but did you know that neither inductive nor deductive reasoning are rationally grounded? they work, and they're useful, but logically neither process checks out - so we have an entire system of logic for which the only two modes of reasoning are not, themselves, logically sound. See Susan Haack/David Hume, and any modern epistemologist, they all have lots to say about this.
imo, limiting your beliefs to what logic allows turns out to be as arbitrary logically as limiting them to what the body of scientific knowledge allows. they're both just useful places to "draw the line in the sand" to what you're willing to find plausible.
i say this not to piss in anyone's cereal - i accept that people define themselves by these lines in the sand and you won't find my sand-line too far away from either. but i do have to put up with a lot of pompous logical positivists on my college campus with no knowledge of formal logic who claim they only believe what can be logically deduced or inducted, or worse still, Physics majors with no inkling of the historicity of science who claim they only believe what is "scientific". these people have a tendency greater than that of Creationists to insist their worldview is the only viable one, and that others are insane or just stupid. so i spread the word.
anyway, food for thought