TA112 (Müller)

Response 1 (to C1, Byers)


by Herbert FJ Müller
9 February 2009, posted 21 February 2009


In C1, William Byers comments that he agrees with the following statement from  TA112 [24] :

  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’.     

An interesting point here is, I think, that this assessment of the historical development results from dealing with two quite different questions.  It expresses a central concern in both his concept of what mathematics is or should be,  and in my notion of epistemology in more general terms, as needed for the purpose of finding an access to the mind-brain puzzle.   CP Snow’s problem of the ‘two cultures’ re-appears, surprisingly, at the center of mathematics :  mathematical problems and ideas versus algorithms and computers.   And also, Byers’ proposal evidently means a break with the metaphysical-ontological assumptions which have prevailed in occidental thought since the Greek classics.  


For purposes of discussion, I will summarize the conceptual situation as follows, with inclusion of the numerical aspects.

(a)  Spontaneous qualia and gestalt-formations, and the distinctions between one, two, and many,  are biological ad-hoc tools for dealing with otherwise unstructured experience, for both animals and humans.  They do not per se imply anything about a mind-independent reality (MIR).

(b)  MIR-belief starts with the assumption of knowledge of complete objects (and events), which is not entirely supported by, and thus transcends, gestalt-formations, toward ontology-metaphysics :  things-in-themselves, noumena.   (A non-metaphysical description would be that :  this and the following steps are mind-internal heuristic completions, reality-designs for comprehension and action).   From here on, language use plays a role in at least two ways.   Firstly, the use of language is a crucial factor in the great increase of communication, and particularly of possibilities for thought and action of humans, with the side-effect of uncertainty of what to do (which is under-determined by instincts).   This in turn results in a wish for guidelines from ‘outside’.   Secondly, the notion of noumena (complete objects), and also of everything having to do with numbers beyond level (a), can only be achieved and stabilized with the help of language (in the general sense, and in the more specialized sense of mathematics-language, for instance). 

(c)  Once a constructed ‘outside’ reality has been accepted as the true reality, it tends to replace the more direct original subject-inclusive experience, and individual structure-creation-as-needed.   And then a wish for more complete knowledge of the imagined MI-reality naturally arises.   In response, holistic structures are designed, they are of theistic, naturalistic, or other, type.   They are thought to be true-in-themselves, for instance on the basis of theistic or other dogma.    For naturalistic MIRs  the idea emerges, mainly since Descartes, that they are mechanical and can become algorithmic, with the more recent consequence that they can be handled by machines.   (This development started from the ‘dream of reason’ of Euclid, Parmenides, Plato, Aristotle;   and was recently renewed in programs of Hilbert, Frege, Russell and Whitehead, etc).

(d)   MIR-belief results in inversion of agency and of thinking :  our tools   -   ascribed authorities, postulated noumena, a mind-independent realm of mathematics, even computers and other machines   -   are thought or implied to be the agents, and humans are in that case only their extensions.    The source of subject-inclusive agency, including of structure-formation, is thereby obstructed.   As Rilke put it, there are structures (Gestaltung) that act as  ‘traps around the free exit’.    That is, instead of dealing with subject-inclusive experience itself   -   the existence of which is often simply denied, and which may even be condemned as a ‘disease of thinking’ (Wittgenstein)   -   thinking becomes confined to accepted and transmitted structures of imagined MI-reality.  

(e)  Difficulties with the MIR-proposition have long been pointed out, for instance that theistic belief, although desired, is absurd (Tertullian);  that logical-mathematical structures are inherently, and thus inevitably, incomplete (Gödel), circumscribed (Feyerabend), local, or paradoxical (Byers).   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.


(f)  The problem of inversion can be addressed by returning to the unstructured :  as the origin, or as a goal such as nirvana.   That does not abolish the structures but it helps us to see them once again as tools of humans who use them in order to master the unstructured.   (Metaphysics-ontology is neither accepted nor rejected as such but instead understood as mind(s)-internal reality design, a change from incomprehensible MIR-belief to a subject-inclusive structuring activity.)   One might add that the question of science versus religion can also be addressed from here :  provided that ‘religion’ is not equated with theism.   A non-theistic religion, based on nirvana, poses no principal difficulties to a unification with science  -  including evolution.




Concerning the other points of Byers’ commentary :


Re.TA112[18] :  Plato said in the cave parable that the forms or ideas are not accessible to humans; we can only know their shades.  This implies that he understood them as mind-independent, so far as I can see.   The term ‘objective’ as it is mostly employed also implies mind-independence;   although one can argue, as I have in TA112, that the scientific method of objectivity does not necessarily exclude subjects; it only brackets them.    The ‘provability’ would seem to be a different question, at least in principle. 


Re.[22] :  I agree entirely that numbers are more than tools for counting, but I cannot see that the philosophical questions have been discussed before counting action began (i.e., long before the Pythagoreans).   That is difficult to study in the absence of written documentation from those times.   But it may be relevant for this question that there are still now some tribes in the Amazon area who have no numbers beyond two or three.   See



Re.[23, 26] :  My question is :  is the ambiguity primary, or secondary to the original lack of structure ?    -   The Lakatos quote  is on p.262 of your book.


Re.[27] :  Popper was an ontologist, and that is necessary for belief in objectivity of the kind which is independent of what people think.  I don’t think there can be something like a ‘relative objectivity’.   Either reality includes subject(s)’ thinking or it does not.   -   The notion of ‘relativity’ is often understood to mean that all opinions are equally valid.    But opinions have to prove themselves to be ‘viable’ (vonGlasersfeld’s term);   if they are not viable they need change or replacement.   In the political and ethical fields, the absence of absolutes is something one has to learn to deal with   -   as it becomes very clear in everyday political negotiation.  




Herbert FJ Müller
     e-mail <herbert.muller (at) mcgill.ca>