Gödel Loop: A New short story by Nathaniel Bates

Nathaniel Bates has a new short science fiction story up for purchase at Scholardarity, called Gödel Loop:

Time loops were predicted by mathematician and close friend of Einstein Kurt Gödel.  The past and future loop in to one.  A former radical turned police detective discovers that the road to solving a murder may be found in a Gödel loop that leads him to the past, future, and to the very edge of what is possible.  

Check out a free preview here.

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.

Singer's "Famine, Affluence and Morality": Exposition and Appraisal: Now on YouTube

I've posted an audio version of an article of mine critiquing Peter Singer's "Famine, Affluence, and Morality" on YouTube:

http://www.youtube.com/watch?v=Dc1j7IMltR0

Timothy Sprigge and the Importance of Subjectivity

Scott Ryan has a new article at Scholardarity, Timothy Sprigge and the Importance of Subjectivity. The article covers panpsychism, eternalism, Absolute Idealism, and ethics. Here is an introductory excerpt:

In this essay I shall offer a brief appreciative overview of the philosophical system of British philosopher Timothy L.S. Sprigge (14 January 1932—11 July 2007). In so doing I shall be emphasizing the importance in that system of subjectivity—of the existence of centers (he writes “centres,” but here I follow the US spelling convention) of consciousness, sentience, and experience, characterized essentially by the fact that there is ‘something that it is like’ to be them.

Sprigge had adopted this way of talking about subjectivity—as involving what it is “like” to be something—before it was made famous by Thomas Nagel in his 1974 paper “What is it Like to Be a Bat?” Subjectivity was a theme of Sprigge’s philosophical work from the very beginning, well before he had fully worked out his mature views. Indeed, “The Importance of Subjectivity” was the title of his inaugural lecture upon his appointment to the Chair of Logic and Metaphysics at the University of Edinburgh in 1982, and was chosen (by his friend, colleague, former student, and literary executor Leemon McHenry, at the suggestion of Pierfrancesco Basile) as the title of a posthumously published collection of his papers.

My aim is to provide, for interested readers, a short and accessible (though of course very far from complete) account of the main lines of Sprigge’s system in a way that will provide a quick and ready grasp both of the overall unity of that system and of the fundamental and far-reaching importance of subjectivity within it.

Looking for guest bloggers

For a while this blog and (ironically) Scholardarity's DiaBlog have, unfortunately, been primarily monologues. In the interest of starting more conversations, both about philosophy and the humanities in general, I've decided to look for guest bloggers. You can contribute one post, a series of posts, or even become a regular contributor--it's entirely up to you. Contributions about philosophy will be posted on both blogs, and contributions on other sub-disciplines of the humanities will be posted only at Scholardarity. If you're interested, you can email me with a post idea or rough draft at jlzarri@scholardarity.com.

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.

A New and Improved version of the Scholardarity Message Board

Check out the new and improved Scholardarity Message Board, now powered by bublaa:

Scholardarity message board

Some Strong Conditionals for Sentential Logics (Circulation Draft)

Here is my latest draft of a paper attempting to give an account of a stronger-than-material conditional which can be adapted to various sentential logics. An abstract is provided below. To see the draft, go here:

Some Strong Conditionals for Sentential Logics (Circulation Draft)

Please keep in mind that the paper is a work in progress, and is still in a fairly rough state. That being said, I appreciate any comments and / or criticism that those who are interested in the subject have to offer.

Abstract:

In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s language with more than one conditional, and it may be that no single conditional will satisfy all of our intuitions about how a conditional should behave. Finally, I will make no claim that the strong conditional is a good model for any particular use of the indicative conditional in English or other natural languages, though it would certainly be a nice bonus if some modified version of it could serve as one.

The basic idea is this: In general, one starts out with with the logic that one  wants to define the conditional for, and describes a meta-language for it. The metalanguage contains ┌(q|p)┐, a “conditional designator” which designates the truth value that q takes given that p is true, i.e., given that p has the value 1. It is to be read as ┌ the value of q given p┐ or ┌the value of q conditional on p┐. The stroke, |, is not a connective; it merely serves to separate the letter q from the letter p. The designator works like this: If p never takes the value 1, then ┌(q|p)┐ designates nothing—for q cannot take a value given that p is true if p can never be true—and is said to be empty. It is also empty if the value of q varies when the value of p is 1, for in that case q doesn’t take a unique value given that p is true. If q always takes the value 1 when p takes the value 1, then ┌(q|p)┐ designates 1, and in our meta-language we can say that ┌(q|p)┐ = 1, which is another way of saying that ┌(q|p)┐ designates 1. Similarly, if q always takes the value 0 when p takes the value 1, then ┌(q|p)┐ designates 0, and in our meta-language we can say that ┌(q|p)┐ = 0. 

