AH:thesis snippets as background - see below for main section on this topic.
With respect to formal descriptive structures, Varela proposes a parallel between phenomenology and mathematics. The nature of this link, he suggests, will be clarified in the process of neurophenomenological research but his principal claim here is that the invariants of experience can be discovered and that this will allow a formalisation of the phenomenal (Varela 1997, p.373). ‘Phenomenal invariants’ refer to the “categorical features of experience that are phenomenologically describable both across and within the various forms of lived experience” (Lutz and Thompson 2003, p.32). In his original formulation of invariants, Husserl drew inspiration from the calculus of variations to form the perceptual, individual and imaginative universal aspects of the concept of invariants (Depraz 1999b, pp. 101-102). Varela frames these differently.
Francisco distinguished three scales of lived time: the 1 scale, of about one second, which corresponds to the time of a conscious moment and to which “nowness” belongs; the 1/10 scale corresponding to minimal separable perceptual events; and the 10 scale corresponding to narrative time. (Rudrauf et al. 2003, p.52)
In the research interviews I am principally concerned with events on the 1 and 10 scale, the now and the narrative time scales.
Importantly, neurophenomenology does not require the invariants of experience to be fixed. Rather, the creativity of consciousness causes invariants to continually emerge.
With respect to the relationship between local and global emergence, Varela claims that neurophenomenology can draw on the language and mechanisms of non-linear dynamical systems. These dynamical tools are creating radical re-configurations within the domains of ontology and reshaping classical mechanical views of causality and explanation (Varela 1997, p.374-5).
The key point I wish to retain here is that these major scientific developments break from the traditional opposition between matter and life, and provide substance to a modern biology where such dialectical contraries are simply no longer relevant. Similarly, in the cognitive sciences, the traditional opposition between body and mind, or between the biological organic base and the mental and cognitive properties is also simply erased as a fundamental gap. In both cases the erasure of the traditional ontological barriers is done in a non-reductive manner since the new theoretical moves actually retain the specific properties of both traditional regions. (Varela 1997, p.375)
In this way, theoretically and methodologically, neurophenomenology makes use of an embodied large-scale dynamic approach to the neurophysiology and neurodynamics of consciousness (Lutz and Thompson 2003, p.31).
Varela (1997) and Lutz (2002a) call for a mathematisation of phenomenology. The experience of conducting this research has highlighted the efficacy of this suggestion. The question is, how should this be achieved? Category theory is proposed in section 12.5 as a foundation for a mathematisation of phenomenology.
Aspects of the experience of CFS are interrelated, some in complex ways. The cluster analysis employed here is an attempt to capture the relationships between processes. Rather than presenting a diagrammatic representation of the structure of the discrete components in the experience the cluster analysis aims to graph the structure of relationships between the node processes that constitute the CFS experience. These relationships are themselves processes. A focus on the relationships between and processes occurring within the structure of an experience will extend existing phenomenological research. Cluster analysis and category theory are potentially useful tools. Other data mining techniques may also prove efficacious.
AH: thesis section 12.5, pp.-351353
Varela (1997) and Lutz (2002a) call for a mathematisation of phenomenology. Kauffman’s (2002) research moves in this direction. How this would be achieved, however, was beyond the scope of this early work. The project of mathematising phenomenology will remain open to criticisms such as that of Brown (2008) until a mathematical and epistemological approach that is showing practical and theoretical promise is established.
Yoshimi (2007) calls for an integration of phenomenology and cognitive science and acknowledges that this will require a mathematised phenomenology.
I believe that a dynamical approach to Husserlian phenomenology holds out considerable promise for integrating phenomenology and cognitive science. … Drawing the parallels properly will require a suitably mathematized phenomenology. (Yoshimi 2007, p. 290)
In contrast to Brown (2008), Yoshimi also demonstrates that mathematising phenomenology is not an incoherent project given the capabilities of modern mathematics, but Yoshimi also does not suggest how this may be achieved.
The neurophenomenological program aims, in part, to relate neurological behaviour to phenomenal data and the structure of experience in mutual constraint (Varela 1997). The challenge neurophenomenology faces is that these realms of knowing are disjoint. Neurological data, phenomenal data and semiotic systems are separate mathematical universes, in that these data are of incommensurate and incomparable kinds. Mathematics, however, provides a tool for working with objects of different kinds that nevertheless exist in and/or behave in mutually constrained relationships: category theory.
A mathematical category consists of a collection of objects, a set of morphisms that map objects to objects, an identity morphism that maps each object onto itself, and the (associative) operation of composing morphisms. Category theory provides a way to proceed from categories and constraints on morphisms to a fully developed mathematics of the categories.
