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CHAPTER VI. THE INDIRECT METHOD OF INFERENCE.

take as an instance of Baroko, the argument

All heated solids give continuous spectra(1)
Some nebulæ do not give continuous spectra(2)
Therefore, some nebulæ are not heated solids(3)

Treating the little word some as an indeterminate adjective of selection, to which we assign a symbol like any other adjective, let

The premises then become

D= DC(1)
AB= AB c(2)

Now from (1) we obtain by the indirect method the contrapositive proposition

and if we substitute this expression for c in (2) we have

the full meaning of which is that “some nebulæ do not give continuous spectra and are not heated solids.”

We might similarly apply the contrapositive in many other instances. Take the argument, “All fixed stars are self-luminous; but some of the heavenly bodies are not self-luminous, and are therefore not fixed stars.” Taking our terms

we have the premises

A= AB,(1)
CD= b CD(2)

Now from (1) we can draw the contrapositive

and substituting this expression for b in (2) we obtain

which expresses the conclusion of the argument that some heavenly bodies are not fixed stars.

Contrapositive of a Simple Identity.

The reader should carefully note that when we apply the process of Indirect Inference to a simple identity of the form

we may obtain further results. If we wish to know what is the term not-B, we have as before, by the Law of Duality,

and substituting for A we obtain

But we may now also draw a

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