About

This page explains the term “complete argument” and the similar term “complete formal argument” and my motivation creating the terms.

Motivation

My motivation for creating these terms and requesting that people present their important arguments in such a fashion is that:

First, avoid unclarity about what their argument really is. If one thinks that an argument is a certain way and it isn't, then one's counter arguments toward the argument are committing the straw man fallacy.

Second, people that present their arguments unclearly are also highly likely to have an unclear idea about what their argument is. Clarity of language and clarity of mind very often comes together (hence the name of my blogs).

Third, examining arguments that are presented clearly makes it easier to spot fallacies (formal and informal) in the argument. When dealing with very complex arguments, intuition is not good enough to verify that the argument has a valid form, not even a logician's intuition. One needs to state the form and verity it. A good way to verify an argument form is using Proof Tools.

The choice of the name was based on the meaning of "complete" being "with everything included" (Wiktionary). "everything included" referring to not having any missing premises.

The term “complete argument”

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 noted what kind of purpose all the propositions have. (Premise, inference or assumption.)

4. All inferences are stated, it is stated form what they follow and what kind of inference it is.

Here is an example argument:

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]

Thus, 4. If the earth exists, then the moon is round. [From 2, 3, HS]

Thus, 5. The moon is round. [From 1, 4, MP]

The term “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:

1. The earth exists. [premise]

P

2. If the earth exists, then the moon exists. [premise]

P→Q

3. If the moon exists, then the moon is round. [premise]

Q→R

Thus, 4. If the earth exists, then the moon is round. [From 2, 3, HS]

⊢ P→R

Thus, 5. The moon is round. [From 1, 4, MP]

⊢ R

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.