The paper focuses on treating partiality within Tichý’s logical system. Tichý’s logic is two-valued and type-theoretic. His simple theory of types (and the deduction system for it) accepts both total and partial functions. Tichý’s late framework is explicitly ramified. So-called constructions (roughly: algorithms) construct, e.g., values of functions at arguments; in some cases, however, they do not construct anything at all. This special partiality phenomenon is discussed in the second part of the paper.

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.

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are not (...) mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. (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)

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality. In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, (...) the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality. (shrink)

Co-hyperintensionality, or hyperintensional equivalence, is a relation holding between two or more contents that can be substituted in a hyperintensional context salva veritate. I argue that two strategies used to provide criteria for co-hyperintensionality fail. I argue that there is no generalized notion of co-hyperintensionality that meets plausible desiderata, by showing that the opposite thesis leads to falsity. As a conclusion, I suggest to take co-hyperintensionality as a primitive and I provide a general criterion of co-hyperintensionality whose content depends on (...) each hyperintensional notion we aim to formalize. (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.

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 paper describes the solution to semantic paradoxes pioneered by Pavel Tichý and further developed by the present author. Its main feature is an examination (and then refutation) of the hidden premise of paradoxes that the paradox-producing expression really means what it seems to mean. Semantic concepts are explicated as relative to language, thus also language is explicated. The so-called ‘explicit approach’ easily treats paradoxes in which language is explicitly referred to. The residual paradoxes are solved by the ‘implicit approach’ (...) which employs ideas made explicit by the former one. (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)

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)

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)

'Propositionalism' is the widely held view that all intentional mental relations-all intentional attitudes-are relations to propositions or something proposition-like. Paradigmatically, to think about the mountain is ipso facto to think that it is F, for some predicate 'F'. It seems, however, many intentional attitudes are not relations to propositions at all: Mary contemplates Jonah, adores New York, misses Athens, mourns her brother. I argue, following Brentano, Husserl, Church and Montague among others, that the way things seem is the way they (...) are, and that propositionalism must be abandoned. (shrink)

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of extensional (...) logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed by a hyperpropositional attitude de dicto. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions. (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)

It was something of a dogma for much of the twentieth century that one cannot validly derive an ought from an is. More generally, it was held that non-normative propositions do not entail normative propositions. Call this thesis about the relation between the natural and the normative Natural-Normative Autonomy. The denial of Autonomy involves the entanglement of the natural with the normative. Naturalism entails entanglement—in fact it entails the most extreme form of entanglement—but entanglement does not entail naturalism. In a (...) ground-breaking paper “The autonomy of ethics” Arthur Prior constructed some intriguing counterexamples to Autonomy. While his counterexamples have convinced few, there is little agreement on what is wrong with them. I present a new analysis of Autonomy, one which is grounded in a general and independently plausible account of subject matters. While Prior’s arguments do establish shallow natural-normative entanglement, this is a consequence of simple logical relationships that hold between just about any two subject matters. It has nothing special to do with the logical structure of normativity or its relation to the natural. Prior’s arguments leave the fundamental idea behind natural-normative Autonomy intact. I offer a new argument for deep entanglement. I show that in any framework adequate for dealing with the natural and the normative spheres, a purely natural proposition entails a purely normative proposition, and vice-versa. But this is no threat to non-naturalist moral realism. In fact it helps ameliorate the excesses of an extreme non-naturalism, delivering a more palatable and plausible position. (shrink)

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates (...) and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (shrink)

Vít Gvoždiak published a reconciliatory analysis of Searle’s social ontology with semiotics in Gvoždiak (2012). Without prior knowledge of his paper, an analysis of the same subject appeared in Msimang (2014). Even though Searle’s social ontology is a common point of reference in the formulation of semiotics in these papers, it also serves as a point of departure in their understanding of semiotics and its development. The semiotic theory expressed in Gvoždiak (2012) is an inherently linguistic (speech act centred) theory, (...) whereas the semiotic theory presented in Msimang (2014) tends more towards a general theory of communicative systems in which social ontology, which follows from speech act theory, is an interesting part. It is my purpose in this note to contrast the two positions of semiotic theory as they appear in the aforementioned papers in reference to their appropriation of Searle’s social ontology. (shrink)

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).

In this paper we revisit Pavel Tichý’s novel distinction between one-dimensional and two-dimensional conception of inference, which he presented in his book Foundations of Frege’s Logic (1988), and later in On Inference (1999), which was prepared from his manuscript by his co-author Jindra Tichý. We shall focus our inquiry not only on the motivation behind the introduction of this non-classical concept of inference, but also on further inspection of selected Tichý’s arguments, which we see as the most compelling or simply (...) most effective in providing support for his two-dimensional account of inference. Main attention will be given to exposing the failure of one-dimensional theory of inference in its explanation of indirect (reductio ad absurdum) proofs. Lastly, we discuss shortly the link between two-dimensional inference and deduction apparatus of Tichý’s Transparent Intensional Logic. (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)

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)

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)

My concern in this paper is with the intentionality of emotions. Desires and cognitions are the traditional paradigm cases of intentional attitudes, and one very direct approach to the question of the intentionality of emotions is to treat it as sui generis—as on a par with the intentionality of desires and cognitions but in no way reducible to it. A more common approach seeks to reduce the intentionality of emotions to the intentionality of familiar intentional attitudes like desires and cognitions. (...) In this paper, I argue for the sui generis approach. (shrink)

A widely held view about Fregean Sense has it that the determination of a sign's referent by the sign's sense is achieved viasatisfaction: the sense specifies a condition (or set of conditions) and the referent is that entity, if any, which uniquely satisfies that (set of) condition(s). This is usually held in conjunction with the claim that the sense is existentially and qualitatively independent of the referent: if the referent did not exist, or did not uniquely satisfy the sense, the (...) sense would still exist and would still specify the same condition(s) that it actually does (and might determine a different referent than its actual one). Proponents of this view give several reasons for holding it. I describe these reasons and argue that they are not convincing. More generally, I try to show that the notion of satisfaction has no useful application within Frege's system. I then suggest an alternative account of the determination of a referent by a sense that I think is truer to Frege and more illuminating. Compared to the satisfaction view, my account construes determination as a more naturalistic and epistemically real relation between speakers and things in the world. (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)

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)

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)