7/31/08

The very first lesson that we have a right to demand that logic shall teach us is, how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. To know what we think, to be masters of our own meaning, will make a solid foundation for great and weighty thought.[CS Peirce,How to make our ideas clear]

Why do logic? So that you can reason properly and evaluate your own reasoning and that of others. (There are plenty of errors in reasoning: such errors are often known as 'fallacies'.)

- Fallacies [This is good, unfortunately they try to bury you in pop-ups and advertising.]
Let me quote from them

"Description of Fallacies

In order to understand what a fallacy is, one must understand what an argument is. Very briefly, an argument consists of one or more premises and one conclusion. A premise is a statement (a sentence that is either true or false) that is offered in support of the claim being made, which is the conclusion (which is also a sentence that is either true or false).

There are two main types of arguments: deductive and inductive. A deductive argument is an argument such that the premises provide (or appear to provide) complete support for the conclusion. An inductive argument is an argument such that the premises provide (or appear to provide) some degree of support (but less than complete support) for the conclusion. If the premises actually provide the required degree of support for the conclusion, then the argument is a good one. A good deductive argument is known as a valid argument and is such that if all its premises are true, then its conclusion must be true. If all the argument is valid and actually has all true premises, then it is known as a sound argument. If it is invalid or has one or more false premises, it will be unsound. A good inductive argument is known as a strong (or "cogent") inductive argument. It is such that if the premises are true, the conclusion is likely to be true.

A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an "argument" in which the premises given for the conclusion do not provide the needed degree of support. A deductive fallacy is a deductive argument that is invalid (it is such that it could have all true premises and still have a false conclusion). An inductive fallacy is less formal than a deductive fallacy. They are simply "arguments" which appear to be inductive arguments, but the premises do not provided enough support for the conclusion. In such cases, even if the premises were true, the conclusion would not be more likely to be true."

- The Atheism Web Logic and Fallacies

Logic is foundational in philosophy, mathematics, computer science and most other academic disciplines.

### First-order logic

The logic you are taught in this course is known as first-order logic (and you will be taught a considerable proportion of it). A case can be made that it is the main, or the one true, logic. Sowa writes:

Among all the varieties of logic, classical first-order logic has a priviledged status. It has enough expressive power to define all of mathematics, every digital computer that has ever been built, and the semantics of every version of logic including itself. Fuzzy logic, modal logic, neural networks, and even higher-order logic can be defined in [first-order logic]....

Besides expressive power, first-order logic has the best-defined, least problematic model theory and proof theory, and it can be defined in terms of a bare minimum of primitives....

Since first-order logic has such great power, many philosophers and logicians such as Quine have argued strongly that classical [first-order logic] is in some sense the "one true logic" and that the other versions are redundant, unnecessary, or ill-conceived. [Sowa [2000]

Knowledge Representationp.41]