Chapter I -- 15
The next passage is critical. St Gregory is speaking:
What then, I said, if, just as the quality of being material is common to the sensible nature of the elements, the difference being great as concerns the particular qualities in each species of matter—for movement in them is from the opposite, the one tending to rise, the other falling to earth; the species is not the same and the quality is different—if according to the same reasoning one were to say that some of these things were the force which, being conjoined, operated these intellectual (noetikas) imaginations and movements from a natural property and force, as truly we see many things set in motion by the makers of machines in which the matter artfully arranged mimics nature—not only in the shape showing the similarity but it even happens to have motion and portrays a certain sound, the machine sounding in the voice-producing part—and we do not see, I presume, any intelligible (noeten) power in those things that happen that would work each aspect of the shape, the appearance, the sound, the motion? If we should say that these things also occur in regard to this very mechanical instrument of our nature, there having been admixed no intelligible substance of any special kind at all, but there lying in the nature of the elements which are in us a certain motive force, and such an operation is the result, which operation is nothing else but a certain impulsive motion set in operation towards the knowledge (gnosis) of those things which are studied—by means of these things what would be more proven: that that intelligible and bodiless substance of the soul existed in itself or that it did not exist at all?
We are several years prior to 400 ad. We have a complete statement of the materialistic and mechanistic paradigm in biology and neurophysiology. In Volume II, we will see that Evagrius, a contemporary of St Gregory, will use dreams to diagnose with precision the psychological condition of the ascetic, and even his stage of ascetical progress. Is this not astonishing? Why should these things be so?
These men and women were trained in Athens, or else trained by those who were trained in Athens, in pagan philosophy—Classical Greek philosophy—, which included the science of the day. This is what we meant in saying earlier that St Macrina shared, as a Christian from a long-standing Christian family, in the intellectual culture of her late Classical peers. That these men and women write and speak in a manner relevant to our own epoch suggests that the intellectual culture of our own time is a return to the sensibility of the late Classical Age of Greece and Rome.
In what might this similarity or return be constituted? We think it might be, on the one hand, the denial of God of our own epoch, and, on the other hand, its emphasis on reason. As to the denial of God, this is evident not only in the universities of the West but even on its streets. As to the emphasis on reason, we are saying nothing new; that was the triumph of the Enlightenment.
There is a tendency today to seek an outlet for more religious, divine or transcendental aspirations in mysticism; these tendencies are perhaps similar to those which prompted the Romantic in his irrational quest and activity. This mysticism is often healthy; sometimes, however, it can be deranged or disturbed, being a naïve reaction against the excessive rationalism of the person’s environment.
We will see mysticism as we progress, a mysticism based on hard work and lucidity, humility and sobriety, a mysticism that is radically Christ-centred, a mysticism that seeks the apprehension of the Divine but avoids excess, ecstasy—here taken to signify loss of self-control and sobriety—and delusion.
To return to the matter at hand, St Gregory is posing the radical rejection of anything other than sensible (material) elements and their forces in human nature. This is his statement of the mechanistic argument against the existence of the human soul that we announced earlier.
St Gregory is saying this: The elements have this in common: they are material. But the elements differ in their various qualities. (Here, St Gregory is following Plato and Aristotle.) Some elements are light, some heavy, and so on. We might say today that various compounds have different chemical properties, but it is true that the elements themselves have different chemical and physical properties. What if the conjunction of these elements or compounds should by its own very nature produce a certain force or power that works the intelligible imaginations and movements? St Gregory clearly is trying to encompass all mental phenomena or events taken either subjectively or objectively, including those operations of mind (nous) in the body that his sister, St Macrina, has said manifest the existence of the immaterial soul (psuche). ‘By its own very nature’ here means: ‘naturally, according to the natural properties of the elements or compounds combined’. St Macrina has said that behind the motions of the living person is the sensibly inapprehensible but nonetheless existent soul (psuche). St Gregory is saying: well maybe that supposed sensibly inapprehensible soul, including its mental acts, is nothing other than the result of a force or power that arises from the conjunction of the elements in the body of the living person?
This is very similar to the argument that is today called ‘epiphenomenalism’, the argument that we already saw to be expressed by the Nobel laureate, Jacques Monod, in Le hasard et la nécessité.
This is molecular biology. The person in this argument is his molecular biology. Let us make the difference precise. St Macrina has said that there is some immaterial mental (noera) substance which sees by means of the instrumentality of the eye, hears by means of the instrumentality of the ear and so forth. St Gregory is saying: well maybe there is no immaterial substance which is the agent of perception, but just as the eye is a mechanical (molecular biological) instrument at the disposal of the supposed mind (nous), so perhaps all the mental phenomena that we associate with this supposed mind (nous) are in fact nothing other than the mechanical operations of molecular biology?
