Self-Inquisitiveness: the Structure and Role of an Epistemic Virtue

The motivating virtue account claims that inquisitiveness or curiosity is the motivating epistemic virtue. In the case of self-knowledge, self-inquisitiveness, intrinsic and instrumental, is the motivating epistemic virtue that mobilizes other virtues, skills, and epistemic character virtues, needed to achieve such knowledge. Its proper object is substantial self-knowledge, knowledge of one’s dispositions and causal powers that has historically played a central role in philosophy, and is now, under various names, investigated by psychologists. It has been, until recently, comparatively neglected within analytical epistemology of self-knowledge. Self-inquisitiveness thus instantiates the general paradigm of curiosity-inquisitiveness that organizes and motivates other epistemic virtues (virtues-abilities and character virtues). And it is perhaps responsible for intrinsic value of self-knowledge.     

Knowledge versus Understanding: The Cost of Avoiding Gettier

In the current discussion on epistemic value, several philosophers argue that understanding enjoys higher epistemological significance and epistemic value than knowledge??the epistemic state the epistemological tradition has been preoccupied with. By noting a tension between the necessary conditions for understanding in the perhaps most prominent of these philosophers, Jonathan Kvanvig, this paper disputes the higher epistemological relevance of understanding. At the end, on the basis of the results of the previous sections, some alternative comparative contrasts between knowledge and understanding are briefly explored, including one in which an analogue to the KK-principle for knowledge, the ??UU-principle??, does not hold for a different reason than that for which the former principle fails.     

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.     

What’s so Good about a Wise and Knowledgeable Public?

Philosophers have been concerned for some time with the epistemic caliber of the general public, qua the body that is, ultimately, tasked with political decision-making in democratic societies. Unfortunately, the empirical data paint a pretty dismal picture here, indicating that the public tends to be largely ignorant on the issues relevant to governance. To make matters worse, empirical research on how ignorance tends to breed overconfidence suggests that the public will not only lack knowledge on the relevant issues, but also wisdom, in the Socratic sense of an awareness of your ignorance. While increasing the knowledge and wisdom of the public might be thought an obvious remedy, there is, as far as sound political decision-making and action are concerned, nothing particularly valuable about knowledge or wisdom per se. In fact, it might just be that what the public needs is nothing but the most basic epistemic good: true belief.     

Bilattice logic of epistemic actions and knowledge

Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further extended to define and axiomatize a bilattice logic of epistemic actions and knowledge (BEAK). Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective.     

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.     

Getting a Grasp of the Grasping Involved in Understanding

This paper investigates some epistemic properties that distinguish understanding from knowledge. In particular, the focus is on how to spell out the notion of grasping the relationships between propositions that constitute objectual understanding: what kind of epistemic access is required for grasping to occur and to what extent is the act of grasping voluntary? A modest form of access is suggested as an answer to the first question and a largely negative answer to the second. The worry that my suggestion is too permissive in crediting subjects with understanding is addressed. The results are then finally briefly contrasted to Ernest Sosa’s notion of knowing full well where one contrast precisely concerns the voluntary character of the respective epistemic states.     

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.     

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.

Varieties of Pragmatic Encroachment

According to a recent view, known as the 'pragmatic encroachment' thesis, an agent’s non-truth-related factors are relevant to the epistemic status of her beliefs. In particular, in addition to truth-related factors, practical factors are said to be relevant to the question whether or not true belief amounts to knowledge. Despite the intuitive appeal of the thesis, however, it is puzzling how practical factors can impact the truth-related factors that ground the epistemic status of one's beliefs. In this paper, I will distinguish between a strong and a weak sense of the way in which practical factors are said to be thus relevant. Their differences are explicated in terms of the nature and the extent to which practical factors are said to impact the epistemic status of one's beliefs. I begin by considering a strong version of the thesis that suggests principles according to which the practical rationality of one's actions is a necessary condition on knowledge and justification. Having noted an inadequacy in the formulation of such principles, the arguments in their support are subsequently stated and criticized. Finally, I identify two modest versions of the thesis of pragmatic encroachment and argue that they, too, fail to explain how practical factors can bear on the epistemic status of one's beliefs.     

In Defense of Epistemic Circularity

In this paper I defend epistemic circularity by arguing that the “No Self-Support” principle (NSS) is false. This principle, ultimately due to Fumerton (1995), states that one cannot acquire a justified belief in the reliability of a source of belief by trusting that very source. I argue that NSS has the skeptical consequence that the trustworthiness of all of our sources ultimately depends upon the trustworthiness of certain fundamental sources – sources that we cannot justifiably believe to be reliable. This is a problem, I claim, because if the trustworthiness of all of our sources depends upon sources that we should not believe to be reliable, then a reflective individual should not trust any of his sources at all. The hidden cost of rejecting epistemic circularity is thus the unacceptable skeptical thesis that reflective individuals like you and I have no justified beliefs whatsoever.     

Existence results for boundary value problems of high order differential equations involving Caputo derivative

We study boundary value problems for differential equations involving Caputo derivative of order ????(n?1,n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the H?lder??s inequality, a suitable singular Gronwall??s inequality and fixed point theorem via a priori estimate method. At last, three examples are given to illustrate the results.     