With our meta-linguistic conditional designator ready to hand, one can now define what I call the strong conditional, or strong implication, for which I will use the symbol ‘→’. Its definition is (where ‘v( )’ is the valuation function, which gives the semantic value of an expression):

If ┌(q|p)┐= 1, then v(p → q) = 1

If ┌(q|p)┐= 0, then v(p → q) = 0

If ┌(q|p)┐ is empty, then v(p → q) = 0

I shall begin by exploring some of the disadvantages of the material conditional, the strict conditional, and some relevant conditionals. I proceed to define a strong conditional for classical sentential logic. I go on to adapt this account to Graham Priest’s Logic of Paradox, to S. C. Kleene’s logic K3, and then to J. Łukasiewicz’s logic Ł, a standard version of fuzzy logic.

The Format of Scholardarity's Submissions Page Has Been Updated

Scholardarity.com has updated the format of its submissions page. Now you can sign in using your Google, Yahoo, Facebook, Twitter, or HeyPublisher account. Also, you no longer have to send in submissions via email; you can upload them directly through the submissions form.

You can submit your contributions here.

We look forward to hearing from you!

Notes on Timothy Williamson’s Lecture “Logics as Scientific Theories”

Over at Scholardarity I've posted my notes on Timothy Williamson’s lecture “Logics as Scientific Theories” which was given at U.C. Berkeley on November 1st.

A Summary of Mackie’s “The Subjectivity of Values”

I've posted a summary of J.L. Mackie's article "The Subjectivity of Values" in Philosophy Notes at Scholardarity.

Here's an excerpt:

In his essay “The Subjectivity of Values”, J.L. Mackie aims to show that values are not built into the structure of the universe. He begins by clarifying his position, addressing possible reactions and trying to prevent misunderstandings. Some would reject Mackie’s thesis as being morally subversive, others would accept it as a platitude, and still others would say that the question of whether there are objective values is itself illegitimate. Mackie’s thesis applies to all purportedly objective values, not just moral ones. Also, his thesis is a second-order rather than a first-order claim: It states that our values have nothing objective corresponding to them, but one who accepts this claim is not thereby committed to adopt any particular attitude towards private conduct or public policy. One can think that values are ultimately subjective while still valuing things, practices, or states of affairs—or perhaps not valuing much of anything at all—because valuing something does not presuppose that valuing it has an ontological ground.

Aristotle’s Theory of the Origin of the State

I've  posted a new article at Scholardarity in Philosophy Notes from my Grandfather, which is a brief explanation of Aristotle’s Theory of the Origin of the State.

A Primer on Logic: Part 4.1

I've published a new article on Scholardarity, A Primer on Logic: Part 4.1, the latest installment of my introduction to formal logic. In it I address some preliminaries to Predicate Logic.

Also, in case you missed Parts 1, 2, 3, and the Interlude, which respectively cover logical preliminaries, propositional logic, Aristotelian logic, and the inadequacies of Aristotelian logic, you can check them out here:

Part 1

Part 2
 
Part 3

Interlude

If you have any comments / criticism, by all means share it!

Announcement of Scholardarity’s First Essay Contest

Announcement of Scholardarity’s First Essay Contest

 

 

Peter Krey and Jason Zarri, co-founders of Scholardarity, are pleased to announce that Scholardarity is now accepting submissions for its first essay contest. The cost of entering the contest is $10.00. There will be prizes for the first, second, and third place winners. The contestant who wins first place will receive at least $200.00, the contestant who wins second place will receive at least $100.00, and the contestant who wins third place will receive at least $50.00; we say “at least” because the money received from the entrance fees will form a “pot”, which will be divided amongst the three winners: 50% of the pot for first place, 25% of the pot for second place, and 10% of the pot for third place.

There are two topics to choose from:

(1) What role should the government play in a society and what is the proper relation of the government and economy in order to best serve the common good? Would new approaches to the discipline of economics—for example, the evolutionary or complexity economics of Eric Beinhocker or other approaches, e.g., the social economics of Anghel Rugina, contribute to the well-being of society?
 

(2) What is the proper relationship between government and religion in a democracy? What are the effects, positive and/or negative, of government on religion, of religion on government, or of both on society as a whole? Essays may include the pros and cons of the separation of church and state, governmental restrictions on certain religious practices, as well as restrictions placed on a religion, such as wanting to impose its will on the whole society.

 

There will be two rounds: In Round 1, contestants will submit a proposal of about 500 words in which they give an outline for a paper on their selected topic. From these proposals, twenty will be selected as finalists to enter Round 2. The finalists will write a paper based on their proposal, of about 2,000 words in length. All twenty of the finalists’ essays will be published on Scholardarity.
The deadline for submissions for Round 1 is November 15th, and the deadline for submissions for Round 2 is January 15th

To enter the contest, go to Scholardarity's Contest Page to enter, then send your proposal to  jlzarri@scholardarity.com, along with your name, address, and any other relevant contact information.

