Semiotica 182 (2010), 69-79
In this study, we characterize a ground of meaning for each relate of a Roentgen sign. In this scheme, each relate ground includes a perceptual domain, a domanial segmentation and a temporal phenomenology. The temporal phenomenology is selected to satisfy the requirements of diagnostic imaging and is based upon the categorical ontology of Pierce and the formal ontology of Grenon and Smith. Our objective is to show that these relate grounds provide the interpreter of Roentgen signs with the minimum collateral knowledge necessary to initiate the process of diagnostic semiosis.
Keywords: relate ground; Peircean categories; formal ontology; temporal phenomenology.
Things that cannot be directly perceived by the senses may be indirectly perceived by means of signs. Charles S. Peirce conceived of a sign as a triadic relation comprised of a binary opposition between a representamen and an object that is mediated by an interpretant i.e. a relation in which a representamen is interpreted as representing or standing for an object in some way to someone (Peirce 1955: 99). In our interpretation, semiosis is the action by which the mind of the interpreter generates the interpretant of a triadic sign (cf. Peirce 1955: 282). This process depends upon the existence of a ground or source of meaning for each relate of the sign. It follows that each relate of a triadic sign is known only in the context of its relate ground. Hence, every sign has a representamen ground, an object ground and an interpretant ground. We propose that these relate grounds jointly provide a meaningful basis for the initiation of diagnostic semiosis. Our notion that there is a separate ground for each relate of a sign is more specific than the Peircean concept of the 'ground of a sign' (cf. Liszka 1996:20-21). Only for mental signs, where the mind of the interpreter is a common ground for all of its relates, do we speak of the ground of a sign (Cantor 2005). In what follows, we shall characterize the relate grounds of visual signs as they present in medical diagnostic images.
The representamen and object grounds
For convenience, the representamen and object relates of a sign will be termed correlates. We first characterize the correlate grounds of material signs i.e. signs in which the representamen and the object are physical entities. Subsequently, we shall characterize the interpretant ground where the interpretant is a thought in the mind of an interpreter. Diagnostic signs presenting in medical images are material signs with images as representamina and anatomic entities as objects. Such signs may be static or dynamic. We propose that each correlate ground of a material sign consists of a perceptual domain, a domanial segmentation and a temporal phenomenology. A perceptual domain includes visualized things or processes together with the regions of space or space-time that contain them. In this way, the perceptual domain provides objects for selective attention. Segmentation partitions the perceptual domain into individual entities that serve as the correlates of material signs. Such segments of the domain are percepts of things or processes and the intervals in space or time that separate them. A temporal phenomenology consists of the basic temporal modes of presentation of real things or processes. Subsequently, a temporal phenomenology that applies to image interpretation will be derived from the formal ontology of Peirce that represents universal categories of being in thought combined with the formal ontology of Grenon and Smith that represents universal categories of being in space-time.
For static material signs, the domain of a correlate ground is a specific region of space together with the entity that occupies it at a specific moment of time. For dynamic material signs, the domain of a correlate ground is a specific region of space-time together with the process that occupies it over a span of time. For static Roentgen signs, the domain of the representamen ground is a part of a Roentgen image formed at a specific moment in time. The domain of the object ground is the represented object together with its location in the body of a specific patient at the time the image was formed. For dynamic Roentgen signs, the domain of the representamen ground is a sequence of images that is perceived by the interpreter over a span of time as a continuously forming image. The domain of the object ground is a process in the body of a specific patient represented by the continuously forming image.
Visual perception partitions the visual field into individual regions or segments that are distinguished by intrinsic visual qualities such as color, luminance and texture. Adjacent regions are visually separated by quality gradients which constitute boundaries. This process of partition or separation is called visual segmentation (Palmer 1999:269-271). Segmentation of the visual field entails the specification of an aspect, a display and a scale.
Visual aspect. Objects that are opaque to light produce segments with only external boundaries. Objects that transmit x-rays produce segments with internal boundaries. Hence, the visual aspect of a segmentation may be extrinsic or intrinsic. An extrinsic aspect presents only external boundaries. An intrinsic aspect presents both internal and external boundaries. The visual aspect of medical diagnostic images is intrinsic.