St Gregory continues with an example. The machine-maker arranges matter artfully and the machine mimics nature—this is a robot—not only in shape (it looks like a man) but also in movement and voice, and all of this without any intelligible force or power—mind (nous)—being present in the machine. The machine operates mechanically but seems alive for all that.
We ourselves are reminded of Turing’s Test, which provides a behavioural criterion for artificial intelligence. Of course Alan Turing (1912–1954), the English mathematician, lived long after St Gregory’s time.
What St Gregory wants to say is this: Well, maybe we’re just fancy machines—molecular biological systems—and what you say is ‘mind’ or ‘soul’—some immaterial substance animating an otherwise dead body—doesn’t exist? This of course is the dominant model in positivist circles, and the dominant model in biology and a fortiori bioethics.
St Gregory continues: In our own body, perhaps there is no special intelligible substance such as mind or soul, but only a certain natural force or power of the chemical compounds of the body able to set things in motion in such a way that the supposed operations of ‘mind’ are the result, which operations are nothing other than a certain natural biological movement of the brain operating on the things that we try to learn such as medicine or astronomy? Here, St Gregory is replying to St Macrina’s assertion that the mind (nous) is led from sense-perceptions to a conception (ennoia) which is above sense-perception in the process of learning medicine or astronomy or in the process of applying that medical or astronomical knowledge. St Gregory is saying: maybe that ‘being led from sense-perception’ which supposedly indicates the hidden presence of mind (nous) as the bearer of intelligible conceptions (ennoies) is simply a ‘certain impulsive movement’ which arises from the natural properties of the molecular compounds of the body? In other words, maybe this supposed mind (nous) is simply the molecular biology of the brain and this supposed ‘being led to an intelligible conception (ennoia) in an immaterial mind (nous)’ is nothing other than a ‘certain impulsive movement’ which arises from the particular chemical properties of the compounds of the brain? We can view this ‘certain impulsive movement’ as an Epicurean habituation or Humean association of sense-perceptions, passions and emotions, actualized in the molecular biology of the brain neurons. This being so, what else would be proved except that that intelligible and bodiless substance—the soul—would be completely nothing at all?
In other words, perhaps the supposed soul (psuche) is reducible to the molecular biology of the body? Or, equivalently, perhaps the supposed mind (nous) is reducible to the molecular biology of the brain?
St Gregory of Nyssa’s argument is similar in structure to the sceptical refutation by Carneades (214–129 bc), the founder of the New Academy, of the Stoic argument from the design seen in the world to the existence of God, the Designer. Moreover, it is similar to attempts by modern materialistic controversialists to refute the argument of the Weaver from the garment by adducing ‘proofs’ that the garment could have come about merely by chance.
As we have remarked, there is a school of psychology—humanistic psychology—which treats religious experiences as natural phenomena on the basis of the materialistic and mechanistic anthropology that St Gregory here is delineating in counter-argument to his sister, St Macrina. This school proceeds to study the induction of religious experience by natural (physical) means. In this view, the Jesus Prayer is simply a mantra—one among many mantras—, and the experience of the Uncreated Light a natural phenomenon that can be induced by any one mantra among the many, or even by other natural means. In this view, religious experience might be considered a matter of short-circuiting the brain in the right way or of altering its molecular biological constitution and operations in the right way. This of course is not the doctrine of the Orthodox Church, nor our own view. Still, in America, one can buy cassettes that teach one to pray the Jesus Prayer as a means of relaxation; one can learn to do T’ai Chi Ch’uan for equilibrated peace of mind. These things are quite real as social phenomena. Their root as social phenomena today in the West is the model that St Gregory is advancing as a counter-argument to his sister’s argument for the existence of the soul: that, in modern terms, the person is merely the molecular biology of his body. We have devoted a considerable part of this work to the anthropology underlying the Jesus Prayer as prayed by monks in order to clarify the differences between the anthropology underlying the Orthodox practice of the Jesus Prayer, especially in its higher forms, and the anthropology today current in the West, derived from materialistic and mechanistic models and paradigms in physics and the biological sciences.
To return to St Gregory, given his epoch, he has given a prescient description of the materialistic and mechanistic paradigm in neurobiology.
What is St Macrina’s answer?
She, then, said, the example also works in alliance with our argument, and the whole construction of the rebuttal brought against us will contribute not a little to the certainty of those things which we have thought.
How do you say this?
She said: For truly that one should thus know how to handle and dispose the soulless matter, so that the art which must be placed in the mechanisms should become almost like a soul in the matter, by means of which things the mechanism makes a pretence of movement and sound and shapes and other such things—this would be a proof that there is something of this sort in man which has the nature, by means of the contemplative and inventive force, to understand in itself these things and to construct in advance in the intellect (dianoia) the mechanisms and then, by means of art, to bring thus into operation, and by means of the matter to show, the thought (noema).
