Neo-Mooreanism,contextualism, and the evidential basis of scepticism

Two of the main forms of anti-scepticism in the contemporary literature—namely, neo-Mooreanism and attributer contextualism—share a common claim, which is that we are, contra the sceptic, able to know the denials of sceptical hypotheses. This paper begins by surveying the relative merits of these views when it comes to dealing with the standard closure-based formulation of the sceptical problem that is focussed on the possession of knowledge. It is argued, however, that it is not enough to simply deal with this version of the sceptical challenge, since there is a more fundamental sceptical problem underlying the standard closure-based sceptical argument that can be expressed in terms of the evidential basis of our beliefs. Whilst it is argued that neo-Mooreanism has a slight edge over attributer contextualism when it comes to dealing with the closure-based formulation of the sceptical problem, it is claimed that this view is in an ever stronger dialectical position when it comes to the more pressing evidential formulation of the sceptical problem. It is shown that this is so even if one adapts the attributer contextualist thesis along the lines suggested by Michael Williams and Ram Neta so that it is explicitly designed to deal with the evidential variant of the sceptical problem.     

The semantics of knowledge attributions

The basic idea of conversational contextualism is that knowledge attributions are context sensitive in that a given knowledge attribution may be true if made in one context but false if made in another, owing to differences in the attributors’ conversational contexts. Moreover, the context sensitivity involved is traced back to the context sensitivity of the word “know,” which, in turn, is commonly modelled on the case either of genuine indexicals such as “I” or “here” or of comparative adjectives such as “tall” or “rich.” But contextualism faces various problems. I argue that in order to solve these problems we need to look for another account of the context sensitivity involved in knowledge attributions and I sketch an alternative proposal.     

The generation of formulas held in common knowledge

Common knowledge of a finite set of formulas implies a special relationship between syntactic and semantic common knowledge. If S, a set of formulas held in common knowledge, is implied by the common knowledge of some finite subset of S, and A is a non-redundant semantic model where exactly S is held in common knowledge, then the following are equivalent: (a) S is maximal among the sets of formulas that can be held in common knowledge, (b) A is finite, and (c) the set S determines A uniquely; otherwise there are uncountably many such A. Even if the knowledge of the agents are defined by their knowledge of formulas, 1) there is a continuum of distinct semantic models where only the tautologies are held in common knowledge and, 2) not assuming that S is finitely generated (a) does not imply (c), (c) does not imply (a), and (a) and (c) together do not imply (b). Received November 1999/Revised version January 2000     

A Priori knowledge contextualised and Benacerraf’s dilemma

In this article, I discuss Hawthorne’s contextualist solution to Benacerraf’s dilemma. He wants to find a satisfactory epistemology to go with realist ontology, namely with causally inaccessible mathematical and modal entities. I claim that he is unsuccessful. The contextualist theories of knowledge attributions were primarily developed as a response to the skeptical argument based on the deductive closure principle. Hawthorne uses the same strategy in his attempt to solve the epistemologist puzzle facing the proponents of mathematical and modal realism, but this problem is of a different nature than the skeptical one. The contextualist theory of knowledge attributions cannot help us with the question about the nature of mathematical and modal reality and how they can be known. I further argue that Hawthorne’s account does not say anything about a priori status of mathematical and modal knowledge. Later, Hawthorne adds to his account an implausible claim that in some contexts a gettierized belief counts as knowledge.     

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.     

On detachment conditions in the problem on the motion of a rigid body on a rough plane

The classical mechanical problem about the motion of a heavy rigid body on a horizontal plane is considered within the framework of theory of systems with unilateral constraints. Under general assumptions about the character of friction, we examine the question on the possibility of detachment of the body from the plane under the action of reaction of the plane and forces of inertia. For systems with rolling, we find new scenarios of the appearing of motions with jumps and impacts. The results obtained are applied to the study of stationary motions of a disk. We have showed the following.

A noncontextualist account of contextualist linguistic data

The paper takes as its starting point the observation that people can be led to retract knowledge claims when presented with previously ignored error possibilities, but offers a noncontextualist explanation of the data. Fallibilist epistemologies are committed to the existence of two kinds of Kp-falsifying contingencies: (i) Non-Ignorable contingencies [NI-contingencies] and (ii) Properly-Ignorable contingencies [PI-contingencies]. For S to know that p, S must be in an epistemic position to rule out all NI-contingencies, but she need not be able to rule out the PI-contingencies. What is required vis-à-vis PI-contingencies is that they all be false. In mentioning PI-contingencies, an interlocutor can lead S mistakenly to think that these contingencies are NI-contingencies, when in fact they are not. Since S cannot rule out these newly mentioned contingencies and since she mistakenly takes them to be NI-contingencies, it is quite natural that she retract her earlier knowledge claim. In short, mentioning NI-contingencies creates a distortion effect. It makes S think that the standards for knowledge are higher than they actually are, which in turn explains why she mistakenly thinks she lacks knowledge. Conclusion: The primary linguistic data offered in support of contextualism can be explained without resorting to contextualism.     

Differentiability of torsion theories

We prove that every perfect torsion theory for a ring R is differential (in the sense of [P.E. Bland, Differential torsion theory, Journal of Pure and Applied Algebra 204 (2006) 1–8]). In this case, we construct the extension of a derivation of a right R-module M to a derivation of the module of quotients of M. Then, we prove that the Lambek and Goldie torsion theories for any R are differential.     

