Can we conceive of mind-body dualism?

In trying to understand the nature of the connections between mind and body, or between ordinary and spiritual minds, many different ideas have been proposed to explain how they are different. Only if we have a serious scientific proposal for this can we give proper evidence for the fact of a difference, as (almost always in science) new kinds of evidence need a related theory in order to justify taking them seriously.
Many people have realized that there are some differences here, but are reluctant to call that a 'dualism', and so produce many analogies for understanding those differences.  Let us, nevertheless, call the relation between minds and body 'a dualism', and then simply seek to understand its nature.

One way to answer the question of dualism is if we have a clear idea about what have been called 'discrete degrees'. Emanuel Swedenborg wrote in his 1763 book Divine Love and Wisdom that this concept is central to answering many questions:

"Without a concept of discrete degrees ... one can know nothing of the difference between the interior faculties in people which are those of the mind, thus nothing of their state in regard to reformation and regeneration; ... and nothing at all of the difference between something spiritual and something natural." [1]

In everyday life, we have formed our own ideas about these discrete degrees, by means of which we attempt to understand what Swedenborg is suggesting here, especially about what is mental, or spiritual, in comparison with what is natural. However, many people have rather individual ideas about the nature of discrete degrees, and some have ideas that are not in fact dual or discrete.
My purpose here is to look at some common suggestions, to challenge various motives that favour some particular misconceptions, and to try to demonstrate some more realistic (and fruitful) ways of thinking about discrete degrees. This should give us a clearer formulation about how to conceive dualism. In the process we will compare and contrast them with continuous degrees of various kinds, such as occur within a monistic framework.
Our need to think in discrete or continuous degrees touches on some broader desires for certain kinds of explanation. We are much more satisfied, for example, by an integrated view of all the natural and spiritual worlds, compared, say, with a fragmented account. Similarly, scientists and philosophers are much happier with a unified theory which sees everything as part of some continuous whole, compared, say, with a theory with unexplained gaps. We might favor an integrated ‘nondual’ world view compared with an account with dual substances whose relation is more hierarchical and somehow less ‘democratic’.
Our initial desires and kinds of knowledge we can accept are typically based on ideas that we can obtain from our senses, and from logical reasoning from sensual ideas. Contemporary science is a rather full development starting from this approach. However, from our senses and logic, it is rather difficult to have a proper idea of discrete degrees. This is our problem! Most of our starting ideas are based on images obtained from sensations of space and time, and Swedenborg tries to persuade us how our these spatial and temporal images ‘attach’ themselves to many of our attempts to think about discrete degrees. One aim here is to help see how spatial ideas attach themselves to our ideas of discrete degrees, and hence of our ideas of what is (or should be) dual. We will see how spatial images (may) correspond, or be analogous, to discrete degrees, but are not identical with them.
Let us look at some ideas that have been used to describe discrete degrees, and examine each in turn to see whether it is discrete or continuous, and whether it is a means for understanding any dualism about what is mental or spiritual:

