If one wears an arc-and-compass breastpin, then he is a Freemason.

Mr. Wilson is wearing an arc-and-compass breastpin.

Therefore Mr. Wilson is a Freemason.5

Is this argument sound? No, not at all. As a deductive argument it is a valid form of a hypothetical syllogism (modus ponens-way of affirmation). But unfortunately for Holmes the consequent is not entailed in the antecedent.6 There are many other reasons that someone might wear an arc-and-compass breastpin. Pojman asks us to consider the possibility that Mr. Wilson, who is not a Freemason, bought a similar arc-and-compass breastpin at a pawn shop and wore it, thinking it was a beautiful bit of Moslem design.7 In that case, premise 1 would be false-one can wear an arc-and-compass breastpin without being a Freemason. Because it is sensible that non-Freemasons wear that pin, the above deductive argument is not sound. Nevertheless the single most plausible explanation for Mr. Wilson wearing the arc-and-compass breastpin is that he indeed belongs to the Freemasons. What Holmes has really done is reason abductively, i.e., reason to the best explanation of the facts.

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Of the three types of reasoning, it is abduction that offers one the most extensive range of reference. Deduction is entirely analogical, or self-referential. It imparts no new information and refers only to what is found within the proposition under consideration. Induction, on the other hand is synthetic in nature, it does refer to objects that exist outside the proposition considered. Nevertheless, it is limited to conclusions that can be reached through repeated or prior experience. Abduction, on the other hand, is able to introduce new ideas, to solve problems, and to lead one to new explanations of life and reality. It is, as Peirce notes, "the only logical operation which introduces any new idea."8 Furthermore, it is not dependent upon prior experience as is induction. Judged in terms of reference, abduction is clearly the most significant type of reasoning.

We must be aware that what abduction gains in terms of reference, it sacrifices in certainty. While abduction is the only type of reasoning that refers one to new information, it is also the least certain. Deduction applied properly yields a necessary conclusion-one that cannot not be true. Induction applied properly yields a probable conclusion-one that is to be preferred over all other possible answers taken together, not simply over any other single option, as is the case with abduction. Abduction, on the other hand, applied properly, yields only the most plausible conclusion. This means that the best available abductive solution might nevertheless be quite improbable-and thus likely to be mistaken. This is not to say that abduction is less important than deduction or induction. It is to say that our listeners need not only a creative word, but also a certain word. After all, biblical prophets declared, "Thus saith the Lord," not "Divine judgment is the likeliest explanation for our present distress." We must therefore maintain balance in our reasoning. All three types of reasoning have their strengths and weaknesses, and they all have their place in our preaching.9