Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...) framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams. (shrink)

In a 2010 paper Daley argues, contra Fodor, that several syntactically simple predicates express structured concepts. Daley develops his theory of structured concepts within Tichý’s Transparent Intensional Logic . I rectify various misconceptions of Daley’s concerning TIL. I then develop within TIL an improved theory of how structured concepts are structured and how syntactically simple predicates are related to structured concepts.

Strawson’s work seems to contain both pragmatic and semantic concepts of presupposition. The former concept has largely been studied by many philosophers and linguists, while the latter has not been properly investigated (van Fraassen being an exception). The present author explicates the semantic concept of existential presupposition in relation to deriving existential statements and distinguishing their de dicto/de re variants (in the rather generalized sense following Tichý).

We formulate a Curry-typed logic with fine-grained intensionality within Turner’s typed predicate logic. This allows for an elegant presentation of a theory that corresponds to Fox and Lappin’s property theory with curry typing, but without the need for a federation of languages. We then consider how the fine-grained intensionality of this theory can be given an operational interpretation. This interpretation suggests itself as expressions in the theory can be viewed as terms in the untyped lambda-calculus, which provides a model of (...) computation. (shrink)

A bare individual was conceived by Tichý as an individual such as if the property the individual instantiates is non-trivial , it is possible for the individual to lack it ; and for any trivial property that it cannot lack this kind of property. The exact readings of Tichý’s original formulations of are subjected to a detailed analysis to reveal that any of them is refutable by means of Cmorejian objection that there exist contingent properties which are partly essential . (...) To avoid such objection, the present paper attempts to rebuild Tichý’s definitions into viable ones. (shrink)

The paper focuses on the problem of identification of laws of nature and their demarcation from other kinds of regularities. The problem is approached from the viewpoint of several metaphysical, epistemological, logical and methodological criteria. Firstly, several dominant approaches to the problem are introduced. Secondly, the logical and semantic explicatory framework – Transparent Intensional Logic – is presented for the sake of clarification of logical forms of sentences that are supposed to express the laws of nature. Finally, a complementary strategy (...) to the demarcation problem is proposed, including reconsideration of relevant metaphysical, epistemological, logical and methodological requirements and principles behind the former conceptions. (shrink)

Carnap’s analysis of the language of science had presupposed too close a connection between the semantics and testability. The core problem of the logical empiricist tradition was to show how to provide the interpretation of theoretical terms and hence the explanation of their application to observable entities by means of observation terms. It is argued that the utilization of a much more expressive semantic theory which identifies meanings with hyperintensional entities leads to a clarification of the competencies of semantics and (...) methodology. It is claimed that the observability or unobservability of term’s referents does not determine the meaning of the term. Carnap’s reduction sentences are therefore conceived only as methodological devices for the determination of unobservables via the theory-presupposed observable aspects. (shrink)

Tichý’s Transparent Intensional Logic (TIL) is an overarching logical framework apt for the analysis of all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural (as opposed to denotational) one, according to which the meaning of an expression is an abstract, extra-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure that is the object denoted by the expression. Such procedures are rigorously defined as (...) TIL constructions. Though TIL analytical potential is very large, deduction in TIL has been rather neglected. Tichý defined a sequent calculus for pre-1988 TIL, that is TIL based on the simple theory of types. Since then no other attempt to define a proof calculus for TIL has been presented. The goal of this paper is to propose a generalization and adjustment of Tichý’s calculus to TIL 2010. First, I briefly recapitulate the rules of simple-typed calculus as presented by Tichý. Then, I propose the adjustments of the calculus so that it be applicable to hyperintensions within the ramified hierarchy of types. TIL operates with a single procedural semantics for all kinds of logical-semantic context, be it extensional, intensional or hyperintensional. I show that operating in a hyperintensional context is far from being technically trivial. Yet, it is feasible. To this end, we introduce a substitution method that operates on hyperintensions. It makes use of a four-place substitution function (called Sub) defined over hyperintensions. (shrink)

From a general semantic point of view, Thomas Bricot and John Mair are proponents of the solution to semantic paradoxes based on appreciation of the contextuality of truth, who differ in their approach to the relations of logical consequence and contradiction. The core of the study is the analysis of Mair's criticism of Bricot presented in the sixth quaestio of his Tractatus insolubilium where the consequences of non-compositional semantics for the concepts of synonymy and logical form are addressed. The polemic (...) between John Mair and Thomas Bricot is construed as having immediate consequences for research in the area of non-compositional semantics. (shrink)