Space

1. We may imagine as discrete degrees those natural things with discrete units, such as a ladder, as a multi-storied house, even as earth + plants/animals + the heavens, etc. Religious and spiritual literature often uses such images. We may use the body, with head+neck+body+legs +feet to represent different discrete degrees, but from looking at human bodies, as from biology alone, we do not thereby understand what are mental or spiritual degrees.
2. Similarly, the whole and its parts may be imagined as discrete degrees and in a relation of duality. The cells, nerves, muscles, skin and whole body of a person may be called discrete degrees. However, the whole body, however it may be controlled by a mental degree, is itself an aggregation of its parts. It is therefore not itself of a different degree to its parts.
3. We may think of discrete degrees as another dimension, even the fourth (or fifth) dimension of space and time. It is true that dimensions can be counted, and so are discrete in some sense, but they can still be continuously transformed into each other, for example by rotations. It is clear that rotating or expanding does not, by that fact, take you to a new spiritual discrete degree.
4. Infinite space, or Space Itself. Spinoza, for example, saw matter and space as the twin aspects of an infinite divinity, from which matter and space are themselves infinite in their details and in their extents. However, space is not mental, but is in a discrete degree distinct from all mental and spiritual degrees.
   Time
5. We may think of discrete degrees as new frequencies of vibration. Entering the mental realm has been called, for example,  ‘entering a new vibrational level’. However, frequencies can also be continuously transformed into each other, since time in nature is on a continuous numerical scale. It is clear that vibrating faster does not, by that fact, take us to a new discrete degree, and does not describe a dualist ontology.
6. Some natural objects have discrete harmonic modes of operation. A guitar or cello string, for example, has fundamental and harmonic vibrational modes, and these resonate among themselves. Electrons in atoms have discrete levels of different energies. However, if we look in detail, we see that all intermediate vibrations and energies are still possible, but just do not last very long. I have above mentioned the possible roles of different frequencies, and in physics, vibrational energy is proportional to frequency.
7. Series of successive processes, such as waterfalls or other emanations, or the stages of a person's life, are often used to represent ‘successive discrete degrees’. We may often represent discrete degrees as ‘successive’, but we should be aware that this is another representation using ‘time’. Discrete degrees (such as mental/spiritual and natural) are still ‘simultaneous’ in many important senses!
8. Infinite time, or the denial of time, as being eternity. Encompassing all time is sometimes seen as a degree above all us ‘time bound’ individuals. However, any mind or spirit is presumed to be the source of life and activity, and certainly not the freezing of time. We may imagine that Divine Wisdom does see all time together (past, present and future) in an eternity, but note that the accomplishment of Divine Love still requires enacting that time successively.
Natural States

9. Solids, liquids and gases are discrete phases of many substances in nature. Ice, water and steam are discrete manifestations of the one chemical H₂O. However, these multiple phases of water can be continuously transformed one into another, and back again, so not describe dualities in a sense from which we can learn about mind and nature.
10. A related suggestion is to use the classic quartet of earth, water, air and fire, especially to identify a mental or spiritual degree as fire.
11. Sometimes we imagine mind or spirit as a fine or subtle substance that pervades and influences ‘coarse matter’. This may be true, but unless we have an independent idea of the mental or spiritual degrees, we cannot properly describe it merely from the idea of ‘fineness’ or ‘subtlety’.
12. Various polarities in nature, such as positive and negative electric charge, or male and female in biology. Opposite electric charges, such as of electrons and its antiparticle the positron, however, are exact mirror images at exactly the same natural level. Male and female organisms, by contrast, have internal complexities that are very similar, differing in particular in the way some of these are ordered. Furthermore, we cannot say that only positive charges, or only females, are connected to (or are) a dual degree.
    Inside and Outside
13. We may think of discrete degrees as the internal and the external of bodies, or of persons. The  words inmost, inner, and outer may be often used to describe discrete degrees in practice, and many of us use these adjectives to contrast spiritual with natural things. However, if we examine the specific meanings of these words, we see that they are essentially spatial images that must be interpreted metaphorically if they are to indicate spiritual and natural as distinct discrete degrees.
14. Connected with the previous suggestion, sometimes the mental or spiritual degree is seen as the ‘first person’ inside view of nature, so physical matter is the ‘outside’ or ‘third person’ view. This is a popular belief among those trying to reconcile science and spirituality, but it does not help, for example, in trying to understand the possibility of life after separation from the physical body. How can there be a life from a coherent inside view if the outside view is of matter broken into pieces?
15. A recent suggestion is based on chaos theory, where we see self-similarity: a similarity of behavior patterns when we compare the whole and the parts. But the whole and the parts, again, are not ontologically dual.

Many of the above distinctions have been adopted in popular culture as sufficient for defining the distinctness of degrees that lead to the mental or spiritual, and there is some satisfaction, for example, with imagining the spiritual as 'higher resonant states in higher dimensions' of reality as yet undiscovered by physics. However, all the above classifications are continuous, not discrete or dual. The desires for continuous spiritual degrees, though widespread in many contemporary and Eastern philosophies today, are what we should call ‘natural’ or even ‘sensual’.
We need to separate our understanding, in some way, from natural and sensual images. This separation may never be complete on earth, but let us at least be aware of the way we presently think.
But let us try to form some more positive accounts. My immediate problem here is that you may be most happy if I produce a new picture which I claim shows discrete degrees most accurately. However, we have just seen that all pictures are based on spatial and temporal images, and by that fact should be called into question! What can we do?
This is a problem that modern quantum physics has faced for much of the last century. Modern physicists have realized that pictures based on ‘particles’, or on ‘waves’, are no longer satisfactory, but have nothing satisfactory to replace them with. Some among them have (wisely) said that ‘we can no longer rely on naive pictorial thinking’. Thus, for minds as well as for physics, we have to rely on some different kind of thinking. Quantum physics can use its mathematical equations, but what can we use?
To understand in a specific way discrete degrees, and the possibility of a real dualism, we can either

1. build on and extrapolate whatever discrete degrees physics and philosophy have discovered, or
2. rely on our own intuitive understandings of causes and effects in ourselves.

