The paper deals with the problem of logical adequacy of language knowledge with cognition of reality. A logical explication of the concept of language knowledge conceived of as a kind of codified knowledge is taken into account in the paper. Formal considerations regarding the notions of meta-knowledge (logical knowledge about language knowledge) and truth are developed in the spirit of some ideas presented in the author’s earlier papers (1991, 1998, 2001a,b, 2007a,b,c) treating about the notions of meaning, denotation and truthfulness (...) of well-formed expressions (wfes) of any given categorial language. Three aspects connected with knowledge codified in language are considered, including: 1) syntax and two kinds of semantics: intensional and extensional, 2) three kinds of non-standard language models and 3) three notions of truthfulness of wfes. Adequacy of language knowledge to cognitive objects is understood as an agreement of truthfulness of sentences in these three models. (shrink)

The paper shows that it is possible to obtain a "slingshot" result in Gödel's theory of positiveness in the presence of the theorem of the necessary existence of God. In the context of the reconstruction of Gödel's original "slingshot" argument on the suppositions of non-Fregean logic, this is a natural result. The "slingshot" result occurs in sufficiently strong non-Fregean theories accepting the necessary existence of some entities. However, this feature of a Gödelian theory may be considered not as a trivialisation, (...) but as an intended consequence of Gödel's ontotheological views. (shrink)

The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.

Two connectives are of special interest in metalogical investigations — the connective of implication which is important due to its connections to the notion of inference, and the connective of equivalence. The latter connective expresses, in the material sense, the fact that two sentences have the same logical value while in the strict sense it expresses the fact that two sentences are interderivable on the basis of a given logic. The process of identification of equivalent sentences relative to theories of (...) a logic C defines a class of abstract algebras. The members of the class are called Lindenbaum-Tarski algebras of the logic C. One may abstract from the origin of these algebras and examine them by means of purely algebraic methods. (shrink)

According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense.A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A deductive system is a second-order matrix over the formula algebra of some fixed but arbitrary language. A second-order matrix A is (...) Fregean if, for any subset X of A, the set of all pairs a,b such that X{a} and X{b} have the same closure is a congruence relation on A. Hence a deductive system is Fregean if interderivability is compositional. The logics intermediate between the classical and intuitionistic propositional calculi are the paradigms for Fregean logics. Normal modal logics are non-Fregean while quasi-normal modal logics are generally Fregean.The main results of the paper: Fregean deductive systems that either have the deduction theorem, or are protoalgebraic and have conjunction, are completely characterized. They are essentially the intermediate logics, possibly with additional connectives. All the full matrix models of a protoalgebraic Fregean deductive system are Fregean, and, conversely, the deductive system determined by any class of Fregean second-order matrices is Fregean. The latter result is used to construct an example of a protoalgebraic Fregean deductive system that is not strongly algebraizable. (shrink)

In an attempt to improve upon Alexander Pruss’s work (The principle of sufficient reason: A reassessment, pp. 240–248, 2006), I (Weaver, Synthese 184(3):299–317, 2012) have argued that if all purely contingent events could be caused and something like a Lewisian analysis of causation is true (per, Lewis’s, Causation as influence, reprinted in: Collins, Hall and paul. Causation and counterfactuals, 2004), then all purely contingent events have causes. I dubbed the derivation of the universality of causation the “Lewisian argument”. The Lewisian (...) argument assumed not a few controversial metaphysical theses, particularly essentialism, an incommunicable-property view of essences (per Plantinga’s, Actualism and possible worlds, reprinted in: Davidson (ed.) Essays in the metaphysics of modality, 2003), and the idea that counterfactual dependence is necessary for causation. There are, of course, substantial objections to such theses. While I think a fight against objections to the Lewisian argument can be won, I develop, in what follows, a much more intuitive argument for the universality of causation which takes as its inspiration a result from Frederic B. Fitch’s work (J Symb Logic 28(2):135–142, 1963) [with credit to who we now know was Alonzo church’s, Referee Reports on Fitch’s Definition of value, in: (Salerno (ed.), New essays on the knowability paradox, 2009)] that if all truths are such that they are knowable, then (counter-intuitively) all truths are known. The resulting Church–Fitch proof for the universality of causation is preferable to the Lewisian argument since it rests upon far weaker formal and metaphysical assumptions than those of the Lewisian argument. (shrink)

