Ricardo Kubrusly / Marina Petric
risk@ ufrj.br /email@example.com
What might have been and what has been
point to one end, which is always present
While cosmology is now recognized as a science, it had not yet gained this status in the 1940s. The debate surrounding its objective was controversial. Critics questioned how a science could seek "everything" -- that is, the cosmos -- for its primary field of study. However, this scenario has changed since it was observed that the universe was really expanding; such observation brought cosmology into scientific territory because it defined, through an objective analysis, the object of that new science (Novello 1997). The Big Bang model was confirmed with the discovery of the so-called background radiation (Wilson 1978), which consolidated the hypothesis of a universe with a beginning. In that model, instead of discussing where matter can be found in time and space, it became clear that time, space, and matter are inside the cosmos; it's not the cosmos that can be described within a time line, but time that should be taken as a consequence of the cosmos. Modern cosmology no longer envisions a scenario wherein space, time, and matter influence cosmic evolution; rather, space, time, and matter have become the cosmos itself. The universe ceases to exist in space and time, and instead becomes "the whole" where space, time, and matter are.
Today, as we walk toward a definition of a science of consciousness, we recall the time when cosmology became a science; the main object of study of a science of consciousness still lacks clear definition because it was not objectively observed as a whole (we're not discussing the easy problems [Chalmers 1995]). If consciousness, in analogy with cosmology, can be considered "the everything" in a human being, then we can also purpose a model with a beginning. The death model would replace the Big Bang model: the simple knowledge that "we are going to die" is the starting point of the conscious human being, and drives man through any thinking process. Man invents infinity in a clear strategy to overcome death, and infinity is inside every human being; it plays, in our analogy, the role of background radiation, which is everywhere in space-time.
Here I want to discuss the possibility of an “objective observation” which could bring consciousness into the scientific territory. That is, I ask which kind of observation we would need to set, in an objective way, something that is by definition subjective.
Like cosmology, which accepts time inside the cosmos, we discuss the hypothesis of accepting the "I" inside consciousness.
1. Cosmology and Background Radiation
Cosmology is a science that has only a few observable facts to work with; it had not yet gained the status of science in the 1940s. The debate surrounding its objective was controversial. Critics questioned how a science could seek "everything" -- that is, the cosmos -- as its primary field of study. However, this scenario has changed since it was observed that the universe was really expanding; such observation brought cosmology into scientific territory because it defined, through an objective analysis, the object of that new science.
Radio astronomy has added greatly to cosmology and our understanding of the structure and dynamics of the universe. The discovery of cosmic microwave background radiation, by Robert W. Wilson, added one important observable fact to cosmology (Wilson 1978).
Such observation was held as decisive to cosmology: background radiation is considered a relic of the explosion at the beginning of the universe some 18 billion years ago. Thus, the so-called Big Bang model was consolidated.
According to contemporary theory, the last scattering of cosmic microwave background radiation occurred when the universe was a million years old, just before electrons and nucleii combined to form neutral atoms (“recombination”). The isotropy of background radiation thus measures the isotropy of the universe at that time and the isotropy of its expansion since then (Wilson 1978).
2. Consciousness and the Infinity
In the 17th century, Descartes brought to the first level the body-mind problem, or, as he would say, the body-soul problem. As he faced the interaction between an immaterial soul and a material body, he made a distinction between "thinking matter" and "extense matter" (res cogitans / res extensa). By Descartes’ time, Ether was the dominant hypotheses, which means that the idea of a "vacuum" was inconceivable. Matter must always exist in some fashion. This assumption led to the model of a material soul, which was placed by Descartes in the pineal gland -- for him, an indivisible structure in a central location in the brain. Therefore, the idea of the soul represented in the body by the pineal gland (Gaukroger 2000).
The mechanical explanations continued as Descartes tried to explain the reactions of the body to external stimuli through the movement of animal spirits (spirits which could travel through the "hollow nerves" from the body to the soul and vice-versa). In any case, the debate surrounded the existence of an immortal soul and its place in the body.
