Formalities (Part 1)

Before I really get into an analysis of what the incredibly logical Holmesian thought process looks like, I thought I'd take a moment to break down exactly what logic is, in the formal sense, just to get a feel for the techniques used to draw inferences and arrive at logical conclusions.

Questions to answer:

What is deduction?
What makes an argument valid?

What is soundness?

Deduction:

This is the type of thought we usually associate with Sherlock Holmes - taking logical premises and applying rational thought to draw out necessary conclusions. For example:

1) Every house in my neighborhood is white.    [ A logical premise, but kind of bleak. ]

2) My house is in my neighborhood.                 [  Makes a good amount of sense. ]

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3) My house is white.                                      [If we believe the first two, we are committed to this one.]

A more Holmesian example of deduction:

1) A man is killed from a blow to the head.
2) His skull has been shattered, which would cause profuse bleeding. 

3) The crime scene had very little blood.
4) The crime scene has not been altered in any way following the mans' death.
5) If 1-4 is true, then the man was killed elsewhere.

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6) The man was killed elsewhere, then must have been placed at the scene later.

As long as your premises are true, and your conclusion follows from the premises (we'll get there), then your deductions (the conclusions you arrive at) can be said to be 100% true. The reason we associate this type of thinking with Holmes is because... well... he's almost never wrong.

Valid v. Invalid:

So why is Holmes right all the time? It's due in large part to the fact that his arguments are always what logicians would call valid. A valid argument is one that is constructed in such a way that if the premises are true, then the conclusion HAS TO BE TRUE. In other words, there is no way for the premises to be true and the conclusion false. If this is the case, we say that the conclusion follows from the premises.

Makes sense, right? But there's another aspect of this that we're missing:

Soundness:

So let's take the argument from earlier about my house:

1) Every house in my neighborhood is white. 

2) My house is in my neighborhood.              

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3) My house is white.                                      

It's definitely valid, right? But hold on. Doesn't it seem silly that every house in my neighborhood is white? What if it wasn't true? Would my conclusion still be true? Not necessarily.

If not all of my premises were true, my argument would lose it's soundness. An argument is sound if it is valid (see above) AND all of the premises are true. So if all of the houses in my neighborhood really ARE white, then my argument is valid and sound.

Note to Future Detectives:  KNOW THESE THINGS!!! Your conclusions are only good if your arguments have both validity and soundness. Otherwise, they are worth next to nothing. In fact, a lot of the comedy in the Holmes adventures stems from the fact that the Scotland Yard Detectives' arguments are often either invalid or unsound, which Sherlock demonstrates rather easily either through providing counterexamples or by presenting a correct argument that ACTUALLY explains what happened.

continued in Part 2...