This paper focuses on the relation between logic and ontology. In particular, it demonstrates how classical logical theory can clarify the ontological part of Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. To this end, the work examines the adequacy of a formal system that was devised by the Polish logician, mathematician and philosopher Roman Suszko (1919–1979) as a model for the Tractatus. Following a brief explanation of the Tractarian ontology, the main ideas of Suszko’s system and its philosophical significance will be considered. The (...) latter will be illustrated in the context of central Tractarian concepts. Finally, two implications for a better understanding of the Tractarian ontology will be pointed out. (shrink)

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its (...) cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L: syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science. (shrink)

The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...) categorial grammar, and also on the ground of its extension to the bi-level, intensional and extensional semantic-pragmatic theory ST for L. In T, according to the token-type distinction of Ch.S. Peirce, L is characterized first as a language of well-formed expression-tokens (wfe-tokens) - material, concrete objects - and then as a language of wfe-types - abstract objects, classes of wfe-tokens. In ST the semantic-pragmatic notions of meaning and interpretation for wfe-types of L of intensional semantics and the notion of denotation of extensional semanics for wfe-types and constituents of knowledge are formalized. These notions allow formulating a postulate (an axiom of categorial adequacy) from which follow all the most important conditions of the language adequacy, including the above, and a structural one connected with three principles of compositionality. (shrink)

The paper applies the theory presented in A Formal Ontology of Situations (this journal, vol. 41 (1982), no. 4) to obtain a typology of metaphysical systems by interpreting them as different ontologies of situations. Four are treated in some detail: Hume's diachronic atomism, Laplacean determinism, Hume's synchronic atomism, and Wittgenstein's logical atomism. Moreover, the relation of that theory to the situation semantics of Perry and Barwise is discussed.

A generalized Wittgensteinian semantics for propositional languages is presented, based on a lattice of elementary situations. Of these, maximal ones are possible worlds, constituting a logical space; minimal ones are logical atoms, partitioned into its dimensions. A verifier of a proposition is an elementary situation such that if real it makes true. The reference (or objective) of a proposition is a situation, which is the set of all its minimal verifiers. (Maximal ones constitute its locus.) Situations are shown to form (...) a Boolean algebra, and the Boolean set algebra of loci is its representation. Wittgenstein's is a special case, admitting binary dimensions only. (shrink)

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a partial (...) solution to the paradox of analysis. (shrink)

This book is a survey of the most important developments in Austrian philosophy in its classical period from the 1870s to the Anschluss in 1938. Thus it is intended as a contribution to the history of philosophy. But I hope that it will be seen also as a contribution to philosophy in its own right as an attempt to philosophize in the spirit of those, above all Roderick Chisholm, Rudolf Haller, Kevin Mulligan and Peter Simons, who have done so much (...) to demonstrate the continued fertility of the ideas and methods of the Austrian philosophers in our own day. For some time now, historians of philosophy have been gradually coming to terms with the idea that post-Kantian philosophy in the German-speaking world ought properly to be divided into two distinct traditions which we might refer to as the German and Austrian traditions, respectively. The main line of the first consists in a list of personages beginning with Kant, Fichte, Hegel and Schelling and ending with Heidegger, Adorno and Bloch. The main line of the second may be picked out similarly by means of a list beginning with Bolzano, Mach and Meinong, and ending with Wittgenstein, Neurath and Popper. As should be clear, it is the Austrian tradition that has contributed most to the contemporary mainstream of philosophical thinking in the Anglo-Saxon world. For while there are of course German thinkers who have made crucial contributions to the development of exact or analytic philosophy, such thinkers were outsiders when seen from the perspective of native German philosophical culture, and in fact a number of them found their philosophical home precisely in Vienna. When, in contrast, we examine the influence of the Austrian line, we encounter a whole series of familiar and unfamiliar links to the characteristic concerns of more recent philosophy of the analytic sort. As Michael Dummett points out in his Origins of Analytic Philosophy, the newly fashionable habit of referring to analytic philosophy as "Anglo-American" is in this light a "grave historical distortion". If, he says, we take into account the historical context in which analytic philosophy developed, then such philosophy "could at least as well be called "Anglo-Austrian" (1988, p. 7). Much valuable scholarly work has been done on the thinking of Husserl and Wittgenstein, Mach and the Vienna Circle. The central axis of Austrian philosophy, however, which as I hope to show in what follows is constituted by the work of Brentano and his school, is still rather poorly understood. Work on Meinong or Twardowski by contemporary philosophers still standardly rests upon simplified and often confused renderings of a few favoured theses taken out of context. Little attention is paid to original sources, and little effort is devoted to establishing what the problems were by which the Austrian philosophers in general were exercised -- in spite of the fact that many of these same problems have once more become important as a result of the contemporary burgeoning of interest on the part of philosophers in problems in the field of cognitive science. (shrink)

Propositional identity is not expressed by a predicate. So its logic is not given by the ordinary first order axioms for identity. What are the logical axioms governing this concept, then? Some axioms in addition to those proposed by Arthur Prior are proposed.

