Biology Reference
In-Depth Information
mathematical biology and metabolic control analysis which have been deduced
from underlying principles, to proposed flux patterns (Reed & Palsson, 2003),
or distributions of control (e.g. Hornberg et al., 2005).
By contrast, much of postgenomics and systems biology, in which often
we lack reasons or sufficient background knowledge that might lead us to
realistically plausible hypotheses, has been data-driven, with a good hypothesis
being the result, not the starting point, of the initial investigation. This brings
with it a requirement for a different kind of experimental design, in which
rather than seeking to hold everything constant except one parameter we seek
to vary conditions as much as possible (but in a controlled manner!) to produce
a 'training set' of data to establish rules that are likely to generalize well to
apply to examples not previously encountered (Kell & King, 2000). This entirely
different way of thinking also discriminates the methods of classical statistics
(that start with a model and test the goodness of fit of data to that model) from
those of machine learning (that start with data and determine the model that best
fits those data) (Breiman, 2001).
The chief element of this integrated view of the relation between ideas and
data is the recognition that induction is not simply the reverse of deduction
(Carnap, 1966; Kell & Welch, 1991). Deductive reasoning starts with an axiom
or set of axioms (i.e., a mental construct, the world of ideas, such as 'all swans
are white') and a hypothesis such as 'Alice is a swan' that together allow one
to deduce with logical certainty that provided Alice is a swan one may make
an observation in the expectation that Alice will be found to be white and the
data found to be consistent with the hypothesis. Alternatively if Alice is found
to be black then either Alice is not a swan or the axiom should be modified
(axioms are by definition true). This hypothetico-deductive framework, in which
hypotheses can be falsified by data but not proved true, was the focus of Karl
Popper's agenda to demarcate 'science' from 'pseudo-science' (Medawar, 1982;
Popper, 1992), although one must remark that in the real world some favoured
hypotheses can survive in the face of any number of inconvenient facts (Gilbert
& Mulkay, 1984; Kell, 1988; Kuhn, 1996).
The inductive mode of reasoning generalizes from patterns observed in a
number of actual cases, and thus goes from the world of data to the world of
ideas: If Alice is a Swan and is white, Bob is a swan and is white, and George is
a swan and is white, an induction might be that 'all swans are white'. Now it has
been known since the time of Hume that such induction is logically insecure,
in the sense that a single black swan shows it, and that the fact that the sun has
risen every morning throughout one's life does not mean it will probably do
so tomorrow. However, the existence of black swans is no less harmful to the
hypothesis on which the deduction is based that all swans are white than it is
to the same view arrived at inductively, and it is not at all clear why induction
should in fact be so disfavoured.
