What’s there to do about lying liars who lie about their own lying?

Analytical philosopher Richard Johns’s recent paper in an analytical philosophy journal susses out the fact that if any such liars exist, then the lying part of them must be non-physical. That is, he offers an argument against physicalism, the popular philosophy that only physical things exist and that therefore, if humans exist, we are merely physical.

His argument is deeper version of Captain Kirk’s scheme to defeat enemy robots in I, Mudd, a 1967 episode of Star Trek. Kirk posed a paradox that led to circuit meltdown.

Here’s the plot summary, from a fan site, of the events which lead to the snatch of the episode, pictured above, in which an android—faced with self-contradiction—self-destructs.

Admittedly, Johns’s argument is a bit more intellectually difficult than getting the android to self-destruct but I, Mudd offers a good beginning. Essentially, Johns shows that no completely intelligible entity can think about itself. Otherwise it will end up producing a contradiction and contradictions cannot exist.

So what is a “completely intelligible” entity? It is defined as an entity that can be perfectly expressed by a mathematical formula.

Such an entity can talk about itself. Consider, for example, the sentence that says “This sentence has four spaces.” And, when talking about itself, the sentence can pose a property that contradicts itself, such as “This sentence is false.” Thus, if the sentence does have the property (falseness), then it ceases to have the property because it is true. And if it is true, it is also false. An inescapable contradiction ensues.

But reader, never fear! You will not poof yourself into contradictory non-existence by thinking such a sentence. Some entities are immune to such logical suicide. They exist in some way beyond math. Something about such entities, presumably including yourself, is forever mathematically inexpressible. Because they cannot represent themselves completely mathematically, they cannot generate fundamentally contradictory thoughts about themselves. Hence, the fundamental reason why we exist and have thinking minds is that we are in some degree unintelligible!

Physicalism is the thesis that everything is physical, or as contemporary philosophers sometimes put it, that everything supervenes on the physical. The thesis is usually intended as a metaphysical thesis, parallel to the thesis attributed to the ancient Greek philosopher Thales, that everything is water, or the idealism of the 18th Century philosopher Berkeley, that everything is mental. The general idea is that the nature of the actual world (i.e. the universe and everything in it) conforms to a certain condition, the condition of being physical. Of course, physicalists don’t deny that the world might contain many items that at first glance don’t seem physical — items of a biological, or psychological, or moral, or social nature. But they insist nevertheless that at the end of the day such items are either physical or supervene on the physical.

Daniel Stoljar, “Physicalism” at Stanford Encyclopedia of Philosophy

Johns’s argument goes deeper than physicalism itself, because it targets the idealism implicit in physicalism. The crucial reason that physicalism results in self-contradicting minds is that it ultimately depends on the idealism of a completely mathematical universe. And mathematics, in turn, falls prey to Johns’s argument because mathematics is perfectly intelligible. That in turn means that any view of reality that is completely reduced to intelligible ideas becomes internally illogical.

His argument can be a bit scary, once we understand it. Does it mean that there are aspects of reality forever beyond our ability to understand? Yes it does but Richard is not the first to prove such a result. Mathematicians, philosophers, religious figures, and artists have preceded him.

Logician Kurt Gödel (1906–1978) and Mathematician Georg Cantor (1845–1918) and, going much further back, Plato (429?–347 BCE) all argued for an intelligible reality that is yet, in the end, forever beyond complete understanding. In the new Testament, Paul argues for this perspective when he says that in the end, even knowledge will pass away and the only thing that will be left is love. Similarly, the Paradiso, the third book in medieval Italian poet Dante’s poetic trilogy the Divine Comedy, offers a number of intellectual discussions, including discussions on science topics. But when the hero (Dante himself) gazes into the face of Christ, trying to reconcile the duality of Jesus’s divine and human nature (one of the many paradoxes he addresses), he finds that he is facing a reality that is beyond intelligibility and thus he attains the beatific vision.

Johns’s argument is a powerful one and it can help us break us free of the ideological Matrix of physicalism.

Citation: Johns, R. Why Physicalism Seems to Be (and Is) Incompatible with Intentionality. Acta Analytica (2020). https://doi.org/10.1007/s12136-020-00423-3 Here’s the abstract:

There is a long history of philosophical intuition that the human mind must be more than physical or mechanical. I argue that this intuition arises from the perfect “transparency” of physical and mechanical states, in the sense that such states have no obscure or occult elements, but are fully intelligible in (usually) mathematical terms. In the paper, I derive a contradiction from the claim that such a physical system has genuine intentionality, comparable with an intelligent human. The contradiction arises from the fact that, according to physicalism, the physical properties of a brain state determine the narrow propositional content of any conscious thought occurring in that state. This fact allows a physical property of brain states to be defined using Cantor’s diagonal construction, and then a contradiction results if a physical system is assumed to form thoughts involving that property. – Why Physicalism Seems to Be (and Is) Incompatible with Intentionality Richard Johns 1 Received: 28 May 2019 / Accepted: 20 January 2020/ # Springer Nature B.V. 2020 (paywall)

Further reading: Human intelligence as a halting oracle (Eric Holloway)