Notes

Logic may be defined as the science that evaluates arguments. All of us encounter

arguments in our day-to-day experience. We read them in books and newspapers,

hear them on television, and formulate them when communicating with friends and

associates. The aim of logic is to develop a system of methods and principles that we

may use as criteria for evaluating the arguments of others and as guides in constructing

arguments of our own. Among the benefits to be expected from the study of logic is

an increase in confidence that we are making sense when we criticize the arguments

of others and when we advance arguments of our own.

An argument consists of a sequence of statements. One is the conclusion; the rest are premises. The premises are given as evidence that the conclusion is true. If the conclusion must be true if the premises were true, the argument is valid. A valid argument is sound if its premises are true. Valid arguments result from applying correct rules of reasoning.

An argument, as it occurs in logic, is a group of statements, one or more of which

(the premises) are claimed to provide support for, or reasons to believe, one of the

others (the conclusion). All arguments may be placed in one of two basic groups:

those in which the premises really do support the conclusion and those in which they

do not, even though they are claimed to. The former are said to be good arguments

(at least to that extent), the latter bad arguments. The purpose of logic, as the science

that evaluates arguments, is thus to develop methods and techniques that allow us to

distinguish good arguments from bad.

Common Fallacies of Relevance

Common Fallacies of Evidence

Apriorism: Normally we allow facts to be the test of our principles. When we see what the facts are, we can retain or modify our principles. To start out with principles from the first (a priori) and to use them as the basis for accepting or rejecting facts is to do it the wrong way round. It is to commit the fallacy of apriorism.

"We don't need to look through your telescope, Mr Galileo. We know there cannot be more than seven heavenly bodies"

"Since there are no cats in Tibet, this animal here, with the ears of a cat, the tail of a cat, the fur of a cat and the whiskers of a cat, shows that Tibetan dogs are pretty good actors"

Bifurcation/ False dichotomy: The presentation of only two alternatives where others exist is called the fallacy of bifurcation. Sometimes known as the 'black and white' fallacy, it presents an 'either/or' situation when in reality there is a range of options.

Cum hoc ergo propter hoc: The cum hoc fallacy assumes that events which occur together are causally connected, and leaves no room either for coincidence, or for the operation of an outside factor which separately influences those events.

"A tourist met a Spanish peasant and his wife on a train. They had never seen bananas before, so he offered one to each of them. As the farmer bit into his, the train entered a tunnel. 'Don't eat it,  Carmen,' he shouted, 'They make you blind.' "

Like the post hoc fallacy which links events because they occur consecutively, the cum hoc fallacy links them because they occur simultaneously. It is a fallacy because of its unwarranted assumption that either of the events would not occur without the other one.

Texas Sharpshooter's fallacy:

The Texas sharpshooter fallacy is a logical fallacy in which information that has no relationship is interpreted or manipulated until it appears to have meaning. The name comes from a joke about a Texan who fires some shots at the side of a barn, then paints a target centered on the biggest cluster of hits and claims to be a sharpshooter.

The acclaimed British twentieth-century mathematician J. E. Littlewood defined a miracle as “an event that has special significance when it occurs, but occurs with a probability of one in a million.” He then went on to calculate that people experience miracles at a rate of roughly one per month, which has become known as “Littlewood’s law of miracles.” You can do even better. If you flip a coin 20 times, you will get a sequence of heads and tails. I just did it and got the seemingly unremarkable sequence:

HTTHHTHTTHTTTHHTHTTT

However, each particular sequence of heads and tails has probability ( 1 /2)^20, which is about one in a million. My sequence had 8 heads and 12 tails, which is not that unlikely, but the chance of getting them in exactly this order is still one in a million and I think it bears special significance that I managed to achieve something so highly improbable. Start your morning with a cup of coffee and 20 coin flips, and you can make every day miraculous.

Law of Truly Large Numbers:

he Law of Truly Large Numbers, attributed to Persi Diaconis and Frederick Mosteller, states that with a sample size large enough, any outrageous thing is likely to happen.