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.

An idea regarding charitable giving

Today I had an idea regarding charitable giving that as far as I know hasn't been implemented, at least on a large scale: Why not have "charity cards", credit cards which automatically donate a certain percentage  of what you spend to charity whenever you make a purchase? For example, if you spend $100.00 on something and have a 2% threshold, that would automatically generate a corresponding $2 donation to a charity of your choice. I think that would be good because such "microdonations," which most of us wouldn't bother to make separately, would eventually ad up. They would also require no special effort, which I think is a great psychological  barrier to giving. If a lot of people ended up using charity cards, it could easily generate millions (or more) in donations.  So instead of getting "points" or filer miles, why not have cards that automatically generate microdonations?

On the Announcement of Pope Francis's first Apostolic Exhortation: Evangelii Gaudium

Has anyone else seen this? I don't consider myself Catholic, but it's pretty awesome.

Excerpt:

"As we open our hearts, the Pope goes on, so the doors of our churches must always be open and the sacraments available to all. The Eucharist, he says pointedly, “is not a prize for the perfect, but a powerful medicine and nourishment for the weak” And he repeats his ideal of a Church that is “bruised, hurting and dirty because it has been out on the streets” rather than a Church that is caught up in a slavish preoccupation with liturgy and doctrine, procedure and prestige. “God save us,” he exclaims, “from a worldly Church with superficial spiritual and pastoral trappings!” Urging a greater role for the laity, the Pope warns of “excessive clericalism” and calls for “a more incisive female presence in the Church”, especially “where important decisions are made.” 
Looking beyond the Church, Pope Francis denounces the current economic system as “unjust at its root”, based on a tyranny of the marketplace, in which financial speculation, widespread corruption and tax evasion reign supreme. He also denounces attacks on religious freedom and new persecutions directed against Christians. Noting that secularization has eroded ethical values, producing a sense of disorientation and superficiality, the Pope highlights the importance of marriage and stable family relationships."

Text from pagehttp://en.radiovaticana.va/news/2013/11/26/pope_issues_first_apostolic_exhortation:_evangelii_gaudium/en1-750083 
of the Vatican Radio website


The document itself can be found here.

Daemonodicy: The Problem of Good

Daemonodicy

~ The Problem of Good ~

Jason Zarri

“Leibniz’s solution of the problem of evil, like most of his other popular doctrines, is logically possible, but not very convincing. A Manichaean might retort that this is the worst of all possible worlds, in which the good things that exist serve only to heighten the evils. The world, he might say, was created by a wicked demiurge, who allowed free will, which is good, in order to make sure of sin, which is bad, and of which the evil outweighs the good of free will. The demiurge, he might continue, created some virtuous men, in order that they might be punished by the wicked; for the punishment of the virtuous is so great an evil that it makes the world worse than if no good men existed. I am not advocating this opinion, which I consider fantastic; I am only saying that it is no more fantastic than Leibniz’s theory.”

--Bertrand Russell, A History of Western Philosophy, Simon & Schuster (1972), p. 590

Zigur: Greetings, brother Zead.

Zead: Greetings, brother Zigur. May our lord Malus curse you and smite you on the Day of Pain!

Zigur: (Muttering:) Yes, I certainly hope so...

Zead: You hope so?!

Zigur: That is precisely the reason I came to see you, brother Zead. I am starting to doubt my faith, and have come to you for assurance and for counsel.

Zead: I am glad that you have come to me, Zigur. I will do whatever I can to strengthen you, and keep you in the Dark One's fold. Speak then, and tell me of the cause of these doubts.

Zigur: Well, we are told that the lord Malus is most evil, are we not?

Zead: Indeed, brother Zigur; lord Malus is supremely evil, the first cause of all misery and despair. Not only is he the most evil being in existence, he is that than which no fouler can so much as be conceived.

Zigur: Yes, that has been my instruction from the earliest age, and reflecting upon it has been the chief source of my doubt. If the lord Malus is as wicked as you say—omnimalevolent, as our Daemonologists put it—why do we see so much good in the world? In every nation there are some who thirst after righteousness, and they are not smitten. There are some who help the disadvantaged and fight for the freedom of the oppressed, and our lord does not strike them down. I know of some who go so far as to treat their enemies as well as their friends, and yet they prosper. And not only is all this the case, but the virtuous even outnumber the vicious! Why would the lord Malus allow this mockery of his unholy name? For we are taught that he is not only omnimalevolent, but omniscient and omnipotent. Does he not know of goodness? Then he is ignorant. Is he willing to suppress goodness, but not able? Then he is impotent. Is he able to suppress goodness, but not willing? Then he is beneficent. Is he both able and willing? Then from whence comes goodness? Is he neither able nor willing? Then why call him a Daemon?

