
315355.126059
Consider this Thomisticstyle doctrine:
God’s believing that a contingent entity x exists is the cause of x’s existing. Let B be God’s believing that I exist. Then, either
B exists in all possible worlds
or
B exists in all and only the worlds where I exist. …

884266.126105
In his article “Reassurance via Translation” Marcel Crabbe proposed a formalism to obtain reassurance and classical recapture in the setting of minimal F DE. His formalism proved to be general enough to be extended in order to formalize other forms of nonmonotonic systems based on preference relations. It is the aim of this article to show how his result can be extended in a natural way by combining two different reasoning systems, namely minimal F DE and circumscription, in order to get a paraconsistent and paracomplete version of circumscription, which we will call paracomplistent circumscription, which has the advantages of F DE and circumscription but is neither explosive nor lacks modus ponens in consistent contexts. Furthermore, we will complete a proof Crabbe left unfinished.

1007037.126121
J. D. Hamkins and M. Kikuchi, “The inclusion relations of the countable models of set theory are all isomorphic.” (manuscript under review)
Citation arχiv
@ARTICLE{HamkinsKikuchi:Theinclusionrelationsofthecountablemodelsofsettheoryareallisomorphic,
author = {Joel David Hamkins and Makoto Kikuchi},
title = {The inclusion relations of the countable models of set theory are all isomorphic},
journal = {},
editor = {},
year = {},
volume = {},
number = {},
pages = {},
month = {},
doi = {},
note = {manuscript under review},
eprint = {1704.04480},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/inclusionrelationsareallisomorphic},
abstract = {},
keywords = {},
source = {},
}
Abstract. …

1411016.12614
This paper shows how to conservatively extend theories formulated in nonclassical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s ˙= fA(¯t) and A(¯t, s) even though A( ¯x, y) determines the extension of a function.

1461002.126168
We provide a sufficient frametheoretic condition for a superbiintuitionistic logic to have Maksimova’s variable separation property. We conclude that biintuitionistic logic enjoys the property. Furthermore, we offer an algebraic characterization of the superbiintuitionistic logics with Maksimova’s property.

1461020.126243
This paper reflects on metametaphysics and as such develops a metametametaphysical view: that quietist metametaphysics requires dialetheism, and in turn a paraconsistent logic. I demonstrate this using Carnap’s metametaphysical position in his ‘Empiricism, Semantics and Ontology’ (1950) as an example, with regard to how it exhibits selfreference and results in inconsistency. I show how applying Carnap’s position to itself produces a dilemma, both horns of which lead to a contradiction. Such inconsistency commonly arises from metatheories with global scope, as the ‘meta’ approach aims to transcend the scope of that which it is theorizing about, whilst the global nature will place itself back within the scope of that which it is theorizing about, which together result in the theory referring to itself whilst refuting itself. I argue that any global metametaphysical theory that draws a limit to thought will face selfreference problems leading to contradictory realms. My conclusion is conditional: If we want to metaphilosophize in such a way and treat quietist metatheories as being true, then we need to be dialetheist and utilize a paraconsistent logic in order to accommodate the contradictions that result from such theorizing.

1461058.126269
A theorem from Archimedes on the area of a circle is proved in a setting where some inconsistency is permissible, by using paraconsistent reasoning. The new proof emphasizes that the famous method of exhaustion gives approximations of areas closer than any consistent quantity. This is equivalent to the classical theorem in a classical context, but not in a context where it is possible that there are inconsistent infinitesimals. The area of the circle is taken ‘up to inconsistency’. The fact that the core of Archimedes’s proof still works in a weaker logic is evidence that the integral calculus and analysis more generally are still practicable even in the event of inconsistency.

1461118.126293
This paper investigates the use of neighborhood frames as a semantics for the logics of unknown truths and related nonnormal epistemic systems, including the logic of false beliefs. However, the interest in these logics is not restricted to epistemic settings. As such, this paper is perhaps better viewed as a continuation of the study of reflexiveinsensitive logics (we borrow this terminology from [3]) that was initiated in [5] and further developed in [7] and [3]. In addition to this more systematic motive, it is also our desire to further elucidate (and exploit, in some cases) the connections between these logics and provability logics.

