##### Introduction

The new scientific Intelligent Design Theory (IDT) develops logical and mathematical concepts, methods and tools, which - applied to experimental data - are able to detect design in nature. Hence the goal of IDT is to establish the scientific evidence of the action of an intelligent agent on some natural or biological systems. But it is not the core-business of IDT to investigate the identity and properties of the designers.

To fill the gap we will give here - for whom are interested about - an elementary treatment of the "designer problem". Here we will investigate in general the logical and ontological differences existing between the "designer" and the "designed" thing (for brevity called "design", "project" or ID). In particular, as final cosmological application, we will deal with the so-called "Designer of the universe" and his main attributes.

According to the modern taxonomy of the ontological arguments (G.Oppy[1]), perhaps our argument could be classified as a new modern (8th) kind of proof. The originality of this work is that it is based on the powerful concept of limit, it is related to the results of the recently developed Intelligent Design Theory (IDT) and gets some examples from the Information Algorithmic Theory (AIT). We remember that, for example, all of mathematical infinitesimal calculus is based on the concept of limit. To do the reasoning clear and simple it is developed in modular way, by means of numbered axioms, definitions, theorems and corollaries (yet if of course we do not pretend to give a very mathematical formalization). Some evident axioms stay at the beginning of the reasoning. Besides possible objections are answered when needed.

To evidence the concepts we will use some examples from mathematics and informatics (numbers, sequences, algorithms, programs...). But it must be very clear that, when we are dealing with universal principles, we stay far beyond quantity and mechanics. Examples from mathematics and informatics can be used only as symbols of superior realities. Also if we will consider examples from the field of quantity, the concept of limit can be analogically applied to the higher qualitative order. That's the case eminently for the Designer of the universe, who is an immense reality, in front of whom any reasoning is only a pale sign.

##### #1# Axiom (of Infinity)

The metaphysical Infinity only is without limits. Any other thing has at least one limit. There are not two Infinity because they would limit each other. Infinity is identical to the Total Possibility. Outside the Total Possibility there is only the impossibility, the absurd, i.e. the nothingness. All stays into the Total Possibility. Otherwise any other thing is determined or specified or defined or limited (i.e. it can escape from some limits but does not escape from all limits, as Infinity does).

This axiom is the first one of all axioms. It is logically evident, coherent and is without any contradiction. Hence it does not needs any proof. Infinity pertains eminently to metaphysics. Infinity, the Absolute, is far beyond any existence and in the same time it integrates any existence. Metaphysically speaking the possible coincides with the real. So the Total Possibility is the Total Reality too.

###### Question 1

Is the sequence of all integer numbers {1,2,3...} the same as Infinity?

###### Answer 1

Absolutely not. This is a frequent and big mistake: i.e. the confusion between the mathematical infinite and the metaphysical Infinity. One can say only that this sequence has no last term. But to say that it has no last term does not mean at all that it has no limits. The sequence of all integer number 1,2,3 ... is not the same as Infinity because this sequence is specified and does have limits. For example this sequence does not contain the geometric figures, the elephants and the galaxies, and infinite other things, which are outside it.

##### #2# Axiom (nihil agit se ipsum)

A being or thing cannot act on himself/itself. A being or thing cannot create/design himself/itself.

Being "is". Being is the principle of all that exists, all that is becoming, all that is changing. Being is the invariable principle of the "becoming" (the "unmoved mover" of Aristotle). The theological equivalent of the metaphysical Being is usually named God (but many theologicians call God the Infinity itself). Being contains all of the possibilities of the universe. Being is not equal to Infinity because pertains to the manifestation possibilities only and not to the Total Possibility (e.g. there are things that could exist - i.e. they are "possible" - but that don't stay now in the universe). In other words the fundamental ontological statement "Being is", yet being the first determination, is a determination. Being pertains to ontology (as God pertains to theology).

To speak of the "existence" of the principle of existence is defective. The principle of a thing is not into the thing itself. Instead metaphysically any thing is into its principle. See theorem #13# below.

Universe (universal existence, manifestation, nature, cosmos, world) is all that "exists", all that is varying, all that is changing and varying, the "becoming". It refers to the manifestation of Being, who is its principle. In general all things belonging to nature are natural. In particular all living beings are natural because they belong to nature. In particular individual and over-individual beings are natural too.

One can define as "contingent thing" all that hasn't in itself the own sufficient reason. Such thing is nothing thanks to itself. It owns nothing of what it is. The set of things that are in this condition of dependence (from their principle) constitutes the universe. Universe has a beginning and an end because it cannot be the principle of itself and does not contain its principle, which is necessarily outside itself (see the next theorem #11#). Universe is limited. In fact, containing only that exists, the universe leaves outside, for instance, all that "might" exist but does not exist actually.

