https://ojs.victoria.ac.nz/ajl <p><span lang="EN-US">The Australasian Journal of Logic is an online, open access journal run under the auspices of the Australasian Association of Logic and Victoria University.</span></p> Victoria University of Wellington en-US The Australasian Journal of Logic 1448-5052 https://ojs.victoria.ac.nz/ajl/article/view/8292 <p>This is the culmination of a discussion on Berry's Paradox with Graham Priest, over an extended period from 1983 to 2019, the central point being whether the Paradox can be avoided or not by removal of the Law of Excluded Middle (LEM). Priest is of the view that a form of the Paradox can be derived without the LEM, whilst Brady disputes this. We start by conceptualizing negation in the logic MC of meaning containment and introduce the LEM as part of the classical recapture. We then examine the usage of the LEM in some other paradoxes and see that it is applied to cases of self-reference. In relation to Priest's [2019] paper, we go on to find a similar use of the LEM in Priest's derivation of Berry's Paradox. However, it is found to be deeper and trickier than other paradoxes, requiring a special effort to untangle the relationships between the LEM, self-reference and meta-theoretic influence. We then examine Brady's previous formalization of Berry's Paradox, considering Brady's most recent view of restricted quantification and his recursive account of the least number satisfying a property. We show that neither of these methods can be used to formalize the paradox. We also examine the inductive shapes for the Substitution of Identity Rule for intensional and extensional identities, while conceding Priest's point, made in [2019], that his shape of Substitution of Identity is not relevant to his proof of Berry's Paradox.</p> Ross Brady Copyright (c) 2024 Ross Brady 2024-06-24 2024-06-24 21 3 100 122 10.26686/ajl.v21i3.8292 https://ojs.victoria.ac.nz/ajl/article/view/7409 <p>This paper presents two possibility results and one impossibility result about a situation with three voters under a pairwise majoritarian aggregation function voting on a countably infi nite number of candidates. First, from individual orders with no maximal or minimal element, it is possible to generate an aggregate order with a maximal or minimal element. Second, from dense individual orders, it is possible to generate a discrete aggregate order. Finally, I show that, from discrete orders with a particular property, namely the finite-distance property, it is not possible to generate a dense aggregate order.</p> Matthew Rachar Copyright (c) 2024 Matthew 2024-06-24 2024-06-24 21 3 123 140 10.26686/ajl.v21i3.7409