Semisimple Varieties of Modal Algebras

In this paper we show that a variety of modal algebras of finite type is semisimple iff it is discriminator iff it is both weakly transitive and cyclic. This fact has been claimed already in [4] (based on joint work by the two authors) but the proof was fatally flawed. Dedicated to the memory of Willem Johannes Blok     

Does the Quine/duhem Thesis Prevent Us from Defining Analyticity?

Quine claims that holism (i.e., the Quine-Duhem thesis) prevents us from defining synonymy and analyticity (section 2). In Word and Object, he dismisses a notion of synonymy which works well even if holism is true. The notion goes back to a proposal from Grice and Strawson and runs thus: R and S are synonymous iff for all sentences T we have that the logical conjunction of R and T is stimulus-synonymous to that of S and T. Whereas Grice and Strawson did not attempt to defend this definition, I try to show that it indeed gives us a satisfactory account of synonymy. Contrary to Quine, the notion is tighter than stimulus-synonymy – particularly when applied to sentences with less than critical semantic mass (section 3). Now according to Quine, analyticity could be defined in terms of synonymy, if synonymy were to make sense: A sentence is analytic iff synonymous to self-conditionals. This leads us to the following notion of analyticity: S is analytic iff, for all sentences T, the logical conjunction of S and T is stimulus-synonymous to T; an analytic sentence does not change the semantic mass of any theory to which it may be conjoined (section 4). This notion is tighter than Quine's stimulus-analyticity; unlike stimulus-analyticity, it does not apply to those sentences from the very center of our theories which can be assented to come what may, even though they are not synthetic in the intuitive sense (section 5).     

Inquisitive Heyting Algebras

In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures (prime elements represent declarative propositions, non-prime elements represent questions, join is a question-forming operation) and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra.

     

Leibniz Filters Revisited

Leibniz filters play a prominent role in the theory of protoalgebraic logics. In [3] the problem of the definability of Leibniz filters is considered. Here we study the definability of Leibniz filters with parameters. The main result of the paper says that a protoalgebraic logic S has its strong version weakly algebraizable iff it has its Leibniz filters explicitly definable with parameters.     

On the alleged normative significance of a platitude

It seems to be a platitude that the belief that p is correct iff it is true that p. And the claim that truth is the correct‐making feature of belief seems to be just another way of expressing this platitude. It is often thought that this indicates that truth constitutes a normative standard or criterion of correctness for belief because it seems to follow from this platitude that having a false belief is believing wrongly, and having a true belief is believing rightly or correctly. In this paper, I aim to show that when we judge the platitude in question to be indisputably true, we do not endorse that truth is normative for belief but merely the triviality that the belief that p is true iff it is true that p.     

On The Sense and Reference of A Logical Constant

Syntax precedes truth-theoretic semantics when it comes to understanding a logical constant. A constant in a language is logical iff its sense is entirely constituted by certain deductive rules. To be sense-constitutive, deductive rules governing a constant must meet certain conditions; those that do so are sense-constitutive by virtue of understanders' conditional dispositions to feel compelled to accept certain formulae. Acceptance is a cognitive formula-attitude. Since acceptance requires understanding, and a formula can contain more than one occurrence of logical constants, this account involves a 'local holism', but no circularity. I argue that no logical constant is ambiguous between a classical and a constructive sense; but I allow that one constant may have distinct classical and constructive 'semantic values'. A logical constant's sense helps to determine its semantic value, but only together with certain constraints on satisfaction and frustration; it seems that the latter must include 'convention T'-style schemata.     

Consciousness,Higher-Order Content,and the Individuation of Vehicles

One of the distinctive properties of conscious states is thepeculiar self-awareness implicit in them. Two rival accounts of this self-awareness are discussed. Accordingto a Neo-Brentanian account, a mental state M is conscious iff M represents its very own occurrence.According to the Higher-Order Monitoring account, M is merely accompanied by a numerically distinctrepresentation of its occurrence. According to both, then, M is conscious in virtue of figuring in a higher-ordercontent. The disagreement is over the question whether the higher-order content is carried by Mitself or by a different state. While theNeo-Brentanian theory is phenomenologically more attractive, it isoften felt to be somewhat mysterious. It is argued (i) that the difference between the Neo-Brentanian andHigher-Order Monitoring theories is smaller and more empirical than may initially seem, and (ii) that theNeo-Brentanian theory can be readily demystified. These considerations make it prima faciepreferable to the Higher-Order Monitoring theory.     