A description of those discrete degrees that physics has discovered is given separately, so I will merely mention some of the more obvious discoveries here. Let me first describe some of the discrete degrees and dualities that Swedenborg has described: two from general philosophy, and one from simple physics:
Degrees in Philosophy and Simple Physics

16. Form and substance are a pair of discrete degrees. For a given thing, such as this chair, the form is its position, orientation and shape. And not just the overall shape, but also the shapes and arrangements of all its constituent parts. The substance of the chair is that of which the constituent parts are forms of, are made of. This physics can give us some idea of, namely some kind of energy or propensity to interact. Form and substance cannot be continuously transformed into each other.  Yet they are not ontological dual, in the sense of independently existing.
17. End, cause and effect are a triplet of discrete degrees. The end is the original principle according to which a process starts, the cause is the formulation of means that is poised to act, and the effect is the resulting action. End, cause and effect produce each other in sequence, but cannot be reversibly transformed.
18. Heat and Light, strictly, are radiation in the same electromagnetic spectrum: making them a pair of continuous rather discrete degrees. However, ‘heat’ has a more general meaning: that of energy in general, and light has a more specific meaning: as a form of radiation that can be encoded with very much information. Energy and information do form a discrete pair of degrees, but similar therefore to 'form and substance' above. Thus ‘light’ is a particular form of energy, so light is like form and heat is like substance.
    Other discrete degrees, even within nature, have been discovered by science:
    Degrees in Modern Physics
19. Force and motion are discrete degrees. This was in fact realised in the 18th century by Boscovich and by Kant, Forces may be present even if no movement of matter occurs.
20. Potential energy and force are discrete degrees. This was made clear with the discovery of electromagnetic fields by Faraday and Maxwell. Electric energy fields, for example, only produce forces if a charged particle is present within the field. Similarly, the gravitational fields of the earth and sun are not themselves forces, but only produce forces on planets and satellites should these be present. Physicists often conflate potential energy and force, by saying that forces are simply a description of the gradient of the potential energy surface, but the 'force' here is the force actually operating, not that of a 'force field' that is still waiting to have any effect.
21. Waves and particles, or (better) waves and events are discrete degrees. This is the best way of understanding quantum physics: waves are a description of causes, and specific particle positions (or events) are the actual effects of those causes.
22. Virtual and actual processes are discrete degrees. Electric fields, for example, are generated by a prior degree of virtual photons. I discuss this a little more separately.These dualisms within physics are described elsewhere in more detail.
    Other discrete degrees are seen by our intuitive understanding of causes and effects, for example within ourselves, within our own minds.
    Degrees as suggested by Swedenborg
23. End, cause and effect are a triplet of discrete degrees. The end is the original impetus which motivates us, the cause is that motivation when it has formulated the means and is poised to act, and the effect is the resulting action. End, cause and effect produce each other in sequence, but cannot be reversibly transformed.
24. Affection, understanding and action are discrete degrees. These are analogous to the previous set, but generalised os as to be applicable to processes also of the mind.
25. Soul, mind and nature, are the three discrete degrees, according to Swedenborg [1], describing the production of creation via affections and thoughts to nature.
26. Love, Wisdom and Use are, according to Swedenborg [1], again analogous to discrete degrees, and are applicable even to the Divine.

The classifications 19-22 do describe discrete degrees, but only in nature. By themselves they do not indicate any spirituality, but nevertheless they reflect the true spiritual discrete degrees (23-26) more accurately than the continuous degrees (1-15) since they are themselves discrete and not continuous.
Trying to understand any kind of discrete degree is a useful education toward understanding dualism, and hence to begin to understand what is mind, and what is spiritual.

References
[1] Emanuel Swedenborg, Divine Love and Wisdom, 1763. (online)