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Reductionism versus Holism

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Here I wish to investigate a problem concerning the relationship of the Parts to the Whole, of a uniform being (a uniform thing, a substance). Partly this is already done in the Essay on Being and Essence. But it needs much more consideration.
This problem figures in the Holism-Reductionism discussion and is highly relevant to our investigation into the alleged substance-accident structure of every uniform thing (genuine being, Totality), because Classical Substance-Accident Metaphysics sees these uniform things as strict unities, not consisting of parts. These "parts" are not considered to be parts at all (in that metaphysics), but as qualities distributed within that uniform thing. And this indeed is a strict  h o l i s t i c  conception of such a thing. See for this the ABSTRACT in the HOMEPAGE.
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## The Continuum

To carry out such an investigation about the relationship of the parts to the whole we must first pay our attention to the continuum.
In the Essay on Substance and Accident, subsection Quantity I established that extension (extensum) is undefinable.
But for a continuum we can give a definition :
A continuum is an extensum that is intrinsically (i.e. inherently) ONE.
When such an extensum is an ens extensum, i.e. an extended being, then we have a physical continuum. When it is just an extensum, then it is a mathematical continuum, like a line, a surface or a volume.

### Mathematical continua

In Mathematics these extensa -- and thus these mathematical continua -- (line, etc) are considered as point sets. Strictly speaking however this is not quite correct. A line can never be build up from points alone, and also cannot consist of points alone, because points have no dimensions. And a collection of ' things ' having each for themselves no dimensions cannot constitute a ' thing ' having dimensions. A line is constituted of (smaller) lines only. These smaller lines can be produced by division of the line. The points are the boundaries between the smaller lines.
When we say that a continuum has parts (for example a line has smaller lines as its parts), then this is not entirely correct, because a line as such is not divided. But it is divisible, and when we carry out the division then we obtain the parts. So a line has only potentially parts, its parts have only a potential existence. Only after division are the parts actual, i.e. only then they actually exist (of course only in the way that mathematical objects do exist). The product of such a division is a contiguum. Such a contiguum itself consists of continua. These continua are in contact with each other. A mathematical continuum is indefinitely divisible. The act of division will never encounter a barrier or limit, it can only approach such a limit but never reach it. When the limit would be reached (which is impossible) then the mathematical continuum would be totally divided up by points, i.e. we would end up with a powder of mathematical points. Their number would be an actual infinity. In fact however the number of parts, resulting by repeated division, will always be finite, no matter how long we will proceed with the repeated division.

### Physical (i.e. material) continua

Physical continua come in two varieties : static continua and dynamic continua. Static continua are purely spatial. Dynamic continua also include time, they are movement and (the aspect of) time itself. Because we will focus our attention on wholes, i.e. substances (first substances, as defined in the Essay on Substance and Accident, section Substance ), we will confine ourselves to the static continua.
As we have stated, a continuum is an extensum that is intrinsically ONE. First and foremost this is valid for geometrical continua. But what about real things, i.e. material uniform things, like for instance crystals? Are they also continua? Although they are extensa, they seem at first sight (or, may be better, from one point of view) not to be continua, because they consist of actual parts. A crystal for example consists of atoms, ions, or molecules, arranged in a periodic array. But in the Essay on Being and Essence we saw that a uniform thing is always generated by a dynamical system, and that the (one!) dynamical law governing that particular system can be interpreted as the Essence or Identity of the thing in question. On the basis of this ONE dynamical law we can say that that thing is ONE thing, not a collection of many things (Of course a dynamical law, for instance a particular crystallization law, can produce more than one thing -- more than one crystal -- but that is only a repeated execution of the same law, giving rise to several individual products). So when such a thing -- being ONE thing -- nevertheless seems to consist of actual parts, which seems especially clear in the case of organisms, then we cannot interpret these parts as things. What are they then, what is their status?
As a hypothesis we could cautiously say that they are properties of that one thing. Even when the parts in the thing seem to move, we could speak of a variation (exchanging) of the distribution of those properties over the (extended) thing, the (first) substance.

## Holistic View and Reductionistic View

So when we consider the parts of a thing as properties of one substance (because of the one dynamical law), then we consider that thing in a HOLISTIC fashion. In this way the Whole is ontologically first, the parts are ontologically second (" ontological " means according to nature ). These parts do not exist by themselves, but only by virtue of the thing, of which they are properties. A property, as property, cannot exist by virtue of itself, but only by virtue of the substance. A substance (being itself an individual uniform thing) can and does exist by virtue of itself. A substance, having different properties, and especially properties representing its parts, shows -- according to the location of these parts (here viewed not as things but as properties) -- a non-uniform, or a periodic, distribution of such properties over the thing. A thing so constituted can then be viewed as a heterogeneous continuum.
Such a view can perhaps be characterized as a view of the thing-at-a-high-structural-level.

But when we consider the parts of the thing in question as actually existing things, then we consider that thing in a REDUCTIONISTIC fashion. Then those parts enjoy ontological priority, they are first, the whole comes (also in an ontological sense) later. This represents a view of the thing-at-a-low-structural-level. This does mean that the whole follows from the parts, that the whole is already implicit in the parts, even if they have not yet formed the whole. But this does not automatically imply that we are able to know, and thus predict that whole, from a consideration of the parts alone, i.e. the separated parts (in this case they are not parts of course, but just individual things). Stated in another way, an ontological reduction of the whole to its parts (meaning that the whole has only a derived being, as opposed to its parts) does not necessarily imply an epistemological reduction of the whole to its parts. It is for instance not at all certain that we will ever fully be able to understand self-consciousness from a detailed study of brain cells (neurons).
A thing, viewed as having actual existing parts (seen as things, not as properties) can be denoted as an organised contiguum (if it were not organized, it would be an aggregate, an aggregate of more than one thing, and so the thing in question would not be one thing.

Which one of these views should be the correct one?
A uniform thing is, as stated, generated by a dynamical system. The initial state of the system (i.e. the start configuration of system elements) PLUS the dynamical law (which is inherent in those elements) will generate the thing in question. Thereby it is possible that -- as part of this process -- some elements of the initial state have themselves changed, they then have undergone some change in their inner configurations, or they have joined together, creating larger entities; in both ways the elements form the parts (or properties) of the whole, but the dynamical law has stayed the same throughout. And even in the case where the ' parts ' do not change, the dynamics makes them parts, causes them to be integrated in the Whole. So it seems that the dynamical law has ontological priority relative to the elements, and so to the parts of the generated whole.
It should be emphasized that the dynamical law is not a thing, but a principle, inhering in the system elements. And a principle (staying the same during the process) has ontological priority relative to the items it governs.
So the dispute of Holism versus Reductionism can be provisionally resolved in the following fashion : The question of ontological priority does not concern directly the whole-OR-its-parts, but the dynamical-law-OR-the-whole-and-its-parts. And it seems that the dynamical law has the priority over the whole and its parts.
The ' bottom-up ' view, which is the current view among researchers doing computer simulations of life phenomena or intelligence, should mean that the ' bottom ' is not the parts, but the dynamical law. And because the law is inherent in the elements of the initial condition (starting state), these elements also belong (be it in a secondary way) to the ' bottom '. The parts are themselves already generated by the dynamical-law-plus-initial-condition, so they do not properly belong to the ' bottom '.

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An example of a thoroughly  h o l i s t i c  view of Reality is given in the Third Part of this Website, which is accessible by the following LINK :
HERE (to Third Part of Website).
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