Sherlock holmes and the art of deduction

So-called tense logic can conclude from a premise like РІР‚Сљit is currently the case that oranges are orangeРІР‚Сњ that РІР‚Сљat every point in the future, there was a point in the past when oranges were orange.РІР‚Сњ Other versions of deductive logic include modal logic, which draws conclusions based on necessity and possibility, and doxastic logic, which attempts to deductively describe the relationships between our attitudes and beliefs. For instance, there are versions of logic that can derive conclusions based on time. Over the last 150 years, logicians have developed extremely complex versions of deductive logic that can deductively derive conclusions in all sorts of scenarios. The above examples use an extremely simplified version of deductive logic. This is not the statement a detective might make: РІР‚Сљif the person we are looking for, Sherlock Holmes, is a man, then he will surely be wearing a dearstalker hat.РІР‚Сњ Rather, because the premises stipulate that Holmes is a man and wears a dearstalker, the if-then statement is just a strange way of putting what we already know.Р”ВonРІР‚в„ўt assume from the examples that deduction is weak and always boring. With just a little work we could prove that РІР‚Сљif Sherlock Holmes is a man, then he wears a dearstalker.РІР‚Сњ This might at first look like an interesting conclusion, but it really says nothing. For instance, deductionРІР‚в„ўs reach is quite limited from the premises that Sherlock Holmes is a smart man, smokes a pipe, and wears a dearstalker hat. Only so much is necessarily true given a set of premises, and often the possible conclusions are quite uninteresting.

The necessity of deductive conclusions comes at a cost. Deduction tells us that if the world is composed of x and y, and that x and y are connected by z, then a, b, and c, must also be true. Where math deals with numbers of things, deductive logic deals with the arrangement and existence of things. A math problem takes an unsolved equation as its premise and arrives at a conclusion that must be true. It might be useful to think of deductive logic like math. The statement РІР‚СљSherlock is a man or РІР‚Сњ will always be true given the premises because it will always be the case that Sherlock is a man.

This often strikes people as odd, but if we take Sherlock HolmesРІР‚в„ў manhood as a given, then we can conclude that he is a man or anything else. If we take as our premise that Sherlock Holmes is a man, then we know with absolute certainty that either Sherlock Holmes is a man or he is a cucumber. Many philosophers like to say deduction is РІР‚Сљnecessarily truth preserving.РІР‚Сњ That is, given the premises, the conclusion must absolutely be true. But to come to a satisfactory answer, we have to start at the beginning: what is deductive logic?Р”Вeductive logic is a very careful method of drawing conclusions from premises. Over the next two weeks, IРІР‚в„ўm going to take a look at different types of logic and explore what Sir Arthur Conan Doyle got wrong about deductive logic. Whether or not Sherlock Holmes masterfully uses deduction to solve crimes requires a nuanced answer-one which will take a couple of posts to tackle. Premise 2: If Sherlock Holmes was wrong to think his conclusions were arrived at by deduction, then Sherlock Holmes does not know what deduction is.Р”В¬onclusion: Sherlock Holmes does not know what deduction is. Premise 1: Sherlock Holmes was wrong to think his conclusions were arrived at by deduction.

Sherlock holmes and the art of deduction