§1. On the emergence of informationistic worldview (informatism)

When looking at the development of European thought from bird’s-eye view,  we observe  three great periods  of  mutual  influences  between the state of science (that is, empirical teories with mathematics) and a dominant philosophical worldview: the theistic (or theological)  period of the Middle Ages,  mechanicistic from the Renaissance dawn of modernity, and informationistic as dawning in our times. If we liked to most briefly define each period with one key concept, we could mark them up, respectively, with the key categories: God, hardware, software.

Dependencies between these two intellectual forces are always mutual though in various proportions;  even in the Middle Ages when theology dominated so strongly,  it was influenced e.g. by mathematics in the Pythagorean and Platonian spirit as well as encouraged mathematicians to bold speculations about infinity (which ancient mathematicians were afraid of).  Impressive examples of the impact  of natural theology (of Platonian  brand) on optics and astronomy are found in Kepler who in this respect continued some medieval threads (Grosseteste’s metaphysics of light, etc).

A next nice example of such a feedback is found at the Renaissance eve of modern  science.  Scientists were  then massively influenced by the mechanicist worldview of the ancient atomists. In turn, as a result of successes due to that inspiration, the mechanicist model of the universe has got firmly rooted in science, and in circles of educated public, till our times.

Nowadays  the time is rape for replacing the mechanicist model of the world by what deserves to be called  informationistic worldview.  Before defining this phrase, I  suggest  that we also accept its handy terminological equivalent to be used interchangeably. Let it be the term informatism which has  gained  a noticeable place in the literature.  When using the latter for the sake of convenience, we shall remember that the full meaning is involved in the original version which has been introduced after the following consideration.

The English language offers  quite a number of adjective derivatives from the noun “information”. Thus we have: informational, informatist, informationist, informatic,  informatistic,   informationistic, informatized. Some of them seem to be synonymous, some not. This a real “embarass de richesse”. Fortunately, a convicing hint  as to the choice comes from an article in the  journal “Information, Communication & Society” (Volume 2, Issue 1, 1999) by Jos de Mul. Its title reads: The Informatization of the Worldview, and inside there appears the key term informationistic worldview.   Its author is Professor of Philosophical Anthropology at the Erasmus University in Rotterdam.  Prof. de Mul  depicts  the mechanistic approach  as descending from the historical scene at which there emerges the informationistic worldview as characteristic of the coming  time.

This is also the point  of  the Polish study which appeared in Spring 2011 (with   Academic Publishing House “Exit”  in Warsaw) under the  title: “Umysł – Komputer – Świat. O zagadce umysłu z informatycznego punktu widzenia”.  Part One written by Paweł Stacewicz is entitled  -“Infomatyczna inżynieria umysłu”, Part Two, by Witold Marciszewski – “Światopogląd ery informatycznej“. The term italicized is one to be rendered with “informationistic”, and so the above  phrases get translated as follows. The book title:   Mind  – Computer- World.  On the riddle of mind from an  informationistic point of view.   The Part One: Informationistic engineering of mind;  the Part Two:  The worldview of the  informationistic era.  Moreover, the term “informatism” (Polish “informatyzm”) is frequently employed throughout the book.

Chapter 16 of this book presents the ancient atomism as a paradigm of extreme mechanicism, focussed, so to speak, entirely on a hardware, with negligence of the role of software in natural and social processes.  Moreover,  in agreement with Mul’s point,  it is acknowledged that mechanicism  inspired modern science in its beginnings and several next centuries. However,  in  the last decades the concept of information processing, conceived as computing,  provides a paradigmatic model for natural  and social sciences.

Informatism emerges from several sources: (i) logical research in the foundations of mathematics and computation,  (ii)  merging of computation theory with physics  (iii) computer technology, (iv) biological reaearch  as in genetics  and neurobiology, (v) some  speculative conjectures about computational nature of the universe, inspired  by the earlier listed  points.