Epistemology and the law: why there is no epistemic mileage in legal cases

Philosophical Studies - The primary aim of this paper is to defend the Lockean View—the view that a belief is epistemically justified iff it is highly probable—against a new family of...     

Truth in the Tractatus

My paper takes issue both with the standard view that the Tractatus contains a correspondence theory and with recent suggestions that it features a deflationary or semantic theory. Standard correspondence interpretations are mistaken, because they treat the isomorphism between a sentence and what it depicts as a sufficient condition of truth rather than of sense. The semantic/deflationary interpretation ignores passages that suggest some kind of correspondence theory. The official theory of truth in the Tractatus is an obtainment theory – a sentence is true iff the state of affairs it depicts obtains. This theory differs from deflationary theories in that it involves an ontology of states of affairs/facts; and it can be transformed into a type of correspondence theory: a sentence is true iff it corresponds to, i.e. depicts an obtaining state of affairs (fact). Admittedly, unlike correspondence theories as commonly portrayed, this account does not involve a genuinely truth-making relation. It features a relation of correspondence, yet it is that of depicting, between a meaningful sentence and its sense – a possible state of affairs. What makes for truth is not that relation, but the obtaining of the depicted state of affairs. This does not disqualify the Tractatus from holding a correspondence theory, however, since the correspondence theories of Moore and Russell are committed to a similar position. Alternatively, the obtainment theory can be seen as a synthesis of correspondence, semantic and deflationary approaches. It does justice to the idea that what is true depends solely on what is the case, and it combines a semantic explanation of the relation between a sentence and what it says with a deflationary account of the agreement between what the sentence says and what obtains or is the case if it is true     

Virtue Theory and Ideal Observers

Virtue theorists in ethics often embrace the following characterizationof right action: An action is right iff a virtuous agent would performthat action in like circumstances. Zagzebski offers a parallel virtue-basedaccount of epistemically justified belief. Such proposals are severely flawedbecause virtuous agents in adverse circumstances, or through lack ofknowledge can perform poorly. I propose an alternative virtue-based accountaccording to which an action is right (a belief is justified) for an agentin a given situation iff an unimpaired, fully-informed virtuous observerwould deem the action to be right (the belief to be justified).     

THE LIMITS OF NEO-ARISTOTELIAN PLENITUDE (AND ITS CONCEPTUAL NEIGHBORS)

Neo-Aristotelian Plenitude is the thesis that, necessarily, any property that could be had essentially by something or other is had essentially by something or other if and only if and because it is instantiated; any essentializable property is essentialized iff and because it is instantiated. In this paper, I develop a partial nonmodal characterization of ‘essentializable' and show it cannot be transformed into a full characterization. There are several seemingly insurmountable obstacles that any full characterization of essentializability must overcome. Moreover, these obstacles threaten other views in the conceptual neighborhood such as Counterpart Theoretic Plenitude and Conceptualist Plenitude.     

Color,Relativism, and Realism

It is plausible to think that some animals perceive the world as coloreddifferently from the way humans perceive it. I argue that the best way ofaccommodating this fact is to adopt perceiver-relativism, the view that colorpredicates express relations between objects and types of perceivers.Perceiver-relativism makes no claim as to the identity of color properties;it is compatible with both physicalism and dispositionalism. I arguehowever for a response-dependence version of it according to which an object counts as red (for a type of perceiver) iff it standardly looks red to normal perceivers (of that type). Finally, I develop a notion of minimal realism on which this account counts as realist despite its subjectivist elements, in that it is committed to the objectivityof truth.     