Zead: These are natural questions, brother Zigur, but they have natural answers. Have you not been taught them as well, as a part of your instruction? Do you not know that the lord Malus, though he is wickedness itself, allows there to be some good men and women, so that they may suffer? Some of them receive their due punishment in this life, but in the next they will all receive the greater condemnation. Though all suffering is bad, the suffering of the virtuous is a far worse thing than the suffering of the vicious, because the vicious deserve to suffer and the virtuous do not. This is why the lord Malus, our most beloved Daemon, allows his human creatures free will. Virtue is not truly virtue unless it is freely chosen, and the same is true of vice. This is why he suffers anything good to exist; that out of it, he may bring a greater evil. This too is why we worship him: We also will suffer to satisfy his malice, but not as much as those who are good, for when the vicious receive less punishment than they deserve it is an offense against justice. Let this console you, brother Zigur.

Zigur: All that is well said, brother Zead; so indeed I have been taught, and O how I wish it to be true! But I am afraid that my doubt is greater than you may fear, and extends not only to the wickedness of Malus, but to his existence as well.

Zead: Your doubt is exceedingly great, Zigur! Yet I have in my power the means to dispel it. Surely you can conceive the lord Malus to exist, or you would not have come to me to help strengthen your faith?

Zigur: Yes, I can conceive it.

Zead: And surely you agree that we understand Malus, The Dark One, to be that than which no fouler can be conceived?

Zigur: Certainly, brother Zead.

Zead: Excellent, brother Zigur! It is now within my power to prove to you that our lord Malus exists.

Zigur: How is that?

Zead: I shall tell you, brother Zigur. Suppose that what you fear is true, and that Malus does not exist. Then, since we have acknowledged him to be that than which no fouler can be conceived, does it not surely follow that that than which no fouler can be conceived also does not exist?

Zigur: Most surely, brother Zead.

Zead: Now consider this: Doesn't that than which no fouler can be conceived, though we suppose it not to exist in reality, exist in our understanding, since we can conceive the lord Malus to exist, and he is that than which no fouler can be conceived?

Zigur: Indeed.

Zead: But then, brother Zigur, it follows that one can conceive of that which is fouler than that than which no fouler can be conceived, a contradiction!

Zigur: How so, Zead?

Zead: Like this, Zigur: We suppose that Malus, that than which no fouler can be conceived, does not exist. But we've agreed that that than which no fouler can be conceived can be conceived to exist in reality, which is fouler. But then that than which no fouler can be conceived  can be conceived to be fouler than it is—since it would be fouler if it existed in reality—which is absurd. Therefore our lord Malus, the great Daemon and source of all evil, who on the first day created darkness and saw that it was bad, most assuredly exists in reality, and not in the understanding alone!

Zigur: Your argument is wickedly excellent, brother Zead; too excellent, I fear, to be sound. Could one not argue for all manner of other evil things, in much the same way? Consider the foulest possible island, adorned with volcanoes, deserts, and thickets of thorns, and replete with the greatest possible number of inhabitants in the worst possible agony. Surely this island exists in our understanding. Now, if we suppose it not to exist, we can still conceive it to exist in reality, which is fouler. But the island than which no fouler can be conceived surely cannot be conceived to be fouler than it is, whence it follows that it exists in reality as well. Nice as it would be to know that it exists, I have heard no reports of such an island from any corner of the known world, and even if it were discovered, it seems to me that we shouldn't believe in it just on the strength of the argument I have just presented.

Zead: Surely we should not, Zigur. But there is a flaw in your reasoning: We cannot conceive of an island than which no fouler can be conceived, any more than we can conceive of a number than which no larger can be conceived. We can always conceive of a bleaker, more desolate and larger island, with a larger number of miserable inhabitants in greater agony, and for a longer amount of time. If our imagined island grows too large for the Earth's oceans, we can imagine it to exist on another, larger planet. You have already admitted that the existence of an omnipotent Daemon is possible, and so we may suppose that there are possible circumstances where he does exist, and as there is no limit to the foulness of an island which he could create, there is no limit to the foulness of an island which could exist, even if it could not come to exist by natural means. So there cannot be a foulest conceivable island, while you have already admitted that there can be a foulest conceivable being.