Visual display. Segmentation of the visual world may be displayed in various ways. The natural display of our visual system is projectional; specifically, by perspective projection (Palmer 1999:21). In this format, parts of the visual scene are excluded when opaque objects are located along the line of sight. A cross-sectional or tomographic display does not have this limitation. Tomography eliminates the occlusion effect by forming images in selected planes that are located outside of the opaque object. For static or dynamic Roentgen signs, the visual display is projectional in both correlate grounds. In clinical practice, standardization of projections facilitates visual recognition. For signs in other imaging modalities such as computed tomography or magnetic resonance imaging, the visual display is usually tomographic, although it may be reformatted to be projectional.
Visual scale. A visual scale specifies a grade of segmentation i.e. a range of segment size. We know that visualization with electromagnetic radiation entails the choice of a viewpoint with an unoccluded line of sight. Specifically, perception of a visual scene is derived from an image that is projected upon the retina by the lens and cornea of the eye (Palmer 1999: 28). With this imaging system, the dimensions of a segment in the retinal image vary inversely with the distance of the object from the eye. As the viewing distance of an object becomes smaller, its retinal image becomes larger until its boundaries extend outside of the visual field and the object can no longer be perceived as a whole. Conversely, as the viewing distance becomes larger, the retinal image becomes smaller until its boundaries can no longer be resolved and the object can no longer be perceived. Hence, there are upper and lower limits to the distance at which an object may be seen with the unaided eye. Furthermore, we know that these constraints may be overcome by the use of an artificial lens to magnify or minify the retinal image. These facts provide a basis for grading visual segmentations. Only two grades of visual segmentation are pertinent to clinical practice: the idioscopic (a 'self-produced view') and the cenoscopic (the 'common view'), terms adopted by Peirce from Jeremy Bentham (Peirce 1998:373). In our restricted interpretation of the term, idioscopic segmentation entails the use of a device to modify the range of depth perception. Hence, idioscopy may be microscopic or telescopic. In contrast, cenoscopic segmentation does not entail the use of such a device (cf. Peirce 1998:482). The phenomenology of appearances (Peirce 1998[1903a]:146-147; [1903b]:272) or the common sense world (cf. Smith and Casati 1994; Smith 1995a, 1995b) assume a cenoscopic scale. Medical images are usually interpreted on a cenoscopic scale although magnification or minification techniques may occasionally be used. Hence, a dyadic scale for visual segmentation is adequate for clinical practice. A complex system of 'granular partitions' may be useful in biomedical research (cf. Smith 2004a).
In one sense (Smith 2003), ontology is a representation of entities that exist in reality and are independent of mind. We define phenomenology to be the perceptual presentation of an ontology. Hence, temporal phenomenology involves modes of presentation of things or processes in time. In what follows, we examine two ontologies that provide a basis for the temporal phenomenology of the correlate grounds of Roentgen signs. These ontologies are termed: the Peircean Formal Ontology and the Basic Formal Ontology.
Peircean Formal Ontology (PFO). The PFO is a triadic ontology comprised of three universal categories of being that are accessible by thought. These ontological categories or 'irreducible constituents of thought' were first postulated by Charles S. Peirce and termed Firstness, Secondness and Thirdness (1992:6; 1998[1903a]; 165; 1998 [1903b]:267). In our interpretation, Firstness refers to attribution, Secondness to opposition and Thirdness to mediation. In this categorical hierarchy, Thirdness entails Secondness and Secondness entails Firstness.
