TARGET ARTICLE 112
WITH YOUR MIND AND RESPONSIBILITY :
CONCEPTUAL BASIS OF EXPERIENCE-STRUCTURING
by Herbert FJ Müller
January 2009, posted 7 February 2009
PURPOSE AND OUTLINE
In this essay I outline a general framework for the zero-derivation structuring (0-D) view : principles, levels, and limitations of mental structuring, with an appendix on mathematical thinking, using some material from W. Byers’ recent book.
0-D is required for an access to the conceptual mind-brain (and ‘consciousness’) puzzle, which is the focus of my efforts. It is a central conceptual question not only in psychiatry and psychology but also in other fields like theoretical physics, although in some areas, as in much of biology, it can be safely neglected. The reason for the 0-D proposition is that the mind-brain relation problem has remained unsolved in the accepted conceptual frameworks, specifically in those which postulate that reality is mind-independent (MIR) : because the mind can obviously not be mind-independently real. This traditional MIR-proposition, that reality is certain but mind-independent, actually prompts the question of how one can know something that is not in the mind. The answer is that one cannot; the MIR-assumption is self-contradictory. But a desire for certainty-from-‘outside’ causes people to maintain the MIR-illusion, plus the further illusion of an ontological subject-object split, and also the limitations of critical thinking, that are its prerequisites, but which at the present state of knowledge we can now no longer afford to comply with. In these circumstances, the mind-brain question, which cannot be addressed in an MIR-framework, overrides other needs, and becomes a touchstone for the overall validity of epistemologies. The leading question is : how can subjective experience regain its place at the center of knowledge, and this against the persistent efforts to eliminate it ?
As a conceptual difficulty, the mind-brain problem is more circumscribed but also more demanding and even more radical than some of the more traditional central questions in philosophy like ‘what is being’, ‘what is reality’, ‘what is truth’, or ‘what is my existence’, which are not only compatible with MIR-belief but may even suggest it. 0-D, in contrast, means a change in direction : the aim becomes comprehensibility with maintenance of doubt instead of doubt-free certainty derived from fictitious outside agencies, or by formalisms, which pass by - and may obstruct - the center of creativity, and thus have outlived their time of usefulness. We start from the pre-supposition that what we can know - rather than mind-external realities - are mind-internal structures for handling experience of self, world, and everything, which we create within an unstructured matrix, or accept from others; ‘reality’ consists of those of our structures which we find to be reliable in practice (including for instance our knowledge of the brain and its functions). Since there cannot be more than one generally valid epistemology, this situation prompts my present effort to formulate a general-purpose conceptual scheme for 0-D, which I think is simpler and easier to understand than traditional and recent metaphysics-ontology and their derivatives including realism, exclusive objectivism, positivism, materialism etc. But as it comes at the price of renouncing certainty, it is not necessarily easier in practice. - That reality is constructed does not rule out the possibility of epistemology : we can know about working-reality.
PRINCIPLES OF ZERO-DERIVATION STRUCTURING, COMPARED TO MIND-INDEPENDENT-REALITY BELIEF
Structures Created And Determined By Doing Versus Primary Given Ready-Made Structures
The situation in perception and reality-design is similar to the one in motor coordination development and fine tuning, which finds its optimum in effective doing. All mental structures and their precursors - concerning self, world, and everything - are pragmatically structured, affirmed, posited, and tried out within ongoing experience which is an unstructured matrix or background for structures : zero-derivation (0-D). All structures therefore require and include the subject(s)’ activity. Reality is not found or given in a subject-exclusive mind-independently ready-made state (MIR). Instead of trying to discover an imaginary given single MIReality and world, we devise multiple conceptual designs for structuring and handling experience as it happens; the world is a stage that we build as we can. Instead of either accepting or rejecting metaphysics-ontology (MIR-belief), it is transformed into reality-design (working-metaphysics).
The Biological Basis Of Thinking
The subject’s activity may be difficult to see in the more elementary structures, like qualia and gestalt-formations, because they arise biologically, automatically, and are thus not deliberately influenced or designed by the subject, who starts thinking from the later deliberate stage, and perceives the early one mistakenly as ‘given’ in a pre-structured (ready-made) state. Spontaneous gestalt-generation is indeed a main reason for the prevalent ontological leap of faith to a mind-independent world in the MIR-views. But contrary to this belief, pain, colour, smell, gestalt-formation, touch sensation are produced by the organisms’ activity, and would not occur without it.
And more generally, all biological structures, starting with self-replicating molecules, even before reaching the level of the DNA mechanism, affirm themselves; they sort of assert ‘that is how I am and what I do’. To what extent they will further replicate depends on their success (natural selection, Darwin). The long term overall results of spontaneous-mutation-plus-natural-selection may be misinterpreted as-if acquired individual characteristics were inherited - or also, by the way, as-if they had been purposefully designed by an intelligent agent , such as God or Nature. These views are extensions from the anthropocentric-design view, which is our only available start-point for thinking.
One can understand deliberate intelligent design as a continuation of biological development. That might respond to a question which Byers poses in his book on mathematics (p.321) : whether it is reasonable to say that natural processes are intelligent. Over the long term, they behave as-if they were intelligent.
