Coherentism,Truth, and Witness Agreement

Coherentists on epistemic justification claim that all justification is inferential, and that beliefs, when justified, get their justification together (not in isolation) as members of a coherent belief system. Some recent work in formal epistemology shows that “individual credibility” is needed for “witness agreement” to increase the probability of truth and generate a high probability of truth. It can seem that, from this result in formal epistemology, it follows that coherentist justification is not truth-conducive, that it is not the case that, under the requisite conditions, coherentist justification increases the probability of truth and generates a high probability of truth. I argue that this does not follow.     

An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

Entitlement, Justification, and the Bootstrapping Problem

According to the bootstrapping problem, any view that allows for basic knowledge (knowledge obtained from a reliable source prior to one??s knowing that that source is reliable) is forced to accept that one can utilize a track-record argument to acquire justification for believing that one??s belief source is reliable; yet, we tend to think that acquiring justification in this way is too easy. In this paper I argue, first, that those who respond to the bootstrapping problem by denying basic knowledge succumb to over-intellectualizing epistemology, and secondly, reliabilist views avoid over-intellectualization only at the expense of sanctioning bootstrapping as a benign procedure. Both of these outcomes are difficult to bear. To ward off each of these unsavory outcomes, I propose an alternative solution that draws on a distinction between two separate epistemic concepts: entitlement and justification.     

Virtue -Based Epistemology and the Centrality of Truth (Towards a Strong Virtue-Epistemology)

A strong, strictly virtue-based, and at the same time truth-centered framework for virtue epistemology (VE) is proposed that bases VE upon a clearly motivating epistemic virtue, inquisitiveness or curiosity in a very wide sense, characterizes the purely executive capacities-virtues as a means for the truth-goal set by the former, and, finally, situates the remaining, partly motivating and partly executive virtues in relation to this central stock of virtues. Character-trait epistemic virtues are presented as hybrids, partly moral, partly purely epistemic. In order to make the approach virtue-based, it is argued that the central virtue (inquisitiveness or curiosity) is responsible for the value of truth: truth is valuable to cognizers because they are inquisitive, and most other virtues are a means for satisfying inquisitiveness. On can usefully combine this virtue-based account of the motivation for acquiring knowledge with a Sosa-style analysis of the concept “knowledge”, which brings to the forefront virtues-capacities, in order to obtain a full-blooded, “strong” VE.

Closure,Defeasibility and Conclusive Reasons

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.

Towards an Account of Epistemic Luck for Necessary Truths

Modal epistemologists parse modal conditions on knowledge in terms of metaphysical possibilities or ways the world might have been. This is problematic. Understanding modal conditions on knowledge this way has made modal epistemology, as currently worked out, unable to account for epistemic luck in the case of necessary truths, and unable to characterise widely discussed issues such as the problem of religious diversity and the perceived epistemological problem with knowledge of abstract objects. Moreover, there is reason to think that this is a congenital defect of orthodox modal epistemology. This way of characterising modal epistemology is however optional. It is shown that one can non-circularly characterise modal conditions on knowledge in terms of epistemic possibilities, or ways the world might be for the target agent. Characterising the anti-luck condition in terms of epistemic possibilities removes the impediment to understanding epistemic luck in the case of necessary truths and opens the door to using these conditions to shed new light on some longstanding epistemological problems.     

Reflective equilibrium and underdetermination in epistemology

The basic aim of Alvin Goldman’s approach to epistemology, and the tradition it represents, is naturalistic; that is, epistemological theories in this tradition aim to identify the naturalistic, nonnormative criteria on which justified belief supervenes (Goldman, 1986; Markie, 1997). The basic method of Goldman’s epistemology, and the tradition it represents, is the reflective equilibrium test; that is, epistemological theories in this tradition are tested against our intuitions about cases of justified and unjustified belief (Goldman, 1986; Markie, 1997). I will argue that the prospect of having to reject their standard methodology is one epistemologists have to take very seriously; and I will do this by arguing that some current rival theories of epistemic justification are in fact in reflective equilibrium with our intuitions about cases of justified and unjustified belief. That is, I will argue that intuition underdetermines theory choice in epistemology, in much the way that observation underdetermines theory choices in empirical sciences. If reflective equilibrium leads to the underdetermination problem I say it leads to, then it cannot satisfy the aims of contemporary epistemology, and so cannot serve as its standard methodology.     

