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)

This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...) subject from a rich variety of angles, including the history of logic, the proper interpretation of logical validity, natural deduction rules, the notions of harmony and of synonymy, the structure of proofs, the logical status of equality, intentional phenomena, and the proof theory of second-order arithmetic. All chapters relate directly to questions that have driven Schroeder-Heister's own research agenda and to which he has made seminal contributions. The extensive autobiographical chapter not only provides a fascinating overview of Schroeder-Heister's career and the evolution of his academic interests but also constitutes a contribution to the recent history of logic in its own right, painting an intriguing picture of the philosophical, logical, and mathematical institutional landscape in Germany and elsewhere since the early 1970s. The papers collected in this book are illuminatingly put into a unified perspective by Schroeder-Heister's comments at the end of the book. Both graduate students and established researchers in the field will find this book an excellent resource for future work in proof-theoretic semantics and related areas. (shrink)

It has been common in contemporary logic and philosophy of logic to identify the validity of an inference with its conclusion being a (logical) consequence of its premisses.

Circumstantialists already have a logical semantics for impossibilities. They expand their logical space of possible worlds by adding impossible worlds. These are impossible circumstances serving as indices of evaluation, at which impossibilities are true. A variant of circumstantialism, namely modal Meinongianism (noneism), adds impossible objects as well. These are so-called incomplete objects that are necessarily non-existent. The opposite of circumstantialism, namely structuralism, has some catching-up to do. What might a structuralist logical semantics for impossibilities without impossibilia look like? This paper (...) makes a structuralist counterproposal. We present a semantics based on a procedural interpretation of the typed λ-calculus. The fundamental idea is that talk about impossibilities should be construed in terms of procedures: some yield as their product a condition that could not possibly have a satisfier, while the rest fail to yield a product altogether. Dispensing with a ‘bottom’ of impossibilia requires instead a ‘top’ consisting of structured hyperintensions, intensions, intensions defining other intensions, a typed universe, and dual (de dicto and de re) predication. We explain how the theory works by going through several examples. (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...) of linguistic context in a fully compositional and anti-contextual way. (shrink)

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)

Rigid designators designate whatever they do in all possible worlds. Mathematical definite descriptions are usually considered paradigmatic examples of such expressions. The main aim of the present paper is to challenge this view. It is argued that mathematical definite descriptions cannot be rigid in the same sense as ordinary empirical definite descriptions because—assuming that mathematical facts are not determined by goings on in possible worlds—mathematical descriptions designate whatever they do independently of possible worlds. Nevertheless, there is a widespread practice of (...) treating mathematical definite descriptions as rigid. Apart from this, there might be theoretical reasons for admitting that they are rigid in some sense. The second part of the paper suggests a way out. Borrowing from ideas proposed by Kit Fine, it develops and defends an extended notion of rigidity, which can be applied to mathematical definite descriptions. Importantly, this notion is fully compatible with the claim that mathematical facts are independent of possible worlds. (shrink)

Fregean thoughts (i.e. the senses of assertoric sentences) are structured entities because they are composed of simpler senses that are somehow ordered and interconnected. The constituent senses form a unity because some of them are ?saturated? and some ?unsaturated?. This paper shows that Frege's explanation of the structure of thoughts, which is based on the ?saturated/unsaturated? distinction, is by no means sufficient because it permits what I call ?wild analyses?, which have certain unwelcome consequences. Wild analyses are made possible because (...) any ?unsaturated? sense that is a mode of presentation of a concept together with any ?saturated? sense forms a thought. The reason is that any concept can be applied to any object (which is presented by a ?saturated? sense). This stems from the fact that Frege was willing to admit only total functions. It is also briefly suggested what should be done to block wild analyses. (shrink)

The paper presents an argument against referential treatment of definite descriptions' semantics. Referentialism with respect to semantics of definite descriptions claims that when descriptions are used referentially, then they are semantically referring expressions. It is argued that this picture does not lead to a satisfactory representation of propositions expressed by utterances involving definite descriptions. For if propositions are what primarily enters the relation of entailment, then referentialism is commited to the view that (i) some inferences usually taken as valid are (...) claimed to be invalid; (ii) some inferences usually taken as invalid are claimed to be valid; (iii) some inferences that are by no means trivially valid must be taken to be such. It is argued that Russellian‐ism with respect to definite descriptions gives us a better representation of propositions expressed by utterances involving descriptions. (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)

Drawing upon Martin-Löf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between consequence among propositions and inference among judgements. Derivations in Gentzen’s format with derivable formulae dependent upon open assumptions, stand, it is suggested, for proof-objects, whereas derivations in Gentzen’s sequential format are proof-acts.