Structuring Or Inventing ?
While all mental (mind-and-world-and-all) structures require our automatic or deliberate structuring, only some of them are deliberately invented. Qualia or gestalt-formations are mostly non-deliberate, and thus are not invented in the usual meaning of this word. But there is an increasing proportion of deliberate invention in areas like self- and social identity, language, mathematics, science, technology, religion, art, etc.
Deliberate Thinking : Encompassing Mind At The Center Versus No Mind
Later mental structures are added to the automatic ones. They are designed, with varying degree of subjectively purposeful deliberation, as well as of interpersonal communication. Understanding and deliberate structuring occurs within ongoing subject-inclusive experience, which is not only goal-directed, but also encompassing (umgreifend), as Jaspers emphasized. For 0-D, the encompassment is a fundamental condition and determining feature. In order to deal with the mind-brain question, the encompassment needs to be understood as valid without restriction (and this goes actually further than Jaspers’ proposition, who still maintained some MIR-belief).
Because the mind creates and modifies its structures actively and concurrently within ongoing experience, thinking cannot be confined to already-structured algorithmic processes. For the same reason, the possibility of metaphysics-ontology, i.e., of pre-structured mind-independent ‘outside reality’ is explicitly excluded as such; it is converted into subject-inclusive reality-design. That leads directly to the 0-D position. This consequence of the encompassment aspect of experience may at first come as a surprise, but is inevitable. One can commence thinking only from this anthropomorphic design start-point within ongoing experience : the subject(s)’ activity is always included. The awareness that reality is constructed with subject-participation is itself an aspect of reality. It becomes a fundamental insight of the theory of knowledge (epistemology, Erkenntnis-Theorie).
The Objective Method Of Science Does Not Eliminate Subjects
These considerations include scientific thinking and its objective method where, in order to minimize subjective bias, the subject is bracketed but not excluded : ‘objects’ are described in such a way as to have all ‘observers’ arrive at the same result. Scientific enquiry does not imply nor require subject-exclusion, although this is commonly assumed. Scientific knowledge starts, like art, as free creation (conjectures), as even the ontologist Popper has proposed.
The objective method needs to be distinguished from views which exclude subjects by postulating the existence of a mind-independent reality, as do subject-exclusive objectivism and materialism, and similar opinions which cause confusion in this area; in Nagel’s expression, that is a view ‘from nowhere’ [which however, I think, should be changed to ‘as-if from nowhere’ in order to avoid misunderstandings].
About The Efforts To Eliminate Subjects In Favour Of Objects, And Beyond
The observation of the priority of subjective experience goes directly counter to the opinion of analytic and language philosophy. For instance, an extreme opposite point of view was proposed by Wittgenstein, who wrote that referring to subjective experience is ‘a disease of thinking’ (Philosophical Investigations). The struggle of some exclusive objectivists to eliminate the subject is so intense that one gets the impression that they want to do away with themselves at all cost.
The subject (mind) cannot be objectified, although that has frequently been tried. Due to the pre-occupation with ‘objects’ as the supposed essence of reality, there have recently been attempts to replace the mind, because it cannot be an object, by the body which can be treated as an object, in what has been called ‘embodied cognition’. Another such attempt is talking about ‘the mind-brain’, which implies that mind and brain are the same. A still further recent development is ‘analytic metaphysics’, which wants to translate the view of Parmenides et al., to the quantum age by rejecting not only subjects but objects as well, and replacing them by ‘dispositions’ (see TA110 and its discussion in KJF).
Unstructured Background Of Experience Versus Primary Structures (Metaphysics-Ontology)
The unstructured origin has often been recognized. For example, Anaximander and others called it ‘apeiron’; the Bible ‘tohu va bohu’. Buddhist thinking speaks of a nirvana start and aim; Feyerabend wrote that there can only be islands of logical thinking in an ocean of irrationality. Structured self-contained (that is, mind-independent) theories and algorithms of everything are thus impossible. Ongoing experience is not primarily (ontically) but only secondarily (pragmatically) divided into subject, object, and everything else.
But occidental epistemology since Parmenides, Plato, and Aristotle has been based on the contrary premise that reality is ontic, i.e., mind-independently pre-structured (MIR). This ‘idea’ of reality could only be maintained by postulating that reality, although real, is unknowable, and that only its shadows can be known. Whitehead had noted that all Western philosophy amounts to footnotes to Plato - but one has to add : and to the concomitant attempts, which were quite intense, to get around the side-effects of his opinion. They are the disappearance of the subject, and in particular the impossibility to know the asserted positive pre-structured given entities, which he claimed for the sake of certainty. This opinion needs a thorough overhaul.
The Need For Complete Deconstruction Of MIR-Belief
Understanding of reality confronts us with a paradox. For one thing, one has to start from within present thinking with its already-formed, socially sanctioned, and automatically adopted structures; that is, in my understanding, at least a large part of what Heidegger has called ‘thrownness’ (Geworfenheit). But we also know that all the structures originate within a nirvana-like structure-free matrix of experience (zero-derivation, 0-D).
