[1]
ABSTRACT

This response deals with points discussed by Mark Hubey in his commentary, and, as he suggested, with some emphasis on definitions. The following topics are included: truth and reality (with an excursion on Wittgenstein's Tractatus), numbers, mathematics, and invariability, objects and related terms, matrix, and the mind's center. Definitions are task-oriented, and task-dependent, and it is important to consider their origins. It is suggested that science be defined by its purpose of striving for reliable and comprehensive understanding rather than by mathematical or other methods, or by a wish for impossible ontological ('objective') truth.


[2]
TRUTH AND REALITY

In line with the topic of my paper, and also because they are the foundation for other concepts, I will start with these two concepts. In my opinion (TA1 [31ff]) they both depend on an act of faith in the reliability of the mental structures which are being used. In the case of 'ontology' this reliability is implied to be unconditional - which is I think an error but of course a very common one. Hubey writes <1> about 'imparting' reality to something, such as an object, which I assume means the same as what I just wrote. But it is not clear to me from what he says whether he understands this as operational (as a working property, where the 'reality' quality is constructed, so-to-speak, for experimental purposes) or as unconditional (that is, ontological reality, where we only have the task of finding out about an already existing immutable reality). My impression is that he alternates between the two meanings. Let me present some evidence for my opinion.

[3]
Hubey agrees in <21> that all experience is subjective, and <30> that knowledge is belief, but he makes some statements which conflict with this. For instance, he writes that experience is also 'objective', which he <21> equates with 'commonality', 'and that is not the opposite of subjective'. Further, in <41-42>: ' There is no possibility of starting with zero' because 'our brain is constructed from the real world'. Here by 'real' he appears to mean 'ontological' or at least 'mind-independent'; starting from zero in contrast means (TA1[30,32]) constructing reality within experience. I have proposed that we do that all the time, but we are not usually aware of it. Here too Hubey appears to imply that reality is mind-independent, which conflicts with his earlier statement <30> that knowledge (of reality) is strong belief and thus a mind-function. <42> 'Belief is built up on data which is inputted ... we cannot function without a large set of beliefs'. This is ambiguous with respect to what reality is. What are 'data' ? Here we come close to a communication problem, and I think this is because his definition of reality oscillates between what is fixed by 'knowledge' (strong belief) and ontological absolute (mind-independent) reality.

[4]
<34-37> 'The discussion of who gives data to whom' ... : 'we make theories (tentative) and reject them (if falsified via an example)' since we are born, and science works that way too. But knowledge is not simply about truth or its negation. And '... apparently it is thought that there is no mathematical way of modeling' how the brain works, and he then lists some possible mathematical techniques for this.

[5]
My reply to this is that it may become possible to understand brain functions mathematically, and to model them. What I say is not possible, and I would expect that Hubey agrees, is that such a model has awareness, or experience, and in particular: it cannot have subjective experience. One might refer here to Penrose's book 'The Emperor's New Mind', which makes the same point; unfortunately Penrose then went on to suggest that particle physics could somehow overcome this difficulty (in an objective way, that is), and this same error (I think it is an error) has been engaged in by a number of others, including some participants in the present discussion of my article. The only way I think subjective experience could be produced by computer (and I hope that will forever remain a thought experiment) is the following: if the complete human genome becomes known, and if it then becomes possible to synthesize it in a computer-guided process, the resulting human being would be conscious in the same way as everybody else.

[6]
And <29> 'Infants a few months old ... believe that the world disappears if they close their eyes. I don't think this is a beneficial approach to solving great problems of the world '. Indeed not, an image of mind-independently persisting reality is much more helpful than a world which has to be re-constituted every time we open our eyes. But I also think this is trying to tell us something: children need time and maturation to build up a 'reality' inside their experience, with the help of tools like mental structuring and memory. This built-up reality which goes beyond (transcends) present experience is what is often called metaphysics, or ontology (TA1[35]). Here at any rate Hubey again seems to endorse a mind-independent reality of metaphysical type, and it is not evident how he reconciles this with some of his other statements. In effect he says that reality is both subjective and mind-independent, which is self-contradictory.

