The present paper provides a completeness proof for a system of higher-order logic framed within partial type theory. The framework is a modification of Tichý’s extension of Church’s simple type theory, equipped with his innovative natural deduction system in sequent style. The system deals with both total and partial (multiargument) functions-as-mappings and also accommodates algorithmic computations arriving at various objects of the framework. The partiality of a function or a failure of a computation is not represented by a postulated null object such as the third truth value. The logical operators of the system are classical. Another welcome feature of this expressive system is that its consequence relation is monotonic.

Formal reasoning with non-denoting terms, esp. non-referring descriptions such as "the King of France", is still an under-investigated area. The recent exception being a series of papers e.g. by Indrzejczak and Zawidzki. The present paper offers an alternative to their approach since instead of free logic and sequent calculus, it's framed in partial type theory with natural deduction in sequent style. Using a Montague- and Tichy-style formalization of natural language, the paper successfully handles deduction with intensional transitives whose complements are non-referring descriptions, and derives Strawsonian rules for existential presuppositions of sentences with such descriptions.

The present paper offers the rule of existential generalization (EG) that is uniformly applicable within extensional, intensional and hyperintensional contexts. In contradistinction to Quine and his followers, quantification into various modal contexts and some belief attitudes is possible without obstacles. The hyperintensional logic deployed in this paper incorporates explicit substitution and so the rule (EG) is fully specified inside the logic. The logic is equipped with a natural deduction system within which (EG) is derived from its rules for the existential quantifier, substitution and functional application. This shows that (EG) is not primitive, as often assumed even in advanced writings on natural deduction. Arguments involving existential generalisation are shown to be valid if the sequents containing their premises and conclusions are derivable using the rule (EG). The invalidity of arguments seemingly employing (EG) is explained with recourse to the definition of substitution.

The present paper addresses several puzzles related to the Rule of Existential Generalization, (EG). In solution to these puzzles from the viewpoint of simple type theory, I distinguish (EG) from a modified Rule of Existential Quantifier Introduction which is derivable from (EG). Both these rules are often confused and both are considered as primitive but I show that (EG) itself is derivable from the proper Rule of Existential Quantifier Introduction. Moreover, the latter rule must be primitive in logical systems that treat both total and partial functions, for the universal and the existential quantifiers are not interdefinable in them. An appropriate natural deduction for such a system is deployed. The present logical system is simpler than the system recently proposed and applied by the present author. It utilises an adequate definition of substitution which is capable of handling not only a higher-order quantification, but also (hyper)intensional contexts.

Problem hyperintenzionalnich kontextů, resp. problem logicke vsevědoucnosti, ukazuje na znacnou limitaci možnosvětove semantiky, jež je přijimana i standardni epistemickou logikou. Jako řeseni zde uplatňujeme hyperintenzionalni semantiku, podle niž je významem výrazu abstraktni strukturovaný algoritmus, jmenovitě tzv. konstrukce Pavla Ticheho. Konstrukce determinuji referenty výrazů. Tzv. propozicni postoje tak nejsou v nami prosazovanem přistupu postoji k propozicim, ale ke konstrukcim pravdivostnich hodnot. Tento model explicitniho přesvědceni je inferencně restriktivni, a proto zde navrhujeme model implicitniho přesvědceni. To je vysvětleno jako soubor explicitnich postojů agenta k různým konstrukcim pravdivostnich hodnot, jež jsou propojeny prostřednictvim agentem ovladaneho derivacniho systemu. Derivacni system se sklada předevsim z objektů přesvědceni a derivacnich pravidel, pomoci nichž si agent důsledky svých přesvědceni může odvodit; takove přesvědceni nazývame derivovane. Na množinu přesvědceni a množinu derivacnich pravidel jsou přitom kladeny podminky, jež vystihuji omezeni agentových kognitivnich schopnosti.

The problem of hyperintensional contexts, and the problem of logical omniscience, shows the severe limitation of possible-worlds semantics which is employed also in standard epistemic logic. As a solution, we deploy here hyperintensional semantics according to which the meaning of an expression is an abstract structured algorithm, namely Tichy's construction. Constructions determine the denotata of expressions. Propositional attitudes are modelled as attitudes towards constructions of truth values. Such a model of belief is, of course, inferentially restrictive. We therefore also propose a model of implicit knowledge, which is the collection of a possible agent's explicit beliefs which are related through a derivation system mastered by the agent. A derivation system consists of beliefs and derivation rules by means of which the agent may derive beliefs different from the beliefs she is actually related to. Conditions imposed on the set of base beliefs and the set of rules capture the limitations of the agent's deriving capabilities.

Williamson, Linsky, Paseau and others proposed a solution to Church-Fitch's knowability paradox that is based on typing knowledge; however, it received some criticism. Carrara and Fassio objected that the approach has no paradox-independent motivation, it is thus ad hoc. In the first part of the paper, I dismiss such criticism by carefully stating typing approach principles that are based on non-circular formation of propositions and intensional operators operating on them. In the second part of the paper, I demonstrate that the firm foundation of the approach prevents the variants of the paradox by Florio, Murzi and Jago that were developed as allegedly unresolvable by typing knowledge. The revenge form of Church-Fitch's knowability paradox, which had been proposed by Williamson, Hart, Carrara and Fassio, fares badly as well, since it is likewise based on violation of reasonable typing rules.