On decidable consequence operators

The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.     

Synonymy in sentential languages: a pragmatic view

In this note two notions of meaning are considered and accordingly two versions of synonymy are defined, weaker and stronger ones. A new semantic device is introduced: a matrix is said to be pragmatic iff its algebra is in fact an algebra of meanings in the stronger sense. The new semantics is proved to be universal enough (Theorem 1), and it turns out to be in some sense a generalization of Wójcicki's referential semantics (Theorem 3).     

The logic of ability,freedom and responsibility

The aim of this paper is to offer a rigorous explication of statements ascribing ability to agents and to develop the logic of such statements. A world is said to be feasible iff it is compatible with the actual past-and-present. W is a P-world iff W is feasible and P is true in W (where P is a proposition). P is a sufficient condition for Q iff every P world is a Q world. P is a necessary condition for Q iff Q is a sufficient condition forP. Each individual property S is shown to generate a rule for an agent X. X heeds S iff X makes all his future choices in accordance with S. (Note that X may heed S and yet fail to have it). S is a P-strategy for X iff X's heeding S together with P is a necessary and sufficient condition for X to have S. (P-strategies are thus rules which X is able to implement on the proviso P).Provisional opportunity: X has the opportunity to A provided P iff there is an S such that S is a P-strategy for X and X's implementing S is a sufficient condition for X's doing A. P is etiologically complete iff for every event E which P reports P also reports an etiological ancestry of E, and P is true. Categorical opportunity: X has the opportunity to A iff there is a P such that P is etiologically complete and X has the opportunity to A provided P. For X to have the ability to A there must not only be an appropriate strategy, but X must have a command of that strategy. X steadfastly intends A iff X intends A at every future moment at which his doing A is not yet inevitable. X has a command of S w.r.t. A and P iff X's steadfastly intending A together with P is a sufficient condition for X to implement S. Provisional ability: X can A provided P iff there is an S such that S is a P-strategy for X, X's implementing S is a sufficient condition for X's doing A, and X has a command of S w.r.t. A and P. Categorical ability: X can A iff there is a P such that P is etiologically complete and X can A provided P. X is free w.r.t. to A iff X can A and X can non- A. X is free iff there is an A such that X is free w.r.t. A.     

分次模态传递框架类(英文)

本文证明分次模态逻辑在有穷传递框架类中的Goldblatt-Thomason定理。一个有穷传递框架类可由分次模态公式集定义当且仅当它在不相交并、生成子框架和分次有界态射像下封闭。该定理的证明使用带根的有穷传递框架的分次Jankov-Fine公式。     

Emergent Powers

Topoi - I shall introduce at the beginning of the paper a characterization of strong ontological emergence. According to it, roughly, something strongly emerges from some other thing(s) iff the...     

The Art Type Theory of Art

Abstract

The theory I present and defend in this paper—what I term the art type theory— holds that something is a work of art iff it belongs to an established art type. Something is an established art type, in turn, either because its paradigmatic instances standardly satisfy eight art-making conditions, or because the art world has seen fit to enfranchise it as such. It follows that the art status of certain objects is independent of what any individual or culture might say about it, while the art status of others fundamentally depends on the judgment of the art world. Because of the theory's quasi-institutional component, I conclude by defending it against four objections that have been raised against institutional definitions.     

Temporal Predication with Temporal Parts and Temporal Counterparts

If ordinary objects have temporal parts, then temporal predications have the following truth conditions: necessarily, (a is F) at t iff a has a temporal part that is located at t and that is F. If ordinary objects have temporal counterparts, then, necessarily, (a is F) at t iff a has a temporal counterpart that is located at t and that is F. The temporal-parts account allows temporal predication to be closed under the parthood relation: since all that is required to be F at t is to have a temporal part, a t, that is located at t and that is F, every object that has a t as a temporal part is F at t. Similarly for the temporal-counterparts account. Both closure under parthood and closure under counterparthood are shown to have unacceptable consequences. Then strategies for avoiding closure are considered and rejected.