[7]
Hubey points out <11-13> that my formulation 'if reality were mind-independent, the mind would have to be mind-independent in order to be real' could easily be inverted, to the effect that the mind is not real but the brain is. My main point here is of course that this (erroneous) inversion is actually being used in all seriousness, and in many publications. That (in objective terms) everything is in some way connected to everything else <12> is a different question which has nothing to do with the mind being at the center of experience. What I am proposing is neither a 'grand solution' nor a 'word trick' <13>. I am saying that reality is a product of the mind within the constraints of mind-nature experience.

[8]
(Hubey discusses 'diagonal arguments' <13ff>. The only reference to this term which I could find concerned Georg Cantor's Set Theory. If this is his meaning of the term, and if it really is important, please let me know, and I will try to read up on this, although I am not certain how far I will be able to go in it. For the moment I will stick to Hubey's formula <14-16>: x is a function of x. This works, as far as I can see, when the 'function' is 'one times', or 'divided by one', or 'plus or minus zero', etc.; and Hubey concludes that ' in more abstract settings this becomes the infamous diagonal proof or self-reference '. Fine, but what does this have to do with my statement that 'if reality were mind-independent, the mind would have to be mind-independent in order to be real' which deals with assumptions about mind and reality ? Both of these cannot be treated as numerical units.)

[9]
<40> 'I don't think anyone knows what metaphysics means'. Sure this is a difficult topic, but after all it has been used since Aristotle, so there must be a reason for that. Hubey seems to have a somewhat negative opinion about philosophers - I am not a philosopher by any means, but I agree with Jaspers that everyone has philosophical opinions, whether or not he is aware of it. On the other hand, Hubey is to be commended for engaging in lively discussions about topics which are least in part of philosophical nature. He really dislikes 'postmoderns', and there is perhaps one might say an over-abundance of writing from that side. But still they have a few valid points, in particular concerning the difficulties with the 'referent', which (I think) really refers to the impossibility of ontology, and thus of permanent metaphysics. 'Unobservable' does not catch the meaning of 'metaphysical', because 'observations' themselves are made in conformity with expectations extrapolated earlier from experience and which go beyond ongoing experiences (which they 'transcend', i.e., they are metaphysical) (cf. TA1[35]).

[10]
In <57> Hubey writes that in science there is only one truth, and that more than one is not tolerated. This is somewhat baffling, it seems to be a rather idealized statement, which says more about his convictions than about science. For human matters this is not so, there are oodles of truths offered every day, including by scientists. He also cannot mean, for instance, computer models of the weather. But even some simple arithmetical questions do not comply, for instance for the square root of four you have a choice of true answers between plus two and minus two. But of course 'all ideas are not equally valid', most are more, or less, adequate tools (rather than being true or false). And as he says himself <58> all truth is provisional, and 'only falsity is absolute'. (But how does this fit with his idea that there is only one truth ?)

[11]
However, even that may be an overstatement; it derives from Popper's view that (ontological) truth can only be falsified, not verified. The problem here is, in my opinion, the notion of ontology, as I have suggested previously. Falsification does not defeat ontological truths (which are statements of belief) but indicates that a better tool (concept) is needed. <31-33> Epistemology 'has been already talked about for a long time', machines will take over with lots of knowledge. Truth is defined as whatever cannot be shown to be false, 'truth is temporary and provisional'. In section <60> he suggests that epistemology is being taken out of philosophy and put into the domain of artificial intelligence research. Now here I think is a chief reason why AI gets stuck as far as subjective awareness is concerned. They don't realize what the question is, and go on asking objective questions about a non-objective topic. This can continue for a very long time (namely until they realize that the main question is indeed conceptual in nature). See also his <63>, same point.

[12]
I am aware that some people get upset when it is suggested that there are no pre-existing structures, for instance. However, this I think cannot be avoided, because simply assuming such pre-existence leads into a
blind alley, never mind the mathematics. 'The mind' is not a countable item because of its unstructured center, and neither is reality, which is a result of belief (TA1[31]). 'Compressed' items can be processed by algorithms, and this is one of the ways in which objective science operates. This is though not the same as 'real', because, let us say, pain or joy cannot be compressed in that way but I would assume that even Hubey does not propose that this makes them unreal. This point is evidently difficult to communicate, so let me re-state it in a different form.

