This paper analyzes specific situation in Croatia regarding role, development, and perspectives of employee participation in ownership and financial results. The model of enterprise privatization in Croatia resulted with a large involvement of employees in the enterprises' ownership. As the first phase of privatization in Croatia is approaching to its end, new, genuine mechanisms of development of the employee financial participation are beginning to emerge. Among them, ESOP plans and management and employee buyouts (MEBO) seem to be most appealing. Such (...) practices can be found primarily in enterprises where a functional symbiosis between management and employees has been preserved or developed, where assets of the enterprise have also been preserved, and an organizational culture based on identification with enterprise and confidence with management has been developed. It seems that such a mutual reliance between employees and management can be very successful in assuring good operation and financial results of (especially large) enterprises during and after the process of transition. (shrink)

We describe a KB Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gödel's relation to Kant.

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. As (...) a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

Gödel's philosophical views were to a significant extent influenced by the study not only of Leibniz or Husserl, but also of Kant. Both Gödel and Kant aimed at the secure foundation of philosophy, the certainty of knowledge and the solvability of all meaningful problems in philosophy. In this paper, parallelisms between the foundational crisis of metaphysics in Kant's view and the foundational crisis of mathematics in Gödel's view are elaborated, especially regarding the problem of finding the “secure path of a (...) science” for both mathematics and philosophy. Gödel's temporal subjectivism and metaphysical conceptual objectivism are presented as positively or negatively motivated by Kant's viewpoints. A remark on Gödel's collapse of modalities (in accordance with the collapse of objective time) is added. (shrink)

We claim that Kant's doctrine of the "transcendental ideal of pure reason" contains, in an anticipatory sense, a second-order theory of reality (as a second-order property) and of the highest being. Such a theory, as reconstructed in this paper, is a transformation of Kant's metatheoretical regulative and heuristic presuppositions of empirical theories into a hypothetical ontotheology. We show that this metaphysical theory, in distinction to Descartes' and Leibniz's ontotheology, in many aspects resembles Gödel's theoretical conception of the possibility of a (...) supreme being. The proposed second-order modal formalization of the Kantian doctrine of the "transcendental ideal" of the supreme being includes some specific features of Kantian general logic like "categorical", "hypothetical", and exclusive disjunctive propositions as basic forms. (shrink)

The booklet provides teachers and others who use the textbook "Logic" by Srećko Kovač with basic theoretical and philosophical ideas about logic as a discipline, as well as practical instructions on how to use the textbook.

Kant's theory of transcendental ideas can be conceived as a sort of model theory for an empirical first-order object theory. The main features of Kant's theory of transcendental ideas (especially its antinomies and their solutions) can be recognized, in a modified way, in a religious discourse as exemplified in the dialogue of Jesus and the Samaritan woman (John 4). In this way, what is by Kant meant merely as regulative ideas obtains a sort of objective reality and becomes a religiously (...) founded metaphysics. A metaphysical theory of religious dialogue is formalized on the basis of an extended justification logic of evidence and wish agents. (shrink)

The abstract status of Kant's account of his ‘general logic’ is explained in comparison with Gödel's general definition of a formal logical system and reflections on ‘abstract’ (‘absolute’) concepts. Thereafter, an informal reconstruction of Kant's general logic is given from the aspect of the principles of contradiction, of sufficient reason, and of excluded middle. It is shown that Kant's composition of logic consists in a gradual strengthening of logical principles, starting from a weak principle of contradiction that tolerates a sort (...) of contradictions in predication, and then proceeding to the (constructive) principle of sufficient reason, and to a classical-like logic, which includes the principle of excluded middle. A first-order formalisation is applied to this reconstruction, which reveals implicit modalities in Kant's account of logic, and confirms the implementability of Kant's logic into a sound and complete formal system. (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)

Wittgenstein’s “machines-as-symbols” are considered with respect to their historical sources and their symbolic and logical nature. Among these sources and precursors, along with Leonardo’s drawings of machines, there are illustrated “machine books”, a kind of book published in the period from the 16th to the 18th centuries which consist of pictures and descriptions of a variety of mechanical devices. Most probably, these books were one of Wittgenstein’s inspirations for his view of machines as components of language-games. The picture of homo (...) volans in Vrančić’s machine book possessed by Wittgenstein is taken as an example. In particular, homo volans is shown to contain patterns of logical laws and rules and to be abstractly interpretable as a logical symbol. A machine, taken as a symbol, is shown to be a precondition of a meaningful “overview” of a mechanical work that exceeds the limits of decidability, and to possess causal features if causality is understood teleologically and in a deeper sense of a “binding” life. (shrink)

