An argument consists of premises and a conclusion. Argumentation can consist of chained, supportive arguments. Argumentation contains three places wherein mistakes, tricks or fallacies live. The diagram to the right show the first two:

**Within a premises**: these are called “informal fallacies”**In the logic which connects the premises to the conclusion:**these are called “formal fallacies”.

For a fantastic hyperlinked diagram of formal and informal fallacies, see “The Fallacy Files“.

Even if an argument does not have any informal or formal fallacies, a listener could rightfully demand “proof” (or an argument) for any of the premises which they feel is unsupported. This is fine and good, but unless eventually the arguer and the listener come to some agreed premises, the argument chain could go on forever. This dilemma is called “The Skeptical Regress”. See the diagram below.

Like formal and informal fallacies, the Skeptical Regress and it’s fallacies have been known from antiquity. The first false solution to the dilemma (a fallacy) is to just accept the infinite regress. The second Regress Fallacy is called a circular argument. See below:

The circular argument turns the infinite chain upon itself — like an Ourobus. This method brings back premises to be wrongly dependent upon the original argument’s conclusion.

In summary, here is my classification of argument fallacies:

- Informal Fallacies
- Formal Fallacies
- Regress Fallacies
- Infinite Regress
- Circular Argument

**Question to Readers**: Any corrections or suggestions?

Note to readers: As I tried to sleep last night, I pondered my original post and did not like my explanations or diagrams. I have redone them and significantly changed this post hoping it an improvement.

If the universe is closed, then ultimately it is all circular, (or maybe fractal.)

Formal logic is inadequate to any task but showing internal consistency given a set of axioms. But as soon as the axioms themselves are attempted to be used to verify what is built upon them we get into the problem of Godel’s Incompleteness theorem, (which states that for any non-trivial system, the axioms cannot be proven, and hence the proof of the system is incomplete, which leads to a need for a meta-system to prove the system, but the meta-system suffers from the same deficiency with respect to its axioms, and so on, and so on.)

@ Nicholas:Indeed — I actually did a whole graduate-level philosophy course in symbolic logic which was focused only on Gödel’s Incompleteness Theorem. The final test was being able to reproduce the proof.