What is remarkable about this worldview, it is the fact that nobody does pretend to be its author. It  is rather a content of  spontateous social awarensess shaped by the participation in the society massively saturated  with digital technology and informationistic vernacular.  This state of affairs forms a challenge for philosophers, in particular those concerned with  philosophy of science and epistemology. Informatism is an epistemological position when cognition is conceived  as problem-oriented  information processing, and the latter as a kind of computing — the main concern of informatics.

Informatism can be presented in one of two ways. One of them would take advantage of the fact that there exist  valuable partial approches which  might be merged into a desirable synthesis. However, this ought to be a huge research project to be executed by a team of first-class specialists in the fields of complexity, computability, quanta,  cosmology (universe as a computer), etc. The more difficult would be such a task  that among the views to be considered some opposite other ones;  then we would be bound to precisely analyze their arguments  before trying a synthesis.  As a material to such processing  one should take into accont,  for instance, Ed Fredkin’s digital philosophy,  John Wheeler’s idea about “it from bit”,  likewise opposing their “digitalism” Freeman Dyson who vigorously defends the necessity of analog (i.e. non-digital) computing.

§2. From insight to algorithm, and the other way round

To define a worldview one should  refer to its main tenets,  especially its key concepts and central questions.  The key concepts of informationistic worldview (italicized below)  are grouped around the pair:  algorithm versus insight (i.e. intuition).  Algorithm is  a way of  mechanical  information-processing, or computing,  aimed to solve a certain problem. As insight also has an essential share in problem-solving, hence there arises the central  issue of the informationistic worldview: how insight and algorithm relate to each other?

Once upon the time,  the concept of insight was not much esteemed by those  so-called analytic philosophers who  saw its place rather in the sphere of poetry, metaphysics, religion, etc. However, the situation is different at the start of the 21-st century.  Let me exemplify this fact by a personal remembering.

Several  years ago a friend of mine acted as the editor of a volume on automated theorem proving. Since he knew about my interest in the subject, he asked for a suggestion as to the title of the planned volume. I suggested “From Insight to Proof” — meaning formalized, that is, algorithmized proofs alone;  for  only such proofs are what proof-automation  theorists are aiming at. Thus the suggested phrase might have been generalized as “from insight to algorithm” (obviously, in that project the more specific title version was preferred).  I was happy to see that  my advice has been willingly accepted by the editor and all the contributors (who belonged to the best specialists in the field). The more happy I was when the volume appeared, and I found in it two contributions regarding  a Gödelian approach to the “insight vs proof” issue which is in the centre of my interests. Such an experience  would be incogitable  in the heyday of Vienna Circle,  that is, before Gödel’s discovery of arithmetical sentences which intuitively  prove true,  but  their truth cannot be demonstrated  in an algorithmic way.

To fully express the main tenet of informationistic worldview, the said phrase should be completed  as follows: from insight to algorithm, and  the other way round:  from algorithm to insight.  This is the  case of a positive feedback being, nicely illustrated with the success of arithmetic.  There must have been a very penetrative mathematical  insight  (of an anonymous Hindu more than thousand years ago) that resulted in the discovery that there exists the number zero to precede one (the idea alien to Greek and Roman mathematicians). This made it possible for the Arab scholar Al-Chwarismi to create algorithms for addition etc. This relieved mathematicians from the enormous losses of time and energy  (as those caused by old Roman notation), opening new chances before their creative thought which,  in turn, could have produced new algorithms.

Such mutual support  of insight and algorithm  belongs to the main forces in the dynamics of human knowledge.  In order to perceive  other forces, and have a look at the whole dynamics (as seen by informationistic worldview), a certain conceptual confusion should be removed.  The concept guilty of  this confusion is that of computing  (see the listing of key notions above)  and its derivative computability.  In the idiom of computer scientists “to compute” means:  to process information exactly according to an algorithm. That  is: to mechanically follow its instructions. These tell us:  (1) how to transform physical shapes of formulas,  (2) doing this step by step, without any leaps of intuition,  (3) up to obtaining solution of the problem in  question  (4)  in a finite number of steps.    