1461184.126322
Circular definitions have primarily been studied in revision theory in the classical scheme. I present systems of circular definitions in the Strong Kleene and supervaluation schemes and provide complete proof systems for them. One class of definitions, the intrinsic definitions, naturally arises in both schemes. I survey some of the features of this class of definitions.

1461206.12635
In recent years, two nonclassical views about negation have gained considerable traction in the philosophical literature. The paracomplete view holds that excluded middle (EM) is invalid, while the paraconsistent view holds that explosion (EX) is invalid. Both run contrary to classical logic in distinct but dual ways.

1525812.126379
If $M$ is a model of ZFC set theory, let $I$ be the definable cut of its ordinals, the collection of ordinals that are below an ordinal $\delta$ of $M$ that is definable in $M$ without parameters. This would include all the ordinals of $M$, if the definable ordinals happen to be unbounded in $M$, but one can also construct examples where the definable cut is bounded in $M$. …

1691756.12641
One of the central logical ideas in Wittgenstein’s Tractatus logicophilosophicus is the elimination of the identity sign in favor of the socalled “exclusive interpretation” of names and quantifiers requiring different names to refer to different objects and (roughly) different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier’s account, the first concerning the treatment of individual constants, the second concerning socalled “pseudopropositions” (Scheinsatze) of classical logic such as a = a or a = b ∧ b = c → a = c. We argue that overcoming these problems requires two fairly drastic departures from Wehmeier’s account: (1) Not every formula of classical firstorder logic will be translatable into a single formula of Wittgenstein’s exclusive notation. Instead, there will often be a multiplicity of possible translations, revealing the original “inclusive” formulas to be ambiguous. (2) Certain formulas of firstorder logic such as a = a will not be translatable into Wittgenstein’s notation at all, being thereby revealed as nonsensical pseudopropositions which should be excluded from a “correct” conceptual notation. We provide translation procedures from inclusive quantifierfree logic into the exclusive notation that take these modifications into account and define a notion of logical equivalence suitable for assessing these translations.

2268321.12649
In this paper, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis (1995) that the approach to interpreting quantum theories known as Algebraic Imperialism allows for “too many states”. I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.

2584334.126514
In response to G.Belot’s (2013) criticism that Bayesian theory is epistemologically immodest, we argue that his analysis is misguided. The topological conditions that we understand underpin his criticisms of familiar results about asymptotic Bayesian conditioning are selfdefeating. They require extreme a priori credences regarding, e.g., the limiting behavior of observed relative frequencies. Instead, we offer a rival explication of Bayesian modesty: Rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Using a result of Blackwell and Dubins (1962), we explain how amenability to new evidence may serve as the basis for resolving conflicts among Bayesian investigators. When the new evidence fails to achieve a resolution, that failure can identify epistemologically immodest Bayesian credal states. Also we assess A. Elga’s (2016) rebuttal to Belot’s analysis. He focuses attention on the role that the assumption of countable additivity plays in Belot’s criticism of asymptotic Bayesian learning.

2674145.126531
Let me tell you about a fascinating paradox arising in certain infinitary twoplayer games of perfect information. The paradox, namely, is that there are games for which our judgement of who has a winning strategy or not depends on whether we insist that the players play according to a deterministic computable procedure. …

2724800.126545
Truth values have been put to quite different uses in philosophy and
logic, being characterized, for example, as:
primitive abstract objects denoted by sentences in natural and
formal languages,
abstract entities hypostatized as the equivalence classes of
sentences,
what is aimed at in judgements,
values indicating the degree of truth of sentences,
entities that can be used to explain the vagueness of concepts,
values that are preserved in valid inferences,
values that convey information concerning a given
proposition. Depending on their particular use, truth values have been treated as
unanalyzed, as defined, as unstructured, or as structured
entities.

