'There is much food for thought in McGinn's discussions and each chapter is rich with a series of considerations for thinking that the currently received views on the various topics have some serious difficulties that need confronting... For those interested in metaphysics and the philosophy of logic, this book will stimulate much further thought' -Mind 'The sweep of the book is broad and the pace is brisk... There is much material here to provide the basis for many a deep philosophical (...) discussion' -Mind 'Lucid and provocative little book... clear, direct and well argued' -Times Higher Education SupplementIdentity, existence, predication, necessity, and truth are fundamental philosophical concerns. Colin McGinn treats them both philosophically and logically, aiming for maximum clarity and minimum pointless formalism. He contends that there are real logical properties that challenge naturalistic metaphysical outlooks. These concepts are not definable, though we can say a good deal about how they work. The aim of Logical Properties is to bring philosophy back to philosophical logic. (shrink)

Identity, existence, predication, necessity, and truth are fundamental philosophical concerns. Colin McGinn treats them both philosophically and logically, aiming for maximum clarity and minimum pointless formalism. He contends that there are real logical properties that challenge naturalistic metaphysical outlooks. These concepts are not definable, though we can say a good deal about how they work. The aim of Logical Properties is to bring philosophy back to philosophical logic.

The aim of this short book is to discuss the traditional topics of philosophical logic without the “formalistic fetishism and scholasticism” that McGinn associates with recent work in the field. The writing is indeed crisp, engaging, and free of formalisms. The book consists of five separate essays—one each on identity, existence, predication, necessity, and truth—loosely united by the general theme that these “logical properties” are real and irreducible. “These concepts,” McGinn says, “form a conceptual bedrock; they stand, as (...) it were, underneath all our other concepts. They have no analysis”. (shrink)

A unified answer is offered to two distinct fundamental questions: whether a nonclassical solution to the semantic paradoxes should be extended to other apparently similar paradoxes and whether a nonclassical logic should be expressed in a nonclassical metalanguage. The paper starts by reviewing a budget of paradoxes involving the logical properties of validity, inconsistency, and compatibility. The author’s favored substructural approach to naive truth is then presented and it is explained how that approach can be extended in a (...) very natural way so as to solve a certain paradox of validity. However, three individually decisive reasons are later provided for thinking that no approach adopting a classical metalanguage can adequately account for all the features involved in the paradoxes of logical properties. Consequently, the paper undertakes the task to do better, and, building on the system already developed, introduces a theory in a nonclassical metalanguage that expresses an adequate logic of naive truth and of some naive logical properties. (shrink)

Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably construed, in accordance (...) with an abundant or deflationary conception, Quine’s charge can be resisted. This interpretation need not be seen as precluding the use of model-theoretic semantics for second-order languages; but it will preclude the use of the standard semantics, along with the more general Henkin semantics, of which it is a special case. To that extent, the approach I recommend has revisionary implications which some may find unpalatable; it is, however, compatible with the quite different special case in which the second-order variables are taken to range over definable subsets of the first-order domain, and with respect to such a semantics, some important metalogical results obtainable under the standard semantics may still be obtained. In my final section, I discuss the relations between second-order logic, interpreted as I recommend, and a strong version of schematic ancestral logic promoted in recent work by Richard Heck. I argue that while there is an interpretation on which Heck’s logic can be contrasted with second-order logic as standardly interpreted, when it is so interpreted, its differences from the more modest form of second-order logic I advocate are much less substantial, and may be largely presentational. (shrink)

Since Kit Fine presented his counter-examples to the standard versions of the modal view, many have been convinced that the standard versions of the modal view are not adequate. However, the scope of Fine's argument has not been fully appreciated. In this paper, I aim to carry Fine’s argument to its logical conclusion and argue that once we embrace the intuition underlying his counter-examples, we have to hold that properties obtained, totally or partially, by application of logical (...) operations are not essential to non-logical entities. I also demonstrate that most of the post-Finean versions of the modal view, which were developed to accommodate Fine’s counter-examples, entail that such properties are essential to the entities, and so fail to capture the notion of essence at issue in Fine's counter-examples. Additionally, I explore the consequence of my argument for Fine’s proposed logic of essence. The logic turns out to be inadequate in its present shape as it represents such properties to be essential to the entities. I conclude by developing a modification to the logic to overcome the shortcoming. (shrink)

Trenton Merricks argues that on any reasonable account, warrant must entailtruth. I demonstrate three theses about the properties ofwarrant: (1) Warrant is not unique;there are many properties that satisfy the definition of warrant. (2) Warrant need not entail truth; there are some warrant properties that entailtruthand others that do not. (3) Warrant need not be closed under entailment, even if knowledge is. If knowledge satisfies closure, then some warrant properties satisfy closure while others do not;if knowledge (...) violates closure, then allwarrant properties violate closure. (shrink)