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)

This paper provides an account of co-identification with fictional names, the way in which a fictional name can be used to talk about the same fictional character on disparate occasions. I develop a version of the view that fictional characters are roles constituted by sets of properties that is couched within a dynamic understanding of fictional discourse. I argue that this view captures what is right about both so-called name-centric and information-centric approaches to co-identification with fictional names. I show how (...) the dynamic view in addition accounts for a number of uses of fictional names, including fictional uses, assertoric uses, metafictional uses. (shrink)

It is not a common practice to postulate meaning entities treated as objects of some kind. The paper demonstrates two ways of introducing meaning-objects in two logics of natural language, Tichy’s Transparent Intensional Logic and Zalta’s Intensional Logic of Abstract Objects. Tichy’s theory belongs to the Fregean line of thinking, with what he calls ‘constructions’ as Fregean senses, and ‘determiners’ as object-like meaning entities constructed by the senses. Zalta’s theory belongs to Meinongian logics and he postulates a rich realm of (...) abstract Meinongian objects to play the role of meanings. The paper analyses the mechanisms of reference in both conceptions and it offers a comparison of the mediating meaning-objects and the framework designed to expose this mediation in both theories. An attempt is made to expose how the treatment of the meaning entities depends upon the theory of meaning which is assumed. (shrink)

It is known that the Restricted Predicate Calculus can be embedded in an elementary theory, the signature of which consists of exactly two equivalences. Some special models for the mentioned theory were constructed to prove this fact. Besides formal adequacy of these models, a question may be posed concerning their conceptual simplicity, "transparency" of interpretations they assigned to the two stated equivalences. In works known to us these interpretations are rather complex, and can be called "technical", serving only the purpose (...) of embedding. We propose a conversion method, which transforms an arbitrary model of RPC into some model of the elementary theory TR, which includes three equivalences. RPC is embeddable in TR, and it appears possible to assign some "natural" interpretations to three equivalences using the "Track of Relation " concept. (shrink)

We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.

Ce dialogue confronte deux conceptions qui dominent jusqu’à nos jours la philosophie des mathématiques : d’un côté la conception kantienne qui souligne l’irréductible apport de l’intuition dans la formulation des axiomes, ainsi que l’effectivité des procédés de construction ; de l’autre côté la conception bolzanienne qui s’efforce d’éliminer toute intervention de l’intuition au profit des démonstrations et des procédés purement conceptuels.In this dialogue, two opposed conceptions, which dominate the philosophy of mathematics till today, are confronted. Kant’s account of mathematics is (...) based upon the activity of constructing mathematical objects in pure intuition . In yielding objects for mathematics, our intuition contributes in an essential way to the formulation of mathematical truths. Against Kant, Bolzano argues that intuition has place neither in arithmetic nor in geometry and that mathematical existence consists in the possibility of the defined objects. i.e. in non-contradiction. For Bolzano, the central idea of mathematics is that of rigorous proof. (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)

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)

Zatímco v případě otázek rigidity singulárních termínů panuje obecná shoda, v případě rigidity predikátů tomu tak překvapivě není. Záměrem této statě je opřít distinkci rigidní / nerigidní o jasné pojmy, jmenovitě o pojem reference v určité sémantické teorii. V důsledku toho lze podat rigorózní definici pojmu rigidního designátoru individua. Tato definice je pak přímočaře adaptovatelná pro případ pojmu rigidního designátoru třídy individuí (apod.). Tímto je dosaženo nejen obecnosti, ale i vnitřní jednoty teorie rigidity.

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. The present author explicates the semantic concept of existential presupposition in relation to deriving existential statements and distinguishing their de dicto/de re variants.

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)

Pavel Materna proposed valuable explications of concept and conceptual system. After their introduction, we contrast conceptual systems with (a novel notion of) derivation systems. Derivation systems differ from conceptual systems especially in including derivation rules. This enables us to show close connections among the realms of objects, their concepts, and reasoning with concepts.

Proofs from assumptions are amongst the most fundamental reasoning techniques. Yet the precise nature of assumptions is still an open topic. One of the most prominent conceptions is the placeholder view of assumptions generally associated with natural deduction for intuitionistic propositional logic. It views assumptions essentially as holes in proofs, either to be filled with closed proofs of the corresponding propositions via substitution or withdrawn as a side effect of some rule, thus in effect making them an auxiliary notion subservient (...) to proper propositions. The Curry–Howard correspondence is typically viewed as a formal counterpart of this conception. I will argue against this position and show that even though the Curry–Howard correspondence typically accommodates the placeholder view of assumptions, it is rather a matter of choice, not a necessity, and that another more assumption-friendly view can be adopted. (shrink)

In Transparent Intensional Logic we can recognize two distinct notions of computation that loosely correspond to term rewriting and term interpretation as known from lambda calculus. Our goal will be to further explore these two notions and examine some of their properties.

