Frege famously argued that truth is not a property or relation. In the “Notes on Logic” Wittgenstein emphasised the bi-polarity of propositions which he called their sense. He argued that “propositions by virtue of sense cannot have predicates or relations.” This led to his fundamental thought that the logical constants do not represent predicates or relations. The idea, however, has wider ramifications than that. It is not just that propositions cannot have relations to other propositions but also that they cannot (...) have relations to anything at all. The paper explores the consequences of this insight for the way in which we should read the Tractatus. In the “Notes on Logic” the insight led to Wittgenstein's emphasis on “facts” in any attempt to understand the nature of symbolism. This emphasis is continued in the Tractatus. It is central to his view that propositions are facts which picture facts which prevent us from construing such picturing as a relation between what pictures and what is pictured. It illuminates the importance of context principle with regard to the distinction between showing and saying to which Wittgenstein attached so much importance and it underlies the non-relational view of psychological propositions which he advocates. Finally, if propositions by virtue of sense cannot have predicates or relations the paradox at the end of a work which consist largely of propositions about propositions becomes intelligible. (shrink)

This book articulates and defends Fregean realism, a theory of properties based on Frege's insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley's Regress and the Problem of Universals, but also to understanding the relationship between states of affairs, propositions, and the truth conditions of sentences. Fregean realism, Trueman suggests, ultimately leads to (...) a version of the identity theory of truth, the theory that true propositions are identical to obtaining states of affairs. In other words, the identity theory collapses the gap between mind and world. This book will be of interest to anyone working in logic, metaphysics, the philosophy of language or the philosophy of mind. (shrink)

The analysis of knowledge and belief has provoked intensive discussions in philosophy and linguistics. One of the issues in this area is the semantics of attitude verbs whose complement expresses a thought about the Self of the thinking person. What is the content of my belief when I think that I am tired? Some philosophers propose it is a proposition, others think it is a property. It will be shown in this essay that existing proposals in either direction are unsatisfying. (...) The property theorist expells the subject of the predicate "tired" from the analysis; their theory is at best incomplete. The propositionalist has difficulties with the analysis of the pronoun that refers back to the subject of the attitude, as is the case with "he" in "Wolfgang believes he is tired". The present new proposal ventures the idea that a conscious person is endowed with their own Logical Space that deviates from the standard model in providing for a separate entity, the Self, as the object or target of inner thoughts about oneself. Moreover, this Logical Space leaves room for linguistic error: in such a model, subjects may be unable to correctly identify the reference of a name or may fail to identify the Self with its bearer. By contrast, reference to the Self is immune to error through misidentification, it is a paradigm case of brute indexicality. In consequence, de se pronouns are rigid designators in the sense of Kripke. The book solves several puzzles of reference failure and explores numerous consequences for the semantics of attitude reports and for possible world semantics in general. (shrink)

ABSTRACT Section 1 discusses properties and propositions, and some of the motivation for an account in which property instantiation and propositional truth behave ‘naively’. Section 2 generalizes a standard Kripke construction for naive properties and propositions, in a language with modal operators but no conditionals. Whereas Kripke uses a 3-valued value space, the generalized account allows for a broad array of value spaces, including the unit interval [0,1]. This is put to use in Section 3, where I (...) add to the language a conditional suitable for restricting quantification. The shift from a value space based on the ‘mini-space’ {0,, 1} to one based on the ‘mini-space’ [0,1] leads to more satisfactory results than I was able to achieve in previous work: a vast variety of paradoxical sentences can now be treated very simply. In Section 4 I make a further addition to the language, a conditional modeled on the ordinary English conditional, paying particular attention to how it interacts with the restricted quantifier conditional. This is all done in the [0,1] framework, and two alternatives are considered for how the ordinary conditional is to be handled; one of them results from adding a tweak to a construction by Ross Brady. Section 5 discusses a further alternative, a standard relevance conditional (for the ordinary conditional, perhaps for use with a different quantifier-restricting conditional), but argues that it is not promising. Section 6 discusses the identity conditions of properties and propositions (again in the setting of a value space based on [0,1]); the issue of achieving naivety for coarse-grained properties is seen to be more complicated than some brief remarks in Field [2010] suggested, but a way to get a fair degree of coarse-grainedness is shown. (shrink)

In this paper by using a model-theoretic approach, we prove Craig interpolation property for Formal Propositional Logic, FPL, Basic propositional logic, BPL and the uniform left-interpolation property for FPL. We also show that there are countably infinite extensions of FPL with the uniform interpolation property.

