Formation of Interpretants in Roentgen Semiotics
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Formation of Interpretants in Roentgen Semiotics


Semiotica 187 (2011), 277-291


In this study, the principles of Peircean semiotics are used to elucidate the interpretive process for Roentgen signs. We begin with the identification of terminological, propositional and argumental interpretants in the context of Roentgen diagnosis. We examine the contributions of collateral knowledge and principles of inference, both associational and logical, to the formation of diagnostic interpretants. The Peircean modes of logical inference are then adapted to represent their use in clinical practice by a solitary interpreter. It is suggested that this semiotic model of Roentgen diagnosis may also apply to the interpretation of visual signs in other diagnostic domains.

Keywords:    diagnosis, interpretant, inference, association.


In common usage, the word 'sign' denotes something that stands for or represents some other thing. However, this dyadic concept of 'sign' is not adequate for logical inquiry, since it does not define what it means to 'stand for' or to 'represent'. Clearly, if something represents some other thing, it must do so in some way ie. representation necessarily involves a mediating principle. Hence, a logical definition of the word 'sign' that designates its representative function must, at the very least, contain a triadic relation. Charles S. Pierce defined a sign as a triadic relation in which some thing (a representamen) stands for some other thing (an object) in some way (by means of an interpretant) to someone (an interpreter). (cf. "Division of signs" CP 2.228). In this way, we may define a visual sign to be a triadic relation in which a perception (a representamen) and a recollection (an object) are meaningfully connected by a thought (an interpretant) in the mind of an interpreter. In this definition, we have assumed that each relate of a visual sign is a process in the mind of its interpreter. Hence, a visual sign is a tripartite mental process and not an objective entity (Cantor 2006b). Roentgen signs are visual signs that are perceived in the process of Roentgen diagnosis. In this study, we examine the fundamental role played by inference in the formation of the interpretants of Roentgen signs. The entire work is based on Peircean semiotic principles. We begin with an account of the Peircean categorical typology of interpretants as applied to Roentgen signs.

Interpretant types

Perceived as a whole, a Roentgen image is the representamen of a Roentgen sign in the mind of an observer/interpreter.  By selective attention, any part of the image may serve as the representamen of a Roentgen subsign.  One may consider the sign formed by the perception of a whole image as a semiotic union of any number of Roentgen subsigns (cf. Cantor 2003b).  Furthermore, a Roentgen sign may be designated as global, regional or local, depending on the anatomic scope of its representamen (Cantor 2000). In clinical practice, interpretations of Roentgen images consist of the interpretants of Roentgen signs.  These interpretants are represented in language, preserved in a report and communicated in a timely fashion to the referring clinician for use in the clinical diagnosis and management of the imaged patient.  Since diagnostic interpretants are linguistic representations, it is natural to apply in this context Peirce's categorical typology of interpretants as consisting of terms, propositions and arguments. For simplicity, we shall limit our examples to the interpretants of static Roentgen signs that present in one or more thoracic, abdominal or skeletal images.

Terminological interpretants

In Roentgen semiotics, a term is a word or group of words that designates a perceivable entity ("Nomenclature and divisions of triadic relations" EP2: 292). A term does not have a specific spatio-temporal location i.e. terms represent generals. Commonly used diagnostic terms refer to qualities, objects, states, events or processes (cf. Grenon et al 2004). Examples of terms used in Roentgen diagnosis are:

Terms may serve as the subjects or predicates of propositions representing facts ("On reasoning in general" EP2: 20). Terms are neither true nor false.  Only propositions have truth value.  ("The basis of pragmaticism in the normative sciences" EP2: 379).