What is St Macrina saying? In the case of a robot, the art of the robot-maker must become like a soul in the material of the robot so that the robot makes a convincing mimicry of nature. But the robot-maker must apply that art. He must know how to handle and arrange the soulless matter so that his art becomes a kind of soul in the robot, on the basis of which ‘soul’—the robot-maker’s art—the robot makes a convincing pretence of human movement, voice, gesture and so on. But the very fact that a man can do this, that he can design and construct a robot, is proof that there is something in man—mind (nous)—that by means of its contemplative and inventive force or power can understand within itself (‘in the mind’s eye’) the art of robot-making, can design the robot, and, by means of art or skill operating on matter, can actualize the design of the robot in matter. The gist of this argument is that to be able to design and construct a robot—recall that St Gregory has counter-argued that perhaps we are all natural robots without mind (nous)—man must have mind (nous).
Turing’s Test involves placing a candidate machine that might demonstrate artificial intelligence in a closed room, or box, and a man in a separate closed room, or box. A different man who does not know who is who comes and plies each room or box with questions by means of a teletypewriter (or computer terminal). Each room or box replies with answers in the same way. If the questioner cannot distinguish the machine from the man, then the machine is construed to have artificial intelligence.
Let us take a familiar example that is a variant of Turing’s Test, and in which the machine, a computer, has won. Chess programs have been written which have defeated the world chess champion under standard tournament conditions of play. The chess programs, however, were very carefully programmed. Moreover, the chess programs did not mimic the thinking processes of chess masters. They solved a problem—chess—which happens to be susceptible of solution by means of tedious and long-winded computation of all possible consequences of a move. Some work had previously been done with evaluative algorithms (subprograms) which allow a quicker computation by eliminating from further consideration, according to certain preprogrammed criteria, useless or inferior lines of play. However, computers today are so fast that these evaluative algorithms were unnecessary: brute force was enough to beat the best chess player alive, even under tournament time control.
What St Macrina is saying is that the very existence of such chess programs is a major argument in her favour. For, she says, there must be something in man that can, through a contemplative and inventive power, understand in advance in itself, design in advance in the intellect, manifest through matter, and bring into operation through art or skill, the thought of that very chess program. Moreover, that chess program, conceived and executed by the human mind (nous), becomes like a soul in the computer.
One might say that an argument against today’s materialistic controversialists who deny the existence of God and the soul is that there must be something in them that can think up all those arguments against the existence of God and the soul.
St Macrina continues with a detailed description of how the mechanisms that St Gregory has referred to were constructed. We omit it. We continue with the conclusion of her description:
…Is it not manifestly demonstrated, therefore, by means of those things which appear sensibly, that there is a certain mind (nous) in man, some other sort of thing than a thing which appears sensibly, which, by the formless and mental quality (noero) of its own nature, in its own thoughts constructs these things in advance in itself and then brings thus into actuality, by means of the material services, the thought (dianoia) constituted within?
If it were, according to the reasoning opposed to us, that one should ascribe these wonder-workings [i.e. the primitive robots] to the nature of the elements, then at all events the mechanisms would be constituted spontaneously for us: the blacksmith would not await art for a metal puppet to occur, but directly from nature such a thing would be; neither would the air have a requirement for the pipe [i.e. the organ-pipe used in producing the sounds] for the sake of the sound, but the air would always sound by itself, according to the event flowing and being moved; the upward movement of the water would not be forced by a pipe, art pressing hard by pressures the movement towards [a motion] contrary to nature, but spontaneously the water would move towards the mechanism, by its own nature being channelled upward.
These are details of the construction and operation of one of these mechanisms, which existed in St Macrina’s day. What St Macrina is saying is that if the construction of such a mechanism did not require mind (nous) working by means of art actualized in matter, but was due merely to the natural forces of the elements, then such machines would assemble themselves and operate spontaneously. Today we might say that if there were no mind (nous) and the supposed workings of the computer and the chess program were due to the natural properties of the elements, then the computer would assemble itself spontaneously; the chess program would write itself spontaneously; the chess program would load itself into the computer spontaneously; and the computer would begin operation spontaneously, having plugged itself into a wall socket. Evidently St Macrina is dwelling on the difference between purposeful human actions and natural phenomena, and passing from the analysis of mental phenomena as depending on the natural properties of the elements (which we, and, presumably, her brother, St Gregory, would take to be the elements of our bodies) to a consideration of whether these primitive robots could arise from the natural properties of the elements taken in a far more general sense as the elements occurring generally in nature. We will comment on this argument below.
If, then, of these things nothing is set in operation spontaneously by the nature of the elements, but by art each is led in accordance with one’s preference; and if art is a certain firm thought (dianoia) set in motion towards a certain goal by means of materials; and thought (dianoia) is a certain native movement and operation of the mind—then, by those things that have been set against us, the chain of things said has therefore proved that the mind is something other than a thing that appears sensibly.
