In today's article we will explore List of valid argument forms, a topic that has been the subject of interest in different areas and that has sparked debates and reflections in different areas. List of valid argument forms has captured the attention of experts and the general public, generating endless opinions and perspectives around its relevance and impact. Throughout this article, we will examine different approaches and opinions on List of valid argument forms, exploring its importance, its evolution over time and its influence on various aspects of society. Join us on this journey through the world of List of valid argument forms and discover the multiple facets and possible interpretations that this theme presents.
Of the many and varied argument forms that can possibly be constructed, only very few are valid argument forms. In order to evaluate these forms, statements are put into logical form. Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its subject matter.[1]
Being a valid argument does not necessarily mean the conclusion will be true. It is valid because if the premises are true, then the conclusion has to be true. This can be proven for any valid argument form using a truth table which shows that there is no situation in which there are all true premises and a false conclusion.[2]
In syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition. Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.
| Figure 1 | Figure 2 | Figure 3 | Figure 4 |
|---|---|---|---|
| AAA EAE AII EIO |
AEE EAE EIO AOO |
AII IAI OAO EIO |
AEE IAI EIO |
| Figure 1 | Figure 2 | Figure 3 | Figure 4 | Required condition |
|---|---|---|---|---|
| AAI EAO |
AEO EAO |
AEO | Minor term exists | |
| AAI EAO |
EAO | Middle term exists | ||
| AAI | Major term exists |
The following is a list of some common valid argument forms in propositional logic. It is nowhere near exhaustive, and gives only a few examples of the better known valid argument forms.
One valid argument form is known as modus ponens, not to be mistaken with modus tollens, which is another valid argument form that has a like-sounding name and structure. Modus ponens (sometimes abbreviated as MP) says that if one thing is true, then another will be. It then states that the first is true. The conclusion is that the second thing is true.[3] It is shown below in logical form.
Before being put into logical form the above statement could have been something like below.
The first two statements are the premises while the third is the conclusion derived from them.
Another form of argument is known as modus tollens (commonly abbreviated MT). In this form, you start with the same first premise as with modus ponens. However, the second part of the premise is denied, leading to the conclusion that the first part of the premise should be denied as well. It is shown below in logical form.
When modus tollens is used with actual content, it looks like below.
Much like modus ponens and modus tollens, hypothetical syllogism (sometimes abbreviated as HS) contains two premises and a conclusion. It is, however, slightly more complicated than the first two. In short, it states that if one thing happens, another will as well. If that second thing happens, a third will follow it. Therefore, if the first thing happens, it is inevitable that the third will too.[3] It is shown below in logical form.
When put into words it looks like below.
Disjunctive syllogism (sometimes abbreviated DS) has one of the same characteristics as modus tollens in that it contains a premise, then in a second premise it denies a statement, leading to the conclusion. In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true.[3] It is shown below in logical form.
When A and B are replaced with real life examples it looks like below.
Disjunctive syllogism takes two options and narrows it down to one.
Another valid form of argument is known as constructive dilemma or sometimes just 'dilemma'. It does not leave the user with one statement alone at the end of the argument, instead, it gives an option of two different statements. The first premise gives an option of two different statements. Then it states that if the first one happens, there will be a particular outcome and if the second happens, there will be a separate outcome. The conclusion is that either the first outcome or the second outcome will happen. The criticism with this form is that it does not give a definitive conclusion; just a statement of possibilities.[3] When it is written in argument form it looks like below.
When content is inserted in place of the letters, it looks like below.
There is a slightly different version of dilemma that uses negation rather than affirming something known as destructive dilemma. When put in argumentative form it looks like below.