# About Logical (Deductive) Validity in AGORA-net

An argument is logically valid if and only if it follows an argument scheme that is logically valid. An argument scheme is logically valid if and only if it is impossible for any argument following this scheme to have true premises and a false conclusion. See, for example, the logically valid argument scheme that is called modus ponens:

- p
- If p, then q
- Therefore, q

In this modus ponens argument the conditional “if p, then q” is understood as being true under all circumstances: whenever the statement “p” is true, the statement “q” is also true. That means, the statement “if p, then q” is understood here as something like a law of nature that explains an event described by q as a necessary consequence of an event described by p. If it happens, by contrast, that “p” is true but “q” false, then—and only in this case—the connected statement “if p, then q” is false. So, if the conditional “if p, then q” and the statement “p” in the modus ponens argument above are supposed to be true under all circumstances, it should be impossible to find any two propositions p and q (that is, complete and well-formed sentences that can be true or false) that would lead to a false conclusion. Take the following example:

- Paul is a rational being.
- If Paul is a rational being, then Paul is responsible for what he did.
- Therefore, Paul is responsible for what he did

It is obvious that the conclusion of this argument must be true if both the premises are true. Since it is impossible to imagine that this would be different for any argument that is structured according to this modus ponens form, we can conclude that the form itself is logically valid and, thus, any argument that follows this form.

### What logical validity means in the AGORA approach

Please note the following important points that are specific for the AGORA approach:

- The “logical” argument mapping that we can perform in the AGORA-net is not the same as “deductive reasoning.” Logical argument mapping is the process of constructing arguments in deductive form, assessing the acceptability of the premises as they need to be formulated to achieve this deductive form, and revising these premises and/or the structure of the argument as long as it takes to construct the best possible argument. A reconstruction of an argument in logical form can show us how its premises would need to look like if the goal were to guarantee the truth of the conclusion. The point is to get the content of the premises right and to formulate them in their strongest possible form.
- According to the philosophical foundation of the AGORA approach none of the premises of an argument needs to be objectively true. “True under all circumstances” means here only that there is someone—the author of these premises—who believes that the premises are true under all circumstances. If you formulate a statement in the AGORA system you indicate by this very act that you believe that this statement is true. This is the reason why in AGORA every statement appears in a text box that names the author (“AU”) of the statement. The author can be held accountable for what he or she writes. This means, at the same time, that all the statements in an AGORA argument map represent only the beliefs and opinions of certain people at a certain time. They do not represent “knowledge” which is—at least in philosophy—considered to be objectively true.
- Since the AGORA system presents only beliefs, the default assumption is that every statement in an AGORA map can be defeated. Whatever is claimed can be defeated by a counter-argument or can at least be questioned.
^{1}That means, whether a claim, a thesis, a position, or a recommendation is justified by an argumentation or not depends solely on the social situation at a certain point in time. If nobody presents a counter-argument against one of the premises on which the truth of a claim depends, then this claim is considered to be provisionally accepted as being true. If, however, one of these premises is defeated, then the claim that was supposed to be justified by these premises stands unjustified and can itself be attacked by objections.^{2 }Thus, an argument map does not demonstrate the truth of a proposition and it does not represent a system of knowledge; it only represents whether a proposition is accepted at a certain point in time by a certain community of deliberators. An AGORA map is a momentary expressions of what those who constructed it think about a position at a certain point in time. - Since every argument can be defeated, the author of an argument will always be challenged to either justify any reason that might be problematic by further arguments, or to revise the formulations used in the argument so that they are easier to defend. (For a discussion of what could be done to improve an argument, see here.)
- The AGORA system uses natural language to formulate logically valid arguments. Usually, logic uses only symbols to represent logical connections like “if-then.” The reason for the formal approach of logic is that precisely defined symbols can be more easily interpreted in the correct way than every-day words like “if-then” which are easily confused with their less precise every-day meaning. Since the logical validity of an argument depends on a very precise definition of these connectors, it is important to note that in AGORA the natural language versions of these words must be understood in a sense that might differ from interpretations that are possible in common language. The logical validity of AGORA maps depends on the precise, logical definitions of the connectors that are used in arguments. How these are defined is discussed here.

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^{1 }In the literature a distinction between “strict modus ponens” and “defeasible modus ponens” has been proposed. In the defeasible form the law-like premise “if p, then q” is often modified by a qualifier such as “usually” or “as a rule,” or there is an additional premise such as “It is not the case that there is an exception to the rule that if P, then Q” (Walton, Reed, & Macagno, 2008, p. 366). However, the same effect can be achieved by establishing theconvention that every statement is only “believed to be true” by someone whose name is connected to this statement. This convention can be justified within a pragmatist framework according to which all empirical knowledge is fallible. If knowledge is fallible (i.e., it can be false), the focus shifts to improving our beliefs in the long run or to justify what we believe we know. Whether a statement used in an argument is indeed true is thus less important than the question whether we can provide a justification for it, and whether our justification gets accepted. As long as nobody cares to defeat the reasons for our claims, they can be accepted as true. This, for us, is the essence of a dialogical and pragmatist approach to argumentation (see also Pinto, 2001).

^{2} Any statement that is justified by a logically valid argument cannot itself be attacked within an AGORA map. The reason for this design decision is that such a statement is necessarily true if all the premises are true, so that the attention of an opponent should be directed to these premises. However, since any statement—even though necessarily true based on a certain argument—can be “framed” from a different point of view, it is possible to attack such a statement in another argument map.

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Pinto, R. C. (2001). Argument, Inference and Dialectic. Collected Papers on Informal Logic. Dordrecht; Boston: Kluwer Academic.

Walton, D. N., Reed, C., & Macagno, F. (2008). Argumentation schemes. Cambridge ; New York: Cambridge University Press.