"A middle-way approach: toward the mind-body problem via neither duality nor identity
Both John Searle and Gilbert Ryle object to Cartesian dualism, arguing that there is nothing existing over and above the brain or behaviour. Searle sees dualism as a ‘conceptual confusion’, while Gilbert Ryle instead considers the mind-body distinction a ‘categorical mistake’. Buddhism does side with both Searle and Ryle in their rejection of Cartesian dualism, yet this does notmean that the Buddhist outlook accords with the theory of mind and body propounded by either Searle or Ryle.
The Buddhist position with regard to the mind-body problem can be described as ‘neither same nor other’. Although it would be wrong to say that the mental state is merely a brain state and that there is nothing over and above the brain processes, it would also be incorrect to hold that there is something decidedly separate from the biological brain process. Just as a reference and its referent are neither identical to nor different from one another—e.g. the designation ‘book’ is neither identical nor different to an actual book—so mind and body/brain are neither identical to nor different from one another. For this reason, within the Buddhist scheme of things neither an absent-minded body (such as a zombie) nor a disembodied mind (such as a soul) would be a reasonable hypothesis. Put differently, Cartesian dualism admits to a soul or self (atman) apart from the physical body, thus tending towards the extreme of eternalism rejected by the Buddha. Material monism on the other hand, holds that the mental and the physical are of the same nature, so that nothing remains once the physical body has ceased to exist. This view would again lead to the other extreme of nihilism.
…
From the perspective of dualism, minds can continue to exist apart from bodies even after the ‘conscious entity’ has left the body. From a Buddhist viewpoint this causes one to fall into the trap of eternalism, where one mistakenly believes that either the mind or body can exist independently from its own side. Monism, on the other hand, claims that mental states are simply brain states, a view which again causes one to fall into the trap of nihilism, where one mistakenly believes that the reality of mind and consciousness can be disregarded altogether. In matters related to the mind-body problem therefore, the Buddhist position takes a middle way approach in assuming neither the views of dualism nor monism."
(Lin, Chien-Te. "Rethinking Mind-Body Dualism: A Buddhist Take on the Mind-Body Problem." Contemporary Buddhism 14/2 (2013): 239–264. p. 250)
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First of all, the author confuses non-separateness with non-difference, because two things which aren't separate in the sense of being disconnected or independent from each other are still two (numerically) different things.
Words such as "book" are clearly different and even separate from their referents. The word "book" would survive the destruction of all books in the world.
As for the alleged "middle way" between difference and non-difference, identity and non-identity, or dualism and monism: The only logically consistent interpretation of
"x is neither identical with nor non-identical with (different from) y"
is
"x is neither totally identical with nor totally non-identical with (different from) y".
When two things overlap mereologically by sharing some part(s), they are partially identical and also partially non-identical (different). Two numerically different things can be non-distinct or non-separate by overlapping mereologically.
"[T]he real opposite of identity is distinctness; not distinctness in the sense of non-identity, but rather distinctness in the sense of non-overlap (what is called 'disjointness' in the jargon of those who reserve 'distinct' to mean 'non-identical')."
(Lewis, David. "Many, but Almost One." 1993. Reprinted in Papers in Metaphysics and Epistemology, 164-182. Cambridge: Cambridge University Press, 1999. p. 17)
The statement that experiences are neither identical with nor non-identical with (different from) neural processes isn't logically contradictory only if it is interpreted as meaning that experiences are neither totally identical with nor totally non-identical with (different from) neural processes.
But then it's unclear how an experience can be partially identical with a neural process by overlapping with it, i.e. by sharing some parts with it. It seems this can only mean that some experiential parts of an experience are (totally) identical with some neural parts of the neural process with which the experience overlaps. So what we have here is an unusual partial-identity theory of mind and brain: Experiences and neural processes overlap (incompletely) and are thus both partially identical with and partially different from one another.
However, the partial-identity theory doesn't explain how those experiential parts of an experience come into being which are (totally) non-identical with any neural parts of the neural process with which the experience overlaps. Those experiential parts are irreducible by not being identifiable with any neural parts, so the partial-identity theory turns out to be partly monistic and partly dualistic: Some (but not all) experiential parts of experiences are also neural parts, and some other experiential parts of them are non-neural parts.
A basic question: Do all experiences have experiential parts? Are all experiences mereologically nonsimple?
The partial-identity theory presupposes an affirmative answer!
For a simple, partless experience is either (totally) identical with some neural part of some neural process or it is (totally) different from any neural part of any neural process. In the case of simple experiences we no longer have a mind-brain theory which is partly monistic and partly dualistic, but one which is either totally monistic (and reductionistic) or totally dualistic (and non-reductionistic), i.e. either a total-identity theory or a total-difference theory.
By the way, I don't know any philosopher who endorses the partial-identity theory.