Logic is the study of the principles of correct reasoning associated with the formation and analysis of arguments.

In groups use your powers or reasoning and logic to solve the answer to the following puzzles.

LOGIC In Star Trek when Spock is referred to as being ‘logical’ it is usually taken to mean that he is without emotion. Sherlock Holmes is considered similarly ‘cold’. Why is this? And what is being ‘logical’ anyway?

Introduction – The master of deduction  In one mystery concerning the theft of an expensive racehorse, a police officer asks Sherlock Holmes if any aspect of the crime strikes him as significant. ‘Yes’, he says ‘the curious incident of the dog in the night time’. The dog did nothing in the night time’ says the hapless police officer. ‘That was the curious incident’, replies Holmes.  How has Holmes deduced the solution to the crime?

Solution  The solution to the crime hinges on the fact that the watchdog guarding the horse did not bark in the night, and from that Holmes deduces that the thief must have been known to the dog. We can lay out Holmes reasoning formally as follows:  Watchdogs bark at strangers.  The watchdog did not bark at the thief.  Therefore the thief was not a stranger.

Argument We argue in different ways: we quarrel, debate or persuade. In a philosophical sense argument is used to persuade others of your point of view. Although quarrels may not have rules, persuasion arguments do. There are 2 categories of argument: Deductive and Inductive. A deductive argument provides conclusive support for its conclusion as long as it is valid, an inductive argument provides probable support for its conclusion providing it supplies strong evidence.

1. Deductive argument is a method of ascertaining validity. A properly constructed deductive argument is valid so if all its premises are true then its conclusion must be true.

Aristotle ( BC) is credited with inventing deductive arguments as a means to drawing conclusions. By looking at his own example we can see the form deductive arguments take: If the question were asked ‘Is Socrates mortal?’ then the following deductive argument could be applied. All men are mortal (1 st premise) Socrates is a man (2 nd premise) Socrates is mortal (conclusion) The conclusion follows from the premise. A valid deductive argument will always lead to a valid conclusion but the truth of the conclusion relies on the truth of the premises.

Cartman gives us another example. If the boys combine their lost teeth, then they’ll get money from the Tooth Fairy (premise 1) If they get money from the Tooth Fairy, then they can buy a PS3 (premise 2) Hence, if the boys combine their lost teeth then they can buy a PS3 (conclusion)

2. Inductive argument is a method of ascertaining the degree of certainty the premises confer on the conclusion. A properly constructed inductive argument has strength in that if all the premises are true then the conclusion is probably true.

How sure are you that some day you will die? What evidence do you have for your belief? With reference to the above example, my belief that all human beings are mortal is based on the observation that in history, every human being I know of has eventually died, and I have never heard of a human being who didn’t die. Therefore, I can say with confidence that ‘all observed human beings have died’. Our inductive reasoning can therefore lead us to the conclusion that ‘all human beings are mortal’.

South Park offers another example: Because in the past when we mentioned towel related things, Towelie has always showed up. (premise 1) And because we will mention something towel related now. (premise 2) We can conclude that Towelie will show up. (conclusion)

Or, according to Cartman If you do drugs, then you are a hippie (premise 1) If you are a hippie, then you suck (premise 2) If you suck, then that’s bad (premise 3) So, if you do drugs, then thats bad (conclusion)

In groups  Come up with 2 examples of both an inductive and deductive argument

Final Thoughts As students of philosophy you will need to debate and discuss effectively using arguments based on evidence and sound rational thinking. Using well established induced or deduced logic in order to arrive at your truth claims will give far greater weight and importance to your conclusions. On an even more serious note it is through fallacious reasoning or faulty reasoning that many people seem to make poor decisions. In South Park the case is put forward in the episode called Chef Aid where a prominent lawyer successfully applies the Chewbacca defence to prove a point to the jury and acquit the record company of being found guilty of copyright violations of Chefs original song.

This South Park portrayal of absurd reasoning is funny in the cartoon. However its not so funny when we see faulty reasoning at work in the real world. Consider the following conclusions drawn. All Jews are vermin Vermin needs to be destroyed All Jews need to be destroyed OR All terrorists are evil All terrorists are Muslim All Muslims are evil

OR All Americans are immoral Immorality is punishable by death I will sacrifice my life to bring death to Americans. Logic is the study of the principles of correct reasoning associated with the formation and analysis of arguments. The way in which we reason affects the beliefs we have, which ultimately affects the way in which we behave and live our lives. Therefore, it is vitally important to reason correctly.