To think can mean to reason logically, which certainly some machines do, albeit by following algorithms we program into them. Or it can mean "to have a mind" by which we mean it can experience itself as a subject endowed with consciousness, qualia, experiences, intentions, beliefs, emotions, memories. When we ask, could a machine think, we are really asking whether there can be a completely naturalistic account of what a mind is.
I am a naturalist, so I believe the answer must be yes.
Certainly, we are not there yet. Whatever the brain is doing to generate a mind, I doubt it is only running pre-specified algorithms, or doing anything like what present-day computers do. It seems likely we have yet to discover key principles by which a human brain works. I suspect that how and why we think cannot be understood apart from our being alive, so before we understand what a mind is we will have to understand more deeply what a living thing is-in physical terms.
The construction of an artificial mind then probably has to wait until we understand better, in physical terms, what a mind is.
This understanding will have to address what Chalmers calls the hard problem of consciousness: how to account for the presence of qualia in the physical world. We have reason to believe our sensations of the color red are associated with certain physical processes in our brains, but we are stumped because it seems impossible to explain in physical terms why or how those processes give rise to qualia.
A key step towards solving this hard problem is to situate our description of physics in a relational language. As set out by Leibniz, the patron saint of relationalism, the properties of elementary particles have to do with relationships with other particles. This has been a very successful idea, it is well realized by general relativity and quantum theory, so let's adopt it.
The second step is to recognize that events or particles may have properties that are not relational, which are not described by giving a complete history of the relationships they enjoy. Let us call these internal properties.
If an event or process has internal properties, you cannot learn about them by interacting with it or measuring it. If there are internal properties, they are not describable in terms of position, motion, charges or forces, ie in the vocabulary physics uses to talk of relational properties.
You might, however, know about a process's internal properties by being that process.
So let us hypothesize that qualia are internal properties of some brain processes. When observed from the outside, those brain processes can be described in terms of motions, potentials, masses, charges. But they have additional internal properties, which sometimes include qualia.
Qualia must be extreme cases of being purely internal. More complex aspects of mind may turn out to be combinations of relational and internal properties. We know that thoughts and intentions are able to influence the future.
There is much hard, scientific work to do to develop such a naturalistic account of mind, which is non-dualist and not deflationary, in that it doesn't reduce mental properties completely to the standard physical properties or visa versa. We may want to avoid naive pan-psychism according to which rocks and wind have qualia. At the same time we want to remember that if we don't know what its like to be a bat, we also don't know really what a rock is, in the sense that we may only know a subset of its properties-those that are relational.
One troubling aspect of mind from a naturalistic perspective is the impression we have that we sometimes think novel thoughts and have novel experiences that have never been thought or experienced before in the history of the world.
There is little that would make sense about the human world of culture and imagination without allowance for the genuinely novel. A century ago this website did not exist and likely could not have been imagined. Yet it exists and as naturalists we must have a conception of nature that includes it. This must allow novel kinds of things to come to exist in nature.
We are hamstrung by the conviction that nothing truly new can happen in nature because everything is really elementary particles moving in space according to unchanging laws. Without deviating an inch from rigorous naturalism, however, we can begin to imagine how our understanding of nature can be deepened to allow for the truly novel to occur.
First, in quantum physics we admit the possibility of novel properties arising that are shared among several particles in entangled states. In the lab we can make entangled states of complex systems that are unlikely to have natural precedents. Hence we can and do create physical systems with novel properties.
(So, by the way, does nature, when natural selection produces novel proteins, which catalyze novel reactions.)
Second, Leibniz's principle of the identity of the indiscernible implies that there can be no two distinct events with exactly the same properties. This means that the fundamental events cannot be subject to laws that are both deterministic and simple. For if two events have precisely the same past, their futures must differ. This presumes a physics which can distinguish the future from the past.
Note that quantum physics is inherently nondeterministic.
Does this imply quantum physics will play a role in a future naturalistic account of mind? It is too soon to tell, and the first efforts in this direction are not convincing. But what we learn is that a naturalistic account of mind will require deepening our concept of the natural. We can think novel thoughts by which we can alter the future. Novelty must then be intrinsic to how we understand nature, if minds are to be natural. Therefore, to understand how a machine could have a mind we must deepen our concept of nature.