Speaks defends the view that propositions are properties: for example, the proposition that grass is green is the property being such that grass is green. We argue that there is no reason to prefer Speaks's theory to analogous but competing theories that identify propositions with, say, 2-adic relations. This style of argument has recently been deployed by many, including Moore and King, against the view that propositions are n-tuples, and by Caplan and Tillman against King's view that propositions are (...) facts of a special sort. We offer our argument as an objection to the view that propositions are unsaturated relations. (shrink)

I defend the view that propositions are a kind of property which is true iff it is instantiated. I discuss how we should think about propositional attitudes on this sort of view, and explain why I favor this sort of view over the more familiar Chisholm/Lewis view that attitudes are self-ascriptions of properties. I conclude by raising, and briefly discussing, two problems for the kind of view of propositions I favor.

Everyone working on metaphysical questions about properties or propositions knows the reaction that many non-philosophers, even nonmetaphysicians, have to such questions. Even though they agree that Fido is a dog and thus has the property (or feature or characteristic) of being a dog, it seems weird, suspicious, or confused to them to now ask what that thing, the property of being a dog, is. The same reservations do not carry over to asking what this thing, Fido, is. There is (...) a substantial and legitimate project to find out more about Fido, but is there a similar substantial and legitimate project to find out more about the property of being a dog? Metaphysicians know that there is a straightforward way to motivate such a project, and much of the contemporary debate in the metaphysics of properties is in the ballpark of carrying it out. If we agree that Fido has the property of being a dog, then there is something that is a property and that Fido has. Thus we can ask about what this thing is that he has. How does it relate to Fido? Is it concrete or abstract? Is it fully present in each object that has it? And so on and so forth. Maybe the nonphilosophers are merely not used to asking such questions about unusual entities such as properties, but they are equally legitimate for them as they are for any other thing. However, even metaphysicians sometimes have the nagging feeling that something has gone wrong in the metaphysics of properties, and that a substantial metaphysical investigation into their.. (shrink)

In the paper Weaver's method is adapted to prove interpolation properties of many-valued propositional calculi standard in the sense of Rosser and Turquette. The case of n-valued Lukasiewicz calculi is discussed in connection with the results obtained.

In orthodox quantum mechanics, it has virtually become the custom to identify properties of a physical system with operationally testable propositions about the system. The causes and consequences of this practice are explored mathematically in this paper. Among other things, it is found that such an identification imposes severe constraints on the admissible states of the physical system.

A simple model accounting for semantic properties of propositional attitude operators in negative contexts with no reference to possible worlds is proposed. Verbs occurring in such operators denote relations between individuals and specific sets of sentences (of a given natural language) and their negation is defined as the complement within a specific set of cognitively determined sentences. This approach avoids in particular the problem of intensionality of propositional attitude operators and allows to use many tools from the (...) generalised quantifier theory. In that way the negation giving rise to factive presuppositions and to the neg-raising is defined in a natural way. (shrink)

I argue that the best way to solve Russell's problem of the relationship between propositions and their constituents is to think of propositions as properties of worlds. I argue that this view preserves the strengths and avoids some of the weaknesses of the view of the metaphysics of propositions defended by Jeff King in his _The Nature and Structure of Content_, and that it provides an explanation of the representational properties of propositions and the nature of indexical belief. (...) I conclude by discussing some problems about how to think about the semantics of propositional attitude ascriptions, if a view of this sort is correct. (shrink)

This paper discusses a problem for Russellian propositions. According to Russellianism, each word in a sentence contributes its referent to the proposition expressed by the sentence. Russellian propositions have normally been conceived of as problematic for two reasons, viz. they cannot account for the unity of the proposition and they have problems with non-referring singular names. In this paper, I argue that Russellianism also faces a problem with respect to properties. It is inconsistent with both traditional realism and trope-theories. (...) The only theory of properties which is consistent with Russellianism is Platonism. Moreover, it is argued that Russellianism needs a particularly implausible version of Platonism. (shrink)

In this paper we give a rather detailed algebraic investigation of interpolation and Beth’s property in propositional many-valued logics extending Hájek’s Basic Logic [P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, 1998], and we connect such properties with amalgamation and strong amalgamation in the corresponding varieties of algebras. It turns out that, while the most interesting extensions of in the language of have deductive interpolation, very few of them have Beth’s property or Craig interpolation. Thus in the last part (...) of the paper we look for conservative extensions of having such properties. (shrink)

The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: γ, xn → y / γ, xm → y. It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite (...) model property with respect to its algebraic semantics and hence that the logic is decidable. (shrink)

In the paper we give a sucient condition of the Interpolation Property in propositional calculi; then we establish the power of the class of the systems with Craig's property. Next we show that there does not exist a minimal R0-system with Craig-Godel-Lindenbaum's property. Finally, we generalize Sobocinski-Tarskis theorem concerning Sobocinski-Tarski's property.