The recent stories about the so-called multi-universes do not contradict our definition, for it's always possible to do the set union of these hypothetical multi-universes and to obtain the global universe here considered. In other words, whether these multi-universes would exist anyway they would be nothing other that "regions" of the universal existence.

An individual of a specified kind or species of beings is an instance of that kind/species. Species refers to the qualitative "essence"; instead individuals refer to the quantitative "substance". Under the qualitative aspects each individual of a species is equivalent to any others.

According to its general meaning a causative limit of a set (or series or sequence) of any number of entities {e1, e2, e3...} is an entity L outside the set that has the following properties.

###### It is a fixed entity

The limited set represents variability. Meanwhile the limit is fixed. For example, on this difference between variables quantities and fixed quantities (we might call it a "different logical status") the rigorous foundation and accuracy of the infinitesimal calculus is based on.

###### It is unreachable

A limit is unreachable by the variation that converges to it. You may advance in the sequence but you will never reach the limit. You can approach it how much you want but you will never get it. That entails a fundamental discontinuity between the sequence and its limit. Thus a limit is not included into what it limits.

###### It has a synthetic nature (respect the set)

For example, in the infinitesimal calculus an integral can never be exactly calculated analytically, you need a synthetic operation - the integration - to get it. (Notice that meanwhile it is always possible to get the symbolic derivative of a function, it is not always possible - in general - obtaining the symbolic integral. There are deep reasons for that in connection with the synthetic character of integration.) On the contrary the variation that is inclined to its limit has an analytical nature.

###### It has different nature respect what it limits

A limit of a set - assumed in his general meaning - must necessarily have a different nature respect the set itself. Example (a): what limits space is not spatial. Example (b): what limits time is not temporal. Example (c): what limits the increasing sequence of regular polygons with n sides (n => infinite) is circle. Circle has a different nature respect any polygons.

A limit does not necessarily lose all the characteristics of the elements converging to it.

So a number can limit a sequence of numbers. A function can limit a sequence of functions. A square can limit a sequence of squares and so on.

Hence in what sense "a limit of a thing must necessarily have a different nature respect the thing itself"? The "different nature" that is in point here is effective and is based on the general characteristics of a limit we are listing now. These characteristics are peculiar of the limit only and not of the sequence.

###### It is causative

A causative limit contains into itself the potentiality or virtuality of generating all the elements of the set it limits. To do easy examples, here we deal with generative algorithms only. But it must be clear that causality must be considered in its more general sense, which is far beyond algorithms. Take for instance the simple sequence of pair numbers {2,4,8...}. Often one says that "it tends to infinite" or that "its limit is infinite". These expressions are imperfect. It would be yet more absurd to say a number limits the sequence. Simply we can say that this sequence has no last term. Certainly the sequence is limited by something (from the axiom #1#). But this limit is fully different from a number. In fact we might say that a limit for {2,4,8...} is an algorithm based on the formula "2n" (we could write this algorithm in any programming language - in Perl

[2] programming language: $n=1;while(){print $n*2;$n++;}). It has all the general properties of a causative limit and it is causative too. It is easy to verify that.

This algorithm is fixed. It contains the keyword or placeholder "n", which is something of semantically completely different from the elements of the sequence, which are integer numbers. This algorithm is unreachable: you can take 10, 100, 1000 elements of the sequence but you will never get all the potentiality of the algorithm, which contains virtually all the pair numbers. This algorithm is synthetic: you cannot express all that potentiality by means of a minor expression. According to the Algorithmic Information Theory (AIT) one may say this algorithm is the minimum algorithm to get all the sequence. This algorithm has a different nature respect the series and can generate all the even numbers. Here the qualitative difference between synthesis and analysis is particularly evident. The algorithm is hierarchical superior to the outputted sequence. Any yet long finite sequence of even numbers has zero value respect its generating algorithm. The algorithm is synthetic and the sequence is analytical. The causative limits are very important for us here because designers are causative limits (see below theorem #16#). Notice that only some causative limits are algorithms. Here we are using algorithms as examples because they are easy to understand. It's evident that examples from the field of quantity can be only symbols of superior realities.

###### Question 1

The infinite sequence of rational numbers of the form 1/n {1, ˝, 1/3...} converges to zero. What is its causative limit?

###### Answer 1

The causative limit consisting of the algorithm based on the formula 1/n ($n=1;while(){print 1/$n;$n++;}).