2955542.126559
Hybrid logics are logics that result by adding further expressive
power to ordinary modal logic. The most basic hybrid logic is obtained
by adding socalled nominals which are propositional symbols of a new
sort, each being true at exactly one possible world. The history of
hybrid logic goes back to Arthur N. Prior’s work in the 1960s.

3520927.126572
In philosophy of statistics, Deborah Mayo and Aris Spanos have championed the following epistemic principle, which applies to frequentist tests: Severity Principle (full). Data x (produced by process G) provides good evidence for hypothesis H (just) to the extent that test T severely passes H with x . (Mayo and Spanos 2011, pp.162). They have also devised a severity score that is meant to measure the strength of the evidence by quantifying the degree of severity with which H passes the test T (Mayo and Spanos 2006, 2011; Spanos 2013). That score is a real number defined on the interval [0,1]. In this paper, I put forward a paradoxical feature of the severity score as a measure of evidence. To do this, I create a scenario where a frequentist statistician S is interested in finding out if there is a difference between the means of two normally distributed random variables. The null hypothesis (H0) states that there is no difference between the two means.

3646210.126585
Today’s Virtual Colloquium is “Global and Local Atheisms” by Jeanine Diller. Dr. Diller received her PhD from the University of Michigan and is currently an assistant professor in the Department of Philosophy and Program on Religious Studies of the University of Toledo in Ohio. …

3693882.126603
I propose a new definition of identification in the limit (also called convergence to the truth), as a new success criterion that is meant to complement, rather than replacing, the classic definition due to Gold (1967). The new definition is designed to explain how it is possible to have successful learning in a kind of scenario that Gold’s classic account ignores—the kind of scenario in which the entire infinite data stream to be presented incrementally to the learner is not presupposed to completely determine the correct learning target. From a purely mathematical point of view, the new definition employs a convergence concept that generalizes net convergence and sits in between pointwise convergence and uniform convergence. Two results are proved to suggest that the new definition provides a success criterion that is by no means weak: (i) Between the new identification in the limit and Gold’s classic one, neither implies the other. (ii) If a learning method identifies the correct target in the limit in the new sense, any Ushaped learning involved therein has to be redundant and can be removed while maintaining the new kind of identification in the limit. I conclude that we should have (at least) two success criteria that correspond to two senses of identification in the limit: the classic one and the one proposed here. They are complementary: meeting any one of the two is good; meeting both at the same time, if possible, is even better.

3751483.126617
In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow nonHermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a nonBoolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, a notion that we introduce in order to cope with the temporal aspect of the logical structure of quantum theory.

3751499.12663
We discuss generalized pobabilistic models for which states not necessarily obey Kolmogorov’s axioms of probability. We study the relationship between properties and probabilistic measures in this setting, and explore some possible interpretations of these measures.

3959027.126643
There was a period in the 1970’s when the admissions data for the UC–Berkeley graduate school (hereafter, BGS) exhibited some (prima facie) peculiar statistical correlations. Specifically, a strong negative correlation was observed between being female and being accepted into BGS. This negative correlation (in the overall population of BGS applicants) was (initially) a cause for some concern regarding the possibility of gender bias in the admissions process at BGS. However, closer scrutiny of the BGS admissions data from this period revealed that no individual department’s admissions data exhibited a negative correlation between being female and being admitted. In fact, every department reported a positive correlation between being female and being accepted. In other words, a correlation that appears at the level of the general population of BGS applicants is reversed in every single department of BGS. This sort of correlation reversal is known as Simpson’s Paradox. Because admissions decisions at BGS are made (autonomously) by each individual department, the lack of departmental correlations seems to ruleout the gender bias hypothesis as the best (causal) explanation of the observed correlations in the data. As it happens, there was a strong positive correlation between being female and applying to a department with a (relatively) high rejection rate.

