List of valid argument forms
Encyclopedia
Valid argument forms are a subset of the many forms of argument that one can use. In order to evaluate these forms, the statements must first be put in 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 what it talked about. The valid argument forms are the ones that are true every time so long as they fit the template for the argument as opposed to the list of invalid argument forms that may appear to be true but are not always the case. 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 is guaranteed. It does not at any point state that the premises are true. This can be proven for any valid argument form in a truth table
which shows that there is no situation in which there are all true premises and a false conclusion.
, 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 the premises.
When modus tollens is used with actually content, it looks like below.
(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.
When put into words it looks like below.
This is a shortened example of what is known as a slippery slope
. A slippery slope is the idea that if one single event happens, it will inevitably cause a whole list of other things to happen with no way to stop them.
(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. It is shown below in logical form.
When used A and B are replaced with real life examples it looks like below.
Disjunctive syllogism takes two options and narrows it down to one.
. 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. When it is written in argument for 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 argument form it looks like below.
Logical form
In logic, the logical form of a sentence or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a 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 what it talked about. The valid argument forms are the ones that are true every time so long as they fit the template for the argument as opposed to the list of invalid argument forms that may appear to be true but are not always the case. 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 is guaranteed. It does not at any point state that the premises are true. This can be proven for any valid argument form in a truth table
Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their...
which shows that there is no situation in which there are all true premises and a false conclusion.
Modus ponens
One valid argument form is known as modus ponensModus ponens
In classical logic, modus ponendo ponens or implication elimination is a valid, simple argument form. It is related to another valid form of argument, modus tollens. Both Modus Ponens and Modus Tollens can be mistakenly used when proving arguments...
, not to be mistaken with modus tollens
Modus tollens
In classical logic, modus tollens has the following argument form:- Formal notation :...
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.
- If A, then B
- A
- Therefore, B
Before being put into logical form the above statement could have been something like below.
- If Joe does not finish his homework, he will not go to class
- Joe did not finish his homework
- Therefore, Joe will not go to class
The first two statements are the premises while the third is the conclusion derived from the premises.
Modus tollens
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.- If A, then B
- Not B
- Therefore, not A.
When modus tollens is used with actually content, it looks like below.
- If the Saints win the Super Bowl, there will be a party in New Orleans that night
- There was no party in New Orleans that night
- Therefore, the Saints did not win the Super Bowl
Hypothetical syllogism
Much like modus ponens and modus tollens, hypothetical syllogismHypothetical syllogism
In logic, a hypothetical syllogism has two uses. In propositional logic it expresses one of the rules of inference, while in the history of logic, it is a short-hand for the theory of consequence.-Propositional logic:...
(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.
- If A, then B
- If B, then C
- Therefore, if A, then C
When put into words it looks like below.
- If it rains today, I will wear my rain jacket
- If I wear my rain jacket, it will be easy for my friends to find me
- Therefore, if it rains today, it will be easy for my friends to find me
This is a shortened example of what is known as a slippery slope
Slippery slope
In debate or rhetoric, a slippery slope is a classic form of argument, arguably an informal fallacy...
. A slippery slope is the idea that if one single event happens, it will inevitably cause a whole list of other things to happen with no way to stop them.
Disjunctive syllogism
Disjunctive syllogismDisjunctive syllogism
A disjunctive syllogism, also known as disjunction-elimination and or-elimination , and historically known as modus tollendo ponens,, is a classically valid, simple argument form:where \vdash represents the logical assertion....
(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. It is shown below in logical form.
- A or B
- Not A
- Therefore, B
When used A and B are replaced with real life examples it looks like below.
- Either you will see Joe in class today or he will oversleep
- You did not see Joe in class today
- Therefore, Joe overslept
Disjunctive syllogism takes two options and narrows it down to one.
Constructive dilemma
Another valid form of argument is known as constructive dilemma or sometimes just dilemmaDilemma
A dilemma |proposition]]") is a problem offering two possibilities, neither of which is practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable...
. 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. When it is written in argument for it looks like below.
- A or B
- If A then C
- If B then D
- Therefore C or D
When content is inserted in place of the letters, it looks like below.
- Bill will either take the stairs or the elevator to his room
- If he takes the stairs, he will be tired when he gets to his room
- If he takes the elevator, he will miss the start of the football game on TV
- Therefore, Bill will either be tired when he gets to his room or he will miss the start of the football game
There is a slightly different version of dilemma that uses negation rather than affirming something known as destructive dilemma
Destructive dilemma
In logic, a destructive dilemma is any logical argument of the following form: P \rightarrow Q R \rightarrow S \neg Q \lor \neg S \vdash \neg P \lor \neg R where \vdash represents the logical assertion.The argument can be read in this way:...
. When put in argument form it looks like below.
- If A then C
- If B then D
- Not A or not B
- Therefore not C or not D