Variants of Explanatory Filters

Wesley R. Elsberry (welsberr@inia.cls.org)
Fri, 13 Nov 1998 10:45:19 -0600 (CST)

William Dembski's "The Design Inference" features discussion
of an "Explanatory Filter". I'd like to put forward for
discussion Dembski's original and a variant. "Regularity"
is how Dembski refers to the action of law-like physical
processes.

First, the original.

[Quote]

Premise 1: E has occurred.
Premise 2: E is specified.
Premise 3: If E is due to chance, then E has small probability.
Premise 4: Specified events of small probability do not occur
by chance. [Noted as being supported in Ch. 6 -WRE]
Premise 5: E is not due to a regularity.
Premise 6: E is due to either a regularity, chance, or design.
Conclusion: E is due to design.

[... later given a symbolic logic form]

Premise 1: oc(E)
Premise 2: sp(E)
Premise 3: ch(E) -> SP(E)
Premise 4: [forall]X[oc(X)&sp(X)&SP(X) -> ~ch(X)]
Premise 5: ~reg(E)
Premise 6: reg(E) V ch(E) V des(E)
Conclusion: des(E)

[End Quote - WA Dembski, TDI, pp. 48-49]

Note that "des(E)" is simply "~reg(E) & ~ch(E)".

Now, I'll propose an alternative form of EF.

Premise 1: E has occurred.
Premise 2: E is specified.
Premise 3: If E is due to chance, then E has small probability.
Premise 4: Specified events of small probability do not occur
by chance.
Premise 5: E is not due to design by an agent.
Premise 6: E is due to either design, chance, or a regularity.
Conclusion: E is due to a regularity.

And in symbolic logic:

Premise 1: oc(E)
Premise 2: sp(E)
Premise 3: ch(E) -> SP(E)
Premise 4: [forall]X[oc(X)&sp(X)&SP(X) -> ~ch(X)]
Premise 5: ~des(E)
Premise 6: des(E) V ch(E) V reg(E)
Conclusion: reg(E)

And, of course, "reg(E)" is simply "~des(E) & ~ch(E)".

What I find interesting about these two EF variants is that
they share the same logic, but seem to have widely divergent
results.

Wesley