XMH - Logic of Creation

8/11/2019 XMH - Logic of Creation

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CHAPTER 8

The Logic of Creation

1. Docta ignomntia

To the greatest achievements of science of the last one hundred years

belongs the conclusion Which today one cannot doubt that the World

is not so much static as undergoing evolution. This applies not only to

the evolution of life on our planet as much as the Whole universe to the

greatest magnitude available to us. There are nevertheless three places

in this evolution Which remain as discussion points to this day: the genesis

of the World, the birth of life and the aring up of consciousness. It is

hard to doubt that these three places are linked in the plan of the Whole

but, in spite of the remarkable progress in these three elds, we still knowrelatively very little. The aim of the notes to this chapter because it is

hard to call them even an outline of a lecture is to express this lack of

knowledge in a more organised, quasi-logical manner.

1 2 9Its rst version appeared as: I / z ez z ]e / / ee lmT/oeLogic of Creation, in S e z e n e eand z / 9 eFe/lureof Z \ / le z / e / m e l ,Ponti ciae Academiae Scientiarum Scripta Varia

99 ,Vatican

City2001,

pp. 501-506.


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1 36 PART IV Creation and Sense

2. From the logic of language

The logic of language, now traditionally, is divided into three areas:

syntax, semantics and pragmatics. Syntax is concerned with exploringthe relations between utterances in a given language. It is the oldest

thus it is no surprise that it is the most developed part of the logic of

language. Semantics researches the relations between utterances of the

language and what the utterance refers to. Lastly, pragmatics is inter-

ested in the relation between language and its users. Only recently ha s

the growth in pragmatics gathered pace. It is important to stress that all

three of these branches of the philosophy of language are purely formal

sciences i.e. they do not appeal to empirical work on language, limiting

themselves to purely deductive research methods. For the next stage

I will continue to be interested in the interaction between semanticsand syntax and thus pragmatics will be put to one side; I will use both

the terms syntax and especially semantics in a somewhat broader sense

than is usually done in logic. For example, when talking about the real-

ity to which the language is referred, I will in some cases understand it

not as the formally understood domain of language or a semantic model

see below as much as that realm or aspect of the world on which the

given scientific theory expressed in a certain language conducts re-

search. Such a broad treatment of logic is justified to the extent that one

of the most important tasks of logic is the modelling of the reality of

situations and supplying analysis which goes beyond the realm of pure

logic of the schemes of reasoning. I hope that this type of loosening of

rigour will not lead to misunderstandings.

Some languages exist which are completely devoid of semantic as-

pects. These are formal languages which are reduced to symbol games

which refer to nothing? All other languages talk about something, theyhave their own semantics, they have something to relate to . Terms likemeaning, designation denotation and relation reference are ex -amples of semantic terms or so-called semantic operators: they act on

1 3 0It does not mean, of course, that one does not construct formal models of such lan-guages but I am not concerned with this here see below, section 3.


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CH PTER 8. The Logic of Creation 1 3 7

language, having their values in the world model which the given lan-

guage describes. Thanks to these operators, language may be a language

about something.

It may transpire that some kind of language relates to another lan-guage it talks about another language . Therefore, we have two languages

to consider: the language called a meta-language which talks about an-

other language the subject language . It is easy to imagine a whole hierar-

chy of such languages: language subject , meta-language, meta-meta-lan-

guage. .. The discovery of this hierarchy of languages was a considerable

achievement for the development of logic; it enabled linguists to eliminate

a range of antinomies, that is, ostensibly correct statements which lead to

nonsensical conclusions. Antinomies, springing into existence from an un-

controlled jump from language to meta-language or vice versa, are termed

semantic antinomies other antinomies exist as well . An example of such

an antinomy would be the famous liar paradox. Une of its formula-

tions is: that which I now write is false. Is the sentence true or false?

