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)

Bioassessment is the process of using living organisms to assess the ecological health of a particular ecosystem. It typically relies on identifying specific organisms that are sensitive to changes in environmental conditions. Benthic macroinvertebrates are widely used for examining the ecological status of freshwaters. However, a time-consuming process of species identification that requires high expertise represents one of the key obstacles to more precise bioassessment of aquatic ecosystems. Partial automation of this process using deep learning-based image classification is the goal (...) of an ongoing project AIAQUAMI we are participating in. One of the project goals is to develop software support for image classification with visualization and reporting. For that purpose, we developed desktop and web applications that we open-sourced as Imagelytics Suite. Both desktop and web applications rely on a convolutional neural network (CNN) to classify images and the Grad-CAM algorithm to produce heatmaps of the image areas that mostly influenced the network decision. Along with the source code of the applications, we also open-sourced scripts that can be used to train CNN on an arbitrary dataset and produce required metadata, so it can be used with Imagelytics applications. In this article, we presented technical details regarding the design of the applications and the training method that will enable their general use for image classification tasks. As a part of the evaluation, we will show a use case related to species identification of non-biting midges (Diptera: Chironomidae). (shrink)

This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle (...) of compositionality, a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by (...) such devices as multiple indexing or quantification over times. (shrink)

In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds (...) of graded predicates. Finally, we propose a general research program towards a logic-based account of reasoning with graded predicates. (shrink)

'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)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other (...) axioms of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

The problem of the subject-predicte distinction has featured centrally in much of modern philosophy of language and philosophical logic. and the distinction is taken as basic or fundamental in modern philosophical logic. A sortal is a symbol which furnishes a principle of distinction and counting in its own right for particulars (objects).This book explores sortals and their relationship to the subject-predicate distinction; arguing that the nature of sortal symbols has been misconstrued in much modern writing in the philosophy (...) of logic by failing to clearly distinguish sortals from names and predicates; contending that this misconstruction has led to a failure to appreciate what makes the subject-predicate distinction possible; demonstrating logical difficulties which then follow; and expounding an account of sortal symbols which seeks to be immune from the difficulties. Exploring and challenging aspects of the work of Frege, Russell, Geach, Quine, Evans and Strawson, amongst others, Durrant also provides a new challenge to certain popular presuppositions employed in many areas of contemporary philosophical debate, and offers important insights for those studying across philosophical logic, philosophy of language, and metaphysics and epistemology, in particular. (shrink)

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His (...) book will be of great interest to philosophers of language, linguists, metaphysicians, and logicians. (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.

In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence phi according to this permutation should not change our belief in the truth of phi. In this paper we study when a prior probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.

We investigate a rst-order predicate logic based on Wittgenstein's suggestion to express identity of object by identity of sign, and difference of objects by difference of signs. Hintikka has shown that predicate logic can indeed be set up in such a way; we show that it can be done nicely. More specically, we provide a perspicuous cut-free sequent calculus, as well as a Hilbert-type calculus, for Wittgensteinian predicate logic and prove soundness and completeness theorems.

The problem of completeness for predicate modal logics is still under investigation, although some results have been obtained in the last few years . As far as we know, the case of multimodal logics has not been addressed at all. In this paper, we study the combination of modal logics in terms of combining their semantics. We demonstrate by a simple example that in this sense predicate modal logics are not so easily manipulated as propositional ones: mixing two Kripke-complete predicate (...) modal logics results in a Kripke-incomplete system. (shrink)

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or (...) its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. (shrink)

In our previous paper [5], we have studied Kripke-type semantics for propositional logics without the contraction rule. In this paper, we will extend our argument to predicate logics without the structure rules. Similarly to the propositional case, we can not carry out Henkin's construction in the predicate case. Besides, there exists a difficulty that the rules of inference () and () are not always valid in our semantics. So, we have to introduce a notion of normal models.