Propositional interpretants

A factual proposition represents a perceived entity (an object or event) i.e. a factual proposition is the interpretant of a sign that has a real object. The represented object or event is indicated by the subject and described by the predicate ("The categories defended" EP2: 172). A factual proposition is valued as true if it conforms to the real object it represents (" The basis of pragmaticism in the normative sciences" EP2: 380). In Roentgen diagnosis, propositional interpretants may be either perceptual judgments or consequences of perceptual judgments by valid inference. A perceptual judgment is a proposition that represents the direct perception of an object or process to the mind of the observer ("On phenomenology" EP2: 155). Peirce maintained that perceptual judgments are not subject to conscious control. ("The seven systems of metaphysics" EP2: 191). In contrast, inferential judgments, which depend on collateral knowledge and conventions of inference, are subject to conscious control. According to Peirce, belief is the acceptance of a proposition as true, resulting in its use as a guide for action. ("On reasoning in general" EP2: 19). In Roentgen diagnosis, the expected action is the timely communication of relevant beliefs to the referring clinician to serve as an aid in clinical diagnosis and treatment. Propositional interpretants of Roentgen signs represent the existence, location or identity of objects or processes of clinical interest (Cantor 2002). Ignoring stylistic variations, diagnostic interpretants have forms such as: 'There is _________' or 'The ____is_____', where the blanks are filled by terms representing a quality, object or process that may be specified by localizing or identifying terms. Examples of perceptual judgments from thoracic, abdominal or skeletal images are:

The most frequently used propositional interpretants are:

'There is no radiographic abnormality' in a single image and 'There is no change' in serial images. Examples of inferred propositional interpretants will be given in a later section on clinical inference.

Argumental interpretants

In general, an argument is any thought process tending to produce a belief. ("On reasoning in general" EP2: 12). A logical argument may be reduced to a chain of logical inferences. Peirce identified three elementary modes of logical inference which he termed abduction, deduction and induction ("Deduction, induction and hypothesis" EP1: 188-9). These modes of inference are interdependent but essentially different. In the Peircean scheme, abduction forms possible cases, deduction forms necessary results and induction forms probable rules (cf. Cantor 2004, on Peircean logic). Abduction requires deductive inference to verify a possible case or explanatory hypothesis. Induction requires abductive inference to form an induction hypothesis and deductive inference to verify a probable rule or law. Hence, logical abduction and logical induction are both consciously validated by deductive inference ("The three normative sciences" EP2: 206). However, validation of deduction is not under conscious control but depends on a real relation between premises and conclusion ("The nature of meaning" EP2: 212). In Roentgen semiotics, argumental interpretants are formed by clinical inference, which is distinct from Peircean logical inference. It consists of common sense modes of inference that will be defined in later sections.

Collateral knowledge

The formation of an interpretant of any type depends upon collateral observation or knowledge ("Letter to William James" EP2: 494). In semiotics, collateral knowledge is any knowledge that relates in any way to the object of a sign. In Roentgen semiotics, such knowledge may be acquired from prior observations or interpretations, either directly or indirectly. In other words, collateral knowledge may be recalled or inferred from personal experience or from the communicated experience of others. Collateral knowledge may be acquired prior to or during the process of interpretation. Newly acquired collateral knowledge is in the form of prompts. In Roentgen semiotics, prompts are referred to as clinical history.

Effects of collateral knowledge

In a previous study, we examined the effects of Roentgen signs on the mind of the interpreter (Cantor 2006b). These effects are: to induce feelings, to provoke judgments and to impart knowledge. Collateral knowledge also has the effects of inducing feelings and provoking judgments. Of fundamental importance in the process of diagnosis are the feelings of expectation and surprise.

Expectation.  Expectations may be classified as passive or active.  Passive expectation exists in the absence of prompts.  It is a ground state or habit of mind produced by the memory of repeated prior experiences.  Active expectation is produced by prompts.  Non-fulfillment of active or passive expectation is accompanied by a feeling of 'surprise'.

Surprise.  Peirce observed that passive expectation is always based upon some regularity and that finding regularity where regularity is expected produces no surprise ("On the logic of drawing history from ancient documents" EP2:89). However, finding irregularity where regularity is expected or finding regularity where irregularity is expected both produce a feeling of surprise.  Specifically, passive surprise is a response to non-fulfillment of passive expectation and active surprise is a response to non-fulfillment of the active expectation produced by a prompt ('Letter to William James EP 2: 499).

Normality and abnormality.  Recall that the first stage in the process of diagnosis is detection i.e. detection of the normal or detection of the abnormal.  Detection of abnormality is the awareness of a difference between what is perceived and what is expected (Cantor 2006a) and this awareness is accompanied by a feeling of surprise. Normality is a presence of the expected or an absence of the unexpected.  Abnormality is a presence of the unexpected or an absence of the expected (Cantor 2000).  In other words, abnormality is an unexpected presence or an unexpected absence.  These two general conditions are phenomenologically distinct, although they are logically interdependent.

