"vincent p. norris" wrote in message
...
Yup. Also, "deduced reckoning" would be redundant, as reckoning is
inherently deductive.

"Deduction" means going from the universal to the particular, as in
the classic example used in logic textbooks:

All men are mortal. Socrates is a man. Ergo, Socrates is mortal.

INduction is the process of drawing inferences from PARTICULAR
OBSERVATIONS, as in::

Socrates died. Aristotle died. Ptolemy died. Ergo, all men die.

Dead reckoning starts with "inputting" particulars--the airspeed of MY
airplane, the heading I AM going to fly TODAY, the CURRENT wind, and
therefore, it is an example of induction, not deduction.

Reasoning from the general to the particular, as in the syllogism you cited,
is one of the earliest and simplest kinds of deduction to have been
formalized. But any chain of reasoning that follows by necessity from
general axioms constitutes deduction. Hence, deduction includes, for
example, calculating that 2+2=4 (because that equation follows from the
axioms of arithmetic, even though the equation addresses particular
parameters). Similarly, it is deductive to reason from the axioms of
Euclidean geometry that if I start at position x,y and travel in direction
theta for t minutes at v knots, then I am at position x',y'.

Induction, by contrast, involves a supposition that new instances will
continue to resemble old instances (as in your example above), even though
the contrary is logically possible. (To confuse matters, what's known as
"mathematical induction" is actually a form of deduction.)

Science is an inductive process. Statistics is inductive. Philososphy
and theology are deductive.

Science and philosophy make extensive use of both inductive and deductive
reasoning. Mathematics is purely deductive. Statistics, as a branch of
mathematics, is deductive, but using statistical reasoning to make
predictions involves an inductive leap within deduced constraints.

--Gary