The axiom of canonicity was introduced by the famous Polish logician Roman Suszko in 1951 as an explication of Skolem's Paradox and a precise representation of the axiom of restriction in set theory proposed much earlier by Abraham Fraenkel. We discuss the main features of Suszko's contribution and hint at its possible further applications.

Mentalism preserves the triad: brain's state — thought — state of affairs whereas phy‐sicalism identifies the former two elements of it. Both stands meet the famous difficulties. But these presuppose ontological actualism. On the ground of ontological possibilism, claiming the existence of all possible worlds, one may identify a thought with the corresponding state of affairs in a possible world. Yet, possibilism turns out to be too narrow to carry such an identification and requires a significant generalization.

For decades Ryszard Wójcicki has been a highly influential scholar in the community of logicians and philosophers. Our aim is to outline and comment on some essential issues on logic, methodology of science and semantics as seen from the perspective of distinguished contributions of Wójcicki to these areas of philosophical investigations.

The paper presents a formal explication of the early Wittgenstein's views on ontology, the syntax and semantics of an ideal logical language, and the propositional attitudes. It will be shown that Wittgenstein gave a language of thought analysis of propositional attitude ascriptions, and that his ontological views imply that such ascriptions are truth-functions of (and supervenient upon) elementary sentences. Finally, an axiomatization of a quantified doxastic modal logic corresponding to Tractarian semantics will be given.

We present $\in_I$-Logic (Epsilon-I-Logic), a non-Fregean intuitionistic logic with a truth predicate and a falsity predicate as intuitionistic negation. $\in_I$ is an extension and intuitionistic generalization of the classical logic $\in_T$ (without quantifiers) designed by Sträter as a theory of truth with propositional self-reference. The intensional semantics of $\in_T$ offers a new solution to semantic paradoxes. In the present paper we introduce an intuitionistic semantics and study some semantic notions in this broader context. Also we enrich the quantifier-free language by (...) the new connective < that expresses reference between statements and yields a finer characterization of intensional models. Our results in the intuitionistic setting lead to a clear distinction between the notion of denotation of a sentence and the here-proposed notion of extension of a sentence (both concepts are equivalent in the classical context). We generalize the Fregean Axiom to an intuitionistic version not valid in $\in_I$. A main result of the paper is the development of several model constructions. We construct intensional models and present a method for the construction of standard models which contain specific (self-)referential propositions. (shrink)

There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean logic SCI. (...) Then S3 proves to be the smallest Lewis modal system where PI can be defined as SE. We extend S3 to a non-Fregean logic with propositional quantifiers such that necessity and PI are integrated as non-interdefinable concepts. CA is not valid and PI refines SE. Models are expansions of SCI-models. We show that SCI-models are Boolean prealgebras, and vice-versa. This associates non-Fregean logic with research on Hyperintensional Semantics. PI equals SE iff models are Boolean algebras and CA holds. A representation result establishes a connection to Fine’s approach to propositional quantifiers and shows that our theories are conservative extensions of S3–S5, respectively. If we exclude the Barcan formula and a related axiom, then the resulting systems are still complete w.r.t. a simpler denotational semantics. (shrink)

In the paper there is presented the semantic interpretation of idealism/ realism controversy which is one of the most essential issues in Ingarden’s phenomenological project of ontology. The procedure of semantic paraphrase which is contemporary developed by Wolen´ ski, is the main interpretative tool. In the central part of the paper, there is formulated the formal theory of the semantic framework underlying idealism/realism discourse. Finally, there are formulated some notes showing that intentional conception of negation may be used for defending (...) various idealistic positions. (shrink)