The above procedure can be performed by a human calculator using pencil and a sheet of paper, or by a computing machine  as defined mathematically  by Alan Turing in 1936, and for this reason called  Turing machine.  Now its physical realization is present everywhere as electronic digital computer.  The range of possibilities and the mode of proceding of digital computers is exactly what people call camputing in an everyday idiom.

However, such a narrow  notion of computing  induces  the  crisis of conceptual confusion.  While in the main stream resarch  people stick to the equivalence  of the terms “computing” and “algorithmic digital computing”, there is a fairly large group of dissidents who back their claim as follows.  The main stream definition is inconsistent, since in the accepted at large vabulary of computer science we have the term “analog computing”; it  is what is being done by analog devices, and nobody  refuses to call them computers.  Hence we are bound either (i) to accept contradiction that analog devices are computers and are no computers (as not acting algorithmically and digitally), or  (ii) to more broadly define the notion of computing so that it embrace both algorithmic and non-algoritmic information processing as two varieties of computing.

§3.  Insights in analog computing and in perceiving abstract entities

From among the two strategies stated above, we are bound to follow the latter, if we do not like committing contradiction. This, in turn, implies the duty to explain how broadly should we understand analog computing.  Surely this concept is satisfied by what is done by analog computers. These do not operate with  symbolic representations  (as digit sequences) of,  say, physical quantities. Instead,  (1) they  process quantities of a certain kind (eg. electric)  which represent quantities of another kind  (eg. mechanical), and (2)  such quantities may be continuous. Now,  what about the phenomenon of  insights?

With the computing being performed by analog devices  some insights share  the lack of symbolization and the mapping of some quantities into other quantities.  This is  satsfied, for instance, in the case of car driver whose problem-solving consists of a sequence of decisions.  His inference do not need any  representations by linguistic units.  He reasons with visual representations which are mappings of  what happens on the road.  Also the feature of continuity can be satified in mapping: it is shared by a section of road and its mental picture.  The same can be said about a shooter trying to hit a target;  he acts in a continuous  external environment which he maps in his inside.

The things appear less obvious in a case like that of a preacher who feels, and so reproduces in himself,  the mood of his audience and adapts his performance to such a feeling. Moods and atttitudes are not physical quantities.  However, the  instance may be interpreted as follows. The preacher’s insight consists in an empathic sharing of his audience’s  mood, hence a kind of mapping. This information is by him processed to compute  possibly best reactions to listeners’ attitudes  towards his teaching.

Thus both types of  cases, that of car driver and that of preacher, may be subsumed under the category of  analog computing as  information in them processed  is not symbolic. It  consists of pictures of an external reality which are somehow mapped  in the reasoner’s “inside”  (i.e. his mind? brain?). His reasoning operates not with linguistic units but with mapped pictures.  In driver’s case these are spatial  images of  continuous quantities as distance, velocity etc.  In preacher’s case occur less tangible images of audience’s mental and emotional states, but nevertheless they are mapped, and  the reasoning preserves the feature of operating on  such non-symbolic mappings.

It may seem that insights, as being instantaneous, have nothing to do with computing as being a sequence of steps.  Hower, when  we combine an introspective perception of our insights with what we know from neurobiological research, then  there comes the following understanding:  the experience of insight results from a sequence of events occurring in the nervous system. The last element, being an insight, is one whose we are aware, while the preceding ones (a nervous process of analog computing) are  hidden before the “eye” of consciousness. Thus insights  enter into a harmony with analog computing.

What about perceiving abstract entities,  as sets, functions,  numbers, and in particular infinite numbers?   Infinite magnitudes in no way can be derived  by abstraction from sense experiences. Hence  propositions about  infinities rank as the most spectacular truths of reason.

