mary Poppins, who has been suffering from Orofacial Pain for over ten years, with a diagnosis of "Temporomandibular Disorder" (TMD) confirmed by her dentist, or, more specifically, Orofacial Pain associated with TMD. To understand the complexity in arriving at a precise diagnostic definition using Classic Language Logic, it is fundamental to introduce and analyze the concept at the basis of the philosophy of classical language. | In this chapter, we will revisit the clinical case of Mary Poppins, who has been suffering from Orofacial Pain for over ten years, with a diagnosis of "Temporomandibular Disorder" (TMD) confirmed by her dentist, or, more specifically, Orofacial Pain associated with TMD. To understand the complexity in arriving at a precise diagnostic definition using Classic Language Logic, it is fundamental to introduce and analyze the concept at the basis of the philosophy of classical language. | ||
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The fundamental logical operators include: | The fundamental logical operators include: | ||
* '''Conjunction''', denoted by the symbol <math>\land</math> (and): represents the logical operation "AND". A compound proposition formed by two propositions joined with "and" is true only if both propositions are true. | *'''Conjunction''', denoted by the symbol <math>\land</math> (and): represents the logical operation "AND". A compound proposition formed by two propositions joined with "and" is true only if both propositions are true. | ||
* '''Disjunction''', denoted by the symbol <math>\lor</math> (or): represents the logical operation "OR". A compound proposition is true if at least one of the component propositions is true. | *'''Disjunction''', denoted by the symbol <math>\lor</math> (or): represents the logical operation "OR". A compound proposition is true if at least one of the component propositions is true. | ||
* '''Negation''', denoted by the symbol <math>\urcorner</math> (not): reverses the truth value of a proposition. If a proposition is true, its negation is false, and vice versa. | *'''Negation''', denoted by the symbol <math>\urcorner</math> (not): reverses the truth value of a proposition. If a proposition is true, its negation is false, and vice versa. | ||
* '''Implication''', denoted by the symbol ⇒ (if... then): expresses a conditional relationship between two propositions. If the antecedent (first proposition) is true, then the consequent (second proposition) must be true for the implication to be true. | *'''Implication''', denoted by the symbol ⇒ (if... then): expresses a conditional relationship between two propositions. If the antecedent (first proposition) is true, then the consequent (second proposition) must be true for the implication to be true. | ||
* '''Logical consequence''', denoted by the symbol <math>\vdash</math> (it follows that): indicates that a proposition is a logical consequence of the previous ones within a given logical system. | *'''Logical consequence''', denoted by the symbol <math>\vdash</math> (it follows that): indicates that a proposition is a logical consequence of the previous ones within a given logical system. | ||
* '''Universal quantifier''', denoted by the symbol <math>\forall</math> (for all): expresses that the following proposition is true for all elements of a certain set. | *'''Universal quantifier''', denoted by the symbol <math>\forall</math> (for all): expresses that the following proposition is true for all elements of a certain set. | ||
* '''Proof''', often indicated by reasonings that lead to the conclusion symbolized with <math>\mid</math> (thus): indicates the culmination of an argument or logical reasoning that leads to a conclusion. | * '''Proof''', often indicated by reasonings that lead to the conclusion symbolized with <math>\mid</math> (thus): indicates the culmination of an argument or logical reasoning that leads to a conclusion. | ||
* '''Membership''', denoted by the symbol <math>\in</math> (belongs to) or <math>\not\in</math> (does not belong to): used to indicate whether an element belongs or does not belong to a set. | *'''Membership''', denoted by the symbol <math>\in</math> (belongs to) or <math>\not\in</math> (does not belong to): used to indicate whether an element belongs or does not belong to a set. | ||
Quantifier connectors, such as the universal quantifier (<math>\forall</math>) and the existential quantifier (<math>\exists</math>), allow for extending statements to sets of elements, offering a way to express propositions concerning 'all elements' of a certain set or 'at least one element' of such a set. | Quantifier connectors, such as the universal quantifier (<math>\forall</math>) and the existential quantifier (<math>\exists</math>), allow for extending statements to sets of elements, offering a way to express propositions concerning 'all elements' of a certain set or 'at least one element' of such a set. | ||
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|<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>{a \not\in x \mid \forall \text{x} ; A(\text{x}) \rightarrow {B}(\text{x}) \and A( a)\rightarrow \urcorner B(a) }</math> | ||
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{{q2|so the dentist triumphs!|don't take it for granted}} | {{q2|so the dentist triumphs!|don't take it for granted}} | ||
===Compatibility and Incompatibility of Statements=== | ===Compatibility and Incompatibility of Statements === | ||
The complexity arises when the dentist presents a series of statements based on clinical reports, such as stratigraphy and computed tomography (CT) of the temporomandibular joint (TMJ), indicating an anatomical flattening of the joint, axiography of the condylar paths with a reduction of cinematic convexity, and an electromyographic (EMG) interference pattern showing asymmetry on the masseters. These evidences can be considered co-causes of damage to the temporomandibular joint and, consequently, responsible for "Orofacial Pain". | The complexity arises when the dentist presents a series of statements based on clinical reports, such as stratigraphy and computed tomography (CT) of the temporomandibular joint (TMJ), indicating an anatomical flattening of the joint, axiography of the condylar paths with a reduction of cinematic convexity, and an electromyographic (EMG) interference pattern showing asymmetry on the masseters. These evidences can be considered co-causes of damage to the temporomandibular joint and, consequently, responsible for "Orofacial Pain". | ||
Documents, reports, and clinical evidence can be used to make the neurologist's statement incompatible and support the dentist's diagnostic conclusion. To do this, we present some logical rules that describe compatibility or incompatibility according to classical language logic: | Documents, reports, and clinical evidence can be used to make the neurologist's statement incompatible and support the dentist's diagnostic conclusion. To do this, we present some logical rules that describe compatibility or incompatibility according to classical language logic: | ||
# A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically compatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is coherent. | #A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically compatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is coherent. | ||
# A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically incompatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is incoherent. | #A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically incompatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is incoherent. | ||
Let's examine this concept with practical examples. | Let's examine this concept with practical examples. | ||