Scientific inquiries about reality are shaped by technological possibilities: astronomy got started with the telescope, biology with the microscope, and quantum physics with the particle accelerator. But there are also forms of science where technology becomes ontology. Cognitive science was born like this. The computer became the tool and the object of study—cognitive ontology. More recently, as we shall see, the computer has also been suggested to be the ontology of physical reality at large, with the work of physicist John Archibald Wheeler (1911-2008).
These four components figure in the comeback of dualism. We have a strong tradition of metaphysics in the Western world, despite the fact that during the twentieth century, philosophers declared the end of metaphysics. Many pointed to the failure of modern German idealist metaphysics and, in particular, to Kant (as he was the last and the greatest in this tradition). Granted that neither Kant nor any other philosopher in his tradition managed to create an adequate metaphysical foundation for science, and granted that philosophical metaphysics moved off center stage after him, metaphysics never died. As Kant went out of fashion, many scientists came to see aspects of Plato’s metaphysics as appealing, while others had always thought this. Much of the work from the nineteenth century to the twenty-first century in mathematics and physics has been done, and continues to be done, by top researchers who are supportive of Plato’s philosophy of forms. They believe in a nonphysical world of form, one in which physical reality is an expression or reflection—this they see as the ultimate structure of reality. Within philosophy, Quine and Putnam have been influential with their indispensability argument for Platonism. This argument states that entities that are indispensable to our scientific theories, such as mathematical entities, exist and fund reality. Within physics, Roger Penrose has been the strongest advocate of Platonism. But the core of Platonism comes from mathematics.
In the nineteenth century, mathematical logic and set theory emerged as part of a revival of Platonist metaphysics, with the work of mathematician Georg Cantor (1845-1918). Cantor, like many mathematicians, was philosophically inclined. He knew the literature from Plato to Kant (Murawski 2010, p. 16). The topic that most interested him was one that Leibniz had explored: the nature of infinity. When Cantor tried to understand infinity, he found a complex mathematical landscape. He dedicated himself to working out the idea that infinities are organized in a harmonious system—his continuum hypothesis. Struggling, without success, he ended up in a mental ward. One of the reasons he got there might have been that he was a Platonist. His work mattered immensely to him because it was ultimately about the structure of reality. Cantor thought that concepts are real in two senses: immanently and transiently. Immanent reality is comparable to Plato’s forms, and transient reality is comparable to the physical world. Cantor describes the relation between the two realities:
There is no doubt in my mind that these two types of reality will always be found together,
in the sense that a concept to be regarded as existent in the first respect will always in certain, even in infinitely many ways, possess a transient reality as well. (Sweet 2005, p. 82)
His failure in mathematics was, for him, a profound metaphysical failure and an estrangement from God. He understood himself as chosen by God to do work in mathematics on concepts existing not only as Platonic forms but also as God’s ideas.
Cantor’s contemporary Frege gave further support for a Platonic view of concepts. As we saw in chapter “Externalism and Consciousness”, Frege believed we cannot explicate sense and meaning without a realm where senses exist independently of psychology. We grasp senses through our minds, but senses have an independent and objective existence.
In the twentieth century, Austrian logician Kurt Godel (1906-1978) was working on the logical foundations of mathematics. He too was a Platonist and called himself a conceptual realist—something the following remarks bring out:
The set-theoretical concepts and theorems describe some well-determined reality, in which
Cantor’s conjecture must be either true or false. (Godel and Feferman 1990, p. 260)
Classes and concepts may, however, also be conceived as real objects—namely, classes as “pluralities of things” or as structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions. It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies, and there is quite as much reason to believe in their existence (Godel and Feferman 1990, p. 128).
Godel kept working on Cantor’s continuum hypothesis and also ended up in a mental institution. But he made a remarkable discovery before this—one he thought said something about our minds. For a large class of axiomatic systems, there are truths that cannot be proven within them. Godel showed that formal logic is, to some extent, a failure (there is no complete system of logic), and this was a tremendous disappointment to many logicians.