That leads to the conclusion that all present MIReality-structures must be entirely de-constructed, even while being used in an efficient manner : namely in the sense that they are not MIRs, that they are instead working-designs. An approach to the ‘consciousness question’ is not compatible with even remnants of the MIR-assumption, as they are proposed, for instance, in ‘dual-aspect’ views, because in that case the MIR-aspect is inevitably understood as the more real one.
For some other areas of enquiry, like particle physics, the automatic subject-exclusion of the metaphysical method has also now become unworkable; it needs to be replaced by a more suitable instrument of thinking.
Feedback-Evaluation Of Structures Versus Finding Ready-Made Structures ‘Outside’
The overall effect of the de-construction is a change not necessarily in function, but rather in how to understand the structures : from ‘given’, ‘found’, or ‘uncovered’ (‘ἀλήθεια’) as mind-independently (outside) pre-structured reality (MIR) to an active ‘ad-hoc’ or ‘pragmatically’ structured working- or as-if-MIR, reality-design. And in the 0-D view, the difference between inside and outside is also only pragmatic and not ontic, so that there is no wished-for outside in the ontic meaning available.
What one can ‘discover’, according to the 0-D view, is instead how adequate the posited structures are : this happens by feedback, while using them. That ‘feedback-discovery’ includes sudden subjective ‘eureka’ solutions to problems which one has carried around in one’s mind for some time. But these solutions still need explicit scrutiny, although they often turn out to be viable.
If we see 0-D as the more original situation, feedback-discovery is what had prompted the erroneous MIR-opinion that structures are given in ready-made form from ‘outside’ of the subject in the first place. This MIR-interpretation happens to coincide with the wish for certainty guaranteed by some authority outside oneself (like God or Nature). Evidently this MIR-conclusion can only develop in the context of the other error : that subjects and objects (the world) are given as such, and that they are thus ontically separate from each other, rather than only pragmatically, as they are in the 0-D view.
Persistent Agency : Comprehensibility And Creative Doubt Instead Of Fictitious Certainty
0-D replaces the external unknowable entities by mind-internal reality-design, which always remains within reach of knowledge. Thus 0-D obtains comprehensibility by abandoning the obsolete fictitious Platonic certainty. The start from an unstructured origin or background acts also as a back-up position in case of difficulties. That makes 0-D both ‘fail-safe’ and also ‘deep’ as opposed to ‘trivial’. Structures cannot go deeper than their unstructured origin.
The change from MIR-belief to 0-D means abandoning imagined certainty guaranteed by fictitious outside agents like God or Nature, or by inherently limited (incomplete) mind-independent automatisms like algorithms, formalisms, or logic in general. The gain in this exchange is comprehensibility, which includes acknowledging the limitations of mental structures. (See discussion in the appendix).
The reason for the change is mainly that the restrictions on critical thinking, which the traditional MIR-certainties require for their maintenance, are not compatible with the available knowledge in science and elsewhere. The wish for certainty does not disappear but needs to be dealt with in more appropriate ways.
There are statements of intention, mostly from the Vatican, to reconcile religion and science, but this is not likely to be easy to do. Aside from some very belated corrections such as the rehabilitation of Galileo, or an acceptance in principle of evolution, I have not seen any relevant steps. In particular am I not aware of proposals for a conceptual bridge between the two fields - but I would appreciate information about such undertakings if there are any. Metaphysics-ontology had provided certainty at the price of intellectual absurdity (cf. Tertullian). It has by now become obsolete, impossible to maintain; and that forces us once more to face the original doubt, which is a feature of the use of all structures. A nirvana position may be the only contradiction-free possibility.
In the 0-D view we are in principle always in a trial-and-error situation, maintaining doubt. Certainty can, at all levels of structuring, only be the result of thinking that excludes doubt about the validity of one’s structures, either by naϊve trust in reality, or by a deliberate ontological leap-of-faith to some dogma.
And there is another paradox : although we start from anthropocentric thinking, we tend to rely increasingly on subject-exclusive mental formalisms and other (including machine) tools; and in order to be able to act quickly and effectively, we often have to neglect the doubt in the practice of life. But in spite of this very prominent, powerful, and inevitable development toward subject-exclusion, we must realize, contrary to what some objectivists and neo-metaphysicists suggest, that we are the originators of the structures and mechanisms, and have to remain the responsible agents in charge. The subject-inclusion means subject-and-world-and-all; not subject-only, which would imply solipsism. That concerns not only the mechanization of thinking by formalisms but also the effect of machines and world-wide communication on our daily life. (See also the appendix on mathematics.)
LEVELS OF STRUCTURING, FUNCTIONS, RELIABILITY
a. Pre-structures. Qualia, self, group identity, with no or only indistinct defining preliminary spontaneous structures. Complex motor schemes (like playing ping-pong) also have no corresponding (preceding, fixed) perceptual structures. Qualia function as biological devices, of differing reliability.