It is sometimes objected that Tichý’s logic is not a logic because it underestimates deduction, providing only logical analyses of expressions. I argue that this opinion is wrong. First of all, to detect valid arguments, which are formulated in a language, there needs to be logical analysis to ascertain which semantical entities are involved. Entailment is defined as an extralinguistic affair relating those constructions. The validity of an argument, composed of propositional constructions, stems from the properties of the constructions. Such (...) properties are displayed by the derivation rules of Tichý’s system of deduction. (shrink)

In the last few decades of the twentieth century there was a revolution in metaphysics: the intensional revolution. Many metaphysicians rejected the doctrine, associated with Quine and Davidson, that extensional analyses and theoretical resources were the only acceptable ones. Metaphysicians embraced tools like modal and counterfactual analyses, claims of modal and counterfactual dependence, and entities such as possible worlds and intensionally individuated properties and relations. The twenty-first century is seeing a hypterintensional revolution. Theoretical tools in common use carve more finely (...) than by necessary equivalence: two pieces of language can apply to the same entities across all possible worlds but not be equivalent; thoughts can be necessarily equivalent in truth value but not synonymous. This paper argues that hyperintensional resources are valuable in metaphysics outside theories of representation, and discusses some promising areas of hyperintensional metaphysics. (shrink)

Van Heijenoort’s main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schröder, and Löwenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then (...) I describe his way of arguing for the second view (Sect. 2); and finally I come down in favor of the first view (Sect. 3). There, I specify the version of universalism for which I am prepared to argue (Sect. 3, introduction). Choosing ZFC to play the part of universal, logical (in a nowadays forgotten sense) system, I show, through an example, how the usual model theory can be naturally given its proper place, from the universalist point of view, in the logical framework of ZFC; I outline another, not rival but complementary, semantics for admissible extensions of ZFC in the very same logical framework; I propose a way to get universalism out of the predicaments in which universalists themselves believed it to be (Sect. 3.1). Thus, if universalists of the classical period did not, in fact, construct these semantics, it was not that their universalism forbade them, in principle, to do so. The historical defeat of universalism was not technical in character. Neither was it philosophical. Indeed, it was hardly more than the victory of technicism over the very possibility of a philosophical dispute (Sect. 3.2). (shrink)

To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable (...) as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined. (shrink)

Aim of the paper is to present a new logic of technical malfunction. The need for this logic is motivated by a simple-sounding philosophical question: Is a malfunctioning corkscrew, which fails to uncork bottles, nonetheless a corkscrew? Or in general terms, is a malfunctioning F, which fails to do what Fs do, nonetheless an F? We argue that ‘malfunctioning’ denotes the modifier Malfunctioning rather than a property, and that the answer depends on whether Malfunctioning is subsective or privative. If subsective, (...) a malfunctioning F is an F; if privative, a malfunctioning F is not an F. An intensional logic is required to raise and answer the question, because modifiers operate directly on properties and not on sets or individuals. This new logic provides the formal tools to reason about technical malfunction by means of a logical analysis of the sentence “a is a malfunctioning F”. (shrink)

Gregory Landini offers a detailed historical account of Frege's notations and the philosophical views that led Frege from Begriffssscrhrift to his mature work Grundgesetze, addressing controversial issues that surround the notations.

This paper defendsintensional essentialism: a property (intensional entity) is not essential relative to an individual (extensional entity), but relative to other properties (or intensional entities). Consequently, an individual can have a property only accidentally, but in virtue of having that property the individual has of necessity other properties. Intensional essentialism is opposed to various aspects of the Kripkean notion of metaphysical modality, eg, varying domains, existence as a property of individuals, and its category of properties which are both empirical and (...) essential with respect to particular individuals and natural kinds. The key notion of intensional essentialism isrequisite. A requisite is explicated as a relation-in-extension between two intensions (functions from possible worlds and moments of time)X, Y such that wherever and wheneverX is instantiatedY is also instantiated. We predict three readings of the sentence. Every wooden table is necessarily wooden , one involving modalityde re and the other two modalityde dicto. The first reading claims that no individual which is a wooden table is necessarily wooden. The claim is backed up by bare particular anti-essentialism. The two other interpretations claim that it is necessary that whatever is a wooden table is wooden. However, as we try to show, one is logically far more perspicuous thanks to the concept of requisite and thus preferable to more standardde dicto formalizations. (shrink)

Two kinds of individuals are distinguished: abstract and concrete. Whereas abstract individuals belong to our conceptual sphere, concrete individuals (i.e. particulars) individuate the world of matter. A subject investigating the external world projects abstract individuals onto concrete ones. The proposal offers a solution to various metaphysical and epistemological puzzles concerned with individuals, e.g., the Ship of Theseus, the Polish Logician, problems with reidentification, or proper names.