Category theory builds upwards from the structure of connections between categories to the necessary implications of those connections for the algebras of those categories. Once algebras and the nature of the objects of the categories can be identified one can then also show how to connect the dynamical structures of each category in mutual constraint. In effect, this is the co-dependent arising of structure in and between distinct categories.
Decock (2006) argues that because there is evidence to suspect that phenomenal data cannot be represented in a metric space this implies that there is no phenomenal space. It is possible, instead, that phenomenal spaces exist but are non-metric. It is also possible that a correct mathematical representation of phenomenal data would not be contained in a space but rather in some other mathematical object. Category theory may provide the tools to resolve the nature of a representation of phenomenal data that is consistent with and grounded in phenomenology. The key here would be the grounding of the representation in phenomenology rather than a priori assumptions.
In order to mathematise phenomenology it may be necessary to mathematise neurophenomenology. In mathematising neurophenomenology, the categories involved will include the entire array of the disciplined approaches to human experience and their tools and “the entire array of scientific correlates which are relevant in cognitive science” (Varela 1996, p.330). It seems likely that no one of these categories will manifest enough constraints to specify a structure for a mathematised neurophenomenology, however, in combination they are likely to provide sufficient constraints. This implies that mathematising phenomenology alone may be impossible. This could be considered analogous to establishing the shape of a tent where phenomenology, disciplined approaches to human experience, and the scientific correlates which are relevant in cognitive science each contribute guy ropes. Without enough guy ropes specified the dimensions of the tent cannot be realised.
Some of the necessary categories for the mathematisation of phenomenology are relatively straightforward because their formalisations are already well understood. The applications of mathematics to neurology have been extensively studied, for example. There is also a significant literature on algebraic semiotics founded by Goguen’s (1999) category-theoretical discussion of algebraic semiotics.
What is needed is a mathematised phenomenology and mathematised phenomenological research process. Toward this end, basic element analysis proposes a subject, object, relation tuple as the basic structural element of experience. The collection of all possible such basic elements together with such observational constraints as the mental factors, and others, could be formalised into a mathematical category, subjects and objects being the objects of the category and the relations being its morphisms (McGregor 2010).
Introspection (Vermersch 1999; Vermersch 2009) potentially provides detailed access to first-person experience. To explore this in a rigorous manner, two components are necessary. Firstly, an understanding of symbolisation and the way symbolisations derive their meaning from experience in the first person. Gendlin (1962) has provided a description of how meaning arises from the relation between experience and symbolisation, which could generate the basis of a formalisation of the symbolisation of experience. Secondly, rigorous intersubjective processes for gathering phenomenal data that produce authentic and consistent symbolised results are necessary. The explicitation interview technique described by Vermersch (1999; 2009) and Maurel (2009) acts as a starting point and is also similar to methods employed in this research. Similar processes for intersubjective validation have been described by Petitmiengin-Peugeot (1999) in her study of intuition and Petitmiengin and Bitbol’s (2009) work on the validation of first-person interview data.
Finally, what will be required is a means for discovering structure in symbolised first-person data. The semiotics of Greimas and Courtés (1979), as used in this research for example, provides a potentially useful formalisation and nomenclature of practical analytic techniques for systems of symbols such as first-person reports. In providing a theory of algebraic semiotics Goguen (1999) demonstrates how semiotics can be expressed in terms of category theory. For example, there is a very strong connection between commutative diagrams in category theory and the semiotic square of Greimas and Courtés (1979). In this research the application of Greimasian semiotics to a large symbol system (resulting from coded interview data) and the use of graph theory and clustering in doing so is a simple practical example of the benefit of mathematising phenomenological research. In future research, there are a large number of natural language processing techniques from computer science that stand to save much of the labour requirement of a manual process; for examples, see Tagarelli (2008) and Huang et al (2008).
At each step in the process of constructing a mathematised phenomenology, category theory and abstract algebra could be utilised to provide a full mathematical formalisation of phenomenology. Graph theory and linear algebra could provide analysis tools for the structures that arise both during the mathematical formalisation of phenomenology and those structures that arise from the application of the mathematised phenomenology to phenomenological data. The category-theoretic ability to integrate constraints from each level of re-representation of experience is what could give this approach its power.
A fully mathematised phenomenology could potentially demonstrate the mechanisms of action in precise mathematical terms such that they could be directly compared to neurological data, modelled in digital form, and perhaps even executed in software.