Deduction is deduction, regardless of the domain in which it is applied

The principles of deductive reasoning are independent of the content of the propositions.1 What is being expounded here is not the principles of detection as applied to crime but the general principles of scientific research.

Watson claimed that: The stage lost a fine actor, even as science lost an acute reasoner, when he (that is, I) became a specialist in crime [SCAN]. I modestly agree about the stage but not about the larger stage of science.

I have, on a number of occasions, described detection as a science:

Detection is, or ought to be, an exact science and should be treated in the same cold, unemotional manner [SIGN].
Dr. Mortimer insulted me by placing me second to Monsieur Bertillon, because the latter appealed to his precisely scientific mind, whereas I was merely a practical man of affairs [HOUN]. I took offence at that because he failed to recognize that my reputation for practicality was based exactly on my precise scientific mind. There is nothing as practical as a good theory. Later in the case, I teased him by referring to myself as a scientific expert and denouncing his appeals to the supernatural.

Detection is not an ignoble profession , as Colonel Emsworth dismissed it, any more than science is. [BLAN]. It is merely the application of those principles to the domain of crime. I am not being facetious when I use the language of science:

I think there is a small experiment which we may try tomorrow, Watson, which may throw some light on the matter [SHOS].
There is, alas, some truth in the accusations of some clients that those cases were mere intellectual puzzles [SUSS] or little puzzles [HOUN].2 I found them useful exercises for helping evolve my science of detection.

Perhaps my association with Watson made me sensitive to the analogy between the detective and the doctor. There is, of course, the overlap of the two disciplines. I once did considerable research into matters of a medico-criminal aspect [DYIN]. There are many obvious topics within this domain - the effects of various poisons, the damage as a result of blows to the head, the diminished responsibility of criminals with various diseases, and so on.

However, this is not what I am arguing here. When a client appeared to be more mad than criminal, I quipped: This is Baker Street, not Harley Street [SHOS]. However, the methods applied in both streets are the same. This was well captured by Culverton Smith:

He is an amateur of crime, as I am of disease. For him, the villain, for me, the microbe. There are my prisons (pointing to a row of bottles and jars). Among those gelatine cultivations some of the very worst offenders in the world are now doing time [DYIN].
Mr. Gibson, the Gold King, appropriately made the analogy, when he told me: You're like a surgeon who wants every symptom before he can give his diagnosis [THOR].

1   The following short course in logic may help make this clear. A proposition is anything which can be said to be true or false. Imagine two propositions - P and Q - in an empty universe. There are four possible states of affairs: P&Q or P¬Q or notP&Q or notP¬Q. If P, then Q eliminates the second alternative. P eliminates the third and fourth alternatives. Therefore Q must be true since there is only one alternative left, in which Q is true. The argument - if P, then Q and P, therefore Q - is true regardless of whether P and Q are statements about astronomy or biology or crime.

2   In The Structure of Scientific Revolutions (Second Edition) [Chicago: University of Chicago Press, 1962, 1970], Thomas Kuhn argues that the progress of science is not a gradual evolution, as traditionally thought, but a series of revolutions. Each science is organized around a paradigm, until it is displaced by a better paradigm. Thus, in physics, the paradigm of Ptolemy was replaced by that of Newton, which was in turn replaced by that of Einstein. Within each paradigm, much of science is indeed a matter of "puzzle-solving".