The individual and group self-structures too are not reliably prepared by biological mechanisms, but are designed as required in the activity of living.
b. 0-D gestalt-formations, spontaneous phenomena. They arise mostly without doubt, but may nevertheless be unclear (e.g., clouds), ambiguous as in the Necker Cube and similar designs, or misleading (misidentification). Ambiguities mean that the gestalt-formations relate to more than one more complete ‘object’. Gestalt-formations are tools similar to hands, language, mathematics. They function for perception in a way similar to (and in conjunction with) the elaboration of motor patterns.
c. Gestalt-completion, where needed, is also mostly spontaneous, with help of memory and/or imagination, for instance when the perceived gestalt is incomplete, as when one sees one thing behind another one that partly obstructs the view.
d. Object- and event-completion. This is usually understood as-if one could know, beyond phenomena, complete objects and events. But that is impossible; the knowledge can be improved and made more complete, but the completion cannot proceed ad infinitum, as Merleau-Ponty emphasized. This phenomenological refining process differs in principle from ‘noumena’, ‘things-in-themselves’ which are (postulated metaphysical) guiding structures, although in most of daily life this difference is neglected for practical reasons.
Object-completion works as extension of gestalt-function and can become very efficient, despite the mentioned difficulties. For instance you feel an object in the dark, or in your pocket, and you know what it looks like in light. Object-structures are more, or less, reliable as guides for handling and exploration. Objects can be reliable in the sense that successive experiences of differing kinds conform to the object-structure in its more-complete mental form. In case of discrepancies, the mental object-structure needs correction; for instance in the case of misidentification of objects in difficult perceptual conditions, like vision in fog, hearing in noisy environment, etc. The corrections may improve understanding and reliability. The Copernican revolution is an historical example.
This stabilization procedure works well when the object-completion is reliable : for most of everyday life, and also for many sciences, like much of biology including evolution, genetics, also most of chemistry, earth sciences, etc. The reliability of the operation is similar to that of movements.
Noumena (things-in-themselves) can to some extent be treated as-if they were mind-independently structured realities, MIR. This is often more practical than considering the 0-D origin. Everyday thinking and much of science uses noumena as ‘common currency’, without further discussion; but this implies a surreptitious leap from gestalt to completed ‘object’. And here the mental instrument differs from the (gestalt-)experience; in order to avoid theoretical errors the 0-D origin must be acknowledged in principle.
Plato had made the suggestion that noumena (ideas, forms) are real (and complete) but only their shadows can be known. This is one of the early formulations of the traditional occidental metaphysical-ontological MIR-view. It implies the perplexing proposition that one can affirm (know about) the existence of mind-independent unknowable things - a self-contradiction. In addition it pre-supposes a metaphysical-ontological split between subject and object. This belief has had the effect of excluding the subject from reality for the last 2500 years, except in the form of a theological soul. (While in 0-D there is no such contradiction with a pragmatic-only subject-object difference within encompassing experience). Both of these traditional metaphysical assumptions require an ontological leap of faith.
A subject-inclusive structuring view prevents this difficulty : the ‘shadows’ are working-structures (phenomena) in the subject(s)’ mind, those which are really available. And the designed, or guiding, noumena, also in the mind, indicate that there is, within the framework of our idea or form of the object, much more to look for in objects than the available phenomena.
For this and the following levels, language and verbal communication become additional aspects of the structures. In addition to communication between subjects, word-gestalt-concepts stabilize the functions further, particularly the supra-individual aspect, which contributes, however, to the erroneous notion that the word-forms or -ideas have universal mind-independent (absolute) validity.
e. Numbers avoid the problem of gestalt-based thinking, because they are initially language-supported structures which start out by denoting simple counting actions. One can forestall metaphysical connotations by talking about mathematical tools rather than mathematical objects. In contrast to objects, counting-numbers are unambiguous and complete-in-themselves. Thus the actions can be repeated without error, even by others. They allow complex formal subject-free elaborations (formalisms) of the structure-functions, which are also not ambiguous as such. But as Byers points out, at more advanced levels of mathematics, ambiguity of meaning of mathematical structures is an important driving force for studies in mathematics (see appendix).
f. Metaphysics in the wider sense. As-if-MIR beyond objects, including theoretical frameworks and holistic structures typically use anthropoid authoritative structures (gods, mother nature) that have tended to be used as obligatory, by individuals and societies. They are usually mutually exclusive, but inter-changeable by conversion. Theistic holisms deal with the subject-exclusion of MIR-belief by attributing a soul to the subjects, as extension from God.
A recent development is ‘analytical metaphysics’, a return to metaphysics by analytical philosophy, which tries to describe reality as devoid not only of subjects but of objects as well; the latter are replaced by ‘dispositions’.
Holistic structures serve as functional basis, general framework and reference, for individuals and groups. They are required to a large degree because of the great increase in possible ways of thinking and acting, which results from language use. The dogmas may be enforced by coercion in order to guarantee group cohesion.
The ontology- (MIR-) problem with its subject-exclusion can in theistic holistic structures also be dealt with by transformation of the MIR-belief to mysticism, which allows a more direct exchange between God and individual (e.g., Angelus Silesius, Buber). That can be understood, among other things, as a preliminary stage toward acknowledgment of the unstructured nirvana-matrix, which implies a prior deconstruction of metaphysics.
The effect of the leap of faith is made by stronger by unconditional ontological-metaphysical belief, resulting in (fictitious) certainty.