Basic Formal Ontology (BFO). The summary description of BFO that follows is abstracted from multiple publications of Grenon and Smith (Grenon and Smith 2004a; Grenon et. al. 2004b; Smith and Grenon 2004; Smith et.al. 2006). The BFO is a dyadic spatio-temporal ontology consisting of two universal categories of being in time designated as SNAP and SPAN. The SNAP ontology (derived from 'snapshot') represents things as they exist at a single moment and that continue to exist i.e. things that maintain their identity while undergoing change. Such enduring entities are termed continuants or endurants. The SPAN ontology (derived from 'spanning') represents processes as they occur i.e. as their identity presents through time. Such occurring entities are termed occurrents or perdurants. Note that SNAP and SPAN are non-overlapping categories. SNAP entities may be non-substantial or substantial. Non-substantial entities are spatial regions. Substantial entities are contained in spatial regions. Substantial entities are classified as independent or dependent. Independent substantial entities are bearers of dependent entities. In brief, independent substantial entities may be aggregates, objects, boundaries, parts or sites. Substantial aggregates are collections of objects. Objects are distinguished by their boundaries. Boundaries may be natural (physical discontinuities) or conventional (artifactual). Parts of objects and boundaries of parts are conventional. Sites are spaces within objects that may contain other objects. Dependent substantial entities require independent entities to exist. In brief, dependent entities are inherent in independent entities e.g. qualities or functions. SPAN entities are classified as non-processual or processual. Non-processual SPAN entities are spatio-temporal regions. Processual SPAN entities develop their identity in space-time. In brief, processual entities may be processes, events, phases, aggregates or settings. Processes are continuous and have no temporal gaps. Events are momentary processes. An event may be a physical discontinuity such as the beginning or ending of a process or a conventional demarcation such as the momentary part of a process at which a static image of the process is formed. A phase is a conventional part of a process that has conventional boundaries. A processual aggregate is a succession of processes separated by temporal gaps. A setting is the spatio-temporal environment of a process. Furthermore, the history of a SNAP entity is a SPAN entity. Hence, a phase in such a SPAN entity is a stage in the history of the SNAP entity and an event in the SPAN entity is a state of the SNAP entity.
Categorical Temporal Phenomenology (CTP). If we consider phenomenology to be the perceptual presentation of an ontology, we may characterize a CTP by three phenomenal categories:
Opposition of the perception of a continuant with a recollection of the same continuant is the perception of change. If we refer to the comparison of different states of a continuant as an opponent, we may say that a First Category phenomenon is the perception of a continuant, a Second Category phenomenon is the perception of an opponent and a Third Category phenomenon is the perception of an occurrent.
Distinctions between BFO and CTP. Although CTP is based upon BFO, these two representations differ in important respects. The ontological categories represent different modes of being in time and depend upon relations between identity and time: The identity of SNAP entities is preserved over time and the identity of SPAN entities develops over time. In contrast, the phenomenal categories represent different modes of presentation of being in time and depend upon relations between the perception of identity and time: First Category phenomena present in a single moment of time, Second Category phenomena present as a comparison of First Category phenomena and Third Category phenomena present as they occur over time. Furthermore, BFO is a dyadic ontology dealing with universals or entities that are independent of mind (Smith 2004b). In contrast, CTP is a triadic phenomenology dealing with perceptions, which are mental processes. The ontology and the phenomenology also differ with regard to their uses. The BFO was designed to facilitate description in biomedical research by providing a standard ontology and taxonomy. In contrast, CTP was designed to improve our understanding of the process of semiosis in the interpretation of medical images by making explicit its categorical basis.
This completes our characterization of the representamen and object grounds of material signs in terms of a perceptual domain, a domanial segmentation and a temporal phenomenology where:
In the next section, we shall characterize the interpretant ground of material signs.
The interpretant ground of a material sign is characterized by the same scheme as its correlate grounds i.e. by a perceptual domain, a domanial segmentation and a temporal phenomenology.
The perceptual domain of the interpretant ground of a material sign consists of the mind and thought processes of the interpreter. This domain is uniquely determined by the personal experience of the interpreter and its uniqueness is protected by the privacy of personal mind.
