*necessarily*the premises, Toulmin's contributed the

*modal qualifiers*.

**A modal qualifier might turn some sort of fallacies into valid arguments**. That's why they're so important. But that's not it. Aristotle leaves little margin for arguments less than perfect, or premises that carry some uncertainty whereas modal qualifiers weight the quality of the assertion. So what are the "modal qualifiers"? (please refer to my previous post on Toulmin's model below):

"The modal qualifier specifies the degree of certainty, the force of the assertion, the terms and conditions that limit it (the assertion). It is the concession granted to others....the certainty with which the arguments are held varies in degree and force, that is why conclusions are held probable, possible or presumable. The function of a modal qualifier is to establish the likelihood...They reveal the strength of the thesis...establishes the certainty of the author regarding the generality of his assertion." (Rodríguez Bello, 2004)The same author goes on to establish how the modal qualifiers work, namely:

1)

**Adverb**that modify the verb

2)

**Adjective**that modify the substantive

3) The

**mood**of the verb

In a fascinating paper, Inglis et al. (2007), explore the mathematical argumentation of some talented mathematicians, applying the Toulmin model, and specifically the use of modal qualifiers. They argue that: there are at least 3 warrant types. The first two of the listed below

*reduce*the uncertainty of the initial assertions while the last one, actually

*removes*the uncertainty.

1)

**Inductive Warrant**

Here a person works few examples of a particular problem to ascertain the degree of truth assigned to a conjecture. In other words, "a 'crucial experiment' [is worked]... to persuade himself of a statement's probable truth". This approach departs from the particular and makes assertions about the general, i.e. induction. However, it must ineluctably be accompanied/moderated by a modal qualifier since it's not possible to reach a perfect certainty with this type of reasoning. The strength of this warrant is in reducing the uncertainty and clearing the way to keep on a particular argumentative track.

2)

**Structural-Intuitive Warrant**

This warrant relies in the mental structure to provide intuitive insights into a problem. It shares a portion of induction, and therefore, must accompanied also by modal qualifiers. Consequently, this warrant also aims at reducing and not exhaustively proving an assertion. It "...acts to reduce the uncertainty sufficiently to continue the argument in the given direction".

3)

**Deductive Warrant**

This proof scheme departs from axioms, or solid ground, to attain truth without any rebuttal. Unlike the previous schemes, this one aims at

*removing*uncertainty. The modal qualifiers here express total confidence in the warrant, provided it is flawless.

Thus the use of appropriate modal qualifiers furnish the warrant type with the appropriate degree of certainty that it was intended to have.

**References:**

- Rodríguez Bello, L.I. (2004) "El Modelo argumentativo de Toulmin en la escritura de artículos de investigación educativa" [online].
*Revista Digital Universitaria*. 01/31/2004, <http://www.revista.unam.mx/vol.5/num1/art2/art2.htm> [Retrieved: 02/01/2004]. - Pinto, R.C. (2007). On understanding ‘probably’ and other modal qualifiers. In H.V. Hansen, et. al. (Eds.),
*Dissensus and the Search for Common Ground*, CD-ROM (pp. 1-10). Windsor, ON: OSSA. - Inglis, M., Mejia-Ramos, J.P., Simpson, A., (2007) Modelling mathematical argumentation: the importance of qualification.
*Educ Stud Math*(2007) 66:3–21.

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