SOME DIFFICULTIES, LIMITATIONS, AND MALFUNCTIONS OF STRUCTURES
The Paradoxical (Asymptotic) Relation Between Experience And Structures
The structures originate within experience and can therefore not be identical with it. Nevertheless, all structures are freely created within otherwise unstructured experience, with subject-participation, as they are in art, and they are tested in use (they are not discovered ready-made, as metaphysical-ontological foreign bodies, in the flow of unstructured consciousness). Self-structures are formed as needed for individuals and groups : agents of thinking and action. But the center of experience itself cannot become structured; that would seal the fountain of structures.
(i) Experience is wider than the structures that it encompasses.
(ii) But the structures can also go beyond (become wider than, transcend) experience, as tools for designs of action and ‘reality’ (conjectures, guesses), of how things might or should work or ‘be’. In case they are mistaken for ‘reality’ they become metaphysical entities (onta). There is thus a mutually ‘asymptotic’ relation between experience and its structures.
As mentioned above, structures complete objects and functions by transcending present experience; the resulting assumptions can subsequently be tested. But physical objects can only be experienced in an incomplete way. As Merleau-Ponty described it, we can know a stone from various aspects, and in increasing detail, but never completely, only in an asymptotic manner, one might say. (The act of completion would require an ontological leap of faith to MIR-things-in-themselves, noumena).
Structures can also transcend all possible experience by designing needed but un-testable (un-falsifiable) overall epistemological, theological, philosophical, and political structures. If such holistic structures are meant to structure everything they are metaphysical and necessarily self-contradictory (‘credo quia absurdum’, Tertullian; this applies, however, also to naturalism). They require an act of faith with suppression of critical thinking (because it would deconstruct the metaphysics); and in the practice of religion and politics, also reinforcements. Such experience-transcending designs are also needed and created for self- and group-identity, where they are fixed by action (similar to motor patterns). The same happens in art, where the designs remain playful, and their main effect is resonance in others.
Some Examples Of Malfunction :
1. Wrong object-completion - (e.g., tree mistaken for a person in fog, car-wheels go backward on TV while the car moves forward)
2. Wrong event-completion (e.g. to explain the day-and-night cycle, the Egyptian sky-goddess Nut was invented and believed to swallow the sun in the evening, and give birth to it in the morning)
3. Time and space are results of quantifying the flow and extension of experience, with the help of numbers. There is a strong tendency to understand time and space as primary (ontic) entities, which results in endless debates about what time and space are. It can also result in puzzling proposals like the ‘block universe’, where free will disappears, and the subject as well.
4. Wave versus corpuscle - for particle-physics gestalt-function (as implying MIR-entities) is of doubtful help.
5. Qualia - including feelings - have no gestalt. According to strict objectivists they are not real for this reason. Objectivity (a variety of traditional ontology-metaphysics) mistakes object-completion for the basis of reality without examining its 0-D origin.
6. Mind (subjectivity, consciousness, awareness, experience) has no gestalt-basis. Subjectivity is therefore also not real according to strict objectivists. The mind cannot be nor become mind-independent. It is the encompassing background of all structures and can therefore not become completely structured.
The self needs to be pragmatically structured within the encompassing mind, like all structures; it is thus not the same as the encompassing subjective experience, although the self, too, has no gestalt basis.
For this reason, objective studies (and metaphysics-ontology generally, which claims that reality is mind-independent) are not able to deal with the question of consciousness and the mind-brain relation. Exclusive objectivists have made almost heroic efforts to eliminate themselves from thinking, as mentioned earlier.
7. Logical and mathematical formalisms are only one aspect of the ‘truth’ (the aspect that concerns the internal consistency of the structures) and cannot replace subjects’ activity including structure-creation. This is so whether the formalism is handled by machines or by people. Their reach is limited, as is the reach of logic in the wider sense (see appendix).
8. Holism - Extension to theism etc. - In many holistic-belief groups the effectiveness is enforced, since doubt is a threat to the function of the group which bases itself upon its unconditional validity. But it can also produce difficulties of various types, such as clashes with beliefs of others, and interferes with critical thinking. The conflict of the theory of evolution with theistic beliefs is a common example.
Many of the points mentioned in this paper have been described before, for instance by phenomenologists (especially by Jaspers and Merleau-Ponty), but they maintained a simultaneous residual belief in mind-independent reality; and therefore de-construction of metaphysics remained incomplete, and the subject-inclusive constructivist aspect was lacking. The latter was introduced by the Radical Constructivism of vonGlasersfeld and others; their efforts were chiefly prompted by requirements of teaching and of language theory. The 0-D view, centered on the mind-brain question, has to insist additionally on the start of subject-inclusive structuring from an unstructured matrix, which requires complete de-construction-in-principle of MIR, i.e., of metaphysical-ontological structures. All structures, including the exclusively biological ones, arise within the unstructured.
APPENDIX : MATHEMATICS AND 0-D (Discussing some points from W. Byers’ book on mathematical thinking)
In the reflections of this paper I have been much stimulated by William Byers’ remarkable book ‘How Mathematicians Think’. It offers many interesting thoughts about the basic aspects of that field, which is so fundamental to thinking in general and offers more specific formulations of some aspects than epistemology does. Since I am not a mathematician, I may have misunderstood some of what he presents, and some of my suggestions may be erroneous; but I would appreciate discussion.