Before beginning, let us note the definition of ‘dianoia’. This word can be translated ‘intellect’, ‘thought’ or ‘purpose’, and ‘thought’ here better fits the context. Thought (dianoia) is a native movement and operation of the mind (nous). What is being said is this: The mind (nous) is a substance. That substance is here one of a category of substances that can set themselves in motion without there being anything that has previously set them in motion. The mind (nous) is an autonomous mover, a self-mover. Moreover, according to St Macrina it is intelligible and not sensible. It is an intelligible self-mover. Now one of its native movements and operations is thought (dianoia). ‘Movement’ (or, ‘motion’) and ‘operation’ are Aristotelian terms. They are virtually synonymous: ‘movement (kinesis)’ need not mean physical displacement; it does mean change, and one type of change is physical displacement. The word ‘operation (energeia)’ here means ‘function’ in the sense of ‘activity’; ‘function’ as ‘result’ (ergon) we have consistently translated ‘work’. Thus thought (dianoia) is a native movement (kinesis) and activity (energeia) of the intelligible substance called mind (nous). However, we should point out that we normally translate ‘dianoia’ by ‘intellect’. In those cases the above considerations still apply.
Now, what is St Macrina saying?
She is saying that if the chess program is not a spontaneous product of nature engendered without human intervention by the natural forces inherent in the elements, but is created by art or skill, and if art or skill is a certain firm thought set in motion towards a certain goal—here, beating the world chess champion—and actualized in materials—someone must design and write and test and correct the chess program—then mind (nous) is shown to be something other than what appears sensibly. St Macrina’s logic is the following: She has indicated that the fact that the chess program is created proves the existence of mind (nous). She now says that the fact that the chess program and computer do not assemble themselves spontaneously indicates that mind (nous) is not something sensible.
This argument has a flaw.
St Gregory said: well, what if what we call mind (nous) is simply the molecular biology of the brain? St Macrina has answered, since the chess program did not—and cannot—come into being spontaneously, there must be a mind (nous) that created the program and realized it in matter, and that mind (nous) must be other than a sensible thing. The flaw is this: As far as she goes in proving the existence of mind (nous), St Macrina is on solid ground. Her logic that would prove that that mind (nous) could not be sensible is unclear, however. What St Macrina in effect does not address is her brother’s point: maybe the mind (nous) that created the chess program is the molecular biology of the chess programmer’s brain, nothing more? That is, yes, the programmer created the chess program; it did not come into being spontaneously by the natural forces of nature. But when the programmer created the program, was he anything other than a concourse of biochemical reactions?
It might be remarked in St Macrina’s favour that she does not seem to see how one could pass from ‘natural forces of the elements of nature’—surely a deterministic concept—to ‘purposeful human behaviour’, in the present case conceiving, designing, writing and testing a chess program to beat the world chess champion. That is, she does not seem able to conceive the notion that the mind (nous) might be merely a concourse of biochemical reactions in the brain, since the latter are subject to the deterministic laws of nature whereas the former is a purposeful agent. While this problem is today largely ignored in the materialistic mechanistic paradigm, St Macrina is right: an account must be given by the materialist-mechanist of how the purposeful agent can arise out of deterministic chemical reactions. We discuss this further below.
Let us return, however, to the problem: when the programmer created the chess program that beat the world chess champion, was he anything other than a concourse of biochemical reactions?
This is an interesting problem. Let us first look at computers. Here, however, we are interested not in the chess program but in the person who wrote the chess program. The significance of the computer in the consideration of that person will become clear as we proceed.
Computers are programmed with algorithms: fixed sequential sets of instructions with embedded logical rules. Programs can be very complicated—witness the wonders of science—but they all have a ‘fixed sequential sets of instructions with embedded logical rules’ character. Programs, moreover, must be conceived, designed, written, tested and corrected in just the way that St Macrina has said concerning the design and production of primitive robots.
Users of personal computers will have noticed the staleness that develops round a new package or operating system after a time. Perhaps that is why there is always the urge to buy the newest model of the computer or the newest edition of the software package or operating system—to find something new or different, to return to the first challenge of the game. But this staleness is inherent in the fixed logical nature of computer programs mentioned above, no matter how complex the computer program might be.
However, computers and computer programs are inseparable friends; the one needs the other.
There have been some hopes of being able to mimic the more complex forms of human reasoning or judgement by means of sophisticated computer programs; this is the so-called project of expert systems or artificial intelligence. This would be a project in its final form to create a computer program that would by itself, say, write a chess program to beat the world chess champion. We understand that efforts of this type have not borne much fruit.
Here we begin to see the significance of the computer for a consideration of the person who wrote the chess program: if we were able, even theoretically, to write a computer program that mimicked the man who wrote the chess program, so that the computer would by itself conceive, design, plan, execute, test and correct the chess program, then we would have given an account of the mind (nous) of the chess programmer. It should be quite clear that it is much easier to write a computer program to beat the world chess champion than it is to write a computer program that would by itself design, write and test a computer program to beat the world chess champion.