This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close (...) of the paper, the origin of incompleteness in logic is investigated. The culprit is found to be the predication relation, a relation on properties and relations that is expressed in natural language by the copula. (shrink)

A defense of an ontology of propositions and of some logical resources for representing them. It begins with an austere formulation of a theory of propositions in a first-order extensional logic, but then uses the commitments of this theory to justify an enrichment to modal logic - the logic of necessity and possibility - as an appropriate framework for regimented languages that are constructed to represent any of our scientific and philosophical commitments. Both the proof-theory and the model theory of (...) a first-order quantified modal logic are developed in detail, and it is argued that these formal resources help to sharpen questions about ontology and predication. The clarification of predication helps to provide a motivation for extending our ontological commitment to properties and relations that are expressed by predicates, and for extending the logic to a higher-order modal logic that provides a conception of metaphysical modality that allows for the contingent existence, not only of persons and physical objects, but also of properties, relations and propositions. Even though both the specific ontological commitments defended (to propositions, properties and relations) and the logical resources that are used to defend them (modal and higher-order logic) were famously rejected by W. V. Quine, the book adopts a self-consciously neo-Quinean methodology, and argues that the theory that is developed helps to motivate and clarify Quine's naturalistic metaphysical picture. (shrink)

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with (...) propositional functions, crucial fine-grained intensional distinctions would be lost. (shrink)

We introduce and investigate the notion of uniform Lyndon interpolation property which is a strengthening of both uniform interpolation property and Lyndon interpolation property. We prove several propositional modal logics including \, \, \ and \ enjoy ULIP. Our proofs are modifications of Visser’s proofs of uniform interpolation property using layered bisimulations Gödel’96, logical foundations of mathematics, computer science and physics—Kurt Gödel’s legacy, Springer, Berlin, 1996). Also we give a new upper bound on the complexity of uniform interpolants for (...) \ and \. (shrink)

It is shown that two arguments given by Alvin Plantinga, which he offers to refute the existentialist thesis that propositions, states of affairs, and properties are ontologically dependent upon the objects they are directly about, are unsound. The existentialist position is then defended on the basis of both some intuitive considerations and a rigorous argument that does not presuppose any particular theory of the nature of propositions, states of affairs, and properties.

It is shown that two arguments given by Alvin Plantinga, which he offers to refute the existentialist thesis that propositions, states of affairs, and properties are ontologically dependent upon the objects they are directly about, are unsound. The existentialist position is then defended on the basis of both some intuitive considerations and a rigorous argument that does not presuppose any particular theory of the nature of propositions, states of affairs, and properties.

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.

This is a review of "Properties and Propositions: The Metaphysics of Higher-Order Logic" by Robert Trueman. Following an overview of the main themes of the book, I discuss the metaphysical presuppositions of Trueman's Fregean notation for predicate abstraction and evaluate his argument for strict typing.

A central dispute in discussions of self-locating attitudes is whether attitude relations like believing and knowing are relations between an agent and properties (things that vary in truth value across individuals) or between an agent and propositions (things that do not so vary). Proponents of the proposition view have argued that the property view is unable to give an adequate account of relations like communication and agreement. We agree with this critique of the property view, and in this essay (...) we show that the problems facing the property view are much more serious than has been appreciated. We then develop and explore two versions of the proposition view. In each case, we show how facts about the self-ascription of properties may be determined by facts about propositional attitudes in conjunction with certain other facts. (shrink)

Peter Hanks defends a new theory about the nature of propositional content, according to which the basic bearers of representational properties are particular mental or spoken actions. He explains the unity of propositions and provides new solutions to a long list of puzzles and problems in philosophy of language.

Propositions play a central role in contemporary semantics. On the Russellian account, propositions are structured entities containing particulars, properties and relations. This contrasts sharply with the sets-of-possible-worlds view of propositions. I’ll discuss how to extend the sets-of-worlds view to accommodate fine-grained hyperintensional contents. When this is done in a satisfactory way, I’ll argue, it makes heavy use of entities very much like Russellian tuples. The two notions of proposition become inter-definable and inter-substitutable: they are not genuinely distinct accounts of (...) how propositions represent what they represent. Semantic theorists may move freely between the two conceptions of what propositions are. Nevertheless, the two approaches give different accounts of the metaphysical nature of propositions. I argue that the sets-of-worlds view provides an adequate account of the nature of propositions, whereas the Russellian view cannot. (shrink)

This paper is a survey of results concerning the disjunction property, Halldén-completeness, and other related properties of intermediate prepositional logics and normal modal logics containing S4.