In quantum logics, the notions of strong and full order determination and unitality for states on orthomodular posets are well known. These notions are defined for hypergraphs and their state spaces in a consistent manner and the relations between them and to the notions defined for orthomodular posets are discussed. The state space of a hypergraph is a polytope. This polytope is a simplex if and only if every superposition of pure states is a mixture of these same pure states. (...) Isomorphic hypergraphs have convexly isomorphic state spaces. A class of hypergraphs is given whose group of automorphisms is group-isomorphic to the group of convex automorphisms of their state spaces. (shrink)

In the classical account of knowledge, S knows that P if and only if S believes that P, S is justified in believing that P, and P is true (JTB).. In 1963, Gettier presented two problems that casted doubt on this account. Since then, numerous authors proposed modifications or clarifications of JTB, however, these efforts have not produced a satis-factory solution. In this paper, the focus is on logical properties of justification. The Get-tier problem Case II is expressed (...) in sentential logic and Gettier Minimal Assumption (GMA) is introduced. It is shown that Gettier must have used GMA or some other as-sumption that entails GMA in his construction of Case II. Rejection of GMA solves Get-tier problem Case II and it is a step towards a better understanding of the logical proper-ties of justification and knowledge. (shrink)

Each of the topics mentioned in the title has its own chapter. The unifying theme is McGinn’s conception of naive common sense views of identity, existence, predication, necessity, and truth, which are argued for as being correct. McGinn thinks they should replace entrenched rival treatments of these subjects. However, some of the views McGinn takes as naive seem far from naive or in common use to this reader. This is a technical work in philosophical logic, not in the sense that (...) it is strewn with technical symbols of formal logic. It takes up and discusses topics in a sophisticated way suitable for those working in the area and is not intended primarily for novices in the subject. Having said that, it is well written and clear so that there is much that would be rewarding to nonspecialists who wish to come to the subject. There is much in the way of close and interesting argumentation. (shrink)

Since Kit Fine published his famous counter-examples to the modal account of essence, numerous modalists have proposed to avoid the counter-examples by revising the modal account. A sophisticated revision has been put forward by Fabrice Correia. Drawing on themes from Prior’s modality, Correia has introduced a nonstandard conception of metaphysical modality and has proposed to analyze essence in its terms. He has claimed that the analysis is immune to Fine’s counter-examples. In this paper, I argue that there are counter-examples supported (...) by the very intuition underlying Fine’s counter-examples, which are not accommodated by Correia’s account. If my argument is sound, then Correia has not been successful in his defense of modalism. An important corollary of my argument will be that Fine’s consequential conception of essence needs to be modified if it is to capture his own intuitive notion of essence. (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)

This article gives a conceptual review of the e-value, ev(H|X) – the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical (...) desiderata lying at the foundations of this theory. (shrink)

We can distinguish different senses in which a formal language can be said to have been provided with an interpretation. We focus on two: (i) We provide a model (or structure) and a definition of satisfaction and truth in the standard way (ii) We provide a translation into a natural language. We argue that the sentences of a formal language interpreted as in (i) do not have meaning. A formal language interpreted as in (i) models the way the truth of (...) a sentence would be affected by two factors: the interpretation as in (ii) of the language, and a way the world might be. Viewing in this way the relation between interpreting a formal language as in (i) and as in (ii) allows us to justify the conceptual adequacy of the standard model-theoretic definitions of the properties of logical truth and logical consequence. (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)

If an agent is unsure about which moral theory or principle should guide her action in a decision situation, she faces moral uncertainty. In recent years, various strategies have been explored to deal with this type of uncertainty. In this paper, we briefly mention two strategies from the literature that make use of credence distributions over moral theories, namely “my favourite theory” and “maximizing expected choice-worthiness”. As an alternative, we propose a two-step procedure which uses the concept of aggregation over (...) structural properties. It is standard in the theory of collective choice and has recently been applied to the Kuhnian problem of theory choice as well. The idea is to explore how a morally-motivated rational agent may assess different moral theories on the basis of fundamental properties. These properties are ranked on a common scale of qualitative verdicts. This method enables an outside observer to make comparisons across competing moral theories and then conclude to what degree these theories fulfil a set of postulated properties. By doing so, we try to render the reasons more transparent that lie behind different types of credence ascriptions. (shrink)

This paper studies the topological duality between diagonalizable algebras and bi-topological spaces. In particular, the correspondence between algebraic properties of a diagonalizable algebra and topological properties of its dual space is investigated. Since the main example of a diagonalizable algebra is the Lindenbaum algebra of an r.e. theory extending Peano Arithmetic, endowed with an operator defined by means of the provability predicate of the theory, this duality gives the possibility to study arithmetical properties of theories from a (...) topological point of view. We find topological characterization of $\Sigma_1$-sound theories and of sentences that are $\Sigma_1$-conservative over such a theory. (shrink)

. Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a confluence point for many alternative logical frameworks. Different formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over (...) other conflicting arguments. In this context, defeasible consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators Carg and Cwar intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDSar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference operators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. (shrink)