False diagnosis

Passive expectation of the normal and active expectation of the abnormal usually facilitate the interpretation of Roentgen signs. However, false expectations may provoke false clinical judgments.  For example, a normal anatomic variant that simulates disease will not be expected by an unprepared interpreter and consequently result in misinterpretation (cf. Cantor 2003a).  Similarly, a prompt that produces an active expectation may be misleading or false and lead the interpreter to a false diagnosis (cf. Cantor 2005).

Types of collateral knowledge

The collateral knowledge used in Roentgen diagnosis may be generic or specific.  Generic collateral knowledge pertains to classes of patients that share features or conditions regarded as either normal or abnormal.   The interpreter acquires such knowledge from the communicated experience of others or from personal experience.  Specific collateral knowledge pertains to a single patient i.e. the subject of the imaging study.  Specific collateral knowledge may consist of prompts from the referring clinician, when available, or direct observation of the patient, when possible.  On the basis of collateral knowledge, signs may be classified as natural or artifactual.  For natural signs, the object is a consequence of physical causation without human agency.  For artifactual signs, the object involves human agency.  Furthermore, artifactual signs may be either intentional or nonintentional (cf. Cantor 2004).  Hence, Roentgen signs of disease are natural signs while signs of injury may be natural or artifactual.

Principles of association

Mental association is a process by which attention is transferred from one thought to another.  General principles of association were first articulated by Aristotle in his short treatise on memory.  However, these principles were almost certainly derived from the earlier Greek tradition of Artificial Memory.  Artificial Memory is a discipline consisting of mnemonic techniques that involve the arrangement of familiar images, in familiar places, in a familiar order.  (cf. Yates 1974: 31-55).

Aristotelian principles

Aristotle distinguishes between memory that is preceded by forgetting, which he terms recollection, and (? short-term) memory that is not preceded by forgetting (Aristotle 1941: 612).  Recollection is then characterized as a series of thoughts, beginning in the present and ending with the one sought, where each thought is related to the next by the principles of similarity, contrariety or contiguity (Aristotle 1941:612-613).  He also maintains that thoughts follow one another in an order that is determined by either nature or custom (Aristotle 1941: 613).  Natural ordering is the ordering of perceptual experience that entails causation or necessary succession.  Customary ordering does not entail necessity but is determined by belief, habit or rule. Examining these principles, we find that similarity entails a commonality of qualities, contrariety entails logical or physical opposition, contiguity entails physical proximity or contact and ordering may be natural or customary, where natural ordering is the physical opposition of cause and effect.  Hence, the essential principles of memorial succession in Aristotle's concept of recollection may be restated as: similarity, opposition, contiguity and custom.

Humean principles

According to David Hume, there are only three principles of mental association or connecting principles for thoughts:  resemblance, contiguity in space or time, and causation.  These principles are stated repeatedly throughout his "A Treatise of Human Nature" and serve as the foundation of his entire philosophy (Hume 2002[1740]:416).  Hume uses the term 'resemblance', which we assume is synonymous with 'similarity'.  Furthermore, Hume regards causation as a relation determined by the memory of a constant conjunction of events (cause and effect) where the term constant conjunction is defined as repeated conjoint relations of contiguity and succession (Hume 2002[1739]: 61).  Hence, causation is regarded by Hume as a customary ordering (Hume 2002[1739]: 61).  In other words, Hume's principles of association are fundamentally the same as the Aristotelian principles of recollection with opposition excluded i.e. similarity, contiguity in space or time, and custom. However, we note that opposition is implicit in the concept of causation.  With regard to his principles of association, Hume famously declared that "... as these are the only ties of our thoughts, they are really to us the cement of the universe, and all the operations of the mind must, in great measure, depend on them" (Hume 2002, [1740]:417).