My general question is whether his understanding of mathematics fits into the 0-D view. My impression so far is that it does, and actually supports 0-D, but I would like to discuss some of his proposals for my own benefit. (Thus I am here not trying to present a review of Byers’ book.) For me the most remarkable aspect is that he emphasizes the difference between ideas which people have and the formalisms and algorithms that can be used not only by people but by machines as well. This I understand is a break with the recent historical tradition not only in mathematics but also in logical positivism and analytic epistemology.
What Is Mathematics ?
Mathematical ideas are both subjective and objective, and they are at the center of mathematics (p.194). A mathematical entity is never devoid of a point of view (p.343). In Byers’ terms, thinking is global, formal systems are only local. Mathematical truth ‘goes beyond formalism’ (Penrose about Gödel) and has an irreducible element of subjectivity (p.347). This formulation is of course quite compatible with the 0-D position that ongoing experience always deals with structures concerning subject plus world plus everything, which are encompassed by it and only pragmatically (secondarily), not ontically (primarily, Platonically), separate from each other.
Byers proposes a unified definition of mathematics as both invention and discovery (p.362), and he wants to preserve this as a defining ambiguity without deciding for one or the other of them. I wonder though whether that definition has to differ from the one of reality, which I presented earlier about the relation between structuring (which I see as primary) and finding : ‘ What one can ‘discover’, according to the 0-D view, is ... how adequate the posited structures are : this happens by feedback, while using them. ’ This could, I think, also include the ‘objective’ aspect of truth (p.367), and the ‘immediate certainty’ which he sees as a characteristic of discovery (pp.327ff) : it means an internal closure of structures that one senses will be able to deal with a question which one has carried around for some time as a problem to be solved (concerning the encompassing and 0-D as a method to deal with the mind-brain question, this happened to me in early 1994).
The 0-D differentiation between structuring and inventing is relevant here : ‘ while all mental (mind-and-world-and-all) structures require our automatic or deliberate structuring, only some of them are deliberately invented. Qualia or gestalt-formations are non-deliberate. There is an increasing proportion of deliberate invention in areas like self- and social identity, language, mathematics, science, technology, art, etc. ’
Byers calls ‘Platonic’ the traditional view that reality is mind-independent (naϊve realism, p.350, or what I have called MIR, metaphysics-ontology). But he agrees with Davis and Hersh that ‘Platonist, formalist, and constructivist’ views of mathematics are like the ‘proverbial blind men examining the elephant’ (p.347) and that mathematics is ‘a single thing’. It is one single thing as a human enterprise, one might say; the formalist and Platonist views are auxiliary developments (see below).
Subject And Object
What Byers calls the ‘fundamental subject-object duality of human experience’ (p.349) tends to be understood in MIR-Cartesian terms. But according to 0-D, it is secondary, pragmatic, and not always clearly defined. A trivial example : a haircut turns a part of you, hair, into an instant object. A more important point is that the structure-generating center of experience cannot become an object without obstructing the center, causing it to cease its activity. This results from the encompassing aspect of subjective experience, which is indeed fundamental, but on functional, not static, grounds. The subject-object duality, though pragmatic, cannot be overcome by turning the subject into an object.
I perceive a somewhat uneasy relation between the stated global subjective-plus-objective character of mathematical ideas on the one hand and questions like whether mathematical ‘objects’, or structures (like for instance ‘zero’, nothing) ‘exist’ (p.99) or ‘are real’ , and also his discussion of mathematical truth in Chapter 8, on the other. ‘Existence’ questions inevitably imply Platonic (MIR) reasoning. (Instead one can ask : are these ideas useful ?, how far can they be expected to be reliable ?, etc.)
What And Where Is Reality ?
Similarly, Byers discusses (p.153ff) the question (or paradox) whether ‘geometry is real’ : is there ‘something out there’ called ‘space’ ? In that case Euclidian geometry would be a way of discovering and codifying the pre-existing properties of that space. The Greeks thought that this was so, because they were convinced of the (Platonic) MIR-interpretation. This was universally accepted from them, for instance by Newton; and by Kant (who even thought it to ’be hard-wired’ into everybody’s understanding of the physical aspect of mind-independent reality; p.156).
After a change from imaginary given primary structures (Platonic MIR-ontology-metaphysics) to 0-D structuring as required within unstructured encompassing experience there can be no such thing as ‘out-there’ in the ontological sense; though as working-fiction, i.e., as subject-inclusive design, it can still, with the needed precaution, act as a guiding idea. Reality is the ideas (structures) which we accept as trustworthy.
As mentioned in the first part of this paper, time and space are results of quantifying the flow and extension of experience, with the help of counting (numbers). There is strong tendency to understand time and space as primary (ontic) entities, which can result in proposals like the ‘block universe’, where free will disappears.
And as also mentioned earlier, Whitehead had noted that all Western philosophy amounts to footnotes to Plato - but one has to add : and of concomitant attempts to get around the side-effect of Platonism : the impossibility to know the positive pre-structured given realities, which he asserted, for the sake of certainty. The discovery of non-Euclidian geometry finally showed that this cannot be so in mathematics, and that Euclid had instead ‘created’ a version of space (as one would expect from 0-D).