In this context, it is in order to clarify that the informationistic worldview does not expect any infallibility,  or absolute reliability, from human reason. Similarily,  the sound empiricism does not claim that all sense perceptions are unconditionally true.  The name “truth of reason” hints at reason as the sorce of the given statement, and  at  truth as the goal  endeavoured. A mathematical theorem  which has been disproved  as well as mathematical theorems which has been duly demonstrated are at the same footing as propositions born from reason, and not from another source, say, senses or taste.  Therefore, the term judgement of reason  should be recommended instead of that old Leibnizian phrase, but the latter may be used for historical associations,  provided that  no confusion would arise.

One may speculate that there exist abstract entities which are mapped  in minds in a process of mathematical cognition. However, we are not bound to risk such conjectures.  Should they prove true, then we shall state that such insights are analog in their nature;  but if not, then  we shall  treat them as a separate category. What really matters. it the fact that not all truths are attainable in an algoritmic way.

[stextbox id=”info”]To continue enter “It from Bit”  in “Our Pub” Library. [/stextbox]

According to  the viewpoint  which I suggest to call computational rationalism, the first of these questions  should be answered in the affirmative, while the second remains open,  being the subject of a vivid controversy.  To be ranked among computational rationalists, it is not necessary to have  a solution of the latter question, but  it is indispensable  to be aware of the problem,  acknowledge its import, and tend to finding an answer.

The vision of mathematical order of the world is what the modern computational rationalism shares with  its predecessors — ancient, medieval, and  later  (not computational yet).  The very phrase “ordered in number” is taken from the popular biblical verse (Wisdom of Salomon Book, 11:21):  omnia in mensura et numero at pondere disposuisti. This means: “Thou hast ordered all things in measure and number and weight”.  (This sentence is redundant in meanings, according  to a rule of biblical stylistics; saying  “in number” would suffice alone,  when measure and weight are just applications of numbers.) There is a splendid host,  indeed, of rationalist  thinkers fascinated with this idea, from  its first authors, Pythagoras and Plato (who influenced the Book of Salomon) through Augustine, Aquinas, Da Vinci, Copernicus, Ficino, Cusanus, Galileo, Kepler, Leibniz, Newton, up to Georg Cantor who lifted the notion of number up to infinitely many infinite dimensions.

In modern rationalism  of computational brand there appear two completely novel  points, one concerning practical applications,  the other one connected with  a deep theoretical problem, as hinted  with the second  question in the title.

Its practical  implications arise from  combining the idea  “omnia in numero” with titanic powers of digital computers.  If  all things are defined numerically, then all things, i.e. systems, processes, relations, etc. in the universe can be simulated with computers. Even the universe itself  in its entirety, provided a sufficiently strong mathematics and gigantic resources of energy.  Thus the collective human reason,  which amounts to global civilization, owing to mathematical skills and wonderful technology,  can match the creative divine-like potential  of Plato’s  dēmiourgós (as praised in the dialogue “Timaios”).

While some modern computational rationalists believe in such a perspective,  as possible at least in principle, other ones remain sceptical about that.  This difference of opinions is deeply  rooted in some  worldview considerations.

The belief in the possibility of overall simulation stems from what the physicist Ed Fredkin has called digital philosophy . There is quite a number of eminent physicist and computer scientists  to endorse  this point, often connected with the contention that the physical universe may be a giant  digital machine to compute its own evolution (among the first to claim so was Konnrad Zuse, the German  constructor who pioneered  efficient digital computers  about 1940,  before  British and American constructions).  Then “in numero” means “in natural numbers”, that is, in the mode of computing fully available for digital machines, not engaging  into the inexplorable realm of continuum of real numbers.

Now it is in order to recall that in the uncountably infinite set of reals there is the set of uncomputable numbers whose existence has been proved by Alan Turing in 1936 with the help of Cantorian diagonal argument.  This is a mathematical fact.  Now the question arises about the nature of physical reality: are there in it any  functions  having  uncomputable numbers as values?   If  the answer would be  in the negative, then digital computers  should suffice  to computatioanlly map with simulations, or modelling,  the landscape of physical universe.

