The Value of Lesser Goods: The Epistemic Value of Entitlement

The notion of entitlement plays an important role in some influential epistemologies. Often the epistemological motive for introducing the concept is to accommodate certain externalist intuitions within an internalist framework or, conversely, to incorporate internalist traits into an otherwise externalist position. In this paper two prominent philosophers will be used as examples: Tyler Burge as a representative of the first option and Fred Dretske as one of the second. However, even on the assumption that the concept of entitlement is sufficiently clarified, accomplishing these results is easier said than done – especially if we also want to ascribe positive epistemic value to entitlement. It will be shown that the epistemic value of entitlement is either granted at the expense of the epistemic value of justification or the value ends up below the level of value at which the epistemologists employing the concept of entitlement are aiming.     

Can realists know that they know?

Realists typically suppose that nonepistemic truth is an independent condition on propositional knowledge. Few philosophers, however, have seriously questioned the meta-epistemic consequences of combining alethic and epistemic variants of realism. In this paper I aim to show that the truth condition in the customary definition of knowledge presents an important problem for the realist at higher epistemic levels. According to my argument, traditional epistemic-logical analyses of metaknowledge fail because of their extensionalism and certain presuppositions they have about the satisfaction of the truth condition. I further suggest that we need a different approach to metaknowledge if (1) we want to retain alethic realism, and (2) we want our epistemological accounts to adequately explicate the meta-epistemic states of actual, evidence-bound cognitive agents. This paper greatly benefited from the comments and criticisms of an anonymous referee for Acta Analytica.     

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.     

Wisdom, Understanding and Knowledge: A Virtue-Theoretic Proposal

Reaching understanding is one of our central epistemic goals, dictated by our important motivational epistemic virtue, namely inquisitiveness about the way things hang together. Understanding of humanly important causal dependencies is also the basic factual-theoretic ingredient of wisdom on the anthropocentric view proposed in the article. It appears at two levels. At the first level of immediate, spontaneous wisdom, it is paired with practical knowledge and motivation (phronesis), and encompasses understanding of oneself (a distinct level of self-knowledge having to do with one??s dispositions capacities, vulnerabilities, and ways of reacting), of other people, of possibilities of meaningful life, and of relevant courses of events. It is partly resistant to skeptical scenarios, but not completely. On the second and reflective level, understanding helps fuller holistic integration of one??s first order practical and factual-theoretic knowledge and motivation, thus minimizing potential and actual conflicts between all these components. It also participates in the reflective control whose exercise is needed for full reflective wisdom, the crucial epistemic-practical virtue or human excellence.     

Factive Presupposition and the Truth Condition on Knowledge

In this paper I argue, against some recent criticisms, that the factivity of ??knows?? does not support the traditional truth condition on knowledge. I articulate a conception of the factivity of ??knows?? on which it is a matter of cancelable pragmatic presupposition, and consider the epistemological implications of this.     

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.     

Epistemological Disjunctivism and the New Evil Demon

In common with traditional forms of epistemic internalism, epistemological disjunctivism attempts to incorporate an awareness condition on justification. Unlike traditional forms of internalism, however, epistemological disjunctivism rejects the so-called New Evil Genius thesis. In so far as epistemological disjunctivism rejects the New Evil Genius thesis, it is revisionary. After explaining what epistemological disjunctivism is, and how it relates to traditional forms of epistemic internalism / externalism, I shall argue that the epistemological disjunctivist’s account of the intuitions underlying the New Evil Genius thought experiment is incomplete at best. Therefore, as presented, epistemological disjunctivism is unable to accommodate the core guiding intuitions of epistemic internalism. Given the stated aim of not being revisionary on this score, the view is at a dialectical disadvantage over the traditional forms of epistemic internalism the position is meant to replace. Unfortunately, therefore, at present, the impasse between internalism and externalism remains.     

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.     

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.     

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.     

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.     

