Determinism implies materialism — implies that consciousness is material. Cryonics is based on the premise that the preservation of the fine structure of the brain at low temperature will preserve the self — ie, that the self is entirely determined-by and contained-in the physical brain. Determinism would imply that preservation of the material basis of mind/self is theoretically possible. (For an exploration of how the self is encoded in the brain, see my series The Anatomical Basis of Mind. Development of the anatomical argument to explain the functioning of mind is best summarized in Chapter 8, Neurophysiology and Mental Function.)
Defenders of “free will” who say that the self has a spiritual basis independent of the brain often reject cryonics as being unnecessary. There are a few “spiritually” oriented people (like the Fyodorovians) who think that “resurrection of the body” is essential due to an intimate connection between the body and the “soul”, but these are in the minority. The majority of cryonicists do not accept spiritual beliefs, but there are notable exceptions, namely people who regard cryonics as a form of medicine. If cryonics can extend life, it is no more an affront to spiritual belief than other life-extending practices such as exercise and the avoidance of tobacco.
What about anti-determinist materialists who believe in “free will”? Those, like Roger Penrose, who claim that the mind is ultimately rooted in quantum uncertainty might not accept the possibility of biostasis, but Penrose has made no explicit statement about this subject. Penrose writes of the non-computability of mind, but acknowledges that non-predictability does not equate with “free will”.
Predictability is really at the heart of what is required for cryonics. If the mechanical operation of billions of neurons and trillions of synapses result in the phenomena known as the mind, the Self and the Will, then preservation & restoration of this machinery by cryonicists & nanotechnologists is possible in principle. But this also means that human beings are machines whose future actions are, in principle, entirely predictable. The positive side of this is that understanding the machinery in sufficient detail could provide the basis for reconstructing those aspects of the mind (parts of the brain) that were destroyed beyond recognition or repair. The negative side is that many people find it “dehumanizing” to believe that we are nothing but machines.
The proposition that the self/mind has a complete material basis in the mind has practical implications for cryonics, but also raised baffling questions. If it is possible to use a cryopreserved brain as a template for atom-by-atom reconstruction of a new brain, the identity of the person whose brain was cryopreserved would presumably be restored. But if such reconstruction could be done once, there is no reason why it could not be done hundreds of times. Would each reconstruction have the same personal identity (the same self) as the original? (For more detail on this question, see my essay The Duplicates Paradox).