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Ternality Theory

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Hume's Law prevents reductionism

It is well-known to philosophers that there is a logical gap between information and imparity. This gap is the basis of a long-standing controversy in moral philosophy—what is usually called the 'is-ought question'. It was originally pointed out by David Hume (Hume, 1740), and the logical principle that you cannot derive ought from is is often called 'Hume's Law'.


Figure button   Popper's statement of Hume's Law


Closely related to Hume's Law is the Naturalistic Fallacy—the attempt to deduce conclusions about what ought to be from premises that state only what is the case, or the other way about.

For our purposes, it is important to note that the philosophers' arguments have almost all been about this discontinuity as it occurs in ethics, whereas exactly the same arguments apply in all the other fields where evaluation takes place. We have already noted that Spranger's dimensions can be used as a scheme for the various possible kinds of evaluation, and therefore of imparity. It can readily be seen that Hume's Law and the concept of the Naturalistic Fallacy apply to all of them.

Of great importance for our purposes is the fact that Hume's Law implies that considerations occurring in the domain of imparity cannot, even in principle, be reduced to those in the domain of information. This is what makes a ternary conception of mechanism different from the usual cybernetic conception, as well as from the classical one.

Binary cybernetics can be reductionist

Strictly speaking, the familiar two-domain mechanisms of cybernetics can be accused of being reductionist. For example, it is at least in theory possible to describe the activity of a computer in terms of the activity of the electronic components in the hardware, and all of the software considerations could be expressed in those terms. However, in practice, when we work with computers, we very rarely have to think about the physics or the electronics. Computer scientists, and the rest of us, talk about computers at the software level, and could not explain what computers do in a way that would be of use at the hardware level. So, although computer science uses two domains, the second of which is in principle fully describable in terms of the first, it is not in practice reductionist.

But ternary cybernetics cannot


Figure button   The stratified menu


However, reduction is not possible, even in principle, in the case of mechanisms using the three domains. This is because Hume's Law implies that considerations occurring in the domain of imparity cannot, even in principle, be reduced to those in the domain of information. You can never construct a message expressing a judgement from one or more purely descriptive messages or, to put it the other way round, you cannot reduce a message expressing a judgement to a purely descriptive message. This ensures that any theory constructed within this ternary structure can be called 'mechanistic', with all the advantages which that implies but, at the same time, it can never be called 'reductionist'. It cannot be reduced to descriptions which are solely within the first domain. Because a ternary conception of mechanism cannot be reductionist, this makes it importantly different from both the classical and the usual binary, cybernetic, mechanistic conception.

This also means that any practical use of the discontinuity is not merely a matter of definition, of convention, or of convenience, but is forced upon us by the logic of the situation.

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© Copyright D J Stewart 1987, 1998, 2003. All rights reserved.

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