Is consciousness independent of conscious organisms or systems? In other words, is consciousness objective? For scientific psychology the answer is negative, and when the entity "consciousness" is spoken of, it is done simply as the abstract reification of the property to which the term is attributed. We immediately find ourselves in the field of the ontological dispute of universals.
(Video on the Universals:https://www.youtube.com/watch?v=doYHQf6PFQw&list=PLcX5IdGYTx51I5EGmTgOocAHEAxX5Ir31&index=47 )
Within empirical science, the general position rejects consciousness as objective1, as it denies the existence of universals. The paradox that has occurred since the beginning of mathematics and the science that is based on it is that universals are at the very root of rational thought, to the point that it is precisely the reification of properties which has made it possible to develop the powerful systems of abstraction of experience that make mathematics possible and with it science as a whole. But returning to our topic, consciousness as an entity has traditionally been linked to transcendental thought, be it the religious or the humanistic that proclaims the existence of a subject that represents the universe. Consciousness as an entity underlies the psychology of Jung and his followers, as it underlies the very sophisticated psychologies of Advaita Vedanta, Sufism and Buddhism. The widespread exclusion of these systems of ontological and practical psychology from study in Western universities is in no way justifiable by the successes that cognitive psychology, behavioral psychology, and neuroscience are achieving in the fields of psychology dealing with pathological issues. I am referring to its exclusion and integration within psychology programs, not its informative appearance in general culture courses for the humanistic or religious curriculum.
Curiously enough, the universalist positions in relation to consciousness are being taken more seriously, the positions that speak of consciousness as something substantive, and therefore something that occurs outside of its manifestation in conscious entities, since physics has entered to study the subject and tries to incorporate consciousness into its theories about the order and nature of the universe. The mathematician Roger Penrose distinguishes between the following 4 general approaches to consciousness.
A. All thinking is computation; in particular, feelings of conscious awareness are evoked by the carrying out of appropiate computations.
B. Awareness is a feature of the brain’s physical action;and whereas any physical action can be simulated computationally, computational simulation cannot by itself evoke awareness.
C. Apropiate physical action of the brain evokes awareness, but this physical action cannot even be properly simulated computationally.
D. Awareness cannot be explained by physical, computational, or any other scientific terms.
(Roger Penrose. Shadows of the Mind. Vintage Books London.2005. p.12)
And what is computation? It is any action that can be performed by a rather simple machine, usually call a Turing-machine. Let us use the description of a Turing-machine given by Britannica ( https://www.britannica.com/technology/Turing-machine)
(…) the machine performs its functions in a sequence of discrete steps and assumes only one of a finite list of internal states at any given moment. The machine itself consists of an infinitely extensible tape, a tape head that is capable of performing various operations on the tape, and a modifiable control mechanism in the head that can store directions from a finite set of instructions. The tape is divided into squares, each of which is either blank or has printed on it one of a finite number of symbols. The tape head has the ability to move to, read, write, and erase any single square and can also change to another internal state at any moment. Any such act is determined by the internal state of the machine and the condition of the scanned square at a given moment. The output of the machine—i.e., the solution to a mathematical query—can be read from the system once the machine has stopped. (…)
Video: https://www.youtube.com/watch?v=dNRDvLACg5Q&t=3s
If we delve deeper into the question of computation, we arrive at a very interesting mathematical perspective on the ontology of consciousness. In fact, it is an old problem with a very broad implication on the nature of our study of consciousness. In order to follow the argumentation, we need to understand what is an axiomatic system first.
Consider 0,1,2…, the so called natural numbers. They started as adjectives in our human use: 2 trees, 7 persons, etc. But after some millennia (probably more than 100 millennia) they passed from the property ontological status to the substantive ontological status. One could ask: is zero really a natural number? Where is it in nature? Nowhere, and it was never a numeral adjective. It required some philosophical speculation to become a number, o better the foundation of all natural numbers together with 1.
How could the axioms or principles for this set of mental entities be specified? How could the action of counting go without producing errors or contradictions?
We have to start by defining the notion of successor or “adding one”. In mathematical notation:
s(x)= x+1
Then we can state the first axiom
(i) For all x, s(x) ≠ 0.
We should also need a second axiom which states that distinct elements stay distinct when you produce their successors:
(ii) For all x and y, if x ≠ y, then s(x) ≠ s(y).
Then, to finish we should say that there are no other natural numbers that those expressed by our previous two axioms. We could say that:
For every x, either x = 0 or x = s(0) or x = s(s(0)) or · · ·
Or in a more compact way:
(iii) Let A be any subset of the natural numbers with the following properties: 0 ∈ A, and s(x) ∈ A
whenever x ∈ A. Then A must be the set of all natural numbers.
These are called de Peano Axioms for natural numbers. In order to produce a mathematical theorem we need an axiomatic system which is a set of axioms and definitions that give the rules for constructing true mathematical formulas, and the means for proving or disproving any statement produced from that axiomatic system. Any formula or statement, S, of the system has to be consistent, id est, it does not contradict the axioms of the system: we cannot deduce from them S and Not-S.