[13]
You might undertake a self-evaluation, concerning 'where you are coming from', or more exactly, where you believe or imply the origin of your thinking is. For instance, do you think that 'objects' or 'data' are the basis of the world and of knowledge ? (You would then believe in mind-independent reality, of Platonic, of idealist, of empiricist, of materialist, etc. type.) Or do you think 'numbers' are the basis of everything ? (this type of assumption lead the Pythagoreans to number worship.) Or that 'scriptures', including the teachings of Confucius or the Buddha, etc. contain the real truth ? (In which case you would be a theist or something close to it.) Do you think that 'science' furnishes the truth about all that can be done and known ? (This means scientism of some sort.) You might also hope that particle physics will furnish the answer (or theory) for everything (in which case you are probably a materialist, but with doubts whether materialism in its historical incarnations works.)

[14]
Each of these opinions has its, shall we say, 'operational' value, but in case you use them as fundamental truths rather than in an 'as-if they were fundamental' way, in all these instances you will probably have some difficulties bridging the gap to the other fields of belief. My proposal is to start from nothing, and then follow the emergence or crystallization or formation or construction of mental structures - from inside the unstructured matrix of mind-nature experience and in an experimental, reactive (feedback) fashion - to where they are now, in which case it is evident that all structures are secondary to this, their origin.

[15]
<43-44> Hubey writes that transcendence is 'something like inductive generalization'. 'We have tools which know/observe things we can't see directly', like microscopes, telescopes. - I say: tools don't know (i.e., believe) or observe anything, we do, and tools help us with that, for instance the use of icons, or of mathematics. 'The average of all subjective experiences is practically what we mean by objective' - alright, except for the term 'average'; consensus would be more to the point. 'Besides, isn't the whole business of science, the creation of objective, correct, precise truths from subjective experiences ?' This I think is a useful statement: (a) it acknowledges the origin of knowledge in subjective experience, and (b) it shows the function of conceptual structures in creating reliable tools. And <45> math is a public language. The main point is, however, the creation of reliable mental tools. The reliability of scientific belief (knowledge) is crucial;it distinguishes it from other ('loose', and authoritarian) beliefs, and a formulation of this type might be able to deal with anti-science attacks, which are not easily repelled by appeal to mathematical correctness or ontological (so-called 'objective') truth.

[16]
<51-57> Hubey interprets my use of 'positive and negative anchor points' as electric charges or feedback, both of which are rather far from what I had in mind.It also does not mean good or evil, nor arithmetic properties, or quantitative versus quantitative, nor what postmodernist writers may have written about that (I would not know). It appears that at this point we are quite out of touch with each other, and therefore let me re-state what I mean by positive and negative anchors. I guess that the meaning which he would most likely recognize is that of positive knowledge, as in 'positivism'. With positive anchor point I refer to: acceptance of a source of secure knowledge, such as offered by religious teaching or by scientism. By negative anchor point I mean the acknowledgment that such anchor points are fictitious although they can be used on an as-if basis. Now,how can I say this in 'mathematical' terms ? Perhaps: If one recognizes a negative anchor point, the positive knowledge becomes a limit, almost but not quite nothing see [28] below), which still directs thought and action (Jaspers used the word 'ciphers', which is less 'mathematical'). Does that work ? If it does, it might actually be more helpful than 'negative', or 'zero-reference'.


[17]
LUDWIG WITTGENSTEIN'S 'TRACTATUS LOGICO-PHILOSOPHICUS'
seems to have an approach which in some respects is similar to Hubey's, and it may offer some clues why discussion can at times become difficult. For instance, Wittgenstein's formulation (proposition 5ff) 'a proposition (Satz) is a truth function' may be, but does not have to be, understood in the sense that it implies belief in mind-independent truth; it works also for the meaning that truth is a belief product, although the epistemological connotations are different: the 'truth' is then a structure within the constraints of mind-nature experience, which is converted into truth by an act of faith.

[18]
Wittgenstein was concerned with the symbolic-logical structure of language, but not primarily with the formation of reality (the world), which he wrote consists of 'everything that is the case' and 'atomic facts' (propositions 1 and 2). But how does one decide what is and what is not 'the case', and what is, or not, an 'atomic fact' (a somewhat puzzling translation of 'Sachverhalt') ? Wittgenstein described sentences and propositions as pictures of reality; 'in the picture and in the pictured there must be something identical in order that the one can be a picture of the other at all' (2.161), but his opinion that 'there is no picture which is a priori true' (2.225) suggests that he did not believe in absolute reality. 'In logical syntax the meaning of a sign ought never to play a role; it must admit of being established without mention being thereby made of the meaning of a sign; it ought to presuppose only the descriptions of the expressions' (3.33). ('The pictured' is what others call 'the referent', that is, the mysterious metaphysical reality.)