It is not the case, however, that proceeding from a language to a meta-

language always produces antinomies. On the contrary, if we are able to

use them competently then they can serve as a powerful method of

proving theorems. For example, Kurt Godel proved his famous theoremof the incompleteness of the system of arithmetic, which shook the

foundations of the philosophy of mathematics, by cleverly utilising the

strategy of moving from a meta-language to the language of arithme-

tic and back again. He first translated certain sentences on arithmetic

that is, belonging to the meta-language of arithmetic into statements

on numbers which belong to the language of arithmetic . The language

of arithmetic is very functional since it allows one to conduct calcula-

tions. Having completed the required calculations, Godel then translatedthe conclusions acquired into meta-language. He attained in this manner

sentences which expressed his statement of the incomplete nature of

the system of arithmetic. This type of method of proceeding from me-ta-language to language is termed the r e f - 1 e f e 1 e 1 e e emethod and is particu-

larly effective. However, it is necessary to emphasise once again that in

applying this method the slightest inattention may result in, instead of

binding conclusions, the production of antinomies.


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3 . Language and interpretation

Strictly speaking, rigorous control of reasoning is only possible in

formal languages which as we know are completely without seman-tics, that is, the reference to something other than the language itself. We

may, however, add such a reference to formal languages arti cially. If

we want to place this on a logical footing then this relation must also

be purely formal. W e obtain this reference by creating a purely formalsubstitute to reality and establishing the semantic relations between

language theory and this substitute which we term a s e / e e e z m e emodel or,

in short, a model of the given language or theory . When such a model

is constructed then we can say that the given language or theory ha sattained an z m e 1 ] > 1 e z e z z z 0 1 e ,that is it ha s been z m e 1 p 1 e z e e .Having at our dis-

posal the deductive theory and its interpretation semantic model we

may exactly codify the rules of transition from the theory language to

the model and vice versa. Here it is, of course, essential to abide by the

principles of both language and meta-language.

This strategy has very important applications. One is the famous defi-

nition of truth by Tarski. It states that a certain statement which belongs

to a given formal language is true if and only if it asserts something in thesemantic model of the language and this then really occurs in the model. Tar-

skis definition only applies in relation to formal languages but the inspiration

which flowed from it had a considerable effect on general philosophical views

in the 20 century Nevertheless, the moment when we step beyond the safe

realm of deductive language theory, moving from syntax to semantics and

vice versa, we begin to experience difficulties; the ground becomes increas-

ingly awkward but abounding in important problems.

In scholastic philosophy there existed a distinction strongly reminis-cent of that between syntax and semantics. It spoke of logical order andontological order. Logical order related, however, not to language but

rather to what is in the intellect and ontological order not to a deductive

model because they were still unknown as much as to what is in reality.

This distinction w as made, for example, by St Thomas Aquinas when he

argued against the so-called ontological proof of the existence of God

proposed by Anselm of Canterbury. According to St Anselm, God is

something of which nothing greater can be thought Dem e s z e z / z q e z z eg e m


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CH PTER 8. The Logic of Creation 1 39

m /9 z //eeezie/Je 0 g z fe z 1 zpom? but the God that exists according to Anselm

is greater than the God which does not exist and, thus, God exists.131 St

Thomas riposted by drawing attention to the fact that the first premise of

proof God is something of which nothing greater can be thoughtbelongs to the logical order while the conclusion God exists is

part of the ontological order. The error thus stems from as we would

say today an illicit jump from syntax to semantics.

Our sense of logic compels us to sympathise with St Thomas. Indeed,

Anselm gets caught in the trap created by the interweaving of language and

meta-language.132 In any case, we touch on here an extremely important

issue the relation between language and that which it re la te s to . This is

not only an internal ntatter of logic which can be seen from the example

of St Anselms reasoning . In the functioning of the world we encounter

a range of situations in which language or something very reminiscent of

language seems to be an efficient cause of something which exists in

reality. A typical situation of this type is computer programming a nd thus

a certain language and its implementation, that is, what our computer does

in reality, but there also exist analogical situations of significantly more im-

portant philosophical meaning. Utilising certain technical sources from logic

may lead to a deeper discernment of their problematic.

