In this doctoral dissertation, I tackle the issues of the conditions for the possibility of unrestricted quantification and of absolute generality. The text is framed as follows. The first chapter is devoted to reviewing what I call the standard semantics of quantifiers, within the realm of both model and set theories. In such semantics, the idea is, quantificational domains are conceived as sets. It will become clear along the way that, given this construal of quantificational domains, a formal treatment of unrestricted quantification faces insurmountable obstacles. The second chapter focuses on what I take to be the most relevant arguments against unrestricted quantification as well as against our ability to formally deal with so-called absolute generality. Some of them are based on results obtained by Russell and Cantor within set theory – the notorious Russell s paradox and Cantor s theorem. Analogously, in chapter three I review a number of grouped-into-strategic-lines arguments put forward to save unrestricted quantification against its critics. I also elaborate on the metaphysical aspects of the debate and its connections with infinite regress arguments. Lastly, in the fourth chapter I outline an alternative proposal based on paraconsistent set theory to deal with unrestricted quantification. On this approach, the contradictions found in standard semantics are admitted, yet in a controlled way, thus turning absolute quantificational domains available. The proposal is, basically, to allow the existence of inconsistent, yet deductively not trivial formal systems. The present work is broadly guided by the following set of claims: (i) there is a strong correlation between the obstacles set by standard semantics to unrestricted quantification and the structure of infinite regress arguments; (ii) absolute generality is a phenomenon that imposes itself upon our most intuitive conceptions of reality; accordingly, the limitations suffered by our formal languages ought not to lead us to bring such generality into disrepute; (iii) one must choose between adopting classical logic and renouncing to appeal to absolute generality or sticking to our most basic intuitions as described in (ii) and make room for a non-classical treatment of the issue; (iv) we have, after all, good reasons to venture into the landscapes described by the non-classical systems.