Now we have said that we want to address this question: was the human chess programmer anything other than a concourse of biochemical reactions when he conceived, designed, wrote and tested the chess program? St Macrina is saying: no; there is something over and above the body or the biology of the man that conceives and brings to fruition the chess program, and that is the intelligible mind (nous) of the chess programmer. St Gregory has said: well, are we not all just concourses of biochemical reactions in our nervous systems when we do such things, so that there is no such thing as the intelligible mind (nous)? We ourselves are attempting to answer St Gregory’s question and are proceeding, for reasons which will become clear below, from the point of view of artificial intelligence systems, which, indeed, are not biological but logical. The project in the case of an artificial intelligence system is to mimic the mind (nous) with a computer. We have pointed out that all computers, including artificial intelligence systems, work by means of programs or algorithms and we have also pointed out that artificial intelligence projects have not borne much fruit.
Why should these projects not have borne much fruit?
In our view, the problem is in the nature of the algorithm and its relation to the mind—here taken in a simple intuitive sense but with St Gregory’s and St Macrina’s analysis under consideration.
It is evident that the human mind—or brain, even—does not work by algorithms: it is not designed like any known computer. A program can be written to mimic the human mind—witness the chess program that beat the world chess champion—but only in the sense of mimicking the result of the human mind, not its mode of operation. This is, in fact, one of the criticisms that have been directed against Turing’s Test, that it focuses on the result of the human mind’s operation, not on that mode of operation itself: it is a behavioural criterion of artificial intelligence.
However, historically, persons who have wanted to construct machines which would exhibit artificial intelligence have taken the position that the human mind has an algorithmic structure. That is, they take the position, as a matter of philosophy or assumption, that the human mind is a very complicated algorithm. But algorithms have a specific logical definition and structure. Hence, these persons are making the assertion that the human mind works in the same way as an algorithm—that is, in exactly the same way as a computer program.
In our own view, algorithms have a rather limited span of application. While we are here unable easily to render precise the connection between algorithm and formal mathematical system, let us turn to a certain topic in the foundations of mathematics to make our point clear. At the beginning of the Twentieth Century, Bertrand Russell (1872–1970) and A. N. Whitehead (1861–1947) initiated a project to axiomatize arithmetic—to put arithmetic on the same solid foundation as Euclidean geometry. This might be considered to be part of the empiricist program. In 1931, however, Kurt Gödel (1906–1978), the Austrian logician, constructed a proof that any such axiomatization of arithmetic would be imperfect. This proof, quite well known, stopped Russell’s and Whitehead’s project, and all other similar projects, dead in its tracks. What are the implications of this?
We certainly are not experts, but it seems to us that the scope of a formal mathematical system—such as an axiom system for arithmetic—is limited by Gödel’s Theorem, as the above result is known. Moreover, there is a very close connection between the theory of algorithms and Gödel’s Theorem. This is a very technical area, and the easiest thing to do is to quote an article from The Encyclopedia of Philosophy, ‘Recursive Function Theory’ by Martin Davis:
Continuing to accept Church’s thesis, the Kleene–Post form of Gödel’s theorem shows that Gödel’s discovery of the necessary incompleteness of arithmetic cannot be vitiated by even the most radical alteration in the accepted rules of proof; so long as we insist on the existence of an algorithm [i.e. computer program] for checking the credentials of an alleged proof, there will always be a true sentence of arithmetic undecidable by the rules of proof.
This result hinges on the structure of the sets involved; they must have a certain structure for any computer program or algorithm to be able to decide whether a candidate for membership in the set is a member of the set or not; the set of all true statements in arithmetic, under any axiomatization, fails to have this structure—this is Gödel’s Theorem. We are here using Gödel’s Theorem as a result which speaks not so much about the incompleteness of any formal axiomatization of arithmetic—which it does—but as a result which speaks by corollary about a logical limitation of algorithms: they cannot in certain cases decide whether a candidate element is a member of a set or not, in particular whether a candidate sentence in an axiomatization of arithmetic is a member or not of the set of true statements in that axiomatization of arithmetic. In this reading, while, given a particular axiomatization of arithmetic, an algorithm (computer program) might be constructed which could make the decision for some true sentences as to whether they were true or not, there would be at least one true sentence, for every axiomatization and every algorithm, for which the algorithm would be unable to decide. In general, even without reinterpreting Gödel’s Theorem in the way we have suggested, all researchers in the field of the theory of algorithms have accepted that Gödel’s Theorem implies that there are intrinsic logical limitations to the power of an algorithm—without for all that agreeing just what the implications are for the possibility of creating a machine that would exhibit artificial intelligence.
The question of the relation between an algorithm and the human mind can now be posed as follows. Surely Gödel’s Theorem implies—philosophically, now, not mathematically—that the human mind not only does not work by means of algorithms (computer programs) but that it works by methods that surpass the logical potential of any algorithm? Perhaps not as methodically, nor, by comparison with modern computers, as fast, but certainly in greater depth than any algorithm? Of course, this cannot be proven since we have no way to specify just what the mind is and how it operates. In fact, St Macrina herself will speak below of the unknowability of mind.