This clearly written book makes logic interesting and easier to learn without sacrificing content or rigor. It covers symbolization, proofs, counterexamples, and truth trees. These topics are presented in graded steps, beginning with the symbolization of categorical propositions and concluding with the properties of relations. Logic is applied to materials with which readers will be familiar; both examples and exercises are drawn from newspapers, television, and other popular sources. For individuals intrigued by the formal study of 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)

Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clarification of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predica-tivity have since taken a life of their (...) own, but have also produced a deeper understanding of the notion of predicativity, therefore witnessing the " light logic throws on problems in the foundations of mathematics. " (Feferman 1998, p. vii) Predicativity has been at the center of a considerable part of Feferman's work: over the years he has explored alternative ways of explicating and analyzing this notion and has shown that predicative mathematics extends much further than expected within ordinary mathematics. The aim of this note is to outline the principal features of predicativity, from its original motivations at the start of the past century to its logical analysis in the 1950-60's. The hope is to convey why predicativity is a fascinating subject, which has attracted Feferman's attention over the years. (shrink)

In this paper I present a formal language in which complex predicates stand for properties and relations, and assignments of denotations to complex predicates and assignments of extensions to the properties and relations they denote are both homomorphisms. This system affords a fresh perspective on several important philosophical topics, highlighting the algebraic features of properties and clarifying the sense in which properties can be represented by their extensions. It also suggests a natural modification of current logics of properties, (...) one in which some complex predicates stand for properties while others do not. (shrink)

A logic-enriched type theory is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named and , which we claim correspond closely to the classical predicative systems of second order arithmetic and . We justify this claim by translating each second order system into the corresponding LTT, and proving that these translations are conservative. This is part of an ongoing research project to investigate how LTTs may be used to formalise different (...) approaches to the foundations of mathematics.The two LTTs we construct are subsystems of the logic-enriched type theory , which is intended to formalise the classical predicative foundation presented by Herman Weyl in his monograph Das Kontinuum. The system has also been claimed to correspond to Weyl’s foundation. By casting and as LTTs, we are able to compare them with . It is a consequence of the work in this paper that is strictly stronger than .The conservativity proof makes use of a novel technique for proving one LTT conservative over another, involving defining an interpretation of the stronger system out of the expressions of the weaker. This technique should be applicable in a wide variety of different cases outside the present work. (shrink)

In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus . We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀.

A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including donkey sentences and cross-sentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of anaphora, in particular Dynamic Predicate Logic.

We explain two ways of revising a tense logic like kripke's (1963) modal logic by adding predicate modifiers. first we show that modifiers allow us to render valid some mixing formulas--conditionals reversing the order of a quantifier and an operator--within a complete bivalent system. then we show how modifiers enable a tense logic to give analyses close to the surface form for sentences with temporal qualifications of singular terms, e.g., 'toby was fatter then than william is today'.

Predicate modal formulas with non-modalized quantifiers (call them Q-formulas) are considered as schemata of arithmetical formulas, where is interpreted as the provability predicate of some fixed correct extension T of arithmetic. A method of constructing 1) non-provable in T and 2) false arithmetical examples for Q-formulas by Kripke-like countermodels of certain type is given. Assuming the means of T to be strong enough to solve the (undecidable) problem of derivability in QGL, the Q-fragment of the predicate version of the (...) class='Hi'>logic GL, we prove the recursive enumerability of the sets of Q-formulas all arithmetical examples of which are: 1) T-provable, 2) true. In. particular, the first one is shown to be exactly QGL and the second one to be exactly the Q-fragment of the predicate version of Solovay's logic S. (shrink)

In this work we extend results from [4], [3] and [2] about propositional calculi with graded modalities to the predicative level. Our semantic is based on Kripke models with a single domain of interpretation for all the worlds. Therefore the axiomatic system will need a suitable generalization of the Barcan formula. We haven't considered semantics with world-relative domains because they don't present any new difficulties with respect to classical case. Our language will have, as in [1], constant and function symbols, (...) but they will have a rigid interpretation. In this instance the terms will be considered rigid designators, that is, their interpretations will be the same in all possible worlds (cfr. [5]). Nevertheless we will not consider languages with identity: in this way we avoid the problems of identity in modal contexts. On the other hand, we think that in that context would arise essentially the same problems which occur in classical predicative modal logic. Finally we will consider only denumerable languages because the extension to non denumerable ones isn't conceptually problematic. (shrink)

A new class of program-oriented logical formalisms is investigated – renominative logics with extended renominations, equality predicates, and predicate complement composition. Composition algebras and languages of such logics are described; their semantic properties are investigated. For these logics, a number of logical consequence relations are proposed and investigated, in particular, the logical consequence relations with undefinedness conditions. Properties of these relations form the semantic basis for further construction of sequent-type calculi for the proposed logics.

