# The Roles of Inductive & Deductive
Methods

[Chapter 1 Objectives]
BHS
-> Mr. Stanbrough -> Physics
-> About Science ->
this page

"The deductive method is
used exclusively in mathematics, and the inductive
method (it is the scientific method, after all) is used
exclusively in science, right?"

##

No. It's not that simple at all.

As stated previously,
mathematicians do **not** spend their days plodding along from
theorem to theorem - mathematics requires insight, exploration,
intuition, hypothesis, and yes, experiment. Mathematicians use
inductive methods to explore mathematics.

However, what is accepted as evidence in mathematics is proof -
the deductive method rules. You can (and
should) use any method possible to discover new mathematics, but in
order for your discoveries to be accepted, you must be able to fit
them into the deductive structure of mathematics.

On the other hand, physicists use
mathematics all the time. Every major physical theory
of the last 400 years has been mathematical in nature -
*theoretical* physics is *mathematical* physics. To explore
the consequences of their theories, physicists use the tools of
mathematics - deductive methods.

However, what is accepted as evidence in science is observation
- the inductive method rules here. That
doesn't mean that scientists never use deductive reasoning - they do,
profitably and all the time - but that in order for a discovery to be
accepted as a part of science, it must agree with observations of
nature.

So, the statement that began this page turns out to be
*considerably* oversimplified. Oh well, most statements about
the nature of science and mathematics are, by necessity,
oversimplified.

[Chapter 1
Objectives]
BHS
-> Mr. Stanbrough -> Physics
-> About Science ->
this page

last update June 6, 2000 by JL
Stanbrough