Byers calls the resulting view ‘relativistic’; I would call it functional structuring : a change from imaginary given ready-made primary structures (ontology-metaphysics) to structuring as required for handling unstructured encompassing experience.
These considerations become even more important when dealing with certain topics, like randomness and chaos-theory (p.314). Here ‘systems’ are no longer deterministic. Newton thought the world was a machine governed in a predictable manner by differential equations; but in chaos theory each (everyday) system has an event-horizon beyond which it is impossible to predict its behaviour. And there can be no theories of everything (p.318).
I would like to coordinate these points with some ideas from 0-D structuring. We have immediate gestalt-perceptions, trust them as reliable and transcend (extrapolate from) them to complete objects, and use the latter for prediction, acting as if we knew them. But this is an over-extension, we cannot really know complete objects, except as guiding metaphysical speculations. The same has to be said about event-completion, such as Newton’s world-machine. Because we transcend the extent of what we are able to handle, unaware of the limitations of the structures, the unstructured re-enters, uninvited. All structures are limited, but notions like ‘God’ or ‘Nature’ are meant to be universal; as a result of the incompatibility between their limitations as structures and their universal aspirations they are necessarily self-contradictory.
An inadequate over-extension of the gestalt-object-concept may also play a role in particle-physics (p.318), where it is said to be not clear whether a quantum is a wave or a particle. One should note that this is a metaphysical (MIR-Platonic) question, which pre-supposes that the macroscopic notions of waves and particles are ‘certified’ onta, and that they are valid for sub-atomic particles. But there is no basis for this assumption to start with; such an interpretation goes beyond the reach of the gestalt-object structures. Or, in Byers’ terms, ‘the natural world as revealed by quantum mechanics is ambiguous’ (p.319).
In more general terms, we habitually take ordinary gestalt objects to be the non-ambiguous standard, but this too is an implicit metaphysical-ontological assertion which transcends not only ongoing experience, but also safe use of concepts and procedures. We start from gestalt-formation, because it is usually a reliable tool, extrapolate from there to complete-object-certainties, which also tend to work well although they are not really entirely within reach. And then we go still further, to assumptions that are even less warranted in some areas of study. As a result, we finally face puzzling opinions like (p.344) Heisenberg’s ‘atoms are not things’ (although one can nowadays take photographs of gold atoms), or that ‘the quantum world is objective but object-less’ (N. Herbert). Perhaps one can ‘translate’ the last statement as follows : ‘the quantum world includes mind and world, thus it is not solipsistic, but traditional metaphysical ‘objects’ need to be re-functionalized by tracing them to their origin’.
Reification Of Tools
Byers calls the change from mathematical process to mathematical object ‘reification’ (p.67, etc.); that sounds like a promotion; does it imply only res-ification or also real-ification or even rex-ification ? In other words, does it imply abandoning ongoing structuring activity in favour of (Platonic) MIR-belief ?
Numbers start out as tools, made and used by people in their quantifying activity, rather than as metaphysical objects or truths. To see structures as tools has the advantage that one can more functionally deal with some questions which have historically caused much concern to mathematicians : for instance whether zero or the infinite ‘exist’ or are ‘real’ (see above). The ‘zero’ notation started out in India as indicating ‘no entry’, which means a human activity, not a metaphysical entity. Zeno’s paradoxes are further instances of the complications arising from MIR-belief.
One can use a variety of tools to drive a nail into a wall; a hammer is only one of them, though it is usually a good choice. String theory serves to unite general relativity and quantum mechanics which are very accurate but mutually incompatible with respect to black holes and the big bang; it has several distinct versions which work, but they have a ‘hidden unity’ (p.64).
The MIR-view in mathematics reportedly led to the death by drowning of Hippasus of Metapontum, a member of the Pythagorean sect, on the order of Pythagoras, because he proved that the square root of two is not rational. The reason was that the Pythagoreans had accepted the fundamental doctrine that natural and rational numbers, i.e., fractions of whole numbers, were the MIR-essence of reality (in some situations mathematical proofs can be dangerous to your health).
Structures, Formalisms And Thinking
Byers shows that mathematical formalisms and algorithms arise in ambiguity, contradiction and paradox. These terms refer to the function of structures, and thus I see them not as primary (Platonic), but as special instances of functional characteristics of structures in the context of a more global concept like ‘the unstructured’, within which all structures are created. The reach of structures is circumscribed, and often can be understood in more than one way. Numbers can be understood to indicate counting activity, as they did originally; but they and other mathematical concepts can also be understood in other ways, as the Pythagoreans have shown long ago. For instance ‘the one’ (το ἑν) as unity of experience, or of ‘being’, the equal sign as identity or process, etc.
And also, the structure-creating center of experience cannot become structured, because that would seal off the source. If present structures lead into blind alleys, their correction, or the creation of new structures, is required to overcome the difficulties. But the unstructured acts indeed as a stimulus for structure-function and -use.
Byers makes the ambiguities, etc., the center of mathematical progress. How would it be to go one step further back, to the unstructured ?
