First, a couple of definitions:
When I say 'brain' I mean the nervous system, including brain, spinal cord, and peripheral nerves.
I'll define a 'computer' as a deterministic system that transforms an input into an output according to a program.
In that sense, many aspects of brain function are computational. Reflexes such as the knee reflex, the pupillary reflex to light, etc are substantially computational, in the sense that the input stimulus (a tap on the patellar tendon) causes an output (contraction of the quadriceps muscle). Although reflexes can be modified by thought (which as I will show is not computational), some aspects of brain function such as reflexes are mostly computational.
What about higher thought? Reason, judgement, will, etc.? These are not computational. In fact, they cannot be computational.
The explanation for this is intentionality. Intentionality is the central concept in philosophy of the mind. It was recognized by the ancients and the scholastics, and the modern concept of intentionality was formulated by philosopher Franz Brentano in the late 19th century. Brentano:
Every mental phenomenon is characterized by what the Scholastics of the Middle Ages called the intentional (or mental) inexistence of an object, and what we might call, though not wholly unambiguously, reference to a content, direction towards an object (which is not to be understood here as meaning a thing), or immanent objectivity. In presentation something is presented, in judgement something is affirmed or denied, in love loved, in hate hated, in desire desired, and so on.Intentionality is the 'aboutness' of a thought, the fact that the thought refers to something other than itself. A thought refers to an object ('I like this pencil'), or a person ('Sam is running late'), or to a concept ('love is blind'), etc. The only mental acts that are not intentional are qualia, which are pure sensation (the hurt of pain, the smell of coffee, etc)
In Brentano's famous observation, intentionality is the mark of the mental.
There are three kinds of intentionality:
1) Primary intentionality: the intentionality of a mind.
2) Secondary intentionality: intentionality imparted to an object by a mind. For example: a book is secondarily intentional, in the sense that the ink and paper is about something, but only because a person with a mind wrote the book
3) As-if intentionality: an expression comparing an inanimate thing to a mind (the river ran to the sea as if it wanted to go home)
Can a computer have intentionality?
It can certainly have secondary intentionality. Programmers write programs that make computation 'about' things and users do things on a computer that are intentional. But the computer itself isn't intrinsically intentional. Without human minds to program and use them, computers wouldn't be about anything. They would just be assemblages of silicon, tin, glass, etc.
A program is what makes a computer intentional, in the sense of secondary intentionality. Nothing in a computer inherently points to anything. Circuits and movements of electrons are generic. The same circuits that display a picture of the White House also play music and produce word documents. It is the human mind of the programmer/user that creates the intentionality.
So is the brain a computer? To the extent that it mediates reflexes, which are not intentional (your knee reflex isn't about anything. It's just itself- a reflex), the brain is a computer.
To the extent that the brain mediates thought, it is not a computer, because computation is not primarily intentional, whereas thoughts are.
The mind is not adequately described by our current science. This is because our science is largely based on a mechanical understanding of nature, which is restricted to material and truncated efficient causation. We need a deeper understanding of nature to understand the mind. As is obvious in quantum mechanics and in the study of the mind, the materialist paradigm is failed. We just haven't come to grips with it yet.
I believe that the Aristotelian/Thomist understanding of nature does provide a basis for understanding the mind. Grist for future posts.