4199535.126656
It was, I think, till recently broadly assumed among working analytic metaphysicians that metaphysics, or at least that branch of it called ontology, is concerned with issues of existence, and that one’s known arguments that one can resist positing Meinongian unreal objects by accepting his theory of descriptions. However, it would be a mistake to read Russell as nothing more than a protoQuinean. This will no doubt already be conceded for the period of Russell’s career in which he thought there were notions of “existence” not explicable by means of the existential quantifier, or embraced a distinction between existence and mere being or subsistence (e.g., PoM §427, Papers 4, 486–89, PP 100). However, in what follows I want to argue that this is true even for mature Russell, during the period (starting roughly 1913) in which he officially held the position that all existence claims are to be understood quantificationally. In particular, metaphysical position is more or less exhausted by one’s position on while mature Russell understood “Fs exist” as expressing p(∃v)Fvq, the question of what entities there are, or what entities exist. This he would not have taken the truth of this claim necessarily to setlikely stemmed from Quine’s wellknown paper “On What There Is”, tle the metaphysical or ontological status of Fs. Russell had, runviews is determined by what things its quantifiers range over: “To be is to be the value of a variable,” as he succinctly put it (Quine 1948, 15). Of course, Quine’s views were never universal, but at least most ning alongside his account of existence, a conception of belonging to what is, as he variously put it, “ultimate,” “fundamental”, the “bricks of the universe”, the “furniture of the world”, something “really there”.

4436705.126669
We consider a naturallanguage sentence that cannot be formally represented in a firstorder language for epistemic twodimensional semantics. We also prove this claim in the appendix. It turns out, however, that the most natural ways to repair the expressive inadequacy of the firstorder language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal. In this paper we investigate some questions concerning the expressive power of a firstorder modal language with twodimensional operators. In particular, a language endowed with a twodimensional semantics intended to provide a logical analysis of the discourse involving a priori knowledge. We consider a naturallanguage sentence that cannot be formally represented in such a language. This was firstly conjectured in Lampert (manuscript), but here we present a proof. It turns out, however, that the most natural ways to repair this expressive inadequacy render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.

4500651.126682
Traditional monotheism has long faced logical puzzles (omniscience, omnipotence, and more) [10, 11, 13, 14]. We present a simple but plausible ‘gappy’ framework for addressing these puzzles. By way of illustration we focus on God’s alleged stone problem. What we say about the stone problem generalizes to other familiar ‘paradoxes of omni properties’, though we leave the generalization implicit. We assume familiarity with the proposed (subclassical) logic but an appendix is offered as a brief review.

4675395.126695
Is part of a perfectly natural, or fundamental, relation? Philosophers have been hesitant to take a stand on this issue. One of reason for this hesitancy is the worry that, if parthood is perfectly natural, then the perfectly natural properties and relations are not suitably “independent” of one another. (Roughly, the perfectly natural properties are not suitably independent if there are necessary connections among them.) In this paper, I argue that parthood is a perfectly natural relation. In so doing, I argue that this “independence” worry is unfounded. I conclude by noting some consequences of the naturalness of parthood.

4681614.126708
We prove that under some technical assumptions on a general, nonclassical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause Principle against certain attempts of falsification. Some open problems concerning possible strengthening of the common cause completability result are formulated.

4688270.126721
Let me tell you about the game Buckets of fish. This is a twoplayer game played with finitely many buckets in a line on the beach, each containing a finite number of fish. There is also a large supply of additional fish available nearby, fresh off the boats. …

5000922.126739
We offer a defense of one aspect of Paul Horwich’s response to the Liar paradox—more specifically, of his move to preserve classical logic. Horwich’s response requires that the full intersubstitutivity of ‘ ‘A’ is true’ and A be abandoned. It is thus open to the objection, due to Hartry Field, that it undermines the generalization function of truth. We defend Horwich’s move by isolating the grade of intersubstitutivity required by the generalization function and by providing a new reading of the biconditionals of the form “ ‘A’ is true iff A.”