F-Inductive Arguments: A New Type of Inductive Argument

In his extensive writings, the prestigious philosopher Richard Swinburne makes a useful distinction between two types of inductive arguments. Let B be our background information or evidence; E be the evidence to be explained; and H be an explanatory hypothesis.

“C-inductive argument”: an argument in which the premisses confirm  or add to the probability of the conclusion, i.e., P(H | E & B) > P(H | B).

“P-inductive argument”: an argument in which the premisses make the conclusion probable, i.e., P(H | E & B) > 1/2.

It seems to me that there is a third type of inductive argument which should go between C-inductive and P-inductive arguments. I’m going to dub it the “F-inductive argument.”

“F-inductive argument”: an argument in which the evidence to be explained favors one explanatory hypothesis over one or more of its rivals, i.e., P(E | H1 & B) > P(E | H2 & B). Explanatory arguments are F-inductive arguments and have the following structure.

1. E is known to be true, i.e., Pr(E) is close to 1.
2. H1 is not intrinsically much more probable than H2, i.e., Pr(H1 | B) is not much more probable than Pr(H2 | B).
3. Pr(E | H2) > Pr(E | H1).
4. Other evidence held equal, H1 is probably false, i.e., Pr(H1 | B & E) < 0.5.

Good F-inductive arguments show that E is prima facie evidence — that is why (4) begins with the phrase, “Other evidence held equal.” They leave open the possibility that there may be other evidence which favors H1 over H2; indeed, they are compatible with the situation where the total evidence favors H1 over H2.

F-inductive arguments are “stronger” than C-inductive arguments insofar as they show E not only adds to the probability of H2, but that E is more probable on the assumption that H2 is true than on the assumption that H1 is true. They are weaker than P-inductive arguments, however, because they don’t show that E is ultima facie evidence — they don’t show that E makes H2 probable.

One final point. Although I believe I am the first to give F-inductive argument a name and place within Swinburne’s taxonomy of inductive arguments, the structure for such arguments is not mine. Paul Draper deserves the credit for that.

About Jeffery Jay Lowder

Jeffery Jay Lowder is President Emeritus of Internet Infidels, Inc., which he co-founded in 1995. He is also co-editor of the book, The Empty Tomb: Jesus Beyond the Grave.


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