4. Genetic code

The term code in the sense of genetic code is in reality a syno-

nym for the term language. As we know, the alphabet of this language

is made up of four bases represented by their symbols, A, C, G and T

which, in a linear sequence, crea te DN molecules which contain all ofthe information indispensible for the creation of a four leaved clover orAlbert Einstein. Today we are able to a considerable degree to derive the

1 3 1It is worth remembering, however, that even Anselm himself did not regard this viewas a strict proof. He placed it in an asce tic sermon to monks which had as its objective anexhortation to live a perfect life.1 3 2Yet the logician of Godels class was convinced that St Anselms proof could be savedby adding an additional premise that states that the Perfect Being may exist.


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deductive rules which govern these letters of life. It is undoubtedly

a syntactical aspect of the language of genetics.

The real problem, however, stems from the fact that the syntactic ge-

netic code must create its semantics. The information contained withinmust translate itself to certain processes in reality that ultimately produce

the four leaved clover or Albert Einstein. To use more traditional lan-

guage, it is necessary to make a jump from logical order to ontological

order. The living organism is not, after all, a purely linguistic creation as

much as a real object. Genetic code does not simply describe certain ways

of action, it a lso m a ke s them real.

jaques Monod, in his famous book Le hazard e z a e e e s s z z e 1 3 3 ,in the fol-

lowing manner introduces this semantic antinomy: Genetic code would

be completely useless if there did not exist a decoding mechanism which

could be applied to the information which, in turn, would be applied to

biochemical processes. Without this kind of decoding tool, the information

contained in genetic code would never be able to leave the syntax of this

code. However, the information concerning the decoding structural tool is

not present anywhere except within genetic code itself. W e thus have a clas-

sic antinomy: without a decoding tool, the code may not function but it

may not be produced anywhere other than within the encoded information

contained within the code. It is a new version of an old dilemma which

came first : the chicken or the egg? The situation is reminiscent of a vicious

circle. How is it connected with the theory of evolution?131I am not using

this understanding as an argument against the theory of evolution; I only

wish to call attention to the fact that what may seem as illicit jumps in tlte

theory of language from syntax to semantics, do not only occur in reality

in the strategy of evolutionary processes, but manifest themselves at key

points. Can one not make here a certain analogy with the method employed

by Godel in proving his s ta tement? The method of self-reference is effec-

tive under the condition that it is used in a re ned manner.

133 Monod, Le hazard e z 1 e e e e rr z z e ,Du S eu il, P aris 1 9 7 0, p. 1 8 2 .1 3 1On the attempts to resolve this dilemma and the linguistic aspect of genetic infor-mation, john Maynard Smith writes in an interesting manner in his article Ere/aired an dIafer/aaaea, in I/Wager qf the War/d S e z e a e e ,I-Ia/aaaz els; /lrz, ed . A. Koj, P . Sztompka, Uni-wersytet jagiellonski, Krakow 2001, pp. 13-17.


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5. The language of the brain

Another eld in which one may discern the syntactic-semantic con-

juring trick is the functioning of the human brain. In this case, languageis created by electrical signals which travel along the nerve cells and the

illicit jump here is even more radical: it is not based on the transition fromthe linguistic level to something which that language speaks of, as much as

on the transition from language to something which previously did not

exist at all or existed only rudimentarily into consciousness. The problem

which we must assess here is thus even harder and our knowledge of the

eld is yet more insuf cient. One of the main methods of the working of

consciousness is that of the self-referencing method. It gives birth to self-

awareness and along with it all of the problems which we grapple with.

6 .IllicitjumpThe third area in which the linguistic approach may be utilised is

the universe or, more strictly speaking, the laws of nature which govern

it. It is often said that the laws of nature are expressed in the language

of mathematics. Physics handbooks are full of mathematical formulae

which are nothing other than elements of a certain purely formal lan-

guage even though the language of physical theory is rarely recon-

structed as an axiomatic system suitably interpreted. On the strength

of this interpretation, mathematical language gains a semantic refer-

ence to a physical reality and certain formulae of this language be-

come interpreted as laws of nature. In reference to the idea put forward

in section 3 , one may say that the universe or some of its realms is

a semantic model of a given mathematical language. However, the

expression semantic model should be put here in quotation markssince the universe or some of its realms is not a collection of sentences

or symbolical sequences, as is the case in a technical understanding of

a semantic model. Indeed, logicians and philosophers of science often

try to construct semantic models in their technical sense of theories

of physics but physicists, in writing their equations, normally relate them

directly to what they term physical reality.