Were there in the universe  functions  with uncomputable values,  then some regions of it would be  inaccessible for digital computing.  Then — here a new factor would step in:  a real help might be expected from analog computing, somehow neglected at the present stage of computer science,  but not devoid of the chance of a  successful come back.   Some problems have been discovered which  can be tackled with analog computers alone,  but in the moment there remains open the question  of how much are  these issues  significant for the progress of science.

To  learn more, the Reader is advised to enter “Our Pub” Library   in which   the essay  “It from Bit”  introduces prominent parts of the said controversy, their arguments, and some  historical background.

Witold Marciszewski

When describing rationalism as computational,  I mean making a substantial use  of the data-program distinction  in order to elucidate crucial ideas of classical rationalism, to wit that of  the truth of reason  (veritas rationis),  and  that of  the light of natural reason (lumen naturalis rationis).

At first glance, the answer seems to be negative. If there had arisen computational rationalism as a philosophical view, people would invent a name to call it.  But, in fact, such a name  almost does not appear in the literature. With Google I found one postmodernist context, in which this phrase is used but not defined.

Another one is scientifically serious and thought-provoking, but  not one to be directly concerned with the issues in this post.  This term appears in the blog  run by a computer scientist  of MIT in dealing with the question: Can computer programs be understood through reason alone, or there is an empirical approach necessary for understanding?   There might be an interesting relation between this question  and philosophical rationalism,  but only when our discussion reaches  a more advanced stage, that of inquiry into pragmatic aspects of computational rationalism  in  philosophy. In the meantime, let this short mention suffice.

However,  there  happen to be views  or methods of thinking which function  and get influential even before a name for them gets established.  This  is the case of computational rationalism.

Among the authors who paved the way to this new attitude there is the renowned linguist and philosoper of language Noam Chomsky with this teory of universal grammar.  Its concise explanation is given in Wikipedia: “Universal grammar [the entry’s title]  is a theory in linguistics that suggests that there are properties that all possible natural human languages have. Usually credited to Noam Chomsky, the theory suggests that some rules of grammar are hard-wired into the brain, and manifest without being taught”, hence they are inborn to human minds,  and do not require any support from  sense experiences.

Let it be stressed, grammatical rules more resemble programs than data. However, there no clear line of demarcation between  rules  to form knowing  how,   and data, as distinct from programs, and  forming knowledge in the sense of knowing that. Anyone who possesses hard-wired rules  of grammar,  does also possess, at least potentially, an idea that there exists a grammar, hence enjoys a piece  of knowing  that.

This line of argument  does not lead to Plato’s  extreme nativistic view  that human beings come to this world with ready knowledge of a language and some other domains of reality.  Rather, it results in  the moderate Aristotelian brand of rationalism in which the light of natural reason amounts to inborn intellectual skills to attain knowledge through  following certain rule-like principles.  Thus,  people prove equipped with sets of rules (knowing how) like software of a kind, which control mind’s activities in acquiring  data like knowledge (knowing that).  In this way they enable getting knowledge that there are such entities as syntactic rules,  forms of material things, sets, numbers, goals of actions, social relations, moral values, and so on.

To be continued.

This seems to be wrong, indeed.  For authorities claim unanimously that Aristotle was an empiricist who opposed Plato’s rationalism, and that Aquinas followed his viewpoint.  As an evidence they quote Aristotle’s famous maxim about the human mind as an empty board at which  sensory experiences  write down their records.  This is to mean:  the human mind understands nothing that has not been first perceived by senses.  This view happens to be called genetic empiricism.

However, at the same time, both of  them assert  the existence of  truths which are necessary, hence irrefutable by experience,  and ascribe them a fundamental role in forming knowledge — as first principles of logic, mathematics, metaphysics.  It looks as if they lacked the awareness of  contradiction  between that claim and their genetic empiricism (what many centuries later was acutely  discussed  by David Hume).

They may have believed that what prevents  inconsistency it  is  the conception  of intellectus agens (the active intellect)  which performs  the job of extracting general and abstract ideas from  the  concrete stuff of sense data. Psychologically, it is really the case  that  the mind makes such generalizations; that ability may be attributed to what one calls active intellect.  However,  such inductive generalizations too frequently prove to be false. There is no logical warrant to  grant  such inferences the rank of  truths being necessary, and thereby  secure against any empirical counterexamples.