How are we to choose our axioms if they are not proven from other statements? Well, we consider them to be self-evident truths that somehow correspond to basic human intuitions, like our axiom 2 in the Peano system, which corresponds to the sequential intuition of time. Any given moment is followed by another, and we can list those individuated moments given each of them a different sign. But are axioms consistent among themselves? How can we know that non-provable statements do not contradict themselves? We certainly could not prove them within the system to which they belong to2. One could not say. “All of these axioms and rules I perceive (with mathematical certitude) to be correct, and moreover I believe that they contain all of mathematics.”3 Such an statement is contradictory. It would not be contradictory recognize the validity of propositions taken one by one, i.e, the validity of the system (in a kind of act of faith in the system itself), but the axiomatic system as a whole cannot be proven, for if someone perceives the axioms under consideration to be correct, one should also perceive that they are consistent, hence having a mathematical insight not derivable from the axioms. The consistency of a system of axioms cannot be proven from those axioms.
Now let us connect this result with the Turing-machine. According to Kurt Gödel, if the human mind is “equivalent to a finite machine, then there is a finite rule producing all the axioms of demonstrable mathematics. But there is not such rule for there are unsolvable diophantine problems4 of the form “For all x there is a y such that P(x,y)=0” where “x” and “y” are sequences of integer variables and parameters and P(x,y) is a polynomial with integer coefficients. If our minds were computers in its workings, all our axioms could be produce from a finite meta-axiomatic system that could solve all mathematical problems (since they would have been generated mechanically. But this has not been the case. Mathematics has still old unsolved problems of proof)
Our mind surpasses the powers of any finite machine and it is not a question of faster and more powerful processing but of the particular thinking required by axiomatics: creative thinking.
Let us generalized now this result of Gödel to all science in terms of the concept of congruence. Suppose for a moment that we could form a set of meta-axiomatic propositions that state today’s basic foundational assumptions about ourselves and the cosmos, that we could somehow agree on a set U of meta-axiomatic indisputable truths, ranging from ethics to physics, from mathematics to psychology and the arts. It is obvious that we could not deduce theorems out of these axioms, but we can consider them as a set of principles. The Pi propositions of U can be dependent or independent among themselves.
1. If all of them were independent, the human experience would be the addition of disconnected actions, but our vital experience, as well as our science, shows us that this is not the case, for all those sciences and arts are inextricably fused in our way of life, producing not only practical knowledge but also founding our wisdom.
2. Then, at least some Pi are related.
3. But if there is even one proposition totally independent of the others, such proposition would not be intelligible, for it would not have a referent.
4. All Pi are, therefore, somehow semantically related, and the relation is the unifying principle of the thinking-living human being, a principle of human congruence or identity.
5. Now, if all Pi are semantically related, they could be expressed in terms of some meta-meta-principles or meta-meta-axioms.
6. This would imply that our meta-axioms are not final (therefore, not axioms), i.e., that there are other meta-meta-axioms U’, some kind of unknown principles about ourselves and the Universe which are not covered by our intuitions and social agreements, nor by any rational or irrational choices and thinking.
7. The Principle of human congruence implies a field of thinking meta-meta-axiomatic, which it is necessarily above our thinking, a supramental thinking that would imply an objective consciousness beyond the human one that operates at least on U’ basis and that cannot be expressed in our intuitions (for then they would be reducible to axioms in U).
It is not only a matter of the non-consistency of the axioms of a generalized axiomatic system as expressed by Gödel’s theorems but also of a semantic congruence of the system U’ that is not based in the functioning of human mind, and that shows an objective form of consciousness beyond our realm of consciousness but intrincated also in it. We started with the hippotesis of consciousness as a property of the mind and arrived to the existance of an extra-human consciousness, thus an objective consciousness in relation to the human one.
Notes
1With the exception of the theory of Penrose and Hammeroff base in quantum mechanics and cell structure (microtubules within the cell) principles.
2“For well-defined system of axioms and rules(…) the proposition stating their consistency (…) is undemostrable from these axioms and rules, provided these axioms and rules are consistent and suffice to derive a certain portion of the finitistic arithmetic of integers.” (Kurt Gödel. Some basic Theorems on the foundations of Mathematics and their Implications.K-Gódel Collecte Works. Vol.III. Oxford Univeristy Press.1995)
3Gödel. Ibid
4Diophantine problems are related to the algebraic diophantine equations, which contain polynomyals and integer coefficients. Diophantine equations fall into three classes: those with no solutions, those with only finitely many solutions, and those with infinitely many solutions. For example, the equation 6x−9y=29 has no solutions, but the equation 6x − 9y = 30, which upon division by 3 reduces to 2x−3y=10, has infinitely many. For example, x=20, y=10 is a solution, and so is x=20+3t, y=10+2t for every integer t, positive, negative, or zero.
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