Modelling Experiments - Natural and Artificial Reasoning - page 64

5.7 Abductive Systems in Science

The process of creating a model and how it relates to the experimentation is initiated
by abductive inference. Abductive inference proposes a set of models for consider-
ation. It is stimulated by the observation of puzzling phenomena (Peirce C. S.). We
will propose in this next section that abduction does not work in isolation from other
inference mechanisms (such a deduction and induction), and illustrate this through
an inference scheme designed to evaluate multiple hypotheses. We will also use game
theory to relate the abductive system to actions that produce new information. This
will provide us with a formal link between inference and action. To enable evaluation
of the implications of this approach we have implemented the procedures used to
calculate the impact of new information in a computer model. Experiments with this
model display a number of features of collective belief-revision observed in the field
that lead to consensus-formation, such as the influence of bias and prejudice. The
scheme of inferential calculations invokes a Peircian concept that:

'belief' is the propensity to choose a particular course of action.

Of the three types of inference proposed by Peirce, deduction is the one most widely
accepted and understood (Peirce 1966 , p. 92 ff.). In the semantic tradition, scientific
models are reducible to formal systems of propositions. Formal systems invoke
deduction because inferences can be made without reference to anything except the
model itself. Deduction is a self-contained syntactic process in that validation of
an inference depends simply upon a priori semantic truths and the preservation of
truth-values. These can be specified in a truth table. Thus deduction appears to free
us from the vagaries and changeability of an external world.
What makes this possible is that deduction relies upon the existence of well-
defined sets. The members of such sets are known without ambiguity. However,
what is often ignored is how the rules that specify set membership are established.
In practice, it is left to the user of a formal system to devise rules that can be applied
to test a candidate element for membership of a set. If this can be done with a finite
set of rules and without reference to context, then the formal model is considered
unambiguous. Following the model of Wittgenstein's Tractatus, we consider such
sets to be ' rational ' (Wittgenstein 1921 ; Addis and Billinge 2004 ).
By contrast, Peirce's notion of 'abductive' inference does not depend upon truth-
values. Instead, the process of validation depends upon 'induction', the third type of
inference that Peirce recognized. First, abduction generates a model (a hypothesis)
that is used together with deduction to explain some surprising facts and to predict
new ones. Where these are successful, this reduces our uncertainty about the world or,
as Peirce put it—'makes the world a less surprising place'. However, any reference
to the world requires a form of validation that depends upon observation of the world.
Peirce's version of induction involves comparison of expected and actual outcomes to
validate the abduced model of the world. Traditional 'induction', when considered
as generalization from given instances, converges to the combination of the two
Peircian inferences of abduction and validation (see Chap. 3 and Addis 2000 ).