Since then, the biggest challenge was to understand and solve the impasse left by Descartes (the "Cartesian impasse"). Leibniz later raised the question of how that interaction (between an immaterial soul and a material body) could occur. If all changes in matter are caused by collisions in small particles, how could something immaterial in essence produce any material changes in something as material as the body? (Gaukroger 2000). According to this argument, the soul should either not exist or exist as something material. A coherent theory would not question the interaction between the immaterial and material realms; instead, it should offer a complete perspective from only one of the "sides" (material or immaterial). Berkeley, for instance, avoided the problem of interaction by bringing the entire physical realm to the world of mental representations (Papineau 2002).
The situation in the Philosophy of Mind has turned around since the 1950s; the relationship between body and soul was replaced by the relationship between mind and brain – specifically, between mental phenomena and physical phenomena. Dualism, behaviorism, the identity theory, eliminative materialism -- all of these schools followed the "historical natural flow," that is, all came in order to replace the failures of the previously dominant view.
Today, physicalism, which can be found in many different forms, is the dominant view. In Kuhn's perspective, physicalism is the new paradigm (Kuhn 1996).
It seems that the Cartesian deadlock was replaced by a new impasse: that of the absence of a link between the physical world, submitted to physical laws and the experience of consciousness. There is a gap between experience and the account of functions: the so-called "explanatory gap." We need an explanatory bridge to cross the gap between the account of functions of consciousness (with which neuroscience can cope today) and the experience of consciousness (Chalmers 1995).
On the other hand, the existence of the "extra ingredient," in the anti-physicalism's view, would be an essential feature that every conscious being would have as a requirement to become conscious; without the extra ingredient, claims the anti-physicalist, one could not talk about conscious beings, but, rather, about zombies. A zombie is a mental experiment; a zombie looks like a conscious being, yet lacks the experience of consciousness (Hawthorne 2002).
In all of these views, including the dominant physicalist view, there is one consensus: at one point, the debate meets a recurrence, in that at one point a conscious being deals with his way of interacting with the world. The first-person access, or subjectivism, does not count with observable, objective facts with which to work. Furthermore, a science of consciousness also lacks the same observable, objective facts with which to work. Simultaneously, the first-person access is "everything:" in an analogy to cosmology, the experience of consciousness for every conscious being is "everything," and is the primary field of study of what could one day become a science of consciousness.
We would like to discuss consciousness here as departing from "the consciousness of death." We are not referring to biological death itself, which is a physical fact. We are introducing the idea that consciousness is the consciousness of the fact that "we are going to die." This internal knowledge compels and directs men to the process of thinking and creating, in a clear strategy to overcome death. Infinity is everywhere, here and now. In our analogy, it is “consciousness's background radiation”. Moreover, it could also be free will’s “background radiation,” since for us it is striking how naturally some sentences read when we replace “the mind-body problem” with “the problem of free will” (Sosa 2002). Here we can offer the image of a choreographer, whose next movement is still undecided: the possibilities of steps are infinite, however, only one will be chosen.
3. The Infinity in Mathematics
How can one measure what has no size or shape? How can one weigh what has no matter? How can one affirm the existence of things that are not subject to physical laws? Certainly, such answers cannot be framed entirely in a physical way.
Infinity took over human thoughts in its several manifestations. The thought that concerns infinity is not directly caused by any physical activity in our brain, although it is possible that it causes modifications in what is physically measurable in us. Because of this, we will have to look for another way to deal with it. Its essential "nonexistence," as far as materialism is concerned, suits it perfectly in the field of mathematical analysis. Mathematics itself does not exist in a physical sense, nor is it caused by anything but a necessity to understand and organize our search for eternity. In other words, mathematics can be viewed as a logical, and therefore human, abstract model of the manifestation of the infinity. It is not related to nature and has no relation to physical laws.
