In a previous UD discussion I started about incompleteness I made the following affirmation: intelligence and life are not computable. A commenter kindly asked me to provide justifications for my claim. Since at UD usually I try to separate different topics in different discussions, to be more focused and reader-friendly as possible, so here is my answer in a dedicated thread. My answer unavoidably implies to investigate first what intelligence is then what life is (given the latter is an effect and the former is its cause).
A premise: intelligent design theory (IDT) per se doesn’t deal with the deep nature of intelligence or the designer. For what matters in IDT intelligence and designer can be considered as source of information. All basic results of this theory hold true when in its statements we substitute “intelligence” or “designer” or “intelligent cause” with “source of information”. This makes sense because the job of IDT is limited to investigate the signs or outputs (CSI, IC …) evidencing the inputs provided by information sources. In a sense IDT focuses on effects rather than the ultimate meaning of their cause. Despite that here I will try briefly to address something of the nature of intelligence, to satisfy the commenter’s request of explanations.
Countless definitions of intelligence were provided by philosophers and scientists according to different points of view. This very fact is sign that intelligence is complex, multi-faced and controversial topic. It’s likely any of those definitions contains some truth. However among them the pragmatic definitions cover its lower aspects only. In fact to consider intelligence as a mere tool to solve practical problems means to limit the power of intelligence to the material world and lower its ontological status to modest dimensions. We will see below that quite different appears the rank of intelligence when the problem of knowledge in its highest sense is considered. On the ground of narrow pragmatism even there may be no particular controversy between an IDer and a Darwinist. An IDer can well agree with the definitions provided by evolutionists, for example, this one by Stephen Jay Gould (“The Mismeasure of Man”): “Intelligence is the ability to face [and solve] problems in an unprogrammed creative manner”. Gould also rightly added that intelligence cannot be adequately measured (causing the ire of many psychologists). Gould’s remarks about intelligence’s unprogrammability and unmeasurability might also be in relation to the previous UD post I referenced at the beginning and in a sense agree with the thesis I am going to defend here, given the relations between the concepts of measure and computation.
Before to examine a couple of definitions of intelligence I will discuss here I must clarify what I mean for computation in this context: a deterministic finite series of instructions or operations sequentially applied to a finite set of objects. Given this definition, a computation is a mechanistic process that a machine can work out. In computability theory the archetype of such machine is the so-called Turing machine (TM).
Intelligence as generator of what is incomputable
IDT shows that CSI cannot be generated by chance and necessity (randomness and laws). An algorithm (which is a generalization of law) can output only what is computable and CSI is not. The concept of intelligence as “generator of CSI” can be generalized as “generator of what is incomputable”. Obviously, needless to say, intelligence eventually can generate also what is computable (in fact what can do more can do less). Intelligence can work as a machine but a machine cannot work as intelligence. Between the two there is a non invertible relation. This is the reason why intelligence designs machines and the inverse is impossible. To consider intelligence as “generator of what is incomputable” makes sense because we know that intelligence is able for instance to develop math. Metamathematics (Gödel theorems) states that math is in general incomputable. It establishes limits to the mechanistic deducibility but doesn’t establish limits to the intelligence and creativity of mathematicians.
Now it’s straightforward to see that the generator of what is incomputable is incomputable. Let’s hypothesize that it is computable, i.e. can be generated by a TM. If this TM can generate it and in turn it can generate what is incomputable then, given that an output of an output is an output, this TM could compute what is incomputable and this is a contradiction. Since we get a contradiction the premise is untrue, then intelligence is not computable.
The Infinite Information Source (IIS)
Now let’s pass to another more demanding but more deep perspective on our topic: intelligence as interface or link between any intelligent being and what we could call the “Infinite Information Source”. IIS is an aspect of the Metaphysical Infinity (or Total Possibility) that contains all and then contains all information too. Outside IIS there is no information because there is nothing at all. The existence of the IIS is a logical inference. In fact it is common evidence that intelligent beings (humans) routinely produce new information. This production is not creation from nothingness because from nothingness nothing comes, then this information must come from a higher source than the intelligent beings themselves. In a sense never there is new information. Besides we know from our repeated experience that intelligent beings share common information (in two senses: as information they contain inside themselves and as information they know). This proves that intelligent beings share the same higher source of information.