Physicist Roger Penrose takes Godel’s incompleteness theorem to be support for Platonism:
If, as I believe, the Godel argument is consequently forcing us into an acceptance of some form of viewpoint C, then we shall also have to come to terms with some of its other implications. We shall find ourselves driven towards a Platonic viewpoint of things. (Penrose 1994, p. 50)
What pushed Godel to insanity was perhaps not the continuum hypothesis but the question of human intuition. Godel realized that his intuitive mind was not a formal system, as the following remarks make clear:
The human mind is incapable of formulating (or mechanizing) all its mathematical intuitions. That is, if it has succeeded in formulating some of them, this very fact yields new intuitive knowledge, for example the consistency of this formalism. This fact may be called the “incompletability” of mathematics. (Wang 1996, p. 184)
Godel thought of intuition as being on a par with sense perception—that it was a given part of our nature:
But despite their remoteness from sense experience, we do have something like a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don’t see any reason why we should have less confidence in this kind of perception, and more generally, in mathematical intuition [a correction proposed by Godel himself to replace “i.e., in mathematical intuition”] than in sense perception [“taken in a more general sense, including, for instance, looking at a city from an air- plane”—phrase added by Godel November 1975]. (Wang 1996, p. 226)
What, other than intuition, allowed his realization of the incompleteness theorem? Godel nevertheless found himself wanting to provide something like a logical proof of intuition—with serious consequences for his mental health. It is as if his mind was itself divided and there was a fight between logic and intuition. For Godel, intuition was a way—perhaps the only way—to reach into the otherworldly, the realm of form behind reality. But he sought an explication for why it had to be this way. The incompleteness theorem was not that explication. It was a bomb that blew up the formalist program in logic and mathematics but left enigmatic questions behind.
Godel sought to understand intuition but got caught in a loop trying to adequately explicate intuition (which he had demonstrated to be a nonrepresentational capacity) using human explanatory tools: representations. This style of thinking about the mind would later come to influence philosophy and cognitive science. It is a selfreflexive style of thinking about the mind, which acknowledges its own explanatory limits. The researcher under the spell of this style may acknowledge that representations are insufficient to explain the mind, but nevertheless thinks there must be some trick, because representations are all that the mind has available to explain itself. So the style is to continue in a loop, using representations to explain representations, but never getting to what makes them work in the first place.
If, as Searle has pointed out, representations are not self-interpretative, and if intuition is not a matter of algorithms, then we will not be able to explicate the mind in a purely representational model. Any attempt will end up in a representational loop.
Turing faced this representational loop in his own way. Unlike Godel, he saw no need to invoke dualism. Instead he seems to have ignored the representational problems. He came to frame his understanding of the mind altogether computationally—there is no separation between thinking about computation and thinking about the mind. Yet this way of looking at the mind is akin to dualism. Ontologically, Turing doesn’t care about physical underpinnings. Turing cares about computation. By framing questions about the mind in terms of computation (and vice versa), he pioneers AI as a discipline orthogonal to physics. The uptake in the cognitive sciences became concretized in the computational approach to cognition in an age with fresh electronic brains. As we have seen, Turing’s computational approach to the mind also fitted with Shannon’s syntactical, semantically sterile redefinition of information. Like Turing, Shannon does his work on information from a perspective of technology. He is a mathematical systems thinker who frames the question of what it means for something to be information from within a technological perspective. Turing’s algorithmic notion of the mind, married with Shannon’s syntactical notion of information, became the mental metaphysics of their century. It was elaborated in AI and computational neuroscience, and remains king in the cognitive sciences. Turing told us how the mind thought computationally, and Shannon told us what it thought with—its information content. As systems thinkers, Turing and Shannon stayed clear of physical properties in their research. Their work was an expression of their time. During the twentieth century, it became increasingly popular to understand reality in terms of various systems. Many new systems were either discovered or refined, such as in biology (genetics), chemistry (molecular science), and earth science (plate tectonics). Other systems were explored in economics (game-theoretical approaches) and linguistics (recursive grammars), with less clear and often dubious ontological commitments to anything physical. That the ephemeral computational mind of pure mathematical logic came to be received so well was natural.
-  Penrose’s viewpoint C is as follows: “Appropriate physical action of the brain evokes awareness,but this physical action cannot even be properly simulated computationally.” (see p. 12 of the samework).