###### Question 2

The infinite sequence of relative numbers {-1, 1, -1, 1...} does not converge to any numbers because it "oscillates". What is its causative limit?

###### Answer 2

It is the algorithm based on the formula "-1**n" (-1 to power n) ($n=1;while(){$a=(-1)**$n;print $a;$n++;}).

##### #7# Definition (of subset's causative limit)

If a set S has a causative limit L, hence L limits any subset of S.

In fact if L is fixed, unreachable, synthetic, different, causative respect the set S, hence L is fixed, unreachable, synthetic, different, causative respect any subset of S too.

##### #8# Definition (of design)

Design (or project or ID) is that, which, satisfying the "specification/complexity criterion" of Intelligent Design Theory (see W.A.Dembski - "The Design Inference", Cambridge University Press), exists only thank to the intelligence of an intelligent agent. A design cannot be generated by chance, neither it can be generated by laws nor by any combination of them, but by intelligence only.

Any superset of an ID is an ID. Any add-on to an ID cannot delete its property of being an ID. Simply it transforms an irreducible ID to a reducible ID (i.e. an ID with some redundant stuff). About the concept of "irreducible complexity" see IDT text books (for instance M.J.Behe, "Darwin's Black Box", The Free Press). Intuitively: if you carry some stuff on a car, the car remains a designed thing. This definition has some importance. Its application to the universe is straightforward: whether we would find a single natural thing designed in the universe, hence all the universe will be designed.

Of course any designer is free to add any number of (apparently extraneous) parts to his design without his design loses its characteristic of being designed.

##### #10# Definition (of reducibility of an ID)

Any reducible ID contains necessarily an irreducible ID. A reducible ID is an ID that contains some useless things (its functions are not compromised by eliminating that stuff). But whether it is an ID must contain a "kernel" irreducible ID. Otherwise, if it were fully reducible, it would not be an ID at all.

The limit of nature is transcendent.

###### Proof

Remember from axiom #1# that nature must have at least one limit. We have to think that in nature nothing is fixed. Nature is the reign of variability. Everything in nature cannot be fixed because fixedness is a property of principles only, not of their consequences (nature is a consequence of Being - from definition #4#). The changing universe derives from a fixed principle (the famous "unmoved mover" of Aristotle). Nature is the set of all contingencies. If in general a limit does not lose all the properties of the elements it includes, then we have to show that the property of "being natural" is really lost by this limit. Whether any thing in nature is variable, hence, its limit, which is fixed, cannot belong to nature. In other words, the property of being natural is closely related to the property of being variable. Here we have the key to reach our goal. If nature is pure variability, any set of natural things, has a limit, which - being fixed - cannot belong to variability, i.e. nature. Moreover there is discontinuity between nature and its limit. In nature all things are cross-connected by relations. One might say nature is a network, a graph of relationships. In the universe there is nothing disconnected from the other (there are neither islands nor emptiness). But the limit of nature is not a "node", a component, an element or a part of this natural network. It is outside nature why the limit is outside the sequence converging to it. In other words whether nature contains all is natural, hence its limit, being outside nature, is not natural, i.e. it's transcendent.

Q.E.D.

###### Question 1

It seems that in nature there are fixed things, for instance, some mathematical constants (number π, number "e"...) or the mathematical/physical laws.

###### Answer 1

All that is not part of nature. About this we can follow Plato's conceptions about over natural Ideas. Nature is a process. On this process laws and constants are over imposed from the outside. The natural processes are only something continuously changing.

##### #12# Theorem (of uniqueness)

The causative limit of nature is unique.

###### Proof

Suppose for absurd that nature has two different causative limits, L1 and L2. Since L2 is different from L1 suppose L2 having something into itself not included in L1. Since a causative limit synthesizes all that it limits, and L2 contains nature, we would have something in nature that L1 has not. But since a causative limit encloses and integrates all the elements of the limited set, that contradicts the premise that L1 is a limit for nature. Of course we could suppose "L1 having something into itself not included in L2" and we will arrive to the same conclusion of absurdity. So L1 is equal to L2.

For easy understanding of this theorem think of a circumscribed circle as limit of the increasing sequence of regular polygons with n sides (n => infinite). Suppose for absurd that such series has two different limit-circles C1 and C2, i.e. with different diameter. It is obvious that the circle with the bigger diameter - say C2 - cannot be a limit for such series of polygons because the distance among the polygons and C2 would not incline to zero.

Q.E.D.

Being is the causative limit of nature.

