According to the diametric model of cognition, we have two parallel modes of thinking. The first is a mentalistic one we use for understanding people and things resembling them (such as animals) in terms of psychological attributes like intention, emotion, memory, belief, and so on. The second is a purely mechanistic mode of thinking that we apply to inanimate objects and the physical world around us in terms of physical cause and effect.

As applied to mental illness, the model portrays autistic disorders as deficits in mentalism (sometimes with compensations in mechanistic skills, such as maths). Psychotic spectrum disorders are the converse: featuring hyper-mentalism epitomized in symptoms such as paranoia/erotomania (exaggerated interpretation of intention, negatively in the former case and positively in the latter), megalomania (overblown sense of self), or manic-depression (pathological amplification of normal mood swings involved in sensing your own state of mind).

A fundamental difference between the mentalistic and mechanistic universes of discourse already validated in the laboratory is that mentalism tends to be a holistic, top-down, centrally coherent way of thinking simply because it is part and parcel of social skills, which depend crucially on groups and collective, cultural norms. As such, mentalism is completely contrary to the reductive, bottom-up, Devil-in-the-detail mode of mechanistic cognition epitomized, for example, in mathematical logic. Theology provides a telling example.

According to theologians like St Thomas Aquinas (1225/27-74), God’s knowledge is infinite, perfect, and complete, and most other theologies that worship a single God agree. Truth for Aquinas was top-down and centrally coherent on a universal scale, and discrepancies and contradictions mere appearances that his great work, Summa Theologiae, sought to remove through point-by-point refutation. Not surprisingly then, St Thomas’s Summa is regarded as the supreme synthesis of Catholic doctrine to this day, and having proved that “there can be no falsehood or deception or error in the angelic mind as such” (Summa, Prima Pars, Question 58, article 5), the Church confirmed St Thomas’s theological authority by according him the title of “The Angelic Doctor.” 

But the problem here is that you can prove mathematically that there are some things that even God—let alone angels—could not know. Take infinity as a case in point. Most believers would readily accept the proposition that God’s knowledge is infinite. But now the sceptic asks: If so, could God name an infinite number? Not according to mathematical logic: Let God’s infinite number be N. If it is indeed a number, you could always add 1 to it to give N+1, which is 1 more than God’s ostensibly infinite value, which cannot be infinite. Therefore, even God cannot put a value on infinity.

Most believers are not in the least fazed by such arguments. They simply reply: Of course God cannot name a definite value for infinity, because no one can. But God’s knowledge is infinite, and so therefore it encompasses all possible numbers, to infinity and beyond!

To this, a mechanistically minded sceptic replies that you can prove that no such infinite set could be complete, even if it were indeed infinite. Believers would respond by claiming that no human mind could possibly comprehend God’s complete and infinite knowledge, but the sceptic could point out that we don’t need to do so.

All we need to be able to do is to start to list it. Such a list would be infinitely long and each entry would also be infinite, but this does not matter. The critic can prove the point from just the first few entries. Furthermore, let us assume that the items in the list are encoded in binary format: 0s and 1s in other words, and that entries are listed randomly, with a unique, random number assigned to each entry. The first few binary digits of the first three entries might start like this:




If this is the beginning of God’s infinite list, now consider a second, Devil-in-the-detail list in which we simply erase the first digit of the first entry and substitute a zero for a one or a one for a zero. Then we do the same to the second digit of the second number, then to the third digit of the third number and so on ad infinitum… Here I embolden and italicize the changed digits of the first three entries above to make them easier to identify:




Now consider the implications of what we have done. The first entry here cannot be the same as the first entry on the original list because its first digit is different; nor can the second because its second digit is different; nor the third; and so on ad infinitum. On the basis of just 42 digits of an infinite number of digits in an infinite list, we have demonstrated that the seemingly infinite and apparently complete list of God’s knowledge was neither infinite nor complete because we have been able to produce a parallel infinite list different in every entry!

Needless to say, such mechanistic, bottom-up, Devil-in-the-detail logic matters little to believers simply because they are thinking about the problem in a completely different, mentalistic, top-down, the-whole-is-greater-than-the-parts manner. Indeed, they are living in a parallel cognitive cosmos to that of mechanistic logic, and that is what these proofs really prove. Infinite, complete, and consistent truth may seem credible in the mentalistic universe of abstraction and belief, but it is provably impossible in the mechanistic world of reason and reality.

And interestingly, while religious delusions feature prominently in psychosis as the diametric model would predict, autistics have been found to be notably non-religious, as I show in my book and as recent studies have confirmed. Essentially, we can now understand why: theology is the apotheosis of mentalizing: Holy Hyper-mentalism if ever there was. But mathematical logic of the kind used in the arguments above is quintessentially mechanistic—thank God!

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