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As Platt and Brooks (2002) stated "If in dialogic activity the mind undergoes transformation, then the evidence is to be found in the dialogue itself" (p. 374).
This allows us to formulate a notion of linear validity: Linear validity: A formula A is linearly valid iff there is a closed dialogue for P- -A such that the P- -Asitional content of any move has been used (and therefore is bracketed).
There is therefore no genuine dialogue…" (Hurtado 2006, p. 205).
Analyzing the interrelationships between labor law and bioethics through the lenses of their shared implicit contractualism, Cooper and Waldby show, for instance, that "the principle of informed consent has historically evolved in a complex, often overlapping, yet largely undocumented dialogue with contractual consent" (p. 223, original emphasis).
For all the old-fashionedness of its tidy symmetry and Ping-Pong dialogue, the play has the great virtue of respecting what cannot be transmitted by a shapely work of art or even put into words.
There are some systematic tendencies on which greater dialogue and clarity are overdue" (p. 11).
Furthermore, "intrinsic to such an ethos is dialogue and interaction with others" (p. 14).
While a wide variety of approaches may work in different situations, one important lesson from successful experiences in both Europe and elsewhere is the essential nature of broad participation and social dialogue in the process" [58, p. 8].
The reason is that even though one could prove the system sound and complete (i.e., that there is a winning strategy for P in a dialogue for a second order formula A iff A is valid), there is no way to systematically define such a winning strategy.
As we have explained, dialogue and contact differ, a point that Modood (2017) himself acknowledges (p. 6 7).
D(A) denotes the dialogue with, as a thesis, a move of the form P- -A, and we say that D(A) is a dialogue for A. There exists a dialogue for A iff A ∈ FO.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com