An inductive step entails proceeding from the nth to the (n + 1)th case of a sequence of propositions. In this case, it is the step from the closest possible here and now and immediately testable, to the balance of the universe. You may make the steps as small as you like. You will hopefully discover as you proceed, that at small distances, where the situation is still testable, your hypothesis still functions in the same fashion as it did in the beginning. If it doen't, you have falsified your hypothesis (progress!) and you will then create a new hypothesis to cover the added situation. At each step, you are able to design an experiment to "test" your hypothesis. At some point, while your hypothesis is not proven, you will decide that it is "good enough" to work with until such time as new evidence appears which contradicts it (falsifies it). At that time you will need to come up with a new theory of whatever. It should be noted that this process permits and encourages as much testing as is deemed necessary to make the theory a "strong" theory.
Faith is accepting something without proof and generally refers to the untestable. If what you are swallowing is testable, then it would not require faith to accept it.
The difference seems mighty clear to me. I'd suggest that it is a discernable qualitative difference clearly visible to the non-ostrich (to borrow from one of the other threads :-) ).
From: firstname.lastname@example.org [mailto:email@example.com]On Behalf Of Tim Rhodes
Sent: Wednesday, February 10, 1999 3:48 AM To: firstname.lastname@example.org
Subject: virus: Re: Faith and truth in science
>There is nothing fundamentally wrong from postulating that the universe is
>strange, unknown and unknowable environment except in our immediate
>vicinity. We can then analyse the environment in our immediate vicinity and
>develop a rational system to describe our immediate environment. We can
>make the inductive step that all of the universe works the same way as our
>localised model. As and when we discover phenomena which confute our
>hypothesis, we simply modify our model of the localised universe to bring
>into alignment with this new information. As anyone with a smattering of
>exposure to science will recognise, this is the very basis of the
>method. As anyone with a slight exposure to the philosophy of science will
>recognise, this is the basis of the philosophy of science. As anyone with
>common sense will recognise, this does not take "faith".
What is the difference between an "inductive step" and a "leap of faith"? The style of the gait or the length of the stride?