The properties, theoretical magnitudes, and natural kinds which science seeks to characterize, and not the sense or meanings which parts of speech may possess, are the subject of this paper. Many philosophers (e.g., Putnam [1971] and Achinstein [1974]) have agreed that two predicates of different meaning may pick out the same property, but they usually hold that that logically equivalent predicates must pick out the same properties. I propose to deny this thesis. My argument is by way of (...) an example and by appeal to a principle. The principle connects propertyhood with causal efficacy. The example situation I will describe in what follows is intended to show that the property of being a closed straight-sided figure having three sides is not the same property as that of being a closed straight-sided figure having three angles (a triangle). (shrink)

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...) advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

This paper defends a deflationary conception of properties, according to which a property exists if and only if there could be a predicate with appropriate satisfaction conditions. I argue that purely general properties and relations necessarily exist and discuss the bearing of this conception of properties on the interpretation of higher-order logic and on Quine's charge that higher-order logic is ‘set theory in sheep's clothing’. On my approach, the usual semantics involves a false assimilation of the logic (...) to set theory. I conclude with remarks about implications for the programme of founding mathematical theories in higher-order logic plus abstraction principles. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

A family of prepositional logics is considered to be intermediate between the intuitionistic and classical ones. The generalized interpolation property is defined and proved is the following.Theorem on interpolation. For every intermediate logic L the following statements are equivalent:(i) Craig's interpolation theorem holds in L, (ii) L possesses the generalized interpolation property, (iii) Robinson's consistency statement is true in L.

There are two known general results on the finite model property of commutators [L0,L1]. If L is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both L0 and L1 are determined by transitive frames and have frames of arbitrarily large depth, then [L0,L1] does not have the fmp. In this paper we show that (...) commutators with a “weakly connected” component often lack the fmp. Our results imply that the above positive result does not generalize to universally axiomatizable component logics, and even commutators without “transitive” components such as [K3,K] can lack the fmp. We also generalize the above negative result to cases where one of the component logics has frames of depth one only, such as [S4.3,S5] and the decidable product logic S4.3×S5. We also show cases when already half of commutativity is enough to force infinite frames. (shrink)

With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The main theorem (...) of the paper (Theorem 2.2) is analogous to the Wroski's result for equational classes of algebras [13]. It reads that for a large class of logics the conjunction of (AP) and (FEP) is equivalent to (IT) and that the latter property is equivalent to (MIP). (shrink)

In this paper, we introduce a logic based on team semantics, called $\mathbf {FOT} $, whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a sublogic of $\mathbf {FOT} $, called $\mathbf {FOT}^{\downarrow } $, captures exactly downward closed elementary (or first-order) team properties. We axiomatize completely the logic $\mathbf {FOT} $, and also extend the known partial axiomatization of dependence logic to dependence (...) logic enriched with the logical constants in $\mathbf {FOT}^{\downarrow } $. (shrink)

The dialogical games introduced in Jaakko Hintikka, Information-Seeking Dialogues: A Model, (Erkenntnis, vol. 14, 1979) are studied here to answer the question as to what the natural logic or the logic of natural language is. In a natural language certain epistemic elements are not explicitly indicated, but they determine which inference rules are valid. By means of dialogical games, the question is answered: all classical first-order rules have to be modified in the same way in which some of them are (...) modified in the transition to intuitionistic logic. (Furthermore, in some cases quantificational rules have to be modified further.) The rules that are left unmodified by intuitionists are applicable only to the output of certain game rules, but not to others. In. this sense, neither classical nor yet intuitionistic logic is the logic of natural language. We need a new type of nonclassical logic, justified by our information-seeking dialogues. (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.

Based on the results of [11] this paper delivers uniform algorithms for deciding whether a finitely axiomatizable tense logic has the finite model property, is complete with respect to Kripke semantics, is strongly complete with respect to Kripke semantics, is d-persistent, is r-persistent.It is also proved that a tense logic is strongly complete iff the corresponding variety of bimodal algebras is complex, and that a tense logic is d-persistent iff it is complete and its Kripke frames form a first order (...) definable class. From this we obtain many natural non-d-persistent tense logics whose corresponding varieties of bimodal algebras are complex. (shrink)

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

We study interpolation properties for Shavrukov’s bimodal logic $\textbf{GR}$ of usual and Rosser provability predicates. For this purpose, we introduce a new sublogic $\textbf{GR}^\circ$ of $\textbf{GR}$ and its relational semantics. Based on our new semantics, we prove that $\textbf{GR}^\circ$ and $\textbf{GR}$ enjoy Lyndon interpolation property and uniform interpolation property. As a consequence of our proofs, we obtain the completeness and the finite frame property of $\textbf{GR}^\circ$ and $\textbf{GR}$ with respect to our new semantics.

This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize (...) it in terms of an extension property and a syntactical metarule. This is the final part of the investigation started and developed in the papers :417–446, 2010; Arch Math Logic 53:353–372, 2016). (shrink)