Ways Modality Could Be: Revised and Expanded

My article "Ways Modality Could Be: Revised and Expanded" is now up on Scholardarity.

Here's an excerpt:

1. Introduction

            In this paper I introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is modeled in terms of a space of possible worlds—a set of worlds structured by an accessibility relation, i.e., a relation of relative possibility—each world representing a way that the entire universe could have been. A second-order modality would be modeled in terms of a space of spaces of (first-order) possible worlds, each space representing a way that (first-order) possible worlds could have been. And just as there is a unique actual world which represents the way that things actually are, there is a unique actual space which represents the way that first-order modality actually is.

            One might wonder what the accessibility relation itself is like. Presumably, if it is logical or metaphysical modality that is being dealt with, it is reflexive; but is it also symmetric, or transitive? Especially in the case of metaphysical modality, the answer is not clear. And whichever of these properties it may or may not have, could that itself have been different? Could at least some rival modal logics represent different ways that first-order modality could have been?

            To be clear, the idea behind my proposal is not just that some things which are possible or necessary might not have been so at the first order, as determined by the actual accessibility relation, but also that the actual accessibility relation, and hence the nature or structure of actual modality, could have been different at some higher order of modality. Even if the accessibility relation is actually both symmetric and transitive, perhaps it could (second-order) have been otherwise: There is a (second-order) possible space of worlds in which it is different, where it fails to be symmetric, or transitive. We must, therefore, introduce the notion of a higher-order accessibility relation, one that in this case relates spaces of first-order worlds. The question then arises as to whether that relation is symmetric, or transitive. We can then consider third-order modalities, spaces of spaces of spaces of possible worlds, where the second-order accessibility relation differs from how it actually is. I can see no reason why there should be a limit to this hierarchy of higher-order modalities, any more than I can see a reason why there should be a limit to the hierarchy of higher-order properties. There will thus be an infinity of orders, one for each positive integer, and each order will have an accessibility relation of its own. To keep things as clear as possible, a space of first-order points (i.e., of possible worlds) shall be called a galaxy, a space of second-order points, a universe, and a space of any higher order, a cosmos. However, to keep things as simple as possible, in what follows I will deal with but a single cosmos at a time, and hence will not deal with modalities higher than the third order.

            The accessibility relation is not the only thing that might be thought to vary between spaces of worlds: Perhaps the contents of the spaces can vary as well. While I presume that the contents of the worlds themselves remain constant—it makes doubtful sense to suppose that in one space some entity e exists in a world w and in another space e doesn’t exist in that same world w—we may suppose that different spaces may differ as to which worlds they contain, just as different worlds may differ as to which objects they contain. Thus we might have a higher-order analogue of a variable-domain modal logic. There seem, then, to be three ways in which spaces can differ: First, as to the properties of the accessibility relation; second, as to which worlds the relation relates; and third, as to which worlds or spaces are parts of their domains.

            The paper will be structured as follows. In Section 2 I provide some reasons why one might want to pursue this kind of project in the first place. In Section 3 I outline the syntax and semantics of my proposed logic. Section 4 covers semantic tableaux for this system; and after giving the rules for their construction, I construct a few of them myself to establish some logical consequences of the system and give the reader a feel for how it works. In Section 5 I outline a potential application of my framework to the metalogic of modal logics. In Sections 6, 7 and 8 I explore some of  its potential philosophical implications for areas besides logic, namely the philosophy of language; metaphysics, including the metaphysics of modality, the philosophy of time, and laws of nature; and finally the philosophy of religion, before concluding the paper in Section 9.

Peter Krey's Doctoral Dissertation "Sword of the Spirit, Sword of Iron", is now available at Scholardarity

Sword of the Spirit, Sword of Iron

Peter Krey

Go here to purchase:  http://www.scholardarity.com/?page_id=2641

Abstract:

This dissertation is a pamphlet investigation dealing with Martin Luther’s ideology and theology of the Word. It studies Luther as a pamphlet writer, whose popular sermon pamphlets addressed the laity with affective, performative language. His “preaching in print” greatly extended the scope of his spontaneous reforming movement. As a self-representation of Luther, this investigation is a prerequisite for his reception. By number of editions and language, this investigation ranks the popularity of almost 70 of Luther’s publications from 1517-1525.This dissertation contains two parts, a handbook on his pamphlets and a thematic section containing the argument. Part One, containing detailed bibliographical research for 32 of these pamphlets, and for his longer works, Babylonian Captivity of the Church, and for Bondage of the Will, is a helpful handbook for their future study.Part Two, the thematic section, deals with the interrelationship of the four themes from the title: Word of God, Scripture, Gospel, and Law, tracing these themes through the thirty most often published pamphlets. Four pamphlets from the year 1520 receive systematic analysis: “Sermon on the Ban,” i.e., about excommunication; On Good Works, and their spontaneity; “The New Testament, i.e., the Holy Mass;” and “Freedom of a Christian Person,” the popular version, which is mostly unknown among English readers. I argue that Luther carved out an inward realm of Christian freedom that promoted a sense of self and a sense of social agency which stressed spontaneity and freedom against what Luther perceived to be a juridical ethos of the church of his day. [Let alone a juridical ethos, I discovered that he was up against two ecclesiastical courts under the canon law.] Because of the ideological nature of propaganda pamphlets, this ethos could not be connected with the old archdeaconal and episcopal courts, the temporal jurisdiction of prince-bishops, and papal legislation being challenged by temporal authorities. But, surprisingly,since Luther’s term “spiritual law” meant “canon law,” his hostility can be seen to escalate through these pamphlets until he publicly burns the canon law on December 10th, 1520. He felt it excluded the laity from the spiritual estate, making them feel as if they were not even Christians. His pamphlets called for communion in both kinds, demanding an inclusive Christian estate for the priesthood of all believers. The central concern of this dissertation, however, is not the polemics of these pamphlets, but Luther’s awe-inspiring religious contribution.