In our own view, the implication of the above is that algorithms—computer programs, and hence computers—have logically a rather limited span of application. The project of artificial intelligence—precisely the project to mimic the human mind by means of computer programs—does not have any prospects of success. In our own view, the situation is somewhat similar to constructing an airplane that mimics a bird. Certainly aeroplanes fly, more or less as birds do; but they are not artificial birds: they are aeroplanes. The success of aeronautical engineering does not consist in producing an airplane that mimics a bird, but in using the principles of Newtonian mechanics and aerodynamics to produce useful aircraft, according to whatever criteria of usefulness the designer might have. Similarly, the goal of making computers do what they cannot (mimic the human mind, whether this is taken as mimicking the external result of mind or as mimicking the mode of operation of the human mind) is chimerical. Of course, this will not be accepted by students of computing who want to make computers that think. However, while they have, and will have, piecemeal qualitative results, the fundamental limitation on the logical power of algorithms that we have just discussed will prevent them from obtaining a complete solution.
What does this have to do with molecular biology? The problem in molecular biology is this: to complete the materialistic and mechanistic project (or paradigm), the molecular biologist must reduce mind (nous) to the molecular biology of the nervous system. This would involve treating the molecular biology of the nervous system in a materialistic and mechanistic way.
Hence, to complete the project of molecular biology, the molecular biologist must show that the chess programmer does not have a mind (nous) in St Macrina’s formal sense even though that chess programmer created the chess program. Recall that we commented that this was the flaw in St Macrina’s argument. The molecular biologist has to provide a convincing explanation of how the chess programmer’s molecular biology—his neural molecular biology—created the chess program. This is the point that St Macrina did not respond to.
What we ourselves are saying is that those theoretical limitations of algorithms that we have just described above render suspect the project to reduce the mind (nous) to molecular biology in this way.
For there is an equivalence between the theory of algorithms and systems theory. This equivalence is what allows one to use the discipline of systems analysis to design complex computer systems that include more than one computer connected in a network.
The point is this: The dominant paradigm in molecular biology is precisely systems theory, so that the reduction of mind (nous) to molecular biology would be accomplished precisely by means of a systems-theoretical representation of the molecular biological reactions that produced the mental phenomena that interested one. But by the equivalence of the various formulations of the theory of algorithms, such a systems representation would be equivalent to some algorithm. But we have already seen the logical limitation of algorithms, and hence of systems of the sort now being discussed, in the matter of axiomatizing arithmetic. In other words, although algorithms can and have been written to beat the world chess champion at chess, they could not be written to decide all true statements in any particular axiomatization of arithmetic. Any systems representation of the molecular biological processes of the brain that purported to explain mental processes whether in whole or in part would be subject to the same logical limitations as algorithms are. Hence, we consider that any proposed systems representation of the molecular biology of the mind (nous) would be logically limited to the power of an algorithm, which appears to us to be less than the power of the human mind (nous), although we concede that a student in the field might dispute this by alleging that the human mind (nous) is just as limited as an algorithm. Of course, the question could never be decided. On the one hand, we would have the representation produced by the molecular biologist and, on the other hand, we would have St Macrina’s assertion that the mind (nous) was an intelligible and formless thing, an autonomous self-mover, which was the agent that worked through the molecular biology that was being represented, without for all that being the molecular biology. One could only work with the systems representation of the molecular biology of brain function; the connection of such a systems representation of brain function to the existence or functioning of the human mind (nous)—including the question of whether the human mind (nous) was limited or not to the logical power of an algorithm—would remain problematical, as can be seen from the following:
Some efforts have been expended to model learning by neurobiological systems, by means of computer programs that model neural networks. That is, the neurobiological system learns—this is evident: you and I learn—and the scientist seeks to model on a computer the learning that the neurobiological system has done using the concept of neural networks.
We do not know much about this. We do not know how the computer programs were constructed. Hence, we do not know how much real progress—progress in constructing models of neurobiological systems, which models learn in the same way that human beings learn—has been made, or whether such striking results as there are, are not artefacts of the algorithms—as if you or I were to throw sand into the air a hundred times, and each time study the pattern on the ground: a few times we might find the face of your mother, more or less. Were we to apply Turing’s Test to such a computer simulation today, the simulation would most certainly fail. There is no evidence of the attainment by such systems of any degree of human understanding that could be called adequate to fool a human questioner.