From definition #4# we know nature is limited. We have to prove that this limit is Being. So we will prove Being has all the properties of a causative limit.

###### Being is fixed

Meanwhile nature "is becoming", Being "is". Meanwhile nature, being what exists, is the becoming (all that is continuously changing), its principle is "that it is", i.e. it is fixed.

###### Being is unreachable

Nothing in the universal existence (nature) can reach Being. To reach at least a property of Being a natural thing should stop and remain fixed, that is impossible for definition #4#. Being is unreachable, for it stays outside the set of natural things it limits.

###### Being has synthetic nature

Being is the synthesis of nature why, being its principle, it "integrates" all the content of the universe. Aristotelian dictum "effects are in their causes" is relative to this synthetic property indeed.

###### Being has different nature from the universe

If Being would have the same nature of the universe it would stay into the universe. But that is impossible for that affirmed above.

###### Being is causative

Being is the principle of nature. A principle is the cause of all its effects or consequences. Being is the principle of nature and as such it can generate all of the natural effects inherent to the cause it is.

Q.E.D.

##### #14# Theorem (of Being as First Cause)

Being is the First Cause of nature.

###### Proof

The proof of the "first motor" is - simplifying - something like this:

*«That is in motion must be moved by something else. In turn that will be moved by something else, and this one yet by another one. But this cannot continue without limit *[remember what we said before that each series has a limit]

*thus is necessary to postulate a first unmoved motor; that is known by all as God»[3]. *

First Cause, containing all the (secondary) cause and effects (of nature) is the causative limit of nature, i.e. is Being (for theorem #13#). First Cause is unique (for theorem #12#).

###### Question 1

Might the chain of causes return to itself in some circular way?

###### Answer 1

No. The chain of causes cannot return to itself in some circular way, because we would have a caused thing that is in the same time at the beginning of the series of its causes, and hence causative of itself. That contradicts the axiom "

*nihil agit* *se ipsum".*Designs are effects of a cause called "designer". Since the universe contains designs and has a First Cause, we can speak analogically about it as the "First Designer" or "Designer of the universe". Any other designer in the universe (man comprised) is a "secondary" designer only.

Moreover we know from evidence that man is a natural designer of many artificial designs. According to Aquinas:

*«In no order of causes is it found that an intelligent cause is the instrument of an unintelligent one. But all causes in the world stand to the prime mover, which is God, as instruments to the principal agent. Since then in the world there are found many intelligent causes, the prime mover cannot possibly cause unintelligently»**[4]**.*

Nature contains intelligent designers. Hence nature must have a superior intelligent cause. As such this cause can be considered symbolically as the Designer of the universe.

###### Question 1

Could man have been designed by a secondary designer (i.e. a natural designer)?

###### Answer 1

No, he couldn't. A designer has a hierarchical superior rank respect his project. In fact he has a superior ontological degree respect his designs (as cause is ontologically higher than its effects). Consider the following hierarchy: First Cause/Designer (transcendent) => man (natural secondary designer) => artifacts (artificial designs). It is a sequence of type: "transcendent - natural - artificial". If there were a secondary designer of man he would be a natural designer. Thus we would have a sequence "transcendent - natural - natural - artificial". But that's absurd because we would have a natural - natural designing relation. That's impossible for the superiority of ranking would be missing.

##### #16# Theorem (of Designer of the universe as causative limit)

The Designer of the universe is the causative limit of nature.

###### Proof

In fact the Designer has all the properties of a causative limit respect nature (considered as set of his designs).

###### The Designer is fixed

Meanwhile his designs can vary in quality and quantity and can be updated many times a designer remains fixed and unchanged in his function respect his designs. The designer stays fixed upon all the variability of his designs.

###### The Designer has synthetic nature

The designer is the synthesis of all his projects, as a causative limit synthesizes all the sequence toward it. Synthesis cannot be achieved perfectly by analysis. There is between the two a fundamental discontinuity. A designer integrates all the variability of his projects.

###### The Designer has different nature respect his designs

For example, human natural designers design artificial objects (artifacts). An artificial object is a set of arranged natural materials, which one cannot find in the wild nature. An artifact does not derive from natural laws or from chance; instead it derives from a natural intelligent agent. Hence an artificial object has a characteristic, artificiality, which differentiates it from its human designer. Man, differently from artifacts, stays in nature, and derives from the Designer of the universe.

###### The Designer is causative

For definition, a designer contains all the potentiality of his designs.

###### The Designer is unreachable

Here it's an artificial example: any robot (as much it is improved) never will reach the rank of its human creator.