Peircean categories

In his seminal paper "On a New List of Categories" (1867), Charles S. Peirce defines three fundamental types of relation which he calls representations (EP1:7). Peirce conceives of a representation as a triadic relation between a relate, a correlate and a mediating principle. In the first type of representation, initially termed a 'likeness' and in later work termed an icon, there is a commonality between relate and correlate with respect to some quality.  In the second type, which he terms an index, there is a factual relation or real opposition between relate and correlate.  In the third type, which he terms a symbol, there is an imputed connection between relate and correlate.  Hence, the mediating principles of Peircean representations are essentially: sameness, opposition and convention. Clearly, iconic relations entail similarities.  Moreover, indexical relations entail contiguity in space or time, since factual opposition implies being perceivable and distinguishable in the same moment of awareness, which entails spatio-temporal proximity or contiguity.  And finally, symbols as conventional relations are formed by habit or custom.  Hence, the Peircean typology of representations may be thought of as a generalization of the Humean principles of association and a simplification of the Aristotelian principles of mnemonic succession.  By further abstraction, Peirce's three universal categories of thought may be derived from his triadic typology of representations.  These categories are universal in the sense that they are used by the mind to represent all being.  We designate the Peircean categories of thought by the descriptive terms: attribution, opposition and mediation.  Since similarity is a relation that entails a sameness of attributes of a relate and its corelate, attribution is a primary or First Category mental process.  Since factual relations entail an opposition between a relate and its corelate, opposition is a Second Category mental process.  Since convention forms a mental connection between a relate and its correlate, mediation is a Third Category mental process.  In this way, the Peircean categories of thought may be derived from the Aristotelian principles of memorial succession, principles that were probably derived from the earlier Greek tradition of Artificial Memory.  In the same way that Hume believes his principles of mental association have universal significance, Peirce asserts that his universal categories are "...the three irreducible and only constituents of thought "("The categories defended" EP2: 165).

Forms of inference

Aristotle states, in passing, that recollection is a mode of inference that is independent of reason.  (Aristotle 1941: 616).  Hume states that the general principles of association constitute modes of inference that are independent of reason (Hume 2002[1739]: 64-65).  For Peirce, reasoning is a mental process that entails inference and all modes of inference involve association ("Association" CP 7.444).  However, only logical inference is subject to conscious control ("Issues of pragmaticism" EP 21: 347-8).  Inference may be thought of as a connecting principle for beliefs (" Issues of pragmaticism" EP 2: 22).   It is a process by which truth value may be transferred from one proposition to another.  Formally, an inference is a triadic relation between an antecedent, a consequent and a mediating principle.  In abduction, a result is the antecedent, a rule is the mediator and a case is the consequent.  In deduction, a case is the antecedent, a rule is the mediator and a result is the consequent.  In induction, a case is the antecedent, results constitute the mediator and a rule is the consequent (cf. "Deduction, induction and hypothesis" EPI: 188-9).  In both abduction and induction there is inference from a directly perceived antecedent (i.e. objects or processes in the present) to a consequent that cannot be directly perceived (i.e. objects or processes in the past or future).  In deduction, both antecedent and consequent are in the present.  Both abduction and induction are validated by means of deduction.  In common sense reasoning, a deduction is valid if its antecedent and consequent are both valued as true.  Prior to validation by deduction, the consequent of an abduction is valued as possibly true and the consequent of an induction is valued as probably true.

Stages of inference

Peirce distinguishes three stages in the process of deductive inference ("On reasoning in general" EP2: 22).  In the first stage, termed colligation, propositions that are believed to be true are brought together in successive moments of awareness to form a conjunctive proposition or compound assertion.  In the second stage, the conjunctive proposition is contemplated and selective attention is directed toward certain of its features.  In the third  stage, a judgment is made that the selected features are related to the conjunctive proposition by a known rule.  A similar triadic scheme may be applied to abductive and inductive inference.  Both abduction and induction begin with colligation of propositions believed to be true ("The first rule of logic" EP2: 45-6).  In abduction, the colligation of results is followed by contemplation of the colligand together with a known rule which evokes the awareness of a case, not part of the original results, but related to them by the rule.  In induction, the colligation of cases by a controlled process of selection is followed by contemplation of the colligand together with known results which evokes the awareness of a rule relating the selected cases to the results.

