A complete argument is as argument that is stated or presented such that:
1. One can see all the propositions in the argument.
2. All the propositions in the argument are numbered.
3. It is explained what kind of purpose all the propositions have. (Premise, inference or assumption.)
4. All inferences are stated, it is stated form where they follow and what kind of inference it is.
Here is an example argument:
| n | Proposition | Explanation |
| 1 | The earth exists. | Premise. |
| 2 | If the earth exists, then the moon exists. | Premise. |
| 3 | If the moon exists, then the moon is round. | Premise. |
| 4 | If the earth exists, then the moon is round. | From 2, 3, HS |
| 5 | The moon is round. | From 1, 4, MP. |
I find that it is a very good idea to use tables to present arguments with.
Complete formal argument
A complete formal argument is an argument that is a complete argument where the symbols representing the propositions or predicates are stated and the definitions of these symbols or predicates is stated (if needed).
Here is an example argument created by extending the above argument:
| n | Proposition | Symbol | Explanation |
| 1 | The earth exists. | P | Premise. |
| 2 | If the earth exists, then the moon exists. | P→Q | Premise. |
| 3 | If the moon exists, then the moon is round. | Q→R | Premise. |
| 4 | If the earth exists, then the moon is round. | P→R | From 2, 3, HS |
| 5 | The moon is round. | R | From 1, 4, MP. |
Note that it is not necessary to state the definitions of the propositions or predicates. If the argument is complicated and uses predicate logic, then it is wise to define the terms before presenting the propositions.