Imagine a sequence (yet infinite) of versions of IDs {id1, id2, id3...}, with increasing complexity and improvements. Could that sequence reach exactly its designer? It cannot because we would have something that designs itself. The self-design is logically absurd (it contradicts axiom #2# - "nihil agit se ipsum"). See question1 below for a deeper explanation. That will explain also why we have put the unreachability property after the causative one. There is always discontinuity between a designer and all his designs. A designer is outside of the set of IDs he limits.

From the previous five points we have a designer is a causative limit for the set of all his designs.

Q.E.D.

###### Question 1

About "the designer is unreachable". The designer could design an individual, who - yet not being exactly himself - is equivalent to him (e.g. whether the designer is a man, he could design another man). That compromises the unreachability because it does not seem to deny axiom #2# - "nihil agit se ipsum".

###### Answer 1

From definition #5# an individual of any species is equivalent to all other individuals of the same species. "Equivalent" means "with all the same qualitative aspects". To counter-object question 1 is sufficient to remember that a designer is causative too. To easy the proof consider an algorithm generating its outputs. This algorithm contains a set of "keywords" (i.e. qualitative aspects), which cannot be present in the produced outputs with the same meaning. Even whether a "parent" algorithm would write another "child" algorithm with inside the same set of "keywords" of the parent one, the same the "child keywords" meanings would be different. In other words the difference between the algorithm and its results is similar to the difference between meta-language and language, which is fundamental in mathematical logic. Mutatis mutandis, this semantic difference is analogous to the ontological difference between the designer and his designs. Therefore this reasoning, valid for algorithms, is valid a fortiori also in the higher case of designers.

That proves also that a secondary designer cannot design man (we have again here the result obtained above in the answer 1 of the definition #15#). And of course man cannot design man.

The Designer of the universe is unique and transcendent.

###### Proof

The Designer of the universe is the causative limit of nature (from theorem #16#). From theorem #12# the causative limit of the universe is unique. Hence the Designer of the universe is unique. From theorem #11# the causative limit of nature is transcendent. Therefore the Designer of the universe is transcendent.

Q.E.D.

One cannot exclude a hierarchy of designers. Here it's an example: I am a designer. But I have parents.

Parents generate children, but they do not "design" children. An avalanche "generates" or "produces" damages, but it doesn't "design" damages.

###### Question 2

I am the designer of all my projects, but God designed me. Thus there is a hierarchy of designers (I myself and God upon me). Perhaps is there a designer upon God and so on?

###### Answer 2

No, there is no designer upon God. In this hierarchy there is a unique transcendent designer only (God), for you are a natural designer. Our goal is to show that the transcendent designer (God) was not designed and the hierarchy stops at him. The designer must have always a different nature respect its designs. The reason is the designer must be a causative limit, and a causative limit has a different nature respect what it limits (from definition #6#). Natural things are designed by God, who is transcendent (from theorem #11#). We will prove that there is no regression of transcendent designers in the next theorem.

A regress or hierarchy of transcendent designers is absurd.

It is possible to conceive the set of all natural things. Imagine the set of all natural things, the cosmos or universe U, limited by its unique (from theorem #12#) and transcendent (from theorem #11#) limit L: U => L (transcendent). From theorem #16# the Designer of the universe is its limit. Now imagine for absurd that another Designer L2 designed L:

U => L (transcendent) => L2 (?)

Question: is L2 natural or transcendent?

L2 must limit L, thus he must have a different nature respect him (from definition #6#). Since L is transcendent L2 should be natural. There is no third way why the dichotomy "natural/transcendent" is the same as the dichotomy "to exist/not to exist". That's the logical axiom of "tertium non datur". But this is a contradiction: all natural things stay in the set U. In this set no elements can be L2, because we would have L2 limiting itself and that is impossible ("nihil agit se ipsum"). So it is necessarily wrong the premise: "another Designer L2 designed L". Hence L - the Designer of the universe - was not designed. For induction, a hierarchy of not natural designers is absurd.

The Designer of the universe is unique, transcendent and not designed by another Designer (from theorems #12#, #17#, #18#). The Designer of the universe by means of his knowledge integrates in a unique synthesis all of nature, which is full of his projects.

The Designer of the universe is Being (God) (from theorems #12#, #13#, #16#, #17#).

[1] G.Oppy, Ontological arguments and belief in God, New York, Cambridge University Press, 1995.

[2] L.Wall, Programming Perl.

[3] Tomas Aquinas, Summa Theologica, I, 2, 3.

[4] Tomas Aquinas, Summa Contra Gentiles, I, 44.