>Right on target, Glenn. This is all too reminiscent of the medieval
>Muslim philosopher Averroes who maintained that "truths of reason" and
>"truths of faith" existed in two logic-tight compartments, so he could
>"save" both his Aristotelian natural scuence and his faith based on the
>Qur'an. Thomas Aquinas opposed Averroism and argued strongly for the
>unity of truth, and I don't see how he could be wrong about this.
Nor do I. "Double truth" doesn't impress me.
>laws of logic apply accross the board, and if a statement of faith is the
>contradictory of a statement of reason, one of them must be true and the
Agreed. However, the statements we formulate about truth are generally
approximations. The statements can conflict without the underlying truths
>To say they are both true in their own way is to open a
>pandora's box which, if recent history is our guide, will result in
>people denying the Resurrection and still claiming to be Christians; or
>affirming that all religions are equally truthful even though Christians
>affirm the uniqueness of Christ; etc.
I am totally in agreement. I believe there is a widespread, common
tendency to confuse truth with representations of truth that contributes
much heat and no light to debates on origins and a variety of other
A logical proposition is true or false. If it conflicts with another
logical proposition, both cannot be true. However, if a logical
proposition represents real-world facts, it is likely its formulator had to
approximate and abstract in order to formulate it. If two propositions
formulated in this way conflict, they cannot both be true. But because of
the approximation and abstraction involved in formulating them, that does
not necessarily invalidate the truth that one or the other propositions is
intended to represent.
Example. I'm in the process of translating an excel spreadsheet that uses
the optimizer to design CVRTD (Continuously Variable Real Time Damping)
shock absorbers into a c function that can be used in a genetic algorithm.
Excel's optimizer is pretty good, but we want to make sure excel isn't
finding a local optimum. The c function is written and debugged (mostly
:-). One of the tests involved providing the c function with inputs which
yielded known outputs and making sure we got the same outputs.
Unfortunately, in the first series of tests, an integer parameter that
should have had a value of 10 kept turning up as 11. The parameter was
computed by evaluating a floating point value, adding 0.5 to it and
truncating it, so it would round off properly. By changing the 0.5 to
0.499 I could make it agree, and as far as I was concerned I knew the
problem: different floating point representations led to different
roundoff results. There is one number that was computed. No question
about it. And it has a well-defined value. But different representations
of it led to different approximations. In theology/science comparisons of
course, we are usually not so blessed by providence that we are able to
determine exactly how our representations differ. :-).
Bill Hamilton | Chassis & Vehicle Systems
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