If we assume, as shown earlier, that infinity is everywhere and equally dense in ourselves (“isotropy”), the proper way to deal with it in a scientific manner is through mathematics. Indeed, this has been the goal of mathematics throughout history: to understand and explain infinity.
The first manifestation of infinity dates to the beginning of our conscious history. Humans found out, when counting, that there did not exist one last number -- that is to say -- that the set of the so called natural numbers happen to be infinite. This almost natural fact immediately poses a logical paradox, which generates the definition of an infinite set. It is remarkable that such definition only appeared with the work of Cantor in the nineteenth century. Why did so much time transpire between the realization that the set of even numbers and the whole set of natural numbers were in a one-on-one relationship, and the remarkable Cantorian definition, which took advantage of this very unusual property to understand infinite sets as the sets that are in a one-on-one correspondence with proper subsets? The answer is that it took this much time for men to get familiar with paradox as the normal environment for thought. In fact, infinity is a necessity for the development of human thought.
Another way to approach infinity in mathematics is through geometry. As soon as numbers were set and understood by mathematics, measure in geometry created a major problem for the Greek scholars. How to fit the square root of 2 into a number framework? In other words, are all numbers measurable? Once more, in order to solve this question, infinity had to play a decisive role. We had to invent a number to be placed in that hole, created by the absence of a number corresponding to that given measure. However, the price for this artificial invention was ironically high: this number had to have an infinite number of algorithms. In fact, the presence of irrational numbers and the additional discovery by Cantor that they exist in a much larger quantity than natural numbers, suggests the artificiality of a numerical continuum. The numerical continuum only became possible through the massive interference of several layers of different kinds of infinities.
Another major problem in the foundations of mathematics concerns Euclid’s formalization of geometry. In his famous fifth axiom, he assumed as true the statement that for a given straight line and a point not belonging to it, in a certain plane, there exists a unique parallel passing through this point. As soon as he enunciated this postulate, he noticed that it lacked a required property for being a regular axiom, that is to say, it was not self evident, since one could not always verify its validity. For example, if the supposed parallel lines were such that they make a small, but not zero, angle between themselves, how could one be sure that they indeed did not touch each other, which could be happening, perhaps, outside the piece of paper where the draw were made? Imagine a very small angle between the two lines: it could happen that they touched each other outside the town, or even outside the universe -- if one considers it as a finite object.
The surprising question that has stared mathematics in the eye for more than 2000 years can be posed as it follows: does anything that happens outside the universe, outside the place of possible things to happen, really happen? In fact, to make sure that the two lines in the above example do touch each other, one had to examine all the way through infinity in order to confirm whether or not they meet. Infinity is again the key point to understanding and restoring some truth about the famous axiom. It describes one possible universe and leaves room for the existence of many more universes, which are described by the elliptical and hyperbolical geometries.
Whenever infinity appears in mathematics, it rearranges part of its formalization, enlarging and strengthening its structure. In the late-nineteenth century, mathematics started to be comfortable when dealing with infinity. Driven by the success and applicability of the Differential Calculus, countless new results appeared in the Theory of Sets and Series, and with them a great deal of "nonsense results." Infinity was not yet fully understood.
The most important results on the Theory of Infinity were achieved by Cantor; for an example, see J. W. DAUBEN , who showed us that there is an infinite, hierarchically-ordered sequence of infinities, each one with its own size and topology, allowing for a logical qualitative classification of their properties. His work was so impressive that most mathematicians thought that mathematics, as Galileo stated centuries before, was indeed the language of God. In the beginning of the twentieth century the formalists, which consisted of a group of mathematicians led by D. Hilbert, set a plan to prove that mathematics was a complete and consistent set of logical rules, capable of proving all results corresponding to a mathematical truth (M. Kline 1980). Fortunately, their dreams did not come true; otherwise, we would have a positive answer for several important present questions and the existence of paradoxes would be denied. Consequently, most philosophical discussions on consciousness would be meaningless.