The main objective of this paper is to sketch unifying conceptual and formal framework for inference that is able to explain various proof techniques without implicitly changing the underlying notion of inference rules. We base this framework upon the so-called two-dimensional, i.e., deduction to deduction, account of inference introduced by Tichý in his seminal work The Foundation’s of Frege’s Logic (1988). Consequently, it will be argued that sequent calculus provides suitable basis for such general concept of inference and therefore should (...) not be seen just as technical tool, but philosophically well-founded system that can rival natural deduction in terms of its “naturalness”. (shrink)

Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics. The main thrust of the book is to show that it is misguided to understand model theory metaphysically and so to try to base formal semantics on something like formal metaphysics; rather, the book states that model theory (...) and similar tools of the analysis of language should be understood as capturing the semantically relevant, especially inferential, structure of language. From this vantage point, the reader gains a new light on many of the traditional concepts and problems of logic and philosophy of language, such as meaning, reference, truth and the nature of formal logic. (shrink)

In this essay I will consider two theses that are associated with Frege,and will investigate the extent to which Frege really believed them.Much of what I have to say will come as no surprise to scholars of thehistorical Frege. But Frege is not only a historical figure; he alsooccupies a site on the philosophical landscape that has allowed hisdoctrines to seep into the subconscious water table. And scholars in a widevariety of different scholarly establishments then sip from thesedoctrines. I believe (...) that some Frege-interested philosophers at various ofthese establishments might find my conclusions surprising.Some of these philosophical establishments have arisen from an educationalmilieu in which Frege is associated with some specific doctrine at theexpense of not even being aware of other milieux where other specificdoctrines are given sole prominence. The two theses which I will discussillustrate this point. Each of them is called Frege''s Principle, but byphilosophers from different milieux. By calling them milieux I do not want to convey the idea that they are each located at some specificsocio-politico-geographico-temporal location. Rather, it is a matter oftheir each being located at different places on the intellectuallandscape. For this reason one might (and I sometimes will) call them(interpretative) traditions. (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)

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)

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)

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)

'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)

The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified (...) from this proof-theoretic perspective. This paper argues that, while classical logic can be formulated so as to satisfy a number of harmony constraints, the meanings of the standard logical constants cannot all be given by their introduction and/or elimination rules; negation, in particular, comes under close scrutiny. (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)

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 following well-known problem motivated my handling more general problems. As we surely know, our pupils and even students are confronted with much more trouble when learning mathematics (and even physics) than when they learn ‘empirical’ sciences like biology, mineralogy etc. There are many factors that can at least partially explain this phenomenon. I would however mention one factor that is not too frequently adduced: mathematics, logic, and much of physics use concepts that are abstract while the empirical sciences seem (...) to support understanding by using expressions concerning (denoting? expressing?) concrete objects. Therefore the first topic to be explained (or explicated) is: Abstract vs. concrete. The second point will consist of applying the first point to explanation of the trouble with learning mathematics. The third point will ask Logical Analysis of Natural Language how to tell abstract expressions from concrete ones. The fourth point will confront the concept described in the foregoing point with conceptions trying to abandon the distinction between analytic and empirical expressions. Here it will be shown that the empiricism representing this latter conception deprives semantics as applied to Natural language of important features of expressivity. (shrink)

On the one hand, Pavel Tichý has shown in his Transparent Intensional Logic (TIL) that the best way of explicating meaning of the expressions of a natural language consists in identification of meanings with abstract procedures. TIL explicates objective abstract procedures as so-called constructions. Constructions that do not contain free variables and are in a well-defined sense ´normalized´ are called concepts in TIL. On the second hand, Kolmogorov in (Mathematische Zeitschrift 35: 58–65, 1932) formulated a theory of problems, using NL (...) expressions. He explicitly avoids presenting a definition of problems. In the present paper an attempt at such a definition (explication)—independent of but in harmony with Medvedev´s explication—is given together with the claim that every concept defines a problem. The paper treats just mathematical concepts, and so mathematical problems, and tries to show that this view makes it possible to take into account some links between conceptual systems and the ways how to replace a noneffective formulation of a problem by an effective one. To show this in concreto a wellknown Kleene’s idea from his (Introduction to metamathematics. D. van Nostrand, New York, 1952) is exemplified and explained in terms of conceptual systems so that a threatening inconsistence is avoided. (shrink)

If concepts are explicated as abstract procedures, then we can easily show that each empirical concept is a not an effective procedure. Some, but not all empirical concepts are shown to be of a special kind: they cannot in principle guarantee that the object they identify satisfies the intended conditions.

In his paper Bare Particulars, T. Sider claims that one of the most plausible candidates for bare particulars are spacetime points. The aim of this paper is to shed light on Sider’s reasoning and its consequences. There are three concepts of spacetime points that allow their identification with bare particulars. One of them, Moderate structural realism, is considered to be the most adequate due its appropriate approach to spacetime metric and moderate view of mereological simples. However, it pushes the Substratum (...) theory to dismiss primitive thisness as the only identity condition for bare particulars, but the paper argues that such elimination is a legitimate step. (shrink)

I present an analysis according to which the current state of the definition of substitution leads to a contradiction in the system of Transparent Intensional Logic. I entail the contradiction using only the basic definitions of TIL and standard results. I then analyse the roots of the contradiction and motivate the path I take in resolving the contradiction. I provide a new amended definition of collision-less substitution which blocks the contradiction in a non-ad hoc way. I elaborate on the consequences (...) of the amended definition, namely the invalidity of the Church-Rosser theorem. I present a counterexample to the validity of the theorem in TIL with an amended definition of substitution. (shrink)

This paper presents several important results for Transparent Intensional Logic. The conversions that are standardly taken to be valid – namely restricted β-conversion by name and β-reduction...