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There is no doubt that the promise of Artificial Intelligence (AI), could re-shape the world, and by AI I’m follow the definition of the Stanford Encyclopedia of Philosophy (SEP) who defines it like this:

“AI is the subfield of Computer Science devoted to developing programs that enable computers to display behavior that can (broadly) be characterized as intelligent.”

But when one steps back from the hype, there is a debate about whether achieving AI is even possible?

Proposal 1: AI is not possible

From my knowledge the toughest criticism of achieving AI comes from R. Penrose and J.R. Lucas and both refer to “Gödel’s incompleteness theorem” as the reason. The Theorem can be described like this:

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F see SEP

Following the description of SEP and NZZ  the basic idea of Gödel was to create a statement G in a formal system (F) which more or less says:  “G cannot be proved within the theory F”. If such a statement G exists we have a “funny” situation: If G can be proven, then also non-G (and vice versa) and therefore if G is consistent we see G can’t be proved, or disproved, at all. That is the basic idea of the proof of Gödel’s Theorem.

So we have shown G can’t be proved at all. But that is what G claims. Therefore G is true, or more precisely we understand that G is true, but the formal system will never be able to deduce the truth.

On a side note, I personally think that Gödel’s incompleteness theorem is maybe one of the most intelligent, impressive and surprising findings. Gödel’s brilliant idea was to search for a statement G which says “G cannot be proved within the theory F” and then – which was even more difficult – to create such a statement. [For those who are really interested in math and in the Gödel theorems see this book in German: “Einführung in die mathematische Logik”, ISBN: 3827416914.]

Building on that surprising theorem, Lucas & Penrose’s basic idea against AI, based on the arguments as described here in IEP, is the following:

Since there will be always true but unprovable statements (in the meaning above), a machine would be unable to understand the truth of such a sentence. However, a human can “look and see” that the sentence is true (in the meaning above). Therefore, there is at least one thing that a human mind can do that no machine can.  Therefore, “a machine cannot be a complete and adequate model of the mind” (Lucas 1961: 113).  In short, the human mind is not a machine.

Proposal 2: AI is possible – “AND” R. Penrose and J.R. Lucas are right:

One main argument against the above logic and arguing that AI is possible (again mainly referencing IEP), is the following:

Lucas’s argument is based on Gödel’s 1st incompleteness theorem and this is only true if we are in a consistent system. But what happens if the system is not consistent, or if we are consistent but cannot establish this consistency?

One can avoid Lucas’s argument by simply claiming that we are formal systems and therefore, in accordance with Gödel’s 2nd theorem, cannot establish our own consistency (see Wikipedia). Then Lucas argument is not relevant anymore.

Other very interesting arguments against R. Penrose are described by Dennett).

As a result, one could say that R. Penrose and J.R. Lucas are, in fact right, but perhaps are not relevant. On the other hand math can only be practiced if we believe math is consistent, and therefore, Lucas’ argument indeed seems necessary for this mathematical discussion …

What will come next:

I believe the human mind has a unique ability to “step out of any system”, to look from a meta level and to understand there are no final boundaries. Therefore I believe the human mind will always be superior to a machine, but we will see how relevant this will be in the future. It is interesting to think that evolution itself will be impacted by these human & machine interactions and collaborations.

These interactions have already started and are being driven by intelligent combinations of hardware, software and data. As evidenced in e.g.: Predictive and big data solutions, machine learning, natural language processing, social Intelligence … for more see SAP or Wikipedia.


It is up to us to determine the way 🙂

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