Uniform Regularity in a Wedge and Regularity of Traces of CR Functions

We discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs and apply, in Sect. 2, to two situations. First, let W\mathcal{W} be a wedge of ℂ ⁿ with C ^ω , generic edge ℰ: a holomorphic function f on W\mathcal{W} has always a generalized (hyperfunction) boundary value bv(f) on ℰ, and this coincides with the collection of the boundary values along the discs which have C ^ω transversal intersection with ℰ. Thus Sect. 1 can be applied and yields the uniform continuity at ℰ of f when bv(f) is (separately) continuous. When W\mathcal{W} is only smooth, an additional property, the temperateness of f at ℰ, characterizes the existence of boundary value bv(f) as a distribution on ℰ. If bv(f) is continuous, this operation is consistent with taking limits along discs (Theorem 2.8). By Sect. 1, this yields again the uniform continuity at ℰ of tempered holomorphic functions with continuous bv. This is the theorem by Rosay (Trans. Am. Math. Soc. 297(1):63–72, 1986), in whose original proof the method of “slicing” by discs is not used.     

An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

Why contextualists cannot know they are right: Self-refuting implications of contextualism

Conversational contextualism in epistemology is characterized by four main theses: 1. the indexicality of knowledge claims thesis; 2. the attributor contextualism thesis; 3. the conversational contextualism thesis, and 4. the main thesis of contextualism according to which a knowledge claim can be true in one context and false in another context in which more stringent standards for knowledge are operant. It is argued that these theses taken together generate problems for contextualism. In particular, it is shown that there is no context in which the contextualist can truthfully claim to know her theory is true. Since these results were obtained only with principles the contextualist cannot give up—like the principle of epistemic closure and the principle that knowledge implies truth—it seems that contextualism is in need of a thoroughgoing revision if it is to become a successful epistemic theory.     

The power of paradox: some recent developments in interactive epistemology

Paradoxes of game-theoretic reasoning have played an important role in spurring developments in interactive epistemology, the area in game theory that studies the role of the players’ beliefs, knowledge, etc. This paper describes two such paradoxes – one concerning backward induction, the other iterated weak dominance. We start with the basic epistemic condition of "rationality and common belief of rationality" in a game, describe various ‘refinements’ of this condition that have been proposed, and explain how these refinements resolve the two paradoxes. We will see that a unified epistemic picture of game theory emerges. We end with some new foundational questions uncovered by the epistemic program. This survey owes a great deal to joint work and many conversations with Robert Aumann, Amanda Friedenberg, Jerry Keisler, and Harborne Stuart. Scott Ashworth, John Asker, Carliss Baldwin, Heski Bar-Isaac, Pierpaolo Battigalli, Ken Corts, Konrad Grabiszewski, Joe Halpern, Rena Henderson, Martin Meier, Martin Rechenauer, and participants in various seminars provided important input. The associate editor and referees made very helpful suggestions and observations. Financial support from Harvard Business School and the Stern School of Business is gratefully acknowledged.     

The twistor theory of the Hermitian Hurwitz pair (ℂ4(I 2,2),ℝ(I 2,3))

An analogue of the twistor theory is given for the Hermitian Hurwitz pair(ℂ⁴(I _2,2),ℝ(I _2,3)). In Sect. 2 a concept of Hurwitz twistors is introduced and a counterpart of the Penrose correspondence is obtained. It is proved that there exists a one-to-one correspondence between the twistors on the (1,3)-space and the (2,2)-space, which is called the duality theorem for Hurwitz twistors (Theorem 1). In Sect. 3. a concept of spinor equations is introduced for an Hermitian Hurwitz pair (abbreviated as HHP) and the duality theorem for solutions of the spinor equations is proved (Theorem 2). In Sect. 4 we give an elementary proof of the Penrose theory on the base of our Key Lemma. Then we can give the desired correspondence explicitly. In sect. 5 we consider the Penrose theory in the context of HHPs. At first we give a local version. It is proved that every solution of the spinor equation on the (2,2)-space can be represented as a ∂-harmonic one-form. By use of this result, we can get a direct relationship between the complex analysis and spinor theory on some open setM ⁺, which is called as “semi-global version” of the Penrose theory (Theorem 7). Moreover, we can get the original Penrose theory by use of the Penrose transformation (Theorem 5). Research of the first author partially supported by the State Committee for Scientific Research (KBN) grant PB 2 P03A 016 10 (Sections 1, 3 and 5 of the paper), and partially by the grant of the University of Łódź no. 505/485 (sections 2 and 4).     

What Is Entitlement?