Mental segmentation involves perceptual separation and the awareness of difference. We distinguish two fundamental types of mental separation: differentiation and abstraction. Differentiation involves a separation of object from object in thought whereas abstraction involves a separation of attribute from object in thought. Differentiation is the perception of a difference between objects. Two types of mental differentiation are dissociation and discrimination (cf. Peirce 1992: 2-3). Mental dissociation of two objects entails the perception of differences in all of their attributes. Mental discrimination between of two objects entails the perception of differences in some of their attributes. Abstraction involves the conception of an attribute or aggregate of attributes as belonging to an independent entity. Two types of abstraction are prescission and hypostatization (cf. Peirce 1998: 352). Prescissive abstraction is the conception of a single attribute of an object as an independent entity. Hypostatic abstraction is the conception of an aggregate of attributes common to multiple objects as belonging to an independent entity. Independent entities conceived by abstraction are termed generals or universals. This typology of mental separation differs from Peirce's typology of logical separation which is based upon a concept of necessity (cf. Peirce 1992:2-3; 1998:270).
The most frequently asked questions in diagnostic image interpretation are:
Answers to these questions depend upon the tacit assumption of a temporal phenomenology by the interpreter.
First category phenomenology. An answer to the first question depends upon the detection of findings by the interpreter. This is a First Category mental operation i.e. perception or attribution in a single moment of awareness. Findings are judged to be abnormal if they involve the presence of the unexpected or the absence of the expected. Findings are judged to be normal if they involve the presence of the expected or the absence of the unexpected (Cantor 2006a). This phenomenal category applies to the interpretant ground of both static and dynamic Roentgen signs.
Second category phenomenology. An answer to the second question depends upon a comparison of findings that are temporally indexed in common time. This is a Second Category mental operation i.e. opposition in a single moment of awareness of two perceptions. The presentation of findings at different moments of image-time in the same moment of common-time represents change when the findings are discriminable and no change when they are not. The detection of a change is followed by a judgment of its clinical significance (Cantor 2006a). This phenomenal category applies to the interpretant ground of compound signs i.e. signs that are the semiotic union of static signs in images formed at different moments of common-time (Cantor 2003).
Third category phenomenology. An answer to the third question depends upon the inference of an event or process in common time. For static signs, this is a Third Category mental operation i.e. a mediation in a single moment of awareness between a perception and a memory of events or processes. In Roentgen semiotics, events or processes in common time may be inferred from images by the categorical modes of inference designated by Peirce as abduction, deduction and induction (Peirce 1992: 188; Cantor 2004):
Note that in each form of inference, a conjoint antecedent implies a consequent: the antecedent in abduction is a conjunction of a 'result' and a 'rule'; the antecedent in deduction is a conjunction of a 'case' and a 'rule'; and the antecedent in induction is a conjunction of a 'case' and a 'result'. In each mode of inference, the conjunction is produced by an association of thoughts. Hence, the interpretant ground must include the principles of mental association: similarity, contiguity and habit (cf. Association, in Cantor 2004). Furthermore, validation of abductive and inductive inferences depends upon their consistency with subsequent deductive inferences (Peirce 1998: 95, 97, 528 Editors Note 12). For static signs, the categorical modes of inference may be restated as follows:
In other words (cf. Cantor 2002):
For dynamic signs, a process is inferred from a cinematic image by deduction where the observed process (a 'result') is inferred from the memory of similar processes (a 'case') and knowledge that the cinematic image is a real-time representation of such processes (a 'rule'). Hence, deduction is used to infer processes occurring in the image-present.
In a previous study (Cantor 2006b), Roentgen signs were classified by their effects on the mind of the interpreter i.e. by their capacity to evoke feelings, to provoke judgments or to impart knowledge. Furthermore, signs that impart knowledge (gnostic signs) may be classified by their temporal reference i.e. anagnostic signs refer to the past, diagnostic signs to the present and prognostic signs to the future, relative to the moment in common time at which their image was formed (Cantor 2002). In this study, we have specified a ground of meaning for each relate of a Roentgen sign. A relate ground consists of a perceptual domain, a domanial segmentation and a temporal phenomenology. The temporal phenomenology, regarded as the perceptual presentation of an ontology in common-time, was derived from the categorical ontology of Peirce and the formal ontology of Grenon and Smith. In this way, the relate grounds of Roentgen signs provide the minimum collateral knowledge necessary to initiate the process of semiosis in Roentgen diagnosis.