Covering in the lattice of equational theories and some properties of term finite theories

For countable languages, we completely describe those cardinals κ such that there is an equational theory which covers exactly κ other equational theories. For this task understanding term finite theories is helpful. A theoryT isterm finite provided {ψ:Tτϕ≈ψ} is finite for all terms ϕ. We develop here some fundamental properties of term finite theories and use them, together with Ramsey's Theorem, to prove that any finitely based term finite theory covers only finitely many others. We also show that every term finite theory possesses an independent base and that there are such theories whose pairwise joins are not term finite. The paper was written with the support of NSF Grant MCS-80-01778. Presented by B. Jónsson. Received July 22, 1980. Accepted for publication in final form March 19, 1981.     

Star-linear equational theories of groupoids

We prove that there are precisely six equational theories E of groupoids with the property that every term is E-equivalent to a unique linear term. Presented by J. Berman. Received November 11, 2004; accepted in final form March 12, 2006. The first and third authors were supported by the Ministry of Science and Environment of Serbia, grant no. 144011; the second and fifth authors were supported by MŠMT, research project MSM 0021620839, and by the Grant Agency of the Czech Republic, grant #201/02/0594; the fourth author was supported by the NSF grant #DMS-0245622.     

Categoricity of computable infinitary theories

Computable structures of Scott rank are an important boundary case for structural complexity. While every countable structure is determined, up to isomorphism, by a sentence of , this sentence may not be computable. We give examples, in several familiar classes of structures, of computable structures with Scott rank whose computable infinitary theories are each -categorical. General conditions are given, covering many known methods for constructing computable structures with Scott rank , which guarantee that the resulting structure is a model of an -categorical computable infinitary theory. Work on this paper began at the Workshop on Model Theory and Computable Structure Theory at University of Florida Gainesville, in February, 2007. The authors are grateful to the organizers of this workshop. They are also grateful for financial support from National Science Foundation grants DMS DMS 05-32644, DMS 05-5484. The second author is also grateful for the support of grants RFBR 08-01-00336 and NSc-335.2008.1.     

Cantor Diagrams: A Unifying Discussion of Self-Reference

Within the framework of category theory, Cantor diagrams are introduced as the common structure of the self-reference constructions by Cantor, Russell, Richard, Gödel, Péter, Turing, Kleene, Tarski, according to the so-called Cantor diagonal method. Such diagrams consist not only of diagonal arrows but also of idempotent, identity and shift arrows. Cantor theorem states that no Cantor diagram is commutative. From this theorem, all the constructions above can be systematically retrieved. We do this by grouping them into two main classes: the class based on Cantor diagrams with a numerical shift function and the class based on Cantor diagrams with a Boolean shift function.     

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.

Predicate logics of expressively strong theories

It is proved that the logicL(T) coincides with the predicate calculus for the theory of rings, the theory of fields, group theory, and all arithmetically correct theoreies. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 777–788, November, 1999.     

A classification of thin shell theories

This paper gives a modern mathematical analysis of the relationships between several, different linear shell theories. It also discusses the asymptotic role played by membrane theory. It presents theorems on the existence and uniqueness of solutions of membrane equations depending on the concavity of the surface.     

Primitive connected and additive theories of polygons

We study into monoids S the class of all S-polygons over which is primitive normal, primitive connected, or additive, that is, the monoids S the theory of any S-polygon over which is primitive normal, primitive connected, or additive. It is proved that the class of all S-polygons is primitive normal iff S is a linearly ordered monoid, and that it is primitive connected iff S is a group. It is pointed out that there exists no monoid S with an additive class of all S-polygons. __________ Translated from Algebra i Logika, Vol. 45, No. 3, pp. 300–313, May–June, 2006.     

Representability and local representability of algebraic theories

A finitary monosorted algebraic theory is called locally representable (or representable) in a category with finite products if every its initial segment is the domain of a full faithful finite-products-preserving functor into (or if itself is the domain of such a functor). The question of when local representability implies representability is discussed, and theories for which local representability always implies representability are fully characterized. Received December 20, 1996; accepted in final form March 19, 1998.     

Equational theories as congruences of enriched monoids

The problem of characterizing the lattices of equational theories is still unsolved. In this paper we describe a class of monoids enriched by two unary operations and show that a lattice L is a lattice of equational theories if and only if L is isomorphic to a lattice of congruences of some enriched monoid belonging to . The author was supported by INTAS grant 03-51-4110 and The Alexander von Humboldt Foundation.     

The equivalence of theories that characterize ALogTime

A number of theories have been developed to characterize ALogTime (or uniform NC ¹, or just NC ¹), the class of languages accepted by alternating logtime Turing machines, in the same way that Buss’s theory characterizes polytime functions. Among these, ALV′ (by Clote) is particularly interesting because it is developed based on Barrington’s theorem that the word problem for the permutation group S ₅ is complete for ALogTime. On the other hand, ALV (by Clote), T ⁰ NC ⁰ (by Clote and Takeuti) as well as Arai’s theory and its two-sorted version VNC ¹ (by Cook and Morioka) are based on the circuit characterization of ALogTime. While the last three theories have been known to be equivalent, their relationship to ALV′ has been an open problem. Here we show that ALV′ is indeed equivalent to the other theories.      

On the class of flat stable theories

A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence relation, flat theories are defined as an appropriate version of superstability. It is shown that in a flat theory every type has finite weight and therefore flat theories are strong. Furthermore, it is shown that under reasonable conditions any type is non-orthogonal to a regular one. Concerning groups in flat theories, it is shown that type-definable groups behave like superstable ones, since they satisfy the same chain condition on definable subgroups and also admit a normal series of definable subgroup with semi-regular quotients.