Infinitely many intermediate propositional logics with the disjunction property are defined, each logic being characterized both in terms of a finite axiomatization and in terms of a Kripke semantics with the finite model property. The completeness theorems are used to prove that any two logics are constructively incompatible. As a consequence, one deduces that there are infinitely many maximal intermediate propositional logics with the disjunction property.

To be a proposition is to possess propositional properties and to stand in inferential relations. This is the organic intuition, [OI], concerning propositional recognition. [OI] is not a circular characterization as long as those properties and relations that signal the presence of propositions are independently identified. My take on propositions does not depart from the standard approach widely accepted among philosophers of language. Propositions are truth-bearers, the arguments of truth-functions (‘not’, ‘or’, ‘and’, ‘if’), the arguments of (...) propositional-attitude verbs (‘know’, ‘believe’, ‘doubt’, ‘assume’, ‘reject’) and the kind of entity capable of standing in inferential relations (which are basically implication and incompatibility). The aim of this paper is to argue for [OI]. In doing so, I will show that even what is probably the most repeated argument against non-descriptivism, the so-called Frege-Geach Argument (FGA), presupposes something like [OI], a presupposition that Geach shares with his critics. Despite the huge success of FGA, a thorough analysis of the actual scope of this argument has yet to be given. I will provide such an analysis in section 3 below. In this paper, I argue that [OI] is a meta-theoretical principle which is neutral with respect to specific metaphysical debates about the nature of propositions, as well as specific proposals about the semantics of declarative sentences. (shrink)

The simple substitution property provides a systematic and easy method for proving a theorem from the additional axioms of intermediate prepositional logics. There have been known only four intermediate logics that have the additional axioms with the property. In this paper, we reformulate the many valued logics S' n defined in Gödel [3] and prove the simple substitution property for them. In our former paper [9], we proved that the sets of axioms composed of one prepositional variable do not have (...) the property except two of them. Here we provide another proof for this theorem. (shrink)

This is the first part of a paper concerning intermediate propositional logics with the disjunction property which cannot be properly extended into logics of the same kind, and are therefore called maximal. To deal with these logics, we use a method based on the search of suitable nonstandard logics, which has an heuristic content and has allowed us to discover a wide family of logics, as well as to get their maximality proofs in a uniform way. The present part (...) illustrates infinitely many maximal logics with the disjunction property extending the well-known logic of Scott, and aims to provide a first picture of the method, sufficient for the reader who wish to achieve an overall understanding of it without entering into the further aspects developed in the second part. From this point of view, the latter will not be self-standing, but will be seen as a prosecution and a complement of the former, with the aim that the material presented in the whole paper can be used as a starting point for a classification of the subject. (shrink)

This is the second part of a paper devoted to the study of the maximal intermediate propositional logics with the disjunction property , whose first part has appeared in this journal with the title “A method to single out maximal propositional logics with the disjunction property I”. In the first part we have explained the general results upon which a method to single out maximal constructive logics is based and have illustrated such a method by exhibiting the Kripke (...) semantics of maximal constructive logics extending the logic ST of Scott, for which, in turn, a semantical characterization in terms of Kripke frames has been given. In the present part we complete the illustration of the method of the first part, having in mind some aspects which might be interesting for a classification of the maximal constructive logics, and an application of the heuristic content of the method to detect the nonmaximality of apparently maximal constructive logics. Thus, on the one hand we introduce the logic AST , which is compared with ST and is seen as a logic “alternative” to it, in a sense which will be precisely explained. We provide a Kripke semantics for AST and show that there are maximal constructive logics which neither are extensions of ST nor are extensions of AST. Finally, we give a further application of the results of the first part by exhibiting the Kripke semantics of a maximal constructive logic extending AST. On the other hand, we compare the maximal constructive logics presented in both parts of the paper with a constructive logic introduced by Maksimova , which has been conjectured to be maximal by Chagrov and Zacharyashchev ; from this comparison a disproof of the conjecture arises. (shrink)

The simple substitution property provides a systematic and easy method for proving a theorem by an axiomatic way. The notion of the property was introduced in Hosoi [4] but without a definite name and he showed three examples of the axioms with the property. Later, the property was given it's name as above in Sasaki [7].Our main result here is that the necessary and sufficient condition for a logicL on a finite slice to have the simple substitution property is thatL (...) is finite. Here the necessity part is essentially new, for the sufficiency part has been proved in Hosoi and Sasaki [5]. Also the proof of sufficiency part is improved here. (shrink)