Argument Schemes

AGORA provides four logical argument schemes: modus ponens, modus tollens, disjunctive syllogism, and not-all syllogism. Since you have to select one of them in the process of argument construction, this page shows you with examples how each of them looks like. The name of the scheme you selected is always indicated underneath the “therefore.” When you click there, you can change the scheme.

Further down this page you will find a table that shows you which argument scheme should be used in which situation. Additionally, there is also a section on “How non-deductive argument schemes can be transformed into logical ones.”

A. Modus ponens


The modus ponens above is formulated with “if-then” in the enabler. You can also select another language form, they are all logically equivalent. Select the one that fits best. Below is a modus ponens argument that is formulated with “only if.”

B. Modus tollens

Again, the argument can be formulated with different language forms. Below is an example with “only if.”

C. Disjunctive syllogism


 

D. Not-all syllogism


 

Which argument scheme is best for which situation?

As you can see in the pictures above, the four argument schemes can be distinguished with regard to the question whether the conclusion and/or the reason is either negated (“it is not the case that ...”) or affirmed. When you reconstruct an argument in AGORA from a text, you should first analyze reason and conclusion in the text according to the following table. You can find the correct scheme for each situation in the right column.

Conclusion

Reason

Argument scheme

Affirmed

Affirmed

Modus ponens

Negated

Negated

Modus tollens

Affirmed

Negated

Disjunctive Syllogism

Negated

Affirmed

Not-all syllogism

 

How non-deductive argument schemes can be transformed into logical ones

Logically valid arguments form only a very small subset of all possible arguments. If we would try to provide a complete overview of all forms of arguments people are using in all areas of life, it would hardly be a good idea to focus only on some argument schemes of propositional logic.

However, it is well-known that almost all non-deductive arguments can be transformed into deductive ones by introducing an additional premise that simply states that the set of all reasons implies the conclusion. For example, the inductive argument: “All the ravens that I saw in the past were black, therefore all ravens are black” can be transformed into a modus ponens argument by adding the premise: “If all ravens I saw in the past were black, then all ravens are black.” Of course, this additional premise is not really convincing and should be criticized. But that is exactly the point in the AGORA approach: Making those premises visible that would make conclusions necessarily true if all the premises were true helps you to understand that most arguments should be revised to make them more plausible. Thus, you should see that the argument above could be improved, for example, by saying:

  • All the ravens that I saw in the past were black
  • If all ravens I saw in the past were black, then probably all ravens are black
  • Therefore, probably all ravens are black

This means that even though the means of  expression are limited in the AGORA system by the fact that only four argument schemes are available, the overall expressiveness of the system is not much smaller than in other systems. The difference is only that most other systems aim at representing all sorts of everyday arguments directly, whereas the AGORA system challenges you to participate in a reflective dialogue. After you specify reason(s) and claim and selects an appropriate deductively valid argument scheme, the system creates automatically the missing premise. This premise again should stimulate a reflection on its acceptability and about possible objections, which again should lead to a revision of the formulations used as reason and claim. For an example of this dialogical approach in which the proponent of an argument always reacts to objections of an opponent, see the “Tweety can fly” example here.