[19]
Within the Tractatus at least these terms remain somewhat in the air, it seems to me. Perhaps he actually wanted to leave the question - what reality is - open, in part because he thought that (other) philosophers' opinions about such questions did not make sense: 'Most propositions and questions, that have been written about philosophical matters, are not false, but senseless' (4.003). In a letter to Russell he wrote that his 'main contention' was was the distinction between what can be said in propositions - i.e., in language - and what cannot be said but can only be shown ('you have to construct your own world in your experience', I think, is a possible interpretation here). This he said was 'the cardinal problem of philosophy' (Malcolm). And of course, 'Whereof one cannot speak, thereof one must be silent' (7). The Tractatus has been sometimes interpreted as anti-metaphysical, sometimes as profoundly metaphysical in nature (Malcolm), which in itself is interesting.

[20]
For the present topic (the reasons for the difficulties of discussion in this area) one may point to (a) the use of ambiguous concepts of reality, and (b) the emphasis on logical-mathematical procedure and procedural truth rather than on reality, which are implied in a point of view like Wittgenstein's. It seems to me, and here I would appreciate receiving opinions from others, that leaving the question of reality open in such a way (I assume this is the attitude of both Wittgenstein and Hubey) supports, and is in effect equivalent to, the notion of 'working metaphysics' which I have suggested (TA1[28]): concepts, logical and mathematical propositions are used on an (in principle) temporary or ad hoc basis, and to the extent that they work, and this justifies the beliefs in their 'reality' or 'truth', which are opinions about reliability. Inside logical and mathematical systems, 'true' means 'consistent within their rules'. My main difference with respect to this opinion would then be that this position should be explicit instead of implicit.


[21]
NUMBERS, MATHEMATICS, AND INVARIABILITY

In contrast to the above questions, 'two and three is five' is true because we have set the meanings of the words up in that way, and originally the meanings refer to simple counting activity which can easily and reliably be communicated and shared. Mathematics is a central concern in Hubey's argumentation, and this presents particular, and welcome, challenges for the discussion. Since mathematics is, among other things, an experience, and actually an instrumental structure formed within experience, I take it that he agrees that there is a subjective aspect to mathematics, and that belief plays a role in establishing mathematical results; this does not imply that it is 'only subjective', nor that the belief is ad libitum. On the other hand, he proposes that it allows only one truth (see [10] above).

[22]
Hubey points out <7-8> that mathematics can easily deal with changing things. But this it does with the help of 'formulae' which are (for the moment of use) un-changing; they are used on the basis of the same
('working metaphysical') invariability as 'concepts' or 'objects': all of these are invariable mental tools, they are used as needed, ad-hoc, temporarily, but thought to be valid - though open to testing. They are scaffolding (or skeletons) for stabilization and expansion of thinking, and can be constructed and modified as needed.

[23]
Actually this is a good illustration of what I wanted to show: we, that is everybody including mathematicians, master the ongoing flow of experience by using temporarily invariable mental tools ('working metaphysics'). As long as one does not assume an unchanging order this is fine; but many people tend to feel more comfortable when things stay the same, without question.

[24]
Hubey writes: <18-19> '... math is a set of tools for knowledge compression. And sciences are those sets of information/knowledge that have been properly compressed. If some people who read this are looking for specific structures (math) in which the mind works (compresses reality around it and stores it, and operates on it), then I am sure they will take great offense if someone claims that there is no structure (see my discussion on this in [12] above), or that someone says that there is structure after all. The former will draw ire, and the latter might draw 'No kidding'. Compression of data is done via algorithm, and this says that whatever is being compressed has a structure or order. The algorithms take advantage of existing order/structure to compress information/data. It is this compressed form of data/information that we call knowledge.'