I examine the familiar quadruple of categorical statements “Every F is/is not G.”, “Some F is/is not G.” as well as the quadruple of their modal versions “Necessarily, every F is/is not G.”, “Possibly, some F is/is not G.”. I focus on their existential import and its impact on the resulting Squares of Opposition. Though my construal of existential import follows modern approach, I add some extra details which are enabled by framing my definition of existential import within expressively rich higher-order partial type logic. As regards the modal categorical statements, I find that so-called void properties bring existential import to them, so they are the only properties which invalidate subalternation, and thus also contrariety and subcontrariety, in the corresponding Square of Opposition.

Abstract The paper examines Loar's and Bach's defence of Nominal Description Theory against Kripkean Modal Argument (MA). Using formal tools of hyperintensional logic, I discriminate three kinds of nominal description which are possible substitutes for a proper name, thus considering various readings of the MA. On its natural understanding, the MA is valid { contrary to what Loar and Bach say. On the other hand, the soundness of the MA remains doubtful, as pointed out already by Loar and Bach

Language can be modelled in various ways, highlighting either its social or systemic character. I assume that language is a normative phenomenon enabling speakers to communicate. At any particular time language is used, however, we are capable of determining a function which maps the expressions produced using this language to their meanings. In this contribution I propose a functional model of language in a synchronic sense. This model also solves various complications with ambivalence, etc. Then, I also propose a model of language in a diachronic sense as a function from possible worlds and time instants to languages in a synchronic sense. In this way, the intuitive idea that language changes is captured. Both models are constructed to be convenient tools mainly for the investigation of semantic properties of expressions of that language.

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 concerning individuals, e.g., the Ship of Theseus, the Polish Logician, problems with reidentification, or proper names.

In this study, we examine modern reading of the Square of Opposition by means of intensional logic. Explicit use of possible world semantics helps us to sharply discriminate between the standard and modal (‘alethic’) readings of categorical statements. We get thus two basic versions of the Square. The Modal Square has not been introduced in the contemporary debate yet and so it is in the centre of interest. Some properties ascribed by medieval logicians to the Square require a shift from its Standard to Modal version. Not inevitably, because for each of the two squares there exists its mate which can be easily confused with it. The discrimination between the initial and modified versions of the Standard and Modal Square enable us to separate findings about properties of the Square into four groups, which makes their proper comparison possible. The disambiguation so achieved leads to the solution of various puzzles often mentioned in recent literature.

It is already known that David Miller's critique of Pavel Tichý's counting of truhlikeness for its linguistic dependence affects many frameworks (cf., e.g., Oddie 1986). I review the debate between Miller (1976 and passim) and Tichý (1976, 1978, Oddie 1986, my papers). I focus mainly on the fact that it is inevitable to discriminate between primary and derivative concepts. If such distinction is made, one gets not only a solution of the puzzle raised by Miller: one offers also a more adequate picture of scientific languages in general.

Typing knowledge is capable to resolve Fitch's knowability paradox. As I have argued elsewhere, Russellian typing knowledge is immune to the recently raised criticism of the typing approach. This paper focuses on a special form of the criticism proposing a revenge problem raised by Williamson, Hart and also Carrara with Fassio. The basic idea of the revenge Fitch's paradox employs quantification over type levels. However, the formalism used by the critics is ambivalent. I concentrate only on its two most probable readings, explaining also quantification over types and quantification over orders. As I show in details, if such readings went through, they would violate the typing rules in a direct manner. Hence, there is no revenge for the Russellian typing approach to Fitch's knowability paradox.

Pavel Tichy originally published his interesting conception of possible worlds in 1968. Even though he modified it over the following twenty five years, its core remained unchanged. None of his thirty journal papers or books containing the notion of possible worlds was a study in metaphysics. Tichy (and most of his followers) always introduced the notion in the context of other investigations where he applied his Transparent intensional logic either to the semantic analysis of natural language or to the explications of other notions. Tichy presented his conceptions using rather short descriptions occurring on a number of places; his proposal appears not only fragmentary but also somehow incoherent. The main contribution of this paper is thus not only a complete survey of Tichy's development of his conception but also a certain completion of the very proposal.

The approach of Transparent Intensional Logic to truth differs significantly from rivalling approaches. The notion of truth is explicated by a three-level system of notions whereas the upper-level notions depend on the lower-level ones. Truth of possible world propositions lies in the bottom. Truth of hyperintensional entities-called constructions-which determine propositions is dependent on it. Truth of expressions depends on truth of their meanings; the meanings are explicated as constructions. The approach thus adopts a particular hyperintensional theory of meanings; truth of extralinguistic items is taken as primary. Truth of expressions is also dependent, either explicitly or implicitly, on language (its notion is thus also explicated within the approach). On each level, strong and weak variants of the notions are distinguished because the approach employs the Principle of Bivalence which adopts partiality. Since the formation of functions and constructions is non-circular, the system is framed within a ramified type theory having foundations in simple theory of types. The explication is immune to all forms of the Liar paradox. The definitions of notions of truth provided here are derivation rules of Pavel Tichy's system of deduction.

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 Duži and Pavel Materna under the name the “Parmenides Principle”. However, Duži 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 in their meanings. The meanings are explicated by Tichý, and also by Duži 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 the whole net of methodological principles which support it. This is why the topic largely transcends the debate among Tichý’s followers.

The Barber Paradox is often introduced as a popular version of Russell's paradox, though some philosophers and logicians (e.g. Church) have denied their similarity, even calling the Barber paradox a pseudoparadox. In the first part of the paper, we demonstrate mainly that in the standard (Quinean) definition of a paradox the Barber paradox is a clear-cut example of a non-paradox. In the second part of the paper, we examine a probable source of the paradoxicality of the Barber Paradox, which is found in a certain ambivalence in terms of meaning. The two different readings of the crucial phrase yield distinct existential assumptions which produce the paradoxical conclusion.