Zigur: An excellent reply, brother Zead! I must admit that my objection is vanquished, but my doubts live on. I have another worry: Couldn't one give a similar argument for a most perfect possible being, that than which no greater can be conceived? For it is surely greater if it exists in reality than if it exists in the understanding alone, and can it thus not be proved to exist by an argument exactly analogous to your own?

Zead: Ingenious, Zigur! But nevertheless, mistaken. I will tell you a secret: Those of us in the inner circle know a great truth; namely, that goodness, and hence “greatness” of the sort you have mentioned, is nothing positive, nothing existent in its own right, but is a mere privation, a lack of an evil which rot to be present in a thing.

Zigur: Which rot to be present, brother Zead?

Zead: Yes, Zigur; the perverted, those who seek justice and love the good, think that good is positive and that evil is negative; but their minds have been clouded, and the truth is just the opposite. They would say that what is evil or bad ought not to be present in a thing; which, though true, is not the proper mode of expression, for it can make one think that evil is merely negative, an opinion most abhorrent to us. Thus, we in the inner circle say that that which is evil or bad rot to be present in a thing, and that that which is good rot not to be present in it.

Zigur: I see. But isn't happiness good, brother Zead? And happiness is something positive, which exists in its own right.

Zead: Happiness is certainly good, but it is not an instance of goodness itself. That is, while happiness is something positive, its goodness is negative, being the lack of a misery which the happy creature rot to be suffering instead.

Zigur: Interesting. But how does that answer my objection?

Zead: In this way, Zigur: If a good is nothing but the lack of an evil which rot to be present, and a “perfect being” is one which is supremely good, it is one which must needs also be supremely non-existent. To be, is to be evil; to be good is not to be, in a certain respect. Whence it follows that to be perfectly good is not to be in any respect. So this being cannot be conceived of except as being unreal, while just the opposite is true of our lord. Does this satisfy you, brother Zigur?

Zigur: Indeed I am satisfied brother Zead; you have convinced me at last that there is a Daemon, and that I must have been a fool for my heart to say otherwise! 

My new YouTube Video, Viva la Castlevania

Check out my new YouTube video, a tribute to Castlevania: Lords of Shadow 1 and 2, and Viva la Vida by Coldplay:

Hope you like it. ^_^

I've created a page to fight malaria

I've created a fundraising page to prevent needless deaths from malaria.   Please click here to help fight this terrible disease. If you don't have enough to donate, you can still help out by letting others know. I greatly appreciate your help.

The first section of my intro to philosophy text is now available online!

Peter Krey, my co-author, and I have just e-published the first section of our intro to philosophy text, "I Am, Therefore I Think: A Historical Introduction to Philosophy". This section is about the Presocratics, and can be found here:

I Am, Therefore I Think: A Historical Introduction to Philosophy

Many thanks to Mark Krey for his illustrations and to Scott Ryan for reading and editing the text!

We welcome any feedback you may have on this section, as well as suggestions about what you would like to see in future sections. You can send them to jlzarri@scholardarity.com

Petition in support of Iranian philosophy PhD student Abbas Khosravi Farsani

From the petition's webpage  (http://www.gopetition.com/petitions/treat-abbas-khosravi-farsani-humanely-and-justly.html):

Petition Background (Preamble):

We write on behalf of Abbas Khosravi Farsani, a graduate of Imam Sadegh University, who was until recently working on a Ph.D. in Western Philosophy at Isfahan University.

Last June, however, Mr. Farsani was arrested and expelled from the University and forbidden to teach at any Iranian university for writing the blog and book by the name of “Najvahaye Najibane” (“Noble Whispers”) allegedly insulting the Supreme Leader and high officials of the Iranian regime. He has a summons to appear before the Revolution Court of Iran on January 26.

And from Leiter Reports:

... I would urge all readers to sign given the unjust and politically motivated treatment to which he has been subjected.   It was prepared by philosophers Alan Hajek (ANU) and Jeff Jordan (Delaware).  When you sign, put your institutional affiliation in the comment section.
UPDATE:   I hope other bloggers, including those in other academic fields, will publicize this petition.

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.