The main purpose of the paper concerns the question of the existence of hard mathematical facts as truth-makers of mathematical sentences. The paper defends the standpoint according to which hard mathematical facts do not exist in semantic models of mathematical theories. The argumentative line in favour of the defended thesis proceeds as follows: slingshot arguments supply us with some reasons to reject various ontological theories of mathematical facts; there are two ways of blocking these arguments: through the rejection of the (...) principle of extensionality for individual terms or through the rejection of the principle of Wittgenstein; the first way cannot be accepted because it leads to the practice of softening mathematical facts; the second way, called fine-graining facts, cannot be accepted because it also results in the practice of softening facts. Hence, only soft mathematical facts can be introduced into semantic models of mathematical theories. Because they should be rather interpreted as mental representations of mathematical objects, they no longer satisfy the semantic role of truth-makers in relation to mathematical sentences. The argument formulated in the paper is based on the analysis of mathematical extensions of the basic non-Fregean logic. Sixty-two definitions of potential fact-identity connectives are also presented. The paper's conclusion may be interpreted as undermining the situational paradigm of building semantics for mathematical languages. (shrink)

The paper presents a new argument supporting the ontological standpoint according to which there are no mathematical facts in any set theoretic model of arithmetical theories. It may be interpreted as showing that it is impossible to construct fact-arithmetic. The importance of this conclusion arises in the context of cognitive science. In the paper, a new type of slingshot argument is presented, which is called hyper-slingshot. The difference between meta-theoretical hyper-slingshots and conventional slingshots consists in the fact that the former (...) are formulated in the semantic meta-language of mathematical theories without the use of the iota-operator or the lambda-operator as the abstractor, whereas the latter require for their expression at least one of these non-standard term-operators. Hyper-slingshots implement simpler language tools in comparison with those used in conventional slingshots. (shrink)

A logic is selfextensional if its interderivability (or mutual consequence) relation is a congruence relation on the algebra of formulas. In the paper we characterize the selfextensional logics with a conjunction as the logics that can be defined using the semilattice order induced by the interpretation of the conjunction in the algebras of their algebraic counterpart. Using the charactrization we provide simpler proofs of several results on selfextensional logics with a conjunction obtained in [13] using Gentzen systems. We also obtain (...) some results on Fregean logics with conjunction. (shrink)

1. First, a short anecdote. In the mid-1980s, Professor Jerzy Pogonowski gave a series of lectures entitled The Lvov-Warsaw School at the Institute of Philosophy at the Adam Mickiewicz University i...

The twelve original studies collected in this volume examine different aspects of Edmund Husserl's Logical Investigations. They are authored by scholars and specialists internationally recognized for their expertise in the fields of phenomenology, logic, history of philosophy and philosophy of mind. They approach Husserl's groundwork from different angles and perspectives and shed new light on a number of issues such as meaning, intentionality, ontology, logic, etc. They also explore questions such as the place of the Logical Investigations within the whole (...) of Husserl's work, its sources in 19th century philosophy and in particular in the philosophical work of Franz Brentano and Bernard Bolzano, its reception amongst the so-called members of the Munich Circle and its influence on contemporary philosophy. In short, this volume constitutes a "companion" to Husserl's Logical Investigations. (shrink)

"The Tractatus comprises four parts, which correspond to stages of its rocky development: the theory of logic (1912-14), the picture theory (1914), the discussion of science and mathematics (1915-17), and the discussion of the mystical (1916-17). The structure of the book is as follows.

In order to understand consciousness one would benefit from developing a more eclectic intellectual style. Consciousness is, as proposed by almost everyone except the stubborn reductionists, a truly mysterious concept. Its study and dissection merits a multidisciplinary approach. Waving this multidisciplinary flag has positively enlarged the discussion and neurologists, psychiatrists, mathematicians, and so on, have moved to the philosophy of mind arena, first with caution and now with a more powerful voice. Identifying what we mean by consciousness is a first (...) step even when we want to deny its existence. The link between consciousness and some other mental activity is a logical next step and there is abundant literature doing this, but not all of them differentiate among associated yet different phenomena. (shrink)

One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functor-function defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

What's wrong with modalities in (Wittgenstein 1922)? In (Suszko 1968), the writer argued that "Wittgenstein was somewhat confused and wrong in certain points. For example, he did not see the clear-cut distinction between language (theory) and metalanguage (metatheory): a confusion between use and mention of expressions". Furthermore, a modal logic was proposed in (von Wright 1986) as depicting Wittgenstein's bipolarity thesis in a S5 frame. -/- The aim of the present paper is to deal with the specific case of epistemic (...) modal logic: such a logic of propositional attitudes assumes a philosophy of language that would violate Wittgenstein's two main assumptions. (shrink)