Anotace Following Carnap's Principle of Subject Matter, Pavel Tichý proposed a methodological principle I call the "Denotational Principle of Aboutness". It says that expressions are about their denotata. Denotata are modelled as possible world intensions or (common) extensions. Nearly the same principle was recently defended by Marie Duží and Pavel Materna under the name the "Parmenides Principle". However, Duží and Materna did not react to Tichý's late proposal which I call the "Constructional Principle of Aboutness". It says that the subject (...) matter of expressions consists not in their denotata but their meanings. The meanings are explicated by Tichý, and also by Duží and Materna, as so-called constructions; constructions are complex entities akin to algorithms, they construct intensions or extensions. In this paper, I argue in favour of the Constructional Principle of Aboutness. I show that there are not only single arguments, but whole net of methodological principles which support it. This is why the topic largely transcends the debate among Tichý's followers. (shrink)

The beginning of this century hailed a new paradigm in linguistics, the paradigm brought about by de Saussure's Cours de Linguistique Genérále and subsequently elaborated by Jakobson, Hjelmslev and other linguists. It seemed that the linguistics of this century was destined to be structuralistic. However, half of the century later a brand new paradigm was introduced by Chomsky's Syntactic Structures followed by Montague's formalization of semantics. This new turn has brought linguistics surprisingly close to mathematics and logic, and has facilitated (...) a direct practical exploitation of linguistic theory by computer science. (shrink)

Many philosophers still countenance senses or meanings in the broadly Fregean vein. However, it is difficult to posit the existence of senses without positing quite a lot of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are also (...) discussed. In the end, it is concluded that one must divide senses into various ramified-orders in order to avoid antinomy, but that the philosophical justification of such orders is, as yet, still somewhat problematic. (shrink)

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to export existential quantifiers without conceiving attitudes as relations to expressions (sententialism).

The common view has it that there are two families of approaches towards the logical structure of impossible worlds – Australasian and North American. According to the first, impossible worlds are closed under the relation of logical consequence of one of the non-classical logics. The North American approach is more liberal, allowing for impossible worlds where no logic holds. After pointing out the questionable consequences of each view, I propose a third one. While this new perspective allows for worlds where (...) no logical consequence holds, it also imposes some constraints on what worlds are built upon. This renders the proposed view not as restrictive as the Australasian approach and not as liberal as the North American approach. Due to its intermediary nature, I have named this perspective ‘the Pacific’ approach. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

When we experience the world – see, hear, feel, taste, or smell things – we gain all sorts of knowledge about the things around us. And this knowledge figures heavily in our reasoning about the world – about what to think and do in response to it. But what is the nature of this knowledge? On one commonly held view, all knowledge is constituted by beliefs in propositions. But in this paper I argue against this view. I argue that some (...) knowledge is constituted, not by beliefs in propositions, but by awareness of properties and objects. To make my case, I focus on the role of visual perception in reasoning. I start by introducing a principle about the relationship between knowledge and reasoning, which says that to learn something new by reasoning, one must know the bases of one’s reasoning. Then I argue that in some cases of genuine, knowledge-conferring reasoning, the bases of our reasoning are not propositions that we believe; rather, they’re properties or objects that we see. Thus, I conclude that some such knowledge is non-propositional and is rather what some call “knowledge of things”. (shrink)

CAT4 is proposed as a general method for representing information, enabling a powerful programming method for large-scale information systems. It enables generalised machine learning, software automation and novel AI capabilities. It is based on a special type of relation called CAT4, which is interpreted to provide a semantic representation. This is Part 1 of a five-part introduction. The focus here is on defining the key mathematical structures first, and presenting the semantic-database application in subsequent Parts. We focus in Part 1 (...) on general axioms for the structures, and introduce key concepts. Part 2 analyses the CAT2 sub-relation of CAT4 in more detail. The interpretation of fact networks is introduced in Part 3, where we turn to interpreting semantics. We start with examples of relational and graph databases, with methods to translate them into CAT3 networks, with the aim of retaining the meaning of information. The full application to semantic theory comes in Part 4, where we introduce general functions, including the language interpretation or linguistic functions. The representation of linear symbolic languages, including natural languages and formal symbolic languages, is a function that CAT4 is uniquely suited to. In Part 5, we turn to software design considerations, to show how files, indexes, functions and screens can be defined to implement a CAT4 system efficiently. (shrink)