In his seminal paper, “Content Preservation,” Tyler Burge defends an original account of testimonial knowledge. The originality of the account is due, in part, to the fact that it is cast within a novel epistemic framework. The central feature of that framework is the introduction of the concept of entitlement, which is alleged to be a distinctive type of positive epistemic support or warrant. Entitlement and justification, according to Burge, are sub-species of warrant. Justification is the internalist form of warrant, but entitlement is epistemically externalist. My focus in this paper is Burge’s conception of entitlement, and there are three primary issues that I wish to address. What is the relationship between entitlement and the more traditional concept of justification? In what sense is entitlement epistemically externalist? Has Burge introduced a new epistemic concept or merely coined a new term for a familiar epistemic concept?     

Inferior Disagreement

Literature in the epistemology of disagreement has focused on peer disagreement: disagreement between those with shared evidence and equal cognitive abilities. Additional literature focuses on the perspective of amateurs who disagree with experts. However, the appropriate epistemic reaction from superiors who disagree with inferiors remains underexplored. Prima facie, this may seem an uninteresting set of affairs. If A is B’s superior, and A has good reason to believe she is B’s superior, A appears free to dismiss B’s disagreement. However, a closer look will show otherwise. I first distinguish competent from incompetent inferiors and then argue that disagreement from the former often gives superiors reason to adjust credence and reevaluate belief. In other words, epistemic inferiority alone is insufficient grounds for dismissing opinion. More nuanced difficulties arise with incompetent inferiors. When superiors disagree with incompetents, this might provide evidence to bolster belief credence; however, agreement from incompetents can defeat justification. In either instance, inferior opinion carries epistemic weight. Yet, this fails to cover all ground; at times, superiors learn nothing from inferior disagreement. I finish by exploring these uninformative disagreements, how to distinguish them from the informative cases, and the proper epistemic reactions thereof.     

Armchair luck: Apriority,intellection and epistemic luck

The paper argues that there is such a thing as luck in acquisition of candidate apriori beliefs and knowledge, and that the possibility of luck in this “armchair” domain shows that definitions of believing by luck thatp offered in literature are inadequate, since they mostly rely on the possibility of it being the case that not-p. Whenp is necessary, such a definition should be supplemented by one pointing to variation in belief, not in the fact believed. Thus the paper suggests a focus upon the agent and her epistemic virtue in the account of epistemic luck in general.     

ETSAP-TIAM: the TIMES integrated assessment model. part II: mathematical formulation

This article is a companion to “ETSAP-TIAM: the TIMES integrated assessment model. part I: model structure”. It contains three sections, presenting respectively: the simplified formulation of the TIMES Linear Program (Sect. 1), the details of the computation of the supply demand equilibrium (Sect. 2), and the Endogenous Technology Learning Formulation (Sect. 3). The full details of these three formulations are available in the complete TIMES documentation at www.etsap/org/documentation.     

Transglobal Evidentialism-Reliabilism

We propose an approach to epistemic justification that incorporates elements of both reliabilism and evidentialism, while also transforming these elements in significant ways. After briefly describing and motivating the non-standard version of reliabilism that Henderson and Horgan call “transglobal” reliabilism, we harness some of Henderson and Horgan’s conceptual machinery to provide a non-reliabilist account of propositional justification (i.e., evidential support). We then invoke this account, together with the notion of a transglobally reliable belief-forming process, to give an account of doxastic justification.

Cryptosystems based on semi-distributive algebras

We propose a new cryptographic scheme of ElGamal type. The scheme is based on algebraic systems defined in the paper—semialgebras (Sect. 2). The main examples are semialgebras of polynomial mappings over a finite field K, and their factor-semialgebras. Given such a semialgebra R, one chooses an invertible element a ∈ R ^* of finite order r, and a random integer s. One chooses also a finite dimensional K-submodule V of R. The 4-tuple (R, V, a, b) where b = a ^s forms the public key for the cryptosystem, while r and s form the secret key. A plain text can be viewed as a sequence of elements of the field K. That sequence is divided into blocks of length dim(V) which, in turn, correspond to uniquely determined elements X _i of V. We propose three different methods (A, B, and C, see Definition 1.1) of encoding/decoding the sequence of X _i . The complexity of cracking the proposed cryptosystem is based on the Discrete Logarithm Problem for polynomial mappings (see Sect. 1.1). No methods of cracking the problem, except for the “brute force” (see Sect. 1.1) with Ω(r) time, are known so far.