The project, however, has much in common with the project announced by Hume in his theory of concept formation. In other words, the neural network modelled in the computer is taken to model the mind as defined by Hume; and the learning spoken of above is taken to be the establishment of order within networks of computer-simulated neurons, which order is established by the effect of simulated sensory inputs on computer modules that have a partially random response to the simulated sensory input, and ultimately to each other, but which can be frozen in a certain configuration. The result, it is hoped, mimics to a degree concept formation and understanding, that is, intelligence. But this is the Humean philosophical project used as a basis for the conceptualization of the experimental model. That is, the experimental model is based on the Humean philosophical model which states that concept-formation is a matter of the association of sense-perceptions, or, more precisely, the association of ‘ideas’ which are the mental images of sense-perceptions, passions or emotions. Hence, since Hume’s philosophical program dismissed all intelligible conceptions—and even dismissed the existence of mind (nous) itself—, the experimental model has embedded in it from the very beginning a reduced notion of what mental phenomena are or might be. Hence our remark above that the connection between mind (nous) and a systems representation of the molecular biology of the brain which purported to explain mind (nous) would remain problematical: there would always be dispute about just what that mind (nous) really was—its nature and its scope of operations—that the systems representation of the molecular biology of the brain was purporting to explain. This dispute would include the question of whether the human mind (nous) were limited to the logical power of the algorithm. Moreover, there would be the problem of whether a priori the molecular biologist, or even the computer specialist modelling the mind with neural networks, had eliminated from the definition of mind aspects of human life that we ourselves would consider to be intrinsically human mental activities, such as prayer.
An explanation of why the chess programmer wrote the chess program the way he did and with the judgements he made has to be given by the molecular biologist. This is not the same thing as saying that the mind (nous) has no connection to biology. St Macrina is clear that the mind (nous) works through the body; and that if the body is damaged, then the mind (nous) cannot express itself, precisely where the damage prevents it. Nor is it to deny the architecture that exists in the nervous system.
The problem of course is this: DNA does not think. Cortisone—a randomly chosen hormone—does not think. ATP—a randomly chosen organic molecule important in the molecular biology of the cell—does not think. You and I think. How do we get from the one to the other? Moreover, molecular biological systems are chemical systems: they are deterministic systems within the constraints of random occurrences at various levels of analysis. Within the constraints of a stochastic system, they do not choose, love, contemplate God or any such thing. Hence, it is hard to explain purposeful human behaviour by means of chemical reactions. This is the self-movedness of the soul that St Macrina takes from Plato. That is why St Macrina could refute the notion that the operations of mind (nous) were due to the natural properties of the elements within the body by an argument that the primitive robots of her day did not assemble themselves spontaneously and operate spontaneously, but through human art. We ourselves think that St Macrina’s argument is flawed as it stands. We have tried to improve it.
One species of bird builds its nest in one way, and, if the nest is damaged, repairs it according to the model of the species. Can molecular biology explain this? We are humans; our behaviour is much more complex. We build buildings, write poems, build robots, do philosophy, do physics, write and play music—do many things that seem to be beyond mere chemical reactions. It is these things that St Macrina is saying show the existence of mind (nous), because they require comprehension, understanding, planning, art, systematic execution in materials.
We have here gone somewhat further than St Macrina and addressed the point: can the mind (nous) which comprehends, plans and executes in materials through the agency of the body be reduced to the molecular biology of the brain? We have suggested that the inherent logical limitation of the algorithm is such as to call into question the project to reduce mind (nous) to molecular biological reactions, since the molecular biological reduction, according to the current paradigm of molecular biology, would involve a systems representation of that molecular biology which would be logically and mathematically equivalent to an algorithm. But, in fact, the program to reduce mind (nous) to molecular biology is required by the intrinsic philosophical orientation of the molecular biologist today—by the materialistic and mechanistic paradigm that we spoke of earlier.
There is a further fundamental conceptual problem: To return to the chess program, given the nature of chess, the computer program can look ahead many, many moves—and if the machine that runs the program is fast and has much memory, it can give its answer without making you wait. The more moves the program is programmed to look ahead, the better its answer. Someone, however, once asked a chess master ‘How many moves ahead do you look?’ ‘One, but it’s the right one,’ he replied. A facetious reply but one which conceals a truth: the chess master is not a man whose mind is a bigger computer than the minds of all his opponents or a man whose mind looks ahead more moves than all his opponents, but a man whose mind understands the chess game better than all his opponents: the position, the right move—although he certainly may look ahead a number of moves. It is as St Macrina has said in her own examples: the chess master has a conception (ennoia) in his mind (nous).
With much equipment, many programmers and much, much patience, it might be possible to construct a computer system that passed Turing’s Test by means of a computer that operated on a very big algorithm or computer program. But the machine would not be alive; it would not think; merely much human ingenuity would have gone into anticipating the questions that might be put and establishing what answers to give. This is the problem with a behavioural criterion of artificial intelligence: the behaviour can be faked by means of human ingenuity on the part of the computer programmers. And this was precisely St Macrina’s point in the Fourth Century: these things do not happen by themselves; much human ingenuity goes into the conception, design and implementation of even the most simple ‘artificial intelligence’ system—which is precisely what the primitive robot was that she and her brother were discussing in the Fourth Century. Even so, the results of work in artificial intelligence systems have been disappointing. Even if they were encouraging, however, the very nature of the algorithm makes the algorithm, the computer program, inadequate—on the basis of Gödel’s Theorem and the close connection between it and the theory of algorithms—to turn the machine into a mathematician, say, that can reliably decide theorems in arithmetic.
