Axiomatizing geometric constructions

In this survey paper, we present several results linking quantifier-free axiomatizations of various Euclidean and hyperbolic geometries in languages without relation symbols to geometric constructibility theorems. Several fragments of Euclidean and hyperbolic geometries turn out to be naturally occurring only when we ask for the universal theory of the standard plane (Euclidean or hyperbolic), that can be expressed in a certain language containing only operation symbols standing for certain geometric constructions.     

Googled assertion

Recent work in the philosophy of mind and cognitive science can help to explain why certain kinds of assertions—made on the basis of information stored in our gadgets rather than in biological memory—are properly criticizable in light of misleading implicatures, while others are not.     

Axiomatizing the Logic of Imagination

In a recent paper Berto introduces a semantic system for a logic of imagination, intended as positive conceivability, and aboutness of imaginative acts. This system crucially adopts elements of both the semantics of conditionals and the semantics of analytical implications in order to account for the central logical traits of the notion of truth in an act of imagination based on an explicit input. The main problem left unsolved is to put forward a complete set of axioms for the proposed system. In the present paper I offer a solution to this problem by providing a complete axiomatization of a generalization of the original semantics. The difficulty in proving completeness lies in the fact that the modalities that capture the notion of truth in an act of imagination are neither standard nor minimal, so that the construction of the canonical model and the proof of the truth lemma are to be substantially modified.

     

Centered assertion

I suggest a way of extending Stalnaker’s account of assertion to allow for centered content. In formulating his account, Stalnaker takes the content of assertion to be uncentered propositions: entities that are evaluated for truth at a possible world. I argue that the content of assertion is sometimes centered: the content is evaluated for truth at something within a possible world. I consider Andy Egan’s proposal for extending Stalnaker’s account to allow for assertions with centered content. I argue that Egan’s account does not succeed. Instead, I propose an account on which the contents of assertion are identified with sets of multi-centered worlds. I argue that such a view not only provides a plausible account of how assertions can have centered content, but also preserves Stalnaker’s original insight that successful assertion involves the reduction of shared possibilities.     

Axiomatizing Relativistic Dynamics without Conservation Postulates

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc ². The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.     

Axiomatizing logics closely related to varieties

Let V be a s.f.b. (strongly finitely based, see below) variety of algebras. The central result is Theorem 2 saying that the logic defined by all matrices (A, d) with d A V is finitely based iff the A V have 1^st order definable cosets for their congruences. Theorem 3 states a similar axiomatization criterion for the logic determined by all matrices (A, ^A), A V, a term which is constant in V. Applications are given in a series of examples.     

Knowledge and suberogatory assertion

I accomplish two things in this paper. First I expose some important limitations of the contemporary literature on the norms of assertion and in the process illuminate a host of new directions and forms that an account of assertional norms might take. Second I leverage those insights to suggest a new account of the relationship between knowledge and assertion, which arguably outperforms the standard knowledge account.     

Axiomatizing collective judgment sets in a minimal logical language

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula expresses that is collectively accepted, or that is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where holds if a majority of individuals accepts, consensus voting, where holds if all individuals accept, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures.     

Vision,knowledge, and assertion

I report two experiments studying the relationship among explicit judgments about what people see, know, and should assert. When an object of interest was surrounded by visibly similar items, it diminished people’s willingness to judge that an agent sees, knows, and should tell others that it is present. This supports the claim, made by many philosophers, that inhabiting a misleading environment intuitively decreases our willingness to attribute perception and knowledge. However, contrary to stronger claims made by some philosophers, inhabiting a misleading environment does not lead to the opposite pattern whereby people deny perception and knowledge. Causal modeling suggests a specific psychological model of how explicit judgments about perception, knowledge, and assertability are made: knowledge attributions cause perception attributions, which in turn cause assertability attributions. These findings advance understanding of how these three important judgments are made, provide new evidence that knowledge is the norm of assertion, and highlight some important subtleties in folk epistemology.     

Knowledge,certainty, and assertion

Researchers have debated whether knowledge or certainty is a better candidate for the norm of assertion. Should you make an assertion only if you know it's true? Or should you make an assertion only if you're certain it's true? If either knowledge or certainty is a better candidate, then this will likely have detectable behavioral consequences. I report an experiment that tests for relevant behavioral consequences. The results support the view that assertability is more closely linked to knowledge than to certainty. In multiple scenarios, people were much more willing to allow assertability and certainty to come apart than to allow assertability and knowledge to come apart.     

Problems for factive accounts of assertion

The knowledge account of assertion construes assertion as subject to constitutive norms. In its standard version, it combines a wide scope obligation not to assert p without knowing p, with narrow scope principles specifying conditions under which it is permissible to assert p, where the notions of obligation and permission are duals and behave uniformly for variable p. It is argued that, given natural assumptions about the logic of ‘ought’, the account proves incoherent. The argument generalizes to accounts that substitute other factive notions for knowledge. A recent non-standard version of the knowledge account employs proposition-relative norms and circumvents the problem. However, it still leads to intolerable combinations of verdicts. Again, the problem arises because knowledge is factive, and it generalizes to other factive notions. It is shown that non-factive accounts face none of the diagnosed difficulties and can do much of the explanatory work that the knowledge account is alleged to do.     

Epistemic modals, relativism and assertion

I think that there are good reasons to adopt a relativist semantics for epistemic modal claims such as ``the treasure might be under the palm tree', according to which such utterances determine a truth value relative to something finer-grained than just a world (or a <world, time> pair). Anyone who is inclined to relativise truth to more than just worlds and times faces a problem about assertion. It's easy to be puzzled about just what purpose would be served by assertions of this kind, and how to understand what we'd be up to in our use of sentences like ``the treasure might be under the palm tree', if they have such peculiar truth conditions. After providing a very quick argument to motivate a relativist view of epistemic modals, I bring out and attempt to resolve this problem in making sense of the role of assertions with relativist truth conditions. Solving this problem should be helpful in two ways: first, it eliminates an apparently forceful objection to relativism, and second, spelling out the relativist account of assertion and communication will help to make clear just what the relativist position is, exactly, and why it's interesting. Thanks to Brian Weatherson, John Hawthorne, Daniel Stoljar, Frank Jackson, Ben Blumson, Seth Yalcin, Karen Bennett, Kent Bach, Matthew Weiner, Jonathan Kvanvig, Eric Swanson, David Chalmers, Agustin Rayo, Dustin Locke, Aaron Bronfman, Michael Allers, Ivan Mayerhofer, and to the participants at the BSPC 2005 for helpful discussion.