[25]
Mathematics indeed deals with objects or other items which can be counted, and the items must already have been accepted as items before their utilization in this way, that is, pre-fabricated before the mathematical or logical treatment. For instance, Set Theory deals with aggregates of items, which have obviously already been accepted as such. It can say nothing about what goes on before, about the unstructured origin and the formation of structures within it, which is being discussed in my article. The unstructured center of the mind does not qualify for objective scientific, including mathematical, analysis. In mathematics one has to count something, and one can only count 'entities' - which are pre-structured in some way. Without structure there is nothing to count or measure. In other words, the mind does the counting but cannot be measured or counted.

[26]
<46-48> 'Infinite series can have finite sums' - fine, but this does not help Achilles overtake the turtle (which is the topic under discussion here, TA1[41]). He will get stuck beside it. The difficulty does not lie in the answer but in the question. And where and what are time and space ? Are they primary, with a mind-independent existence, or are they, and to what extent, our creations within the confines of experience? 'We move through' them (I think) because they are structures within our (individual and communal) experience, which flows all the time, and organizes itself both longitudinally and laterally, as one might say (see TA1 [42]). Hubey says that we cannot go back in time - that in principle acknowledges the primacy of experience, and it is better than phantasies about 'time travel', which have on occasion been offered by some physicists.

[27]
<49-50> 'Numerology' is discouraged, another good sign. Hubey advocates a mathematical description of velocity, and once you use that type of language, you have to be consistent, including 'zero velocity' rather than 'absence of velocity'. He contrasts that to 'philosophy' in which 'objects' have or don't have 'properties', such as for instance velocity. 'The proper way to do physics and to look at the objects of the world is to think of them as property tensors in which the values of the various components change ... state vectors that describe the system'.

[28]
If I may 'translate' this into my terms: we deal with happenings ('functions' if you prefer) within experience. To fix them for purposes of stability, in static form, in the form of entities or objects, can lead to difficulties, because it may result in (impossible) ontological entities. But numbers need 'entities' to be associated with (e.g. to count), that is how they started in the first place. Is it useful to say that the history of mathematics is a fight with (or maybe against) its own numerical (integer) basis ? It seems to tear numbers down to almost but not quite nothing, for instance in differential calculus. Perhaps this could be compared with the epistemological question of the ontological 'referent' which recently has also a tendency to almost but not quite disappear. In both cases this would illustrate the 'working' (or maybe he would prefer a mathematical term like 'tangential') nature of mental tools, which become less static and more functional in the process of being questioned (elaborated, differentiated).


[30]
OBJECT and related terms

Objects are circumscribed aspects of (or better within) mind-nature experience. They can be handled as-if they were independent of mental activity, although on closer inspection they turn out not to be mind-independent. The use of the term 'objective reality' tends to imply (although it does not have to) that the speaker believes that the object in question is mind-independently and undoubtedly real, without as-if. This 'imparting' of 'actual reality or existence' <1> to objects is an act of faith. Compared to 'subjective' assumptions, the speaker or thinker tends to be more confident in the persistent and 'consensual' <6> reliability of his belief. Many investigators think that objectivity is the only valid way of looking at things ('exclusive objectivism'); in my opinion it is a useful but facultative way of dealing with experiences. (Ayn Rand <1> or Marx <4> need not concern us here; the concepts of 'I', 'soul', or 'ego' attempt something similar with subjective experience). Also, it is nice to be able to feel comfortable with mathematics, but does that necessarily imply that everybody wants to be <4> a mathematician ?

[31]
Sunburn <10> has subjective and objective aspects or 'components'. The subjective part is not open for measuring and calculating, only the objective aspects, which can be observed not only by the person concerned but also (and often better) by others. The center of all subjective experiences including sunburn is not structured, and therefore not available for counting or measuring. (One may of course say that if someone has a severe sunburn he has no time and energy left to think much about the center of experience, he spends all his thinking on the problem.) The objective part (melanin, exposure to sunlight, behavior, words, brain physiology, etc.) can in principle be measured but not the experience per se. This is because we cannot say (although this is commonly tried) that mental experience equals behavior, or skin damage, or brain activity.

[32]
The opinions of Nagel and Price <8-9> are in my opinion not attempts to confuse. They try to describe a non-mental nature, which I believe does not work because the mind is always at the center. Is this 'God's view' ? I suspect that there is a fear of being interpreted in this way, and that this might contribute to making some writers put the emphasis so strongly on 'objects'.

