Page 149 - MODES of EXPLANATION

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“Living in the midst of ignorance, and considering themselves intelligent and enlightened,
the senseless people go
round and round
, following
crooked courses
just like the blind led
by the blind.”
The evident suggestion is that a more
direct
course to the truth would be better. Granted that one
cannot go
straight
to the truth, one should, at least, pursue the truth
as directly as possible
.
The
ancients even helpfully suggest two precise
measures
of indirectness of approach to the truth:
reversals
of opinion and
cycles
of opinion
Alas, nobody discussing the simplicity puzzle for the
past two and a half millennia has heeded the hint. Until now, that is. In accordance with the ancient
hint, we will explain, without any appeals to Providence, how a
fixed
bias (i.e., a broken compass)
can keep you on the straightest possible path to your goal.
Asking for Directions
Suppose that you become lost in a small town on a road trip, returning from Niagara Falls. You
stop to ask a local resident for directions to your home town to the south. But before you can even
say where you are headed, he responds: “Turn around. The freeway ramp is on the left.”
The advice is useful, even though the local resident didn’t know which city you were
headed to. In rural Pennsylvania, the freeways run through the main valley system, and otherwise
the rural routes twist and meander through the hills and mountains. The freeway is not straight by
any means, since it follows the valley floor. But whichever city you are headed to, the freeway is
the best route. That remains true, even if you have to backtrack to get on to it, which is very often
the case.
Suppose that you disregard the resident’s advice. To up the ante, suppose that your hunch
was
right
, in the sense that you headed south when the nearest freeway entrance ramp was to the
north. Sticking to your guns, you would end up on one of the small, circuitous mountain routes,
and things would get worse and worse. Figuring that out, you would do a U-turn and head back to
the freeway entrance ramp, just as the resident originally advised. So, at the minimum, you would
have added one U-turn to all of the other twists and turns in the freeway system. You would have
done worse by ignoring the resident’s advice
even though you violated it by heading directly
toward your goal.
Therefore,
fixed
advice can help you reach a
hidden
goal, unknown to the
adviser. Moreover, violating that advice can result in doing worse, even if you guessed
right
about
the direction of your ultimate goal. No magic is required. It remains only to transfer that moral to
the vexed problem of justifying Ockham’s razor.
Asking Ockham for Directions
Think about reversals of prior opinion as
epistemic
U-turns. A
reversal
of opinion is defined as
choosing a theory
T
and then choosing a theory
T’
that contradicts
T
after more information has
been received. Reversals of opinion are unpleasant and wreck one’s scientific reputation, but there
is a deeper, epistemological reason to minimize them. Since inductive methods cannot approach
the truth directly, the most reliable inductive methods are the ones that find the truth
most
directly,
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