Book Information Resemblance Nominalism: A Solution to the Problem of Universals. By Gonzalo Rodriguez-Pereyra. Clarendon Press. Oxford. 2002. Pp. xii + 238. £35.

Resemblance Nominalism: A Solution to the Problem of Universals

Individuality: An Essay on the Foundations of Metaphysics.

The paper develops an interface between syntax-based logical models of awareness and dynamic epistemic logic. The framework is shown to be able to accommodate a variety of notions of awareness and knowledge, as well as their dynamics. This, it is argued, offers a natural formal environment for the analysis of epistemic phenomena typical of multi-agent information exchange, such as how agents become aware of relevant details, how they perform inferences and how they share their information within a group. Technically, the logics presented are all simple refinements of the logic of public announcements.

Syntactic awareness in logical dynamics

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

 $$\square \varphi$$
 expresses that
 $$\varphi$$
 is collectively accepted, or that
 $$\varphi$$
 is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where
 $$\square \varphi$$
 holds if a majority of individuals accepts
 $$\varphi$$
 , consensus voting, where
 $$\square \varphi$$
 holds if all individuals accept
 $$\varphi$$
 , and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures.

Axiomatizing collective judgment sets in a minimal logical language

How are objects of different logical types re-identified in time? For instance, how are physical objects re-identified? What is the role of continuity – and what is meant by continuity? The notion of the boundary of a persistent physical object is reminiscent of the notion of stable singularity (in this case, a surface of stable singularities) in the stability theory of differential equations. Is this theory the true logic of the re-identification of physical objects? How are particles re-identified in quantum physics?

哲學問題 = The problems of philosophy

In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence

Modal Logic: An Introduction to its Syntax and Semantics

A formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. The absolute consistency of the system is proved. A completeness proof for the system is also constructed. This proof is relative to a concept of logical validity provided by a semantics, which assumes as its philosophical background an approach to sortals from a modern form of conceptualism.

A Complete and Consistent Formal System for Sortals

With the past and future tense propositional operators in its syntax, a formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. A completeness proof for the system is constructed and its absolute consistency proved. The completeness proof is given relative to a notion of logical validity provided by an intensional semantic system, which assumes an approach to sortals from a modern form of conceptualism.

A Temporal Logic for Sortals

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.

A modal sortal logic

We shall distinguish between sortal predication and standard predication. The former kind of predication necessarily involves sortal concepts but the latter, as it is customarily viewed, does not. It is generally thought that the only essential occurrence of a concept in a standard predication is the concept being predicated. In this paper, we shall put forward an alternative view. We shall propose to understand standard predication as a cognitive act essentially requiring sortal concepts. We shall call this view conceptual predication sortalism and ground it on the basis of epistemic-semantic reasons. Concepts are understood as intersubjectively realizable capacities or abilities that fulfill particular cognitive roles, such as those of classification, categorization, individuation, and referring.

Predication and sortal concepts

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