[33]
One aspect which needs examination is the enormous pull of objectivity. It is not that one 'decides' to use the objective method for thinking: it happens automatically, and if one is uncritical about it, one gets stuck in it, although it is a (secondary) differentiation within experience. It may be possible though to devise a technique to make it easier to remain aware of this problem. One can ask how particular mental structures, for instance opinions or statements (or 'sentences', 'propositions', as the logical positivists called them), originate within experience, and then remember that they always imply subjective experience including its unstructured center, and that exclusive objectivity is a fiction.

[34]
<20-29> 'Objective and invariable': in the discussion of this, Hubey again implies that mathematics is the basis, even though 'animals can see objective reality' to enough degree to live, etc. He agrees that 'all experience is subjective, commonality of experience is what people mean by objective, and that is not the opposite of subjective', but does not like 'objectification' because it is 'postmodernist confusion'. He also agrees <30> that 'knowledge' is strong belief, 'but what is belief ? Actually in philosophy knowledge is said to be 'justified true belief''. I think that depends on whose philosophy is discussed.

[35]
<38-39> 'Because experience is subjective does not mean that the experience cannot be objective': What I say is that the subjective aspect of experience cannot be objective. The important question in Hubey's statement is what he means by 'objective'. Of course we use inductive generalizations (in the form of conjectures and refutations) all the time. For this, experience (or if you prefer, the mind) uses the method of commuting experiences into as-if mind-independent entities ('objectification' for short), and this is fine as long as it is seen as a method which uses temporary structures, rather than as an ontology.

[36]
<61-62> Concerning the meaning of 'objective' and 'subjective': Hubey says that I use it first in a 'linguistic' meaning (operator, input, output), as in subject/object split, and then in the sense of 'quantitative' (as in 'hard science'). What makes hard science hard, he implies, is mathematics, but that is not the original meaning. An object is an entity which is handled as-if it were mind-independent. Objective science uses this assumption, often without considering the 'as-if' qualification. But the Cartesian subject/object split is the underlying assumption here as it is elsewhere. The use of the meaningin the quantitative sense stems from the necessity of entities (such as objects) to be available for counting. And besides, math is less 'hard' than he suggests (see [10] above). I am not sure what he means by 'linguistic', except probably 'unscientific'. That is true in the sense that one may call the subject/object split 'pre-mathematic', that is: some such procedure is a pre-condition for the use of mathematics. But on the other hand, his terms 'input-output' already presuppose an objective image of some sort.

[37]
<64-65> 'Limitations of empiricism': he agrees, but does not seem to accept my point about the need to discuss the conceptual basis, instead refers to non-invasive medical procedures, which are a different question.


[38]
MATRIX

This term <3> was introduced as a mathematical concept in 1850, and had been in other use long before that. For non-mathematicians such as myself there is no clear need to limit the meaning of this word to mathematics. Mathematical language is a specialization of everyday language, and in general discussions (i.e., those which are not limited to mathematical topics) this etymology should be open for discussion. The term means the mother-substance or form, which is not the same as container (like a shoe carton).


[39]
The 'MIND'S CENTER'

is not a figurative trick <4>, it is a concept of central importance; but I agree that it is not clear; the reason for that is that it has no structure. There are several other words available if desired (as listed in Table 1, TA1 [8]).


[40]
CONCLUSION

Definitions of terms are important for consistent work, and for discussion. But they are by nature temporary structures, and the need for definition should not interfere with the need for the scrutiny of the origin of the concepts, because otherwise one may remain caught in some forms of thinking which for the question of mind and reality have proven to be non-functional.


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NUMBERS RULE

The 8th Gaius, Gaius Octavius, was the august ruler of the Roman Empire from minus 31 to plus 14, and thus he evidently ruled in zero. Now, although the Roman Empire was well established at that time, zero was invented only a few hundred years later. And this prompts the following test question: how was Augustus able to rule in something which had not yet been invented ?

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REFERENCES

Malcolm, N. (1967-72), Wittgenstein LJJ, in Encyclopedia of Philosophy,
New York: Collier MacMillan, Vol. 8, pp.327-340.

Wittgenstein, L. (1922-86), Tractatus Logico-Philosophicus,
transl. C.K.Ogden, London: Routledge and Kegan Paul.


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[Author: Herbert F J Muller
e-mail <mdmu@musica.mcgill.ca>]