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**These are excerpts and elaborations from my book "The Nature of Consciousness"**

A very powerful argument in
favor of common sense is that logical reasoning alone would be utterly
impossible. Classical Logic deduces all
that is possible from all that is available, but in the real world the amount
of information that is available is infinite: the domain must be somehow
artificially “closed” to be able to do any reasoning at all. And this can be
achieved in a number of ways: the “closed-world assumption” (all relations relevant
to the problem are mentioned in the problem statement), “circumscription”
(which extends the closed-world assumption to “non-ground” formulas as well,
i.e. assumes that as few objects as possible have a given property), “default”
theory (all members of a class have all the properties characteristic of the
class if it is not otherwise specified).
For example, a form of default theory allows us to make use of notions
such as “birds fly” in our daily lives. It is obviously not true that all birds
fly (think of penguins), but that statement is still very useful for practical
purposes. And, in a sense, it is true, even if, in an absolute sense, it is not
true. It is “plausible” to claim that birds fly (unless they are penguins). At the same time, common sense
reasoning introduces new problems in the realm of Logic. For example, John
McCarthy's "frame problem”: it is not possible to represent what does
“not” change in the universe as a result of an action, because there is always
an infinite set of things that do not change. What is really important to know
about the new state of the universe, after an action has been performed? Most likely, the position of the stars has
not changed, my name has not changed, the color of my socks has not changed,
Italy’s borders have not changed, etc. Nevertheless, any reasoning system,
including our mind, must know what has changed before it can calculate the next
move. A reasoning system must continuously update its model of the world, but
McCarthy suggests that this is an
impossible task: how does our mind manage? Complementary paradoxes are
the "ramification problem" (infinite things change, because one can
go into greater and greater detail of description) and the "qualification
problem" (the number of preconditions to the execution of any action is
also infinite, as the number of
things that can go wrong is infinite).
Somehow we are only interested in things that change and that can affect future
actions (not just all things that change) and in things that are likely to go
wrong (not just all things that can go wrong). “Circumscription” (McCarthy’s solution to the frame problem) deals with default inference by
minimizing abnormality: an axiom that states what is abnormal is added to the
theory of what is. This reads as: the
objects that can be shown to have a certain property, from what is known of the
world, are all the objects that satisfy that property. Or: the only individuals
for which that property holds are those individuals for which it must
hold. (This definition involves a
second-order quantifier. Technically,
this is analogous to Frege's method of forming the
second-order definition of a set of axioms: such a definition allows both the
derivation of the original recursive axioms and an induction scheme stating
that nothing else satisfies those axioms). For similar reasons Raymond
Reiter introduced the
"closed-world axiom" (what is not true is false), or "negation
as failure to derive": if a formula cannot be proven using the premises,
then assume the formula's negation. In other words, everything that cannot be
proven to be true must be assumed to be false. His “Default Logic” employs the
following inference rule: "if A is true and it is consistent that B is
true, then assume that B is also true" (or "if a premise is true,
then the consequence is also true unless a condition contradicts what is
known"). Ultimately, these are all
tricks to account for how the mind can do any reasoning at all in the face of
the gigantic complexity that surrounds it. Back to the beginning of the chapter "Common Sense" | Back to the index of all chapters |