The Social Virtues: Two Accounts

Social (epistemic) virtues are the virtues bound up with those forms of inquiry involved in social routes to knowledge. A thoroughly individualistic account of the social virtues endorses two claims: (1) we can fully characterize the nature of the social virtues independent of the social factors that are typically in play when these virtues are exemplified, and (2) even when a subject’s route to knowledge is social, the only epistemic virtues that are relevant to her acquisition of knowledge are those she herself possesses. A social (or anti-individualistic) account of the social virtues, by contrast, denies one or both of these claims. I will offer some reasons for thinking that the individualistic account is not acceptable, and that one or the other social account provides a better understanding of the social virtues. The argument is not decisive, but it does suggest that the social dimension of social epistemic virtues is not fully characterizable in individualistic terms.     

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.     

Reflective Luck and Belief Ownership

A belief is reflectively lucky if it is a matter of luck that the belief is true, given what a subject is aware of on reflection alone. Various epistemologists have argued that any adequate theory of knowledge should eliminate reflective luck, but doing so has proven difficult. This article distinguishes between two kinds of reflective luck arguments in the literature: local arguments and global arguments. It argues that local arguments are best interpreted as demanding, not that one be reflectively aware of the reliability of the sources of one’s beliefs, but that one’s beliefs be attributable to one as one’s own. The article then argues that global arguments make illegitimate demands, because they require that we be ultimately answerable for our beliefs. In the end, the article argues that epistemologists should shift their focus away from reflective luck and toward the conditions under which beliefs are attributable to cognitive agents.     

Why the Logical Hexagon?

The logical hexagon (or hexagon of opposition) is a strange, yet beautiful, highly symmetrical mathematical figure, mysteriously intertwining fundamental logical and geometrical features. It was discovered more or less at the same time (i.e. around 1950), independently, by a few scholars. It is the successor of an equally strange (but mathematically less impressive) structure, the ??logical square?? (or ??square of opposition??), of which it is a much more general and powerful ??relative??. The discovery of the former did not raise interest, neither among logicians, nor among philosophers of logic, whereas the latter played a very important theoretical role (both for logic and philosophy) for nearly two thousand years, before falling in disgrace in the first half of the twentieth century: it was, so to say, ??sentenced to death?? by the so-called analytical philosophers and logicians. Contrary to this, since 2004 a new, unexpected promising branch of mathematics (dealing with ??oppositions??) has appeared, ??oppositional geometry?? (also called ??n-opposition theory??, ??NOT??), inside which the logical hexagon (as well as its predecessor, the logical square) is only one term of an infinite series of ??logical bi-simplexes of dimension m??, itself just one term of the more general infinite series (of series) of the ??logical poly-simplexes of dimension m??. In this paper we recall the main historical and the main theoretical elements of these neglected recent discoveries. After proposing some new results, among which the notion of ??hybrid logical hexagon??, we show which strong reasons, inside oppositional geometry, make understand that the logical hexagon is in fact a very important and profound mathematical structure, destined to many future fruitful developments and probably bearer of a major epistemological paradigm change.     

Understanding, Integration, and Epistemic Value

Understanding enjoys a special kind of value, one not held by lesser epistemic states such as knowledge and true belief. I explain the value of understanding via a seemingly unrelated topic, the implausibility of veritism. Veritism holds that true belief is the sole ultimate epistemic good and all other epistemic goods derive their value from the epistemic value of true belief. Veritism entails that if you have a true belief that p, you have all the epistemic good qua p. Veritism is a plausible and widely held view; I argue that it is untenable. I argue that integration among beliefs possesses epistemic value independent from the good of true belief, and so has value veritism cannot account for. I argue further that this integration among beliefs comprises the distinctive epistemic value of understanding.     

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.     

Level sets of the Takagi function: local level sets

The Takagi function ??: [0,1] ?? [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y)?=?{x : ??(x)?=?y} of the Takagi function ??(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a ??generic?? full Lebesgue measure set of ordinates y, the level sets are finite sets. In contrast, here it is shown for a ??generic?? full Lebesgue measure set of abscissas x, the level set L(??(x)) is uncountable. An interesting singular monotone function is constructed associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly ${\frac{3}{2}}$ .     

A (Different) Virtue Responsibilism: Epistemic Virtues Without Motivations

Debate rages in virtue epistemology between virtue reliabilists and responsibilists. Here, I develop and argue for a new kind of responsibilism that is more conciliar to reliabilism. First, I argue that competence-based virtue reliabilism(s) cannot adequately ground epistemic credit. Then, with this problem in hand, I show how Aristotle’s virtue theory is motivated by analogous worries. Yet, incorporating too many details of Aristotelian moral theory leads to problems, notably the problem of unmotivated belief. As a result, I suggest a re-turn to Aristotle to develop a distinctively epistemological virtue theory that does not require any motive or affect for epistemic virtue. Nevertheless, my theory affirms that virtues are acquired, agent-expressive traits. The result is a conciliar responsibilism that leans closer to reliabilism. I end by arguing that my virtue responsibilism can solve worries facing both reliabilism and (extant) responsibilism.