Gödel’s theorem (Gödel 1931, see also Nagel and Newman 1958) put an end on the speculation of having a mathematical system both complete and consistent, by proving that one has to choose between completeness and consistency. Moreover, if one makes the obvious choice of keeping consistency for granted, this consistency could never be proven within mathematics. On the other hand, Gödel’s theorem opens a whole new universe of philosophical expectations about human systems of logical inferences which could reach infinity -- not by being God’s model of nature, but a creation of ourselves, certainly closer to a useless, ordered hallucination than to a physical conception of our universe. Infinity has no place in nature but within us, as a plan to overcome death. We can read Gödel’s theorem this way: if we wish to deal with consciousness as we have dealt with infinity, we must lower our expectations of being the “masters and the creatures” while simultaneously giving up the tragic idea of reducing persons to physics and physical laws. Instead, we should start looking at ourselves as a complex endless structure, in some degree analogous to mathematics -- a subject both mysterious and incomplete.
4. Conclusion and Analogy
The comparison between cosmology and a possible science of consciousness led to the conclusion that there exists an “everywhere presence” which is invariant in both fields. In each case, it plays a decisive role in understanding the “whole” (the universe or consciousness).
Background radiation in the cosmos corresponds to the infinity in consciousness. Background radiation and infinity are invariant and omnipresent (isotopy). In order to measure background radiation, cosmology needed radio astronomy. In order to measure infinity, a science of consciousness needs a powerful tool, a method with which the idea of infinity can be somehow captured or understood. That tool, in our analogy, is mathematics, which is applied to observe infinity. Thought has logical laws, acquired by culture, learning processes, language etc. These logical laws correspond to the physical laws in our analogy.
Radio Astronomy – Analysis
This analogy does not contest physicalism. However, it is not a continuation of the established paradigm. Rather, it first accepts today’s impasse between mind and brain in order to start an analogy between the science of the cosmos and the science of consciousness.
Infinity has no place in nature but within us, as an unconscious plan to overcome death. Back to Gödel’s theorem: if we want to deal with consciousness like we have been dealing with infinity, we must lower our expectations of being “masters and creatures” at the same time and give up the tragic idea of reducing persons to physics and physical laws. Instead, we should start viewing ourselves as a complex, endless structure, in some sense analogous to mathematics, which is by essence incomplete.
The process of thinking is not a mechanism caused by the existence of consciousness; rather, consciousness needs the process of thinking to meet infinity. The "I," a product of thought, is inside consciousness -- which means that there is no point in seeking the consciousness inside the "I."
Chalmers, D. (1995). "Facing Up To The Problem of Consciousness." The Journal of Consciousness Studies(Special Issue).
Dauben, Joseph Warren (1979). Georg Cantor - His Mathematics and Philosophy of the Infinite. Princeton, Princeton University Press
Gaukroger, S. (2000). Descartes - Uma Biografia Intelectual. Rio de Janeiro, Ed. Contraponto.
Gödel, Kurt (1962) On Formally Undecidable Propositions of Principia Mathematica and Related Systems New York, Dover, 1962
Hawthorne, J. (2002). Physicalism and Consciousness, COPPE, UFRJ. 2002.
Kline, Morris (1958) Mathematics - The Loss of Certainty New York, Oxford University Press
Kuhn, T. (1996). The Structure of Scientific Revolutions, University of Chicago Press (Trd).
Nagel, Ernst and Newman James R. Gödel’s Proof Ney Ney York, York University Press,
Novello, M. (1997). O Círculo do Tempo. Rio de Janeiro, Editora Campus.
Papineau, D. (2002). Introducing Consciousness. Oxford, Oxford University Press.
Sosa, D. (2002). "Free Mental Causation."
Wilson, R. (1978). The Cosmic Microwave Background Radiation. Holmdel, N.J., Nobel Lecture.