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It doesnt matter which manner of describing the method we use: just

as logicians and philosophers with their deductive models, as physicists,

appealing to the research experience what is surprising is that this model

functions so well. With its help, for example, we are able to foresee withremarkable precision surpassing by many orders of magnitude the pre-

cision which our senses allow the events of the quantum world and el-

ementary particles of which we would know nothing were it not for this

method. It is hard to oppose the impression that here we are also dealing

with an illicit jump from the syntax of mathematical language to its se-

mantics, which combines an unusual explanatory effectiveness and ability

to predict phenomena stemming from the real world.It seems to me that the problem which we must assess here is of even

deeper nature than that of genetic code or neurological code. Both the struc-

ture of DNA and the structure of electric signals between neurons are lan-

guages of nature and, if we wish to understand the shift from the syntax of

these languages to their semantics, we may appeal to the as yet unresearched

secrets of nature. In the case of mathematical language of the laws of na-

ture, the situation is all the more complicated since mathematical language is

our own creation; it has been created by people as part of a long process of

the development of human culture. It may transpire that the questions stem-

ming from the shift from the syntax of this language to its semantics may be

no more complex than in other human languages but everything indicates,

however, that it touches on the deepest secrets of existence.

If our empirical-mathematical method of researching the world is effec-

tive, and to date its successes seem to con rm this, then all of the properties

of the world are able to be deduced from the appropriate collection of the

laws of nature, namely the appropriate set of correctly interpreted mathemati-ca l formulae. All of the properties of the world with one exception its ex-

istence. It is true that todays theoretical physicists are in a position, with thehelp of the laws of quantum physics, to create a model of the origin of the

universe from nothingness but in doing so, they must assume that the laws

of quantum physics exist a p r z 0 r zin relation to the world which they want

to reproduce a ] > r z e r zin a logical sense, not necessarily as a temporal con-

sequence . Not accepting that from the start we have at our disposition

the laws of physics means that we would not be able to make any steps in


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the construction of our model.135 Nevertheless, the universe de nitely ex-

ists. The illicit jump from non-existence to existence must have somehow

been made. This is exactly the Mystery of Creation.

7. New logic

I feel compelled at this point to caution the Reader against the all too

easy temptation of treating these illicit jumps, as I have described above,

as a place which should be lled by the God hypothesis. If science does

not wish to betray its calling, it may never become entangled in a chain of

questions and utilise a strategy of examination which does not appeal to sci-

enti c method. I think that what we now regard as illicit jumps e.g. fromnon-life to life or unconsciousness to consciousness is something only re-

garded as illicit from the perspective of our contemporary logic but actually

serves as a fundamental strategy of nature in solving its hardest problems.

The limits of our logic today are too well known for us to keep needing to

remind ourselves of them see the above mentioned theorem of Godel and

other limiting theorems . Everything indicates that our current post-Aris-

totelian logic is too simplistic to be able to address the most fundamental

problems uncovered by the development of science. I would be inclined tobelieve that we need a radical new perspective on logic a perspective which

would not be concerned with questioning or rejecting this or that rule, one

or another axiom but rather perceiving logic in an entirely new light. I do not

think that this may be conducted via experimentations with purely deduc-

tive operations, which may subsequently be applied to a concrete scienti c

problem e.g. to the problem of the creation of life or consciousness . This

new logic must rather be developed in the course of resolving scienti c

problems as a fully binding partner of other elements of scienti c method.Would the new logic throw a brighter shaft of light on the most im-

portant question of why there exists something rather than nothing? W esh ou ld h op e so but I think that the question will always remain a sourceof metaphysical fascination. For, after all, we exist and it would be much

easier if nothing existed at all.

1 3 5I write on this subject in more detail in chapter 1 4 of my book: C r g y igj//ajesz aaa/ea/ e a / r e a a z l r g y e q / e a.9 ,0 ,1 ) .ea .

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