Hypothetical knowledge and counterfactual reasoning

Samet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information structures used to model it bear some resemblance to the way philosophers have used conditional logic to model counterfactuals, hypothetical knowledge cannot be reduced to conditional logic together with epistemic logic. Here it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator “>” and the knowledge operator “K”, provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed.     

A Renaissance Reading of Aquinas: Thomas Cajetan on the Ontological Status of Essences

Aristotelian philosophers have been always puzzled by the ambiguous status of essences: it is not clear whether an Aristotelian should admit that an essence, taken in itself, is real, even though essences do not exist over and above particular things, as Platonists posit; furthermore, it is not clear whether an Aristotelian should endorse the view that essences have a certain unity, even if they are taken in themselves, namely, by abstracting from the individuals of which they are essences. I tackle Thomas Cajetan??s analysis of this problem: this analysis is more sophisticated than that developed by Aquinas??whose texts had been commented upon by Cajetan. Cajetan distinguishes two senses of ??real?? and of ??unity,?? in order to speak of the reality and of the unity of essences, taken in themselves, though not endorsing a Platonist??s ontology. I suggest that his solution is appealing for the contemporary debate about this problem.     

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.     

Expressivism about Knowledge and the Value of Knowledge

The aim of the paper is to state a version of epistemic expressivism regarding knowledge, and to suggest how this expressivism about knowledge explains the value of knowledge. The paper considers how an account of the value of knowledge based on expressivism about knowledge responds to the Meno Problem, the Swamping Problem, and a variety of other questions that pertains to the value of knowledge, and the role of knowledge in our cognitive ecology.     

Imprecise probabilities for representing ignorance about a parameter

This paper distinguishes between objective probability—or chance—and subjective probability. Most statistical methods in machine learning are based on the hypothesis that there is a random experiment from which we get a set of observations. This random experiment could be identified with a chance or objective probability, but these probabilities depend on some unknown parameters. Our knowledge of these parameters is not objective and in order to learn about them, we must assess some epistemic probabilities about their values. In some cases, our objective knowledge about these parameters is vacuous, so the question is: What epistemic probabilities should be assumed? In this paper we argue for the assumption of non-vacuous (a proper subset of [0, 1]) interval probabilities. There are several reasons for this; some are based on the betting interpretation of epistemic probabilities while others are based on the learning capabilities under the vacuous representation. The implications of the selection of epistemic probabilities in different concepts as conditioning and learning are studied. It is shown that in order to maintain some reasonable learning capabilities we have to assume more informative prior models than those frequently used in the literature, such as the imprecise Dirichlet model.     

Varieties of Multiple Antecedent Cause

A great deal has been written over the past decade defending ??higher-level?? causes by arguing that overdetermination is more complex than many philosophers initially thought. Although two shooters overdetermine the death of a firing squad victim, a baseball and its parts do not overdetermine the breaking of a window. But while these analyses of overdetermination have no doubt been fruitful, the focus on overdetermination??while ignoring other varieties of causal relation??has limited the discussion. Many of the cases of interest resemble joint causes or a cause necessitating a simultaneous epiphenomenon as much as they resemble overdeterminers. If we are to fully understand higher-level causation, we need to distinguish it from these causal relations as well. This paper is dedicated to the task, focusing especially on the ??threat?? that higher-level causes are epiphenomena necessitated by lower-level causes.     

Meta-mathematical rhetoric: Hero and Ptolemy against the philosophers

Bringing the meta-mathematics of Hero of Alexandria and Claudius Ptolemy into conversation for the first time, I argue that they employ identical rhetorical strategies in the introductions to Hero's Belopoeica, Pneumatica, Metrica and Ptolemy's Almagest. They each adopt a paradigmatic argument, in which they criticize the discourses of philosophers and declare epistemological supremacy for mathematics by asserting that geometrical demonstration is indisputable. The rarity of this claim—in conjunction with the paradigmatic argument—indicates that Hero and Ptolemy participated in a single meta-mathematical tradition, which made available to them rhetoric designed to introduce, justify, and bolster the value of mathematics.     

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.