Aristotle’s categorical syllogistic is the first formal deductive system in the history of formal sciences. Most parts or elements of the system are validated by modern (first-order) mathematical logic, but the system is quite limited in scope, as it is incapable of analyzing inferences other than the ‘figure syllogisms’ consisting of a couple of_ a-e-i-o_ premises and an _a-e-i-o_ conclusion, containing three ‘moderately’ universal terms – terms that express neither a highest genus nor a lowest species – each of (...) which is common to a different couple of propositions out of the three. Logicians in the following ages dealt with various questions concerning the addition of various (novel) logical forms into this limited system, among which are singular predications, i.e. categorical propositions with a singular term as subject, and the most common choice has been interpreting singular predications as _universal _predications. This paper tries to take a strictly formal perspective on the system of categorical syllogisms, and argues in detail for a much simpler and fairly effective assimilation or translation scheme for singular predications. The key to the proposed scheme is the preservation of the supposed inferential relation between opposite singular predications, namely _contradiction_. It is argued that the resulting _singularized _syllogistic moods, which are also validated by first-order logic (under its standard renderings of _a-e-i-o_ and singular predications), promote in turn the mentioned type of treatment, since they call for the employment of two of the four subaltern moods of the system, disregarded by Aristotle, which are _formally _there. (shrink)

Predicates are supposed to slice reality neatly in two halves, one for which the predicate holds, the other for which it fails. Yet far from being razors, predicates tend to be dull knives that mangle reality. If reality is a tomato and predicates are knives, then when these knives divide the tomato, plenty of mush remains unaccounted for. Of course some knives are sharper than others, just as some predicates are less vague than others. “x is (...) water” is certainly sharper than “x is beautiful.” But perfect sharpness, perfect boundaries, and perfect separation seem only to obtain in mathematics. The vagueness inherent in many predicates became particularly evident in the twentieth century. Quantum mechanics, the revival of certain ancient paradoxes, and the philosophy of science all contributed to a growing awareness that vagueness was ineliminable from many predicates. Quantum mechanical superposition seems to allow mutually exclusive simultaneous states. In searching for plausible interpretations of quantum mechanics, some researchers attempted to do away with classical bivalent logic. In its place they substituted multivalent quantum logics. Any logic with more than two values forces its predicates to slice reality into more than two parts. Ancient paradoxes involving heaps and baldness also pointed up the 1 Random Predicate Logic 2.. (shrink)

In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give a characterization of the relations on assignments that can be generated by composition from tests and random resettings in the case that we are working over an infinite domain. These relations are precisely the ones expressible in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the (...) way these extensions interact with our notion of context. (shrink)

Kant said that existence is not a predicate and Russell agreed, arguing that a sentence such as ‘The king of France exists’, which seems to attribute existence to the king of France, really has a logical form that is not reflected in the surface structure of the sentence at all. While the surface form of the sentence consists of a subject and a predicate, the underlying logical form, according to Russell, is the formula given in. This formula obviously has no (...) subjectpredicate form and in fact has no single constituent that corresponds to the verb phrase ‘exists’ in the surface sentence. ∃x∀y The importance of Russell’s analysis becomes clear when we consider ‘The king of France does not exist’. If this sentence would attribute non-existence to the king it should entail that there is someone who does not exist, just as ‘Mary doesn’t like bananas’ entails that there is someone who doesn’t like bananas. Thus the idea that all sentences have subject-predicate form has led some philosophers to the view that there are objects that lack existence. This embarrassing position can be avoided once Russell’s analysis is accepted: if ‘The king of France does not exist’ is formalised as the negation of formula, no unwanted consequences follow. (shrink)

In his 2000 book Logical Properties Colin McGinn argues that predicates denote properties rather than sets or individuals. I support the thesis, but show that it is vulnerable to a type-incongruity objection, if properties are (modelled as) functions, unless a device for extensionalizing properties is added. Alternatively, properties may be construed as primitive intensional entities, as in George Bealer. However, I object to Bealer’s construal of predication as a primitive operation inputting two primitive entities and outputting a third primitive (...) entity. Instead I recommend we follow Pavel Tichý in construing both predication and extensionalization as instances of the primitive operation of functional application. (shrink)

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting (...) them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)