The philosopher, Colin McGinn has listed five characteristics of mental states, which purportedly prevent them from being identified with brain states. Mental states are, he claims:1. Unobservable — in the sense that they are not perceptible by means of the senses.
2. Asymmetrically accessible — in the sense that the owner of a mental state has a kind of immediate access to it that other people do not.
3. Subjective — in the sense that the nature of a mental state is knowable only from a single 'point of view'.
4. Non-spatial — in the sense that mental states do not take up a well-defined region of space.
5. Subject-dependent — in the sense that mental states only exist for a subject of awareness.
Now, as I argued a few weeks ago, non-commutative geometry is the best candidate for a mathematical structure which provides a common generalisation of the structures employed in quantum theory and relativity. And the crucial thing to note about non-commutative geometry is that it provides an algebraic representation of space, rather than a manifold of spatial points. Relationships between points in a manifold, such as spatial extension, are rendered obsolescent, and replaced with purely algebraic relationships. Hence, non-commutative geometry has the potential to dissolve one of the apparent barriers to resolving the mind-brain issue. McGinn's fourth point, that mental states are not spatially extended, is only a problem if brain states are held to be the states of spatially extended systems. Non-commutative geometry suggests that the spatial extension of any physical system, including the brain, is an illusion.
— Non-commutative geometry suggests that the spatial extension of any physical system, including the brain, is an illusion. —
ReplyDeleteNonsense, you're confusing the map for the territory.
If a map of the world requires a Mercator projection to accurately represent distances, then it suggests that the world is round rather than flat. Similarly, if a representation of the structure of space-time requires non-commutative geometry to be accurate at small as well as large scales, then it suggests that space-time is not a manifold of points.
ReplyDeleteClearly, but your post was about using non-commutative geometry to describe mental states, not space-time. That would lead to the claim that mental states do not have spacial extent, but that's begging the question in light of point (4).
ReplyDeleteA better analogy would be the claim that my computer can't fit on my desk because I can run Google Earth on it and clearly the Earth is bigger than my desk.
No, my post wasn't about using non-commutative geometry to describe mental states. My post was about using non-commutative geometry to describe space-time, and, perforce, all the physical systems in space-time, of which brains are one example.
ReplyDeleteThe claim that mental states have no spatial extent is a separate premise, endorsed by McGinn. I sought to re-conceptualise the brain, using non-commutative geometry, in a way which would make it easier to reconcile the nature of mental states with the nature of the brain.
Ah - my mistake.
ReplyDelete