In what follows, I focus my argument on  St.Thomas’ views as, presumably, more remote from  empiricism  than those of Aristotle (a more personal reason is that I better understand Latin than Greek).  At the very start of his Summa Theologiae (Question One, 2nd Article) he puts the following statements. Physics is a science which logically follows from geometry, while the latter consists of principles  known to mind owing to the natural light – lumen naturale.

This concept of natural light (more Platonian, after Augustine, than Aristotelian) plays a key role in Aquinas’ epistemology.  Let us read a passage from the same work  which runs as folows (first I quote the Latin original  so that readers may check my interpretation).

Anima humana omnia cognoscat in rationibus aeternis; per quarum participationem omnia cognoscimus: ipsum enim lumen intelectuale, quod est in nobis, nihil est aliud, quam quaedam participata similitudo luminis increati, in quo continentur rationes aeterne.  (S.Th., pars I, q.84, a.5).

Here is a translation. “The human soul perceives all things in eternal principles  by participating in them.  The  light of natural reason we have within us  is nothing else  than a certain participated likeness of the uncreated light in which are contained eternal principles.” (The phrase  “lumen intellectuale”  may be replaced,  in Aquinas’ own language  by  “light of natural reason”,  which is more useful for the present discussion.)

Let us compare this notion with Descartes’ conception of the light of natural reason. For the lack of his original  definition, let us take advantage of the following conjectural interpretation.

“Descartes dwells on the notion of natural light (lumen naturalis, or lumiere naturelle), intuition. For him, it does not make some exceptions to the laws of nature. Rather, it is part of nature. Although Descartes never gives clarification to this concept, he supposed, God creating the universe, had a certain plan that is fully embodied in the universe as a whole and in part – in its separate parts. This plan is also embedded in the human mind, so that the mind can know nature, and even have a priori knowledge about nature, because the mind and objectively existing nature are reflections of the same divine plan.”

The  doctrine of Descartes  has created a firm paradigm of rationalism. Therefore, were  Aquinas’ views in accordance with Descartes’ approach to the light of reason,  this would evidence the rationalistic core of  Aquinas’  thought.  Is it  truly  the case?

In the quest for answer,  I suggest an excursion into the realm of biological a priori as a case of programming  in Nature.  Let us  compare  the whole world to a colony of ants, and  an  individual brain to the brain of an ant specimen. There has to be something like  a software – a plan  to organize the whole colony’s activity,  while some microscopic subprograms would be distributed among particular ants, corresponding to the tasks  to be performed by them.  Such a whole may resemble  what computer scientists call distributed computing.  If we agree to apply the emphatic word “lumen” to any set of instructions  which throw light on the question “how to do that?”,  then we approximate the nature of participation of those microscopic procedures in a giant global program.

In the interpretation regarding Descartes, as quoted above, one speaks of  “a certain plan  which — according to Descartes — gets embodied in the universe as a whole”, and gets distributed into some elements of the universe.  Any portion of such a plan embedded in a mind would be this mind’s aprioric konowledge. So far as regards Descartes.

As to Aquinas, he speaks of participating  of natural reason in eternal principles, and  its acquiring  from that source some pieces of knowledge, independently of any sense data. This is certainly an argument for the existence of aprioric knowledge. Aquinas, like Aristotle, and unlike Plato, does not claim that this has to be a ready knowledge. It may be something like an ability, or a set of rules followed by the mind to attain knowledge, but nevertheless there is something being a priori (whose special case may be instincts of animals).

And this is why there are  reasons to acknowledge Aquinas as a genuine rationalist in spite of all the distance, shared with Aristotle, which he held towards Plato.

What do you, Benevolent Reader, think about that? If you are not happy with the argument of this post, have a look at its sequel titled  “Is it the case that there has arisen computational rationalism?” Any comments of yours will be welcome.

Witold Marciszewski