The logic of the classical language Abstract

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The logic of the classical language

Abstract

This chapter introduces the logic of classical language as a conceptual tool for understanding how medicine constructs “certain” diagnoses from signs, symptoms, and instrumental data. The goal is not to deny the effectiveness of traditional semiotics, but to show that clinical language—even when it appears rigorous—remains anchored to interpretive contexts that may generate divergent conclusions without any change in biological reality.

The chapter revisits the clinical case of Mary Poppins, already discussed in the introductory chapter on the logic of medical language and on the concept of an encrypted “machine message.” Here, however, the same problem is approached differently: we observe how the classical approach tends to transform clinical observation into a system of “if… then” propositions, supported by the law of the excluded middle (true/false) and by proof by contradiction. In other words, classical logic naturally pushes toward a dichotomous diagnosis: “TMD yes / TMD no.”

To make the mechanism transparent, the chapter builds a formal framework based on propositions and predicates, where instrumental evidence (CT, stratigraphy, axiography, EMG pattern) becomes the premise $A(x)$, and the diagnosis of temporomandibular disorder becomes the consequence $B(x)$. If Mary Poppins is included in the set of “normal patients” within the dental context, the deduction is coherent: $A(a)\to B(a)$. Here the strength of classical logic appears as an advantage: it enables internal coherence, local validation, and the construction of protocols.

The difficulty arises when another specialist—e.g., the neurologist—proposes an alternative interpretation: Mary Poppins may not belong to the set $x$ of “normal patients” for dentistry, and therefore the deductive rule would not apply. From this mismatch emerges the most important theme of the chapter: a diagnosis can be logically correct within a context and yet not clinically exhaustive in a broader context. For this reason, the chapter introduces the concepts of logical compatibility and incompatibility between sets of assertions ($\mathrm{\Im }$, ${\delta }_1...{\delta }_n$): internal coherence can grow indefinitely without guaranteeing universality.

The chapter concludes by suggesting that classical logic, although indispensable, shows structural limits when it encounters complex biological systems and early, non-observable phenomena. The need to move beyond “black or white” prepares the transition toward more flexible logics, especially probabilistic logic.

2nd Clinical Approach

(Hover over the images)

• 
  Figure 2: Patient reports "orofacial pain" on the right facial hemisphere.
• 
  Figure 3: Stratigraphy of the temporomandibular joint (TMJ) of the patient showing signs of condylar flattening and presence of osteophytes.
• 
  Figure 4: Computed tomography of the TMJ
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  Figure 5: Axiography of the patient showing a flattening of the masticatory pattern at the level of the right condyle.
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  Figure 6: Interfering EMG activity. Overlapping upper traces corresponding to the right masseter, below to the left masseter.

Three guiding questions (with short answers)

1️⃣ Why is medical language structurally fragile, even when it seems rigorous?
Because it is a hybrid language: it borrows words from everyday speech, but assigns them technical meanings that vary across disciplines. The same “sign” can therefore be interpreted through different clinical grammars.

2️⃣ Why can one clinical case generate conflicting diagnoses without any change in the facts?
Because classical reasoning often depends on the reference set being used (“normal patients” for dentistry vs. “atypical patients” for neurology). The logic may be coherent inside each context, yet the contexts are not equivalent.

3️⃣ How can classical logic be internally correct and still be clinically incomplete?
Because internal coherence can be expanded indefinitely by adding compatible assertions (${\delta }_1...{\delta }_n$) without guaranteeing that the same conclusion remains valid outside the original domain. Complex systems can require broader—and probabilistic—interpretive frameworks.

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