Molecular biological systems, when they are represented by systems-theoretic models, are intrinsically able to be represented in a computer by an algorithm; this is the equivalence of the various formulations of the theory of computing, of which two formulations are systems theory and the theory of algorithms. Any attempt to reduce mind to a systems-theoretic representation in molecular biology will founder on the intrinsic theoretical limitation of the algorithm. For if such a project were to be able to succeed, then necessarily mind would be representable by an algorithm, and that would be to imply that all human mental phenomena were reducible to algorithms. There would be the fundamental philosophical problem, however, whether the reduction had not been achieved at the cost of eliminating some mental phenomena—such as prayer—as being unreal or otherwise illusory. In other words, there is the danger in such projects of an insistence a priori that only mental phenomena that can be represented by algorithms are genuine mental phenomena and of a refusal a priori to accept other mental phenomena, such as prayer, as genuine human mental phenomena. This approach is already foreshadowed in Hume’s own rejection of miracles as spurious.
Let us take a final example: I can write an algorithm to play jazz. If I am patient, I can gather many musicologists, systems analysts, computer programmers and electronics engineers, and I can get them to program a computer to play every known piece of jazz ever played. I might even design some ‘spontaneous’ algorithms for improvisational pieces, using randomizing functions in the algorithms. To the layman and even to the experienced musician it might sound like jazz. To the man who programmed it, however, it would simply be a computer program. Jazz is a very long way from all that. When the nightingale sings, is it just a machine?
St Gregory has his own response:
 This certainly would be considered sound in our own age: the proposition of Albert Einstein, e = mc2, establishes not only the equivalence of all matter but also its equivalence with energy; the findings of particle physics certainly do not dispute the notion that all matter is the same sort of thing.
 In the broad Aristotelian sense.
 See Copleston Volume I, p. 415.
 See http://www.research.ibm.com/deepblue/learn/html/e.8.1.html. The author makes the following remarks which put the victory of the computer over the world chess champion into context:
‘It turns out that the Japanese board game “go” will not succumb to such brute force methods—there are simply too many possible moves for even the most powerful supercomputer imagined to ever examine. Instead, “real” AI [artificial intelligence] will be needed—intelligence based on pattern recognition, “insight” and strategy. Indeed, for those of us who work in pattern recognition, machine learning, or various fields allied with artificial intelligence, it is the weaknesses of Deep Blue [i.e. the computer that beat the world chess champion] that are the most interesting. How should we program computers to recognize and understand the style of their opponent’s play and adapt accordingly? How should we program the machine to distinguish the most promising lines of attack from the ones that are not likely to pay off? How do we program machines to make complex plans? Whereas there are some aspects of the Deep Blue system that employ crude versions of methods we know are important in human intelligence (in particular when scoring the quality of a position), their weaknesses are compensated by the brute force search through possible moves.
‘It must be emphasized, too, that even if such subtle and complicated techniques of pattern recognition, reasoning and so forth are ultimately achieved in chess, there would still remain an enormous gulf between their use in chess and in other general aspects of intelligence, for instance, in planning a story or recognizing a scene. For these, we may have to duplicate the human, at least at some level of abstraction.’
 ‘Program’ and ‘algorithm’ are synonymous.
 One imagines that introducing a stochastic element—a range of outcomes according to a probability density function—might to an extent cure this problem of staleness. The computer manufacturer would arrange that the operating system would behave just a little differently each time a command were entered, on the basis of the probability functions mentioned. In cases where the results were not disastrous, they would be interesting—and challenging—to the user of the computer.
 We use the informal and imprecise word ‘imperfect’ to avoid a formal statement of incompleteness.
 This is the hypothesis that any one of the many equivalent formulations of the theory of algorithms is in fact adequate to cover any intuitive notion of ‘mechanical procedure’ as it might be encountered in practical life.
 Encyclopedia Vol. 7, p. 94.
 This was evidently Gödel’s own view.
 Now and henceforth taken in St Gregory’s and St Macrina’s formal sense.
 Here and below, ‘systems theory’ is taken not as ‘theory of formal mathematical systems’—this was Russell’s and Whitehead’s project for arithmetic—but as one formulation of the theory of algorithms useful for the design of complex computer systems. We must mention in addition that we do not know what happens when one introduces probability functions into the systems representation: a systems representation without probability functions is equivalent to an algorithm, but we are not aware of any work on, or results concerning, systems representations or even algorithms which contain a probabilistic element. Let us therefore restrict the argument to a systems representation of the molecular biology of the chess programmer which is ‘classical’—which does not use probability functions in its formulation.
 Common acceptation.
 The random element.