Farewell to Suppression-Freedom

Abstract

and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. This paper shows that their suggestions for how to understand it, either as the Anti-Suppression Principle or as the Joint Force Principle, turn out to yield properties strictly weaker than that of variable sharing. A suggestion for how to understand some of their use of the notion of suppression which clearly is not in line with these two mentioned principles is given, and their arguments to the effect that the Anderson and Belnap logics T, E and R are suppressive are shown to be both technically and philosophically wanting. Suppressionfreedom, it is argued, cannot do the job Plumwood and Sylvan intended it to do.

Routes to relevance: Philosophies of relevant logics

“…Once one moves beyond FDE to the full relevant logics, it is not clear that suppression‐freedom is equivalent to sufficiency. Øgaard (2020) provides a natural way of formalizing suppression‐freedom in terms of the two principles 34 Anti‐Suppressive Principle : For every formula A , there are formulas B and C such that ( A ∧ B ) → C is valid but B → C is not. Joint Force Principle : For every formula A , there are formulas B and C such that ( A ∧ B ) → C is valid while neither A → C nor B → C is.…”

Relevance through topical unconnectedness

“…Plumwood's formal suppression-principles-the Anti-Suppression Principle and the Joint Force Principle-were analyzed in [16] where it was shown that these formal principles are in fact properly weaker than the variable sharing property. 1 This paper shows first of all that Plumwood's suppression principles are equivalent to principles motivated by one of Ackermann's motivational spins on his notion of rigorous implication.…”

“…1 This paper shows first of all that Plumwood's suppression principles are equivalent to principles motivated by one of Ackermann's motivational spins on his notion of rigorous implication. Even though the formal suppression principles used in [16] turn out to be too weak to do the job they were thought to do, it could be that tweaking the principles slightly would be sufficient to rectify this. [16] did not explore any such tweaked principles.…”

“…Even though the formal suppression principles used in [16] turn out to be too weak to do the job they were thought to do, it could be that tweaking the principles slightly would be sufficient to rectify this. [16] did not explore any such tweaked principles. This paper shows forth ways of tweaking the Plumwoodian and Ackermannian principles so as to at least deliver on one of Plumwood and Sylvan's promise, namely to deliver the variable sharing property, and variant thereof, as a corollary.…”

Val (Routley) Plumwood: Work in Logic

“…With the resulting technical detail "[light] is cast on, and sometimes solutions delivered for, a number of other linked problems". 15 For example, "paradoxes of commitment", so-called Good Samaritan paradoxes and Robber paradoxes. 16 Other paraconsistent approaches to moral dilemmas soon followed.…”