CAT4 is proposed as a general method for representing information, enabling a powerful programming method for large-scale information systems. It enables generalised machine learning, software automation and novel AI capabilities. It is based on a special type of relation called CAT4, which is interpreted to provide a semantic representation. This is Part 2 of a five-part introduction. The focus here is on defining key mathematical properties of CAT2, identifying the topology and defining essential functions over a coordinate system. The analysis (...) is from first principles. This develops on from the axioms introduced in Part 1. The interpretation of fact networks is introduced in Part 3, and the full application to semantic theory comes in Part 4, where we introduce general functions, including the language interpretation or linguistic functions. In Part 5, we turn to software design considerations, to show how files, indexes, functions and screens can be defined to implement a CAT4 system efficiently. (shrink)

CAT4 is proposed as a general method for representing information, enabling a powerful programming method for large-scale information systems. It enables generalised machine learning, software automation and novel AI capabilities. This is Part 3 of a five-part introduction. The focus here is on explaining the semantic model for CAT4. Points in CAT4 graphs represent facts. We introduce all the formal (data) elements used in the classic semantic model: sense or intension (1st and 2nd joins), reference (3rd join), functions (4th join), (...) time and truth (logical fields), and symbolic content (name/value fields). Concepts are introduced through examples alternating with theoretical discussion. Some concepts are assumed from Part 1 and 2, but key ideas are re-introduced. The purpose is to explain the CAT4 interpretation, and why the data structure and CAT4 axioms have been chosen: to make the semantic model consistent and complete. We start with methods to translate information from database tables into graph DBs and into CAT4. We conclude with a method for translating natural language into CAT4. We conclude with a comparison of the system with an advanced semantic logic, the hyper-intensional logic TIL, which also aims to translate NL into a logical calculus. The CAT4 Natural Language Translator is discussed in further detail in Part 4, when we introduce functions more formally. Part 5 discusses software design considerations. (shrink)

An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a range of debates that (...) attention to hyperintensional constructions has generated. (shrink)

Role realism is a promising realist theory of fictional names. Different versions of this theory have been suggested by Gregory Currie, Peter Lamarque, Stein Haugom Olsen, and Nicholas Wolterstorff. The general idea behind the approach is that fictional characters are to be analysed in terms of roles, which in turn can be understood as sets of properties. I will discuss several advantages and disadvantages of this approach. I will then propose a novel hyperintensional version of role realism, according to which (...) fictional names are analysed in terms of individual concepts that cannot be matched by a reference. I will argue that this account avoids the main disadvantages of standard role realism. (shrink)

This paper defends a version of the realist view that fictional characters exist. It argues for an instance of abstract realist views, according to which fictional characters are roles, constituted by sets of properties. It is argued that fictional names denote individual concepts, functions from worlds to individuals. It is shown that a dynamic framework for understanding the evolution of discourse information can be used to understand how roles are created and develop along with story content. Taking fictional names to (...) denote individual concepts provides accounts of a number of uses of fictional names. These include non-fictional uses, fictional uses, metafictional uses, interfictional uses, counterfictional uses, and negative existentials. It is argued that this account is not open to objections that have been raised in the literature. (shrink)

We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...) introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of proofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence. (shrink)

This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...) and were influential in their communities, but produced relatively little. In Australia, materialism gained prominence through the work of John Anderson, who arrived in Australia in 1927, and continues to be influential. John Anderson had been a student of Henry Jones, who might therefore be said to have influenced both main strands of Australian philosophical thought. (shrink)

The paper examines two possible analyses of fictional names within Pavel Tichý’s Transparent Intensional Logic. The first of them is the analysis actually proposed by Tichý in his (1988) book The Foundations of Frege’s Logic. He analysed fictional names in terms of free variables. I will introduce, explain, and assess this analysis. Subsequently, I will explain Tichý’s notion of individual role (office, thing-to-be). On the basis of this notion, I will outline and defend the second analysis of fictional names. This (...) analysis is close to the approach known in the literature as role realism (the most prominent advocates of this position are Nicholas Wolterstorff, Gregory Currie, and Peter Lamarque). (shrink)

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions. Instead they are higher-order, fine-grained structures. (...) I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed λ-calculus, whose λ-terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context. (shrink)