Clinical inference

Peirce's categorical typology of inference applies to logical inference in any scientific domain.  However, criteria for logical inference cannot be directly applied to clinical practice, due to the severe experiential constraints under which a diagnostician must operate.  In general, Roentgen diagnosis involves the state of a single patient at a single moment of time whereas scientific enquiry does not apply to isolated or non-reproducible events. Furthermore, being an early stage in a process the purpose of which is the relief of pain or disability, Roentgen diagnosis must be performed rapidly, as well as accurately.  For these reasons, Roentgen diagnosis is based on clinical inference, which is essentially common sense applied to a clinical domain.  We propose a typology of clinical inference that is analogous to the Peircean typology of logical inference.

Clinical abduction.  In clinical enquiry, abduction is inference from present to past or from effect to cause.  In clinical abduction, antecedent results are directly perceived as representamina of Roentgen signs, the mediating rule involves unconscious principles of association and the case is not directly observable, having occurred in the past.  In clinical practice, logical abduction is only applicable to unfamiliar results.  But for an experienced interpreter, this is an infrequent occurrence.  Usually, clinical inference of past events is a learned convention or habit that is just assumed to be valid. However, for unfamiliar results, the consequent case is valued as possibly true.  Clinical abduction may be validated at a later time by deductive inference from knowledge obtained by other imaging modalities, such as computed x-ray tomography or magnetic resonance imaging.

Clinical deduction.  In clinical enquiry, deduction is inference in the present or inference from cause to effect.  Clinical deduction is common sense deductive inference.  The antecedent cases are directly perceived as the representamina of Roentgen signs, the mediating rule is based on physical principles derived from collateral knowledge and the consequent result may or may not be immediately observable.  For valid clinical deduction, the antecedent and consequent are both valued as true.

Clinical induction.  In clinical enquiry, induction is inference from the present to the future.  Clinical induction is used to predict the course of a disease process or to anticipate the future occurrence of clinically significant events. In clinical induction, a single antecedent case is directly perceived as the representamen of a Roentgen sign, the mediating results are recalled from personal memory of similar cases, and the consequent rule is used to predict future states or conditions of the patient.  Due to temporal constraints, clinical induction cannot be immediately validated by deduction.  Hence, for true antecedent cases, the consequent rule is valued as probably true.

Examples of clinical inference

In what follows, we present examples of clinical inference based on thoracic, abdominal and skeletal images.

Clinical abduction.

Clinical deduction.

Note that in this example, the existence of a fracture is inferred but not directly visualized. The result may be confirmed by a follow-up wrist study.

Clinical induction.

Formation of arguments

An argument is a chain of elementary inferences (abductive, deductive or inductive). A link in such a chain is a relation between an inference and its successor such that the consequent of the inference is the antecedent or mediator of its successor. The conclusion of an argument is the consequent of its final inference. A simple argument consists of a single elementary inference.

Validation of arguments

An argument is valid if it is comprised exclusively of valid inferences. We have seen that there are essentially three distinct degrees of acceptance or grades of validity for clinical inferences: possible, for abductive inference with a consequent that is possibly true; probable, for inductive inference with a consequent that is probably true; and valid, for deductive inference with a consequent that is true. Clearly, a clinical argument or chain of clinical inferences is only as strong as its weakest link. Therefore, an argument consisting of a probably true induction and a true deduction can be, at most, probably true.

Clinical arguments

As examples, we present three clinical arguments derived from thoracic, abdominal and skeletal images.  All three arguments make use of local separation signs, as defined by Cantor (2000).  The inferences that constitute a given argument are numbered consecutively.


In this study, we have examined the process of interpretation of Roentgen signs from a Peircean perspective.  We have seen that terminological, propositional and argumental interpretants are formed in the interpretation of Roentgen signs.  We have reviewed the modes of associational and logical inference that are commonly used in the formation of argumental interpretants. We have observed that the modes of inference used in clinical practice are analogous to the modes of logical inference proposed by Peirce, although they differ in important respects.  These differences are due to limitations of time and capacity that hold for solitary interpreters in contrast with the unlimited collective capabilities of a community of inquirers dispersed in time and place (cf. Cantor 2009).  Since Roentgen diagnosis is ultimately based on principles of association and common sense logic, it is likely that a similar adaptation of Peircean principles would provide a semiotic model for the interpretation of visual signs in other diagnostic domains.


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