It remains to show that this higher source (say it S) is the IIS. The demonstration is for absurdum:
(1) Let’s hypothesize that S is finite. With “finite” I mean non Infinite (i.e. “non containing all information”). As such S is different from IIS.
(2) Since S is finite let’s consider its complement set ~S containing all information not belonging to S. Obviously ~S is included into IIS.
(3) S and ~S are disjoint sets for definition.
(4) Now consider an information ‘a’ of S and an information ‘b’ of ~S.
(5) If a and b are information, also c = (a AND b) is information.
(6) The question is: c belongs to S or ~S? It cannot belong to both because they are disjoint sets.
(7) Let’s hypothesize c belongs to S. Then S contains ‘b’, contrary to #4. Then this hypothesis is untrue.
(8) From #7 we have that c must belong to ~S. Then ~S contains ‘a’, contrary to #4. Also this hypothesis is untrue.
(9) Since we have obtained a contradiction the premise #1 is false. S is IIS.
At this point we have three basic elements in the scenario: the IIS, the being and what connects them (the channel through which information passes from the former to the latter, like a stream from a source to a sink). A classic symbolism that can help to understand their relation is the Sun that creates an image on the surface of water. The Sun is the IIS, the image is the intelligent living being and the beam connecting the Sun to its image is the channel (over-individual intellect). As the Sun is the cause of its image on water (which wouldn’t exist without it) the IIS is the cause of the intelligent living being. In particular, the intersection of the beam with the plane of our layer of existence, causes at the center of the human state the arise of human soul or psyche (with all its faculties: mind, reason, consciousness, thought, free will, emotions, sentiments …). The intersections of the beam with the center of other layers of existence cause different faculties of knowledge to other non human beings. The vertical hierarchical stack of all parallel planes represents symbolically all multiple states of being. The physical body is only the last by-product, the final unproductive production in the causality chain from IIS to matter. Warning: here the Sun is only a symbol for the knowledge’s source (traditionally light was always symbol of knowledge); obviously intelligence doesn’t really come from the physical Sun and soul is not a reverberation upon physical water. I say this because in a previous discussion about thermodynamics I defended the obvious position that the Sun does not send us information, rather energy only.
IIS is eminently incomputable because it is even un-derivable from any system (and all what comes from the development of its potentialities). In fact any system F leaves outside all what is “non F”. IIS leaves outside nothing then IIS is in principle absolutely unachievable by any systematization. Continuing the Sun’s symbolism, as the beam’s light is not really different from the source’s light, so also intelligence participates of the incomputability of IIS.
The above proof evidences also another only-seemingly odd thing: the IIS is not properly composed of parts because when we, for hypothesis, divide it into parts we obtain contradictions. It is our analytic reason that divides IIS in parts, which really don’t exist distinctively in IIS because it is eminently synthetic. IIS is essentially indivisible, and this necessarily excludes any composition and entails the absolute impossibility to be conceived as composed of parts. IIS is an aspect of the Absolute and the Absolute cannot have relations whatsoever with the relative. Since IIS really has no parts, also the link and the linked being are only apparently its “parts” and at the very end are the IIS itself. As such they directly participate of the incomputability of IIS. Again we have got the same deduction.
The same conclusion is got from yet another point of view. Let’s suppose that we find a finite process outputting intelligence. At this point nobody can a priori avoid or exclude that, through its link to IIS, intelligence receives some data that the finite process is unable to output. One can express this situation by saying that intelligence is “open” to Infinity, while, to be computable, a thing must be “closed”. Its “opening” makes intelligence virtually infinite. This is only another way to state the fundamental principle of “universal intelligibility” that sounds: there is nothing of really unknowable, all things are in principle knowable. Of course there may be countless things actually unknown to an intelligent being. But this is only a de facto temporary situation not an in principio definitive destiny. Thus we see that, as I noted above, intelligence is something far more powerful and higher than a simple tool for solving practical problems, because virtually can know all. Since intelligence is virtually the knower of all what is incomputable, in turn it cannot be computable because the knower cannot be lower in rank than the known.
