Is the Mind Reducible to Structures and Procedures?
Do the limits of what can be modelled using structures and procedures define the boundaries of scientific investigation?
An algorithm is a sequential step-by-step procedure involving calculations, comparisons and logical operations. It may involve branching and selective execution of steps depending on the results of comparisons.
All algorithms have associated datastructures, though these may be implicit rather than explicitly declared. For example, even the simplest functions, such as square root, have an implicit associated datastructure consisting of the paired dependent and independent variables. In contrast, not all datastructures have associated procedures.
An algorithm's functionality must be definable in terms of mathematical or logical operations, sequential and conditional execution of steps, and operations on datastructures. All systems subject to the laws of physics can be simulated by algorithms. Hence any system which cannot in principle be simulated by an algorithm must have a non-physical component.
The ability to demonstrate any non-algorithmic function of the mind would be evidence that some of the mind's activities have a non-physical basis. For more detailed analyses, see:
....'Algorithms do not contain within themselves any meaning. For example, the following two statements reduce to exactly the same algorithm within the memory of a computer
(i) IF RoomLength * RoomWidth > CarpetArea THEN NeedMoreCarpet = TRUE
(ii) IF Audience * TicketPrice > HireOfVenue THEN AvoidedBankruptcy = TRUE
Such considerations have led critics of computationalism to claim that algorithms can only contain syntax, not semantics [SEARLE 1997]. Hence computers can never understand their subject matter. All assignments of meaning to their inputs, internal states and outputs have to be defined from outside the system.'...
'The unreasonable effectiveness of mathematics in science and engineering
So we are left with something of a mystery. According to the physicalist worldview, the mind (including mathematicians' minds) is an epiphenomenon of matter which has evolved solely to ensure the survival of the selfish genes which code for it. Why should this 'top-level' phenomenon have such intimate access to the 'bottom level' phenomena such as quantum physics? After all, the two levels are supposedly separated by less well-understood (in some cases) explanatory layers such as evolutionary psychology, neurology, cell biology, genetics, molecular biology, and chemistry.'
Generation of numbers by bootstrapping out of the empty set
....'Numbers have causes - the algorithms that perform the operations on the sets. Numbers have parts and aspects. The number 1 is defined as the set which contains the empty set and so on. But in the final analysis the entire number system has been generated by the play of mind on emptiness, in the complete absence of the need to refer to any material thing, or things, which are being counted.'...
...'It is fairly obvious how Kadampa philosophy maps onto physicalism. It agrees that things-in-themselves are unfindable and can only be known by interdependence with other things. It agrees that the first of these ways of interdependence is algorithmic - IF ... THEN... ELSE - cause and effect. It agrees that the second way of interdependence is by analysis into structured information. However it goes further by pointing out that physicalism is an inadequate explanation for all phenomena. A third mode of interdependence - dependence on the mind - is necessary to explain the phenomena of awareness.'...
...'The great difficulty in talking about non-algorithmic phenomena is that although we can say in general terms what they do, it is impossible by their very nature to describe how they do it. (If we could describe in a stepwise manner what was going on, then the phenomenon would be algorithmic).'..
...'Nagasena said this was because the chariot had no power to define itself from its own side. Nor was there any ideal chariot form 'in the sky' which engaged and disengaged with the timber at definite stages of assembly and disassembly. Milinda's mind was the only thing that could make the distinction between vehicle and firewood. And there were no logical rules, stepwise procedures or decision trees for Milinda to decide when to cease imputing one thing and impute another.'...
Algorithms and datastructures of the mind visualized in meditation
...'You'll become aware of the datastructures in your mind - the associations or 'hyperlinks' which link all mental objects together. Then you'll become aware of the algorithm - the automatic process which like a webcrawler follows all these associations and presents them to your awareness. You don't (at present) control this webcrawler. You will notice that the webcrawler has certain preferred types of links, those that lead to objects of anger, fear or desire. It doesn't pay too much attention to bland associations, and there's no family filter on what it dredges up. You have now begun to understand the algorithms and datastructures of the mind/brain. What you still need to experience is pure mind - the actual awareness which is viewing all the trivia which the webcrawler is displaying to it....'
Qualitative subjective experience
...'The Buddhist does not doubt that the brain does some very sophisticated ordering of its incoming nerve impulses into the datastructures which are the objects of knowledge. But when all is said and done, those datastructures remain as objects. They are not themselves knowledge, neither are they that which performs the function of knowing.'...
...'There is a Western school of philosophy known as dualism which claims that only humans experience qualitative mental states, and animals are automata with no subjective experiences, so it doesn't matter what you do to them. This view originates from the old Christian dogma that humans are qualitatively different from all other animals (because only humans have immortal souls). Dualism is not only contrary to Buddhist teachings, but also to the modern scientific understanding of evolution.'...
- Sean Robsville
If we regard Buddhism as a combination of a philosophy, psychology and religion, then how much mileage can we get from the first two aspects before we have to start invoking religious faith?