The Dream Of Reason And Its Limits
The idea of formal (i.e., mind-independent) proof being equal to mathematical truth has played an important role in the 19th and 20th century, as seen mainly in the work of Hilbert, Frege, Russell, and Whitehead, until Gödel showed their inherent incompleteness (pp.205, 272f). Remarkable features of Gödel’s incompleteness result are firstly that he showed the limitations of logical thinking starting from within logical thinking itself (p.282), and secondly that he did it despite his Platonic bias (p.271; later on in his life he worked on an ontological proof of the existence of God).
The wish of the formalists had been to complete the ‘dream of reason’, the wish for order and predictability, in the work of not only Euclid but also of Parmenides, Plato and Aristotle. In effect this is a part of what could be called a 2500 year long search for ‘truth without people’, or at least without minds, which, as mentioned in the first part of this paper, has recently produced puzzling results such as wanting to replace the mind by ‘embodied cognition’, or by the ‘mind-brain’, and the development of ‘analytic metaphysics’.
The dream of reason, it turns out, was not only a pie in the sky, but beyond that a potentially counter-productive idea which would have made human thinking superfluous, and replaced it by mind-less algorithms or machines.
The Unreasonable Effectiveness Of Mathematics In The Sciences
Wigner suggested that mathematical definitions captures deep aspect of reality, and that this is the reason for the effectiveness of this method (p.381). Byers emphasizes that ambiguity and paradox are aspects of mathematical thought that differentiate the ‘trivial’ from the ‘deep’, and that new unified frameworks of thinking spring from there.
One might also consider the difference between the problems related to the transcendence of gestalt-object-tools in traditional thinking, mentioned above, versus the digital (counting) aspect of numbers. At least initially this avoids the transcendence difficulty of gestalt-formations and ‘objects’ (the ‘digital method’ also functions biologically, for instance for DNA, in synaptic transmission, or in the retina).
Later-on, of course, something similar to transcendence happens in mathematics too, when the limits of determinism are transgressed, in form of the ‘event-horizon’. But there is a large field where the numbers and the digital principle have the advantage over gestalt-object-function. That may be behind the admonition to researchers in physics to ‘shut up and calculate’ - the shut up concerns trying to ‘understand’ reality in the traditional gestalt way.
Computers Cannot Do Mathematics
For computers the formal proof is all there is to mathematics (p.368ff); while mathematical ideas are non-algorithmic (p.253), and logic is not the absolute standard (p.257). For the mathematician there is a whole universe of intuition and understanding that lies behind the formal proofs. And mathematical procedures differ from the experience they deal with. Formal systems are local, not global (p.282). These ideas agree quite well with Feyerabend’s conclusion that there are only islands of rationality in an ocean of irrationality. Or as Lakatos put it (p.265) there is an alternation between doubt and certainty; thinking creates structures at the edge of paradox or of chaos (Byers), or - I would add - within the unstructured.
And Hannah Arendt pointed out that totalitarianism is dangerous not because it is irrational but on the contrary because it is too rational, with logic suppressing the necessary insecurity of thinking (p.259). Of course the irrationality is at the start, in the purported over-all reach of the general political idea which is then promoted ‘rationally’, and by force.
Ideas Versus Formalisms
Thus it is an important new departure when Byers sees the essence of mathematics in the development of ideas in mathematicians’ minds, and not in mind-free algorithms or formalisms, nor even in logic per se. One might add : this also concerns the essence of thinking more generally, which is not defined as only following rules (as for instance Pinker had proposed, p.371; that could become a sort of self-fulfilling prophesy-metaphor). Thinking still requires subjects and their creativity, despite all the power and ubiquity of algorithms and machine-functions. That is also implied in the 0-D principle that ongoing experience encompasses all structures (and machines, by the way).
Byers’ view makes mathematics a more human enterprise than one would assume from the many discussions of artificial intelligence and related matters (see also Byers’ discussion of this topic, p.260). Thus the main thrust of his opinion is, I think, very similar to what I have proposed in this paper, and earlier ones. Humans have to remain the responsible agents (Müller 2004) - or else our tools may use us, as their mind-less extensions.
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Byers, W. (2007) How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics. Princeton University Press. See also TAs 98 and 99 in KJF, where Chapters 7 and 8 have been posted for discussion.
Feyerabend, P. K. (1999) Conquest of abundance. A tale of abstraction versus the richness of being (Edited by Bert Terpstra). University of Chicago Press: Chicago.
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Müller H. F. J. (2004) : People, Tools, and Agency : who is the Kybernetes ? TA78 in the Karl Jaspers Forum. An enlarged version (78CF) of this paper (same title) is in ‘Constructivist Foundations’, 1.1, 1 Nov 2005.
Müller, H. F. J. (2007) Brain In Mind - The Mind–Brain Relation with the Mind at the Center. ‘Constructivist Foundations’ 3.1, 30-37. An earlier version is available in the Karl Jaspers Forum as TA45 by Muller : Brain in Mind - Hypotheses for Discussion (28 September / 6 November 2001)
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I am interested in commentaries, critiques, and suggestions.
Herbert FJ Müller
e-mail <herbert.muller (at) mcgill.ca>