We look forward to hearing from you!

Philosophy Notes from my Grandfather

I’ve started a new section of Scholardarity in Open Source Study Notes, Philosophy Notes from my Grandfather. It’s a page dedicated to the memory of my late grandfather, who graduated Summa Cum Laude with a Bachelor’s in Philosophy from USF. I’ve also added its first entry, An Overview of the History of Philosophy: Part 1.

On the Relativity of “Reallys” -- Now at Scholardarity

I've just posted my article "On the Relativity of “Reallys”: A Critique of Strawson" at Scholardarity in the Philosophy of Mind section, in which I criticize P. F. Strawson's attempt to reconcile the standpoints of science and common sense, insofar as they concern perception .

Philosophy of Language Notes Part 1: Wittgenstein

Over at Scholardarity I've posted Part 1 of my notes on the Philosophy of language, the first contribution to Scholardarity Student’s subsection Open Source Study Notes. This  part deals with the philosophy of Ludwig Wittgenstein. Here's an excerpt:

~ Prelude ~

Why philosophers study language–

1) Philosophers have been accused of “making mistakes” based on language. Consider the sentences:

i) “Santa Claus does not exist.”

ii) “Santa Claus wears a red suit.”

a) “How can one talk about something”, philosophers sometimes ask, “and say something true or false about it, if it isn’t real or doesn’t ‘have being’ in some sense? In order for statements like (i) or (ii) to be true, they have to be about something—Santa Claus, in this case. Granted, in light of the fact that (i) is true, Santa Claus doesn’t exist, but nevertheless he is some kind of being and has properties—including the properties of being non-existent and wearing a red suit.” However, at least since Bertrand Russell published his famous article “On Denoting” in 1905, most philosophers think that arguments like this are based on linguistic confusions. It can be true that Santa Claus does not exist without Santa Clause being real in any sense.

b) From time to time philosophers also ask: Is there such a thing as “goodness”, or something like Plato’s “Form of the Good”? Able philosophers have thought so, but others–emotivists, in particular, such as A. J. Ayer, C. L. Stevenson, Richard Hare—have held that to call something good or bad, or to say that an action is right or wrong, is not to say that it objectively has some moral feature—“goodness”, “wrongness”, etc.—but to express how the speaker feels about the thing or action in question.  For example, on this view a sentence like “Lying is wrong” is neither true nor false; nor, when properly understood, is it purported to be. It merely evinces that the speaker who uttered the sentence disapproves of lying. It does not even say that the speaker disapproves of lying—that would be a sentence that is apt to be true or false; true if the speaker disapproves of lying and false if they do not. On the emotivists’ view, to say that lying is wrong is more like saying “Boo lying!”, “Screw lying!”, “Down with lying!”, or something of the sort.

(Personal note: Words like ‘good’ and ‘bad’, ‘right’ and ‘wrong’, may have an expressive function, but it doesn’t follow that they only have an expressive function. Sentences involving ‘good’ and ‘bad’ might sometimes attribute objective goodness or badness to some entity, and it may be that it is in virtue of one’s belief that the entity in question is objectively good that one can use the term ‘good’ or ‘goodness’ to express how one feels about it. For it may be that if one had no belief concerning the entity’s moral value, one might not have any feelings about it, whether positive or negative.)

2) What are the limits of human knowledge? What can we conceive? The “early” Ludwig Wittgenstein, for example, thought there was a connection between the limits of conception and the limits of what can be expressed in language:

The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought).

The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.—Tractatus Logico-Philosophicus, p. 3

3) Language is inherently interesting.

Open Source Study Notes

Open Source Study Notes, a new feature of Scholardarity.com, is opening. Anyone can contribute their study notes, study guides or study aids, and even overviews or introductions. All contributions will be free to read, and no registration is required. Submissions can be about specific courses, books, or articles; but they can also be about broader topics within a discipline. All areas are welcome—however, submissions may be subject to review and/or editing before they appear, and it will be easier for us to evaluate submissions in the humanities because that is the area in which we have the most experience. Also, anyone can suggest additions or changes to contributions through comments or email. At first, only the administrators will be able to actually make changes, but our plan is that in the future anyone can register (for free) to be an editor, and could then be able to make changes themselves.

Contributions should be submitted to jlzarri@scholardarity.com. Files should be an MS Word, an MS Works, or a Rich Text Document—or, if you have exceptionally clear handwriting, you can scan your contribution and send it as an image. Finally, contributors should accompany their submission with a brief description of its contents, along with its number of pages or words.

We look forward to hearing from you!