Modal Qualification and the Speech-Act of Arguing in LNMA: Practical Aspects and a Theoretical Issue

LNMA distinguishes between ‘semantic conditions, determining the correctness of a claim, and pragmatic conditions, determining how far a particular communicative act is a good means for showing something –namely, that a given claim is correct’ (Bermejo-Luque 2011, 40). Semantic conditions are related to the semantic appraisal of argumentation (considered in this paper), pragmatic conditions to the pragmatic appraisal of argumentation.

Other explanations on ontological and epistemic modals can be found in (Bermejo-Luque 2018, p. 22–23), (Bermejo-Luque 2012, p. 10–11) or (Bermejo-Luque 2011, p. 170–176).

(Bermejo-Luque 2011, p. 109) seems to imply that em depends on both om_i and om_r, not only on om_i. However, further on, in the same text and later papers presenting LNMA, she considers that em depends solely on om_i, thus I take this as the actual position defended by LNMA.

In practice, it is not mandatory for those modals to be explicitly employed, or even with the same words. For example, in a legal context, ‘necessary’ can be expressed as ‘proven beyond reasonable doubt’. In a discussion among mathematicians, ‘necessary’ will be used differently, and with other alternative expressions as ‘therefore, it is proven that’.

For the sake of simplicity, I do not consider in this example the negation of modals (e.g. ‘it is not necessary’ or ‘it is not possible’), which can produce more modals (e.g. ‘it is not possible’ as ‘impossible’).

Function θ could be also defined as θ(em, om c) = om’ c. I omit the propositional content for the sake of simplicity.

At first glance, modal qualification in LNMA can look like ‘unnatural’: distinction between ontological and epistemic modals does not seem to fit into actual speakers’ intuitions. The existence of θ ‘smoothens’ the translation between LNMA and ordinary language, but at the cost of raising doubts about modal qualification, as discussed below.

In this particular example, θ returns the weaker modal (ontological or epistemic) from the input. I think it makes sense in some well-known contexts. E.g., let us consider Golbach’s conjecture: its modern version asserts that (it is necessary that) ‘every even integer greater than 2 can be written as the sum of two primes.’ It has been proved to be true for integers up to 4 × 10¹⁸. But such a proof just allows us to say that, probably, the conjecture is a necessary truth (there are infinite integers, we just tried with a huge, but finite set). So, we have em = probably and om = necessary (‘probably, it is necessary that…’). The outcome for θ(probably, necessary) will be ‘probable’ (‘It is probable that every even integer…’). Of course, there may be other contexts where θ works differently.

Strictly speaking, a non-bijective function has no inverse function, but the notation θ ⁻¹ is, in this context, useful for a better understanding.

Perhaps only constative speech-acts should be considered here.