Given we are dealing with universal intelligibility it is necessary to clear a possible misunderstanding. To avoid it we must carefully distinguish reason and intellect. This distinction, which was well clear to most ancient philosophers, was lost at the arise of rationalism and humanism in the modern era. As someone said: “it was reason to betray intellect”. The first product of rationalism in the scientific field was Cartesian mechanicism, which is in relation with computability I deny here when applied to intelligence and life. Reason is merely an individual human faculty. It is a discursive indirect form of analytical knowledge that takes as support logic and argumentative tools. Reason cannot be universalized as is. Quite differently intellect is a higher universal faculty of direct synthetic knowledge pertaining to all states of being. This explains because with the arise of rationalism and humanism the knowledge of universal principles (as the Metaphysical Infinity) was lost: what is universal can be known only by a universal faculty. Reason is only the lower individual part of intelligence (the horizontal image), while intellect is its higher over-individual part (the vertical beam). Intellect is over-rational. Warning: over-rational is not at all irrational as some believe! The universal intelligibility makes sense only when addressed by intellect. If we remain on the plane of human reason, there is no universal intelligibility. In other words it is not reason to be omniscient and there is no such thing as universal reasonability.
The key point to focus is that all the above definitions of intelligence agree and support each other. They are consistent because represent different viewpoints of the same reality. Hence also the respective demonstrations of incomputability show the same impossibility seen from different perspectives. The above argument has corollaries. The incomputability of intelligence and its non mechanistic nature debunks once and for all any illusion of the so-called Artificial Intelligence to create real intelligence. The IIS can be considered an aspect (expressed in term of information) of the Universal Intelligence or Divine Intellect and since it is also the Source of the universe, which is a design, the symbolism of the Great Designer can be applied to it.
Life as carrier of intelligence
Now let’s consider life (specifically life of conscious living beings) and give of it the following definition: the physical carrier or support of intelligence, what allows intelligence to manifest and operate on the physical plane. If the carrier (living soul and body) were mechanistic only they could not adequately express intelligence, which is not mechanistic. It is a claim of IDT that physical signs manifest the non physical nature of intelligence. These signs (CSI, IC, etc.) are non mechanistic and what displays such signs cannot be mechanistic too. Living soul and body display such signs and then we can conclude that life is non mechanistic.
To illustrate with an example the concept, let’s consider a clear manifestation of intelligence in a living being: language. Also Noam Chomsky admits that language is structural and hardwired in its physical carrier, the brain. Language is not mechanistic: the high expressions of literature cannot be created by a machine. The classic objection of materialists to this claim is: also machines can output literature works. Machines can output texts (strings of characters), but their outputs fully lack meaning and indeed this proves that they are not true manifestation of intelligence (which is the only source of meanings). For instance, when a writer writes the four-chars word “love” he has in mind all the meanings of the idea, instead when a machine writes “love” it has nothing in mind for the simple fact that it has no mind. And here what stays in the “background” (the semantic) is more important and essential of what stays in the “foreground” (the syntax), so to speak. Moreover if a machine writes “love” it is because was programmed to do so, not because it wanted that (as a human writer does). Just a curiosity: an ancient Hebrew legend speaks of the Golem, a sort of automaton that they say Cabalists were able to vitalize by mean of esoteric rituals. The Golem was able to simulate a living being (a robot ante litteram) but it wasn’t able to speak because language is an advanced ability that only real intelligent living beings have.
Of course all that I have written here is light-years from the materialist and reductionist Darwin’s idea of “thought, being a secretion of the brain”. Modern evolutionists believe to be more sophisticated saying that “thought is emergent property of the brain”. But if we examine it their claim is not more explicative. In fact emergent properties involving information (and mind eminently implies information) don’t spontaneously “emerge” from the bottom like a secretion (as they think) but come from the top, from an intelligent source. About this topic see my previous post on emergence.
To sum up about intelligence (like many other things) we are before two diametrically opposite worldviews: the ID non materialist and the materialist (with all its consequence, evolutionism included). The former is a top-down worldview while the latter is a bottom-up approach. Non materialism states that matter itself comes from information. Materialism, at the very end, denying any higher principle than matter, believes that information arose from matter. These two opposite worldviews cannot be both true. I hope these brief notes may help some to know which of them is on the side of truth.