List of valid argument forms

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.

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.

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.

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. 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. It is shown below in logical form.

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