This paper proposes a possible reconstruction and philosophical-logical clarification of Gödel's idea of causality as the philosophical fundamental concept. The results are based on Gödel's published and non-published texts (including Max Phil notebooks), and are established on the ground of interconnections of Gödel's dispersed remarks on causality, as well as on the ground of his general philosophical views. The paper is logically informal but is connected with already achieved results in the formalization of a causal account of Gödel's onto-theological theory. (...) Gödel's main causal concepts are analysed (will, force, enjoyment, God, time and space, life, form, matter). Special attention is paid to a possible causal account of some of Gödel's logical concepts (assertion, privation, affirmation, negation, whole, part, general, particular, subject, predicate, necessary, possible, implication), as well as of logical antinomies. The problem of mechanical and non-mechanical procedures in the work with and on concepts is addressed in terms of Gödel's causal view. (shrink)

Se propone una lectura de los textos del filósofo chileno Carlos Ruiz Schneider que presta atención a las citas que contiene y asume que éstas exceden su uso ilustrativo y autorizador, para funcionar como modo de expresión estético-político de un pensar filosófico comprometido con una democracia radical. Para ello se proyectan y reformulan categorías de análisis de crítica cultural y artística extraídas del trabajo de Nelly Richards (complementadas con aportes de la filosofía contemporáneas: Heidegger, Derrida, Foucault y Butler), pertinentes para (...) configurar lo que podría denominarse un ‘estilo epocal’ en el pensamiento crítico chileno de fines del siglo XX. A partir de esta lectura, se abre una reflexión más general sobre la posibilidad de la democracia en la indecible y, por tanto, secreta complicidad pensante desencadenada por las enunciaciones. _Palabras claves:_ Filosofía – Democracia – Cita – Obscenidad – Estética. (shrink)

Obituary for Berislav Žarnić, an outstanding, internationally influential, Croatian logician and philosopher. His main contributions are in logic of practical inference, logic of imperatives, logic of norms and philosophy of education.

Goran Švob was an influential Croatian logician and philosopher or language. According to him, logic should be based on a theory of meaning, propositions and truth, and, in its core, is inseparable from central philosophical questions. Švob was especially inspired by Frege's early logical philosophy. According to Švob, the concept of identity should include naming and knowledge and has self-identity of objects as its "degenerate" case.

What would happen if we could stroll through the revolutionary history of the 20th century and, without any fear of the possible responses, ask the main protagonists - from Lenin to Che Guevara, from Alexandra Kollontai to Ulrike Meinhof - seemingly naïve questions about love? Although all important political and social changes of the 20th century included heated debates on the role of love, it seems that in the 21st century of new technologies of the self we are faced with (...) a hyperinflation of sex, not love. By going back to the sexual revolution of the October Revolution and its subsequent repression, to Ches dilemma between love and revolutionary commitment and to the period of 68 and its commodification in late capitalism, the Croatian philosopher Srecko Horvat gives a possible answer to the question of why it is that the most radical revolutionaries like Lenin or Che were scared of the radicality of love. What is so radical about a seemingly conservative notion of love and why is it anything but conservative? This short book is a modest contribution to the current upheavals around the world - from Tahrir to Taksim, from Occupy Wall Street to Hong Kong, from Athens to Sarajevo - in which the question of love is curiously, surprisingly, absent. (shrink)

The article focuses on Kant's formal logic (formal theory of concepts, judgments, and inference, general methodology) in the systematic order of logical forms and presents the main characteristics of his transcendental logic (theory of categories and transcendental ideas). Kant's problem of the foundations of logic and its completeness is addressed. The relevance and influence of Kant's account of logic in the development of modern logic is outlined. The article gives a selection of primary and secondary sources.

We want to show that Aristotle’s general conception of syllogism includes as its essential part the logical concept of necessity, which can be understood in a causal way. This logical conception of causality is more general then the conception of the causality in the Aristotelian theory of proof (“demonstrative syllogism”), which contains the causal account of knowledge and science outside formal logic. Aristotle’s syllogistic is described in a purely intensional way, without recourse to a set-theoretical formal semantics. It is shown (...) that the conclusion of a syllogism is justified by the accumulation of logical causes applied during the reasoning process. It is also indicated that logical principles as well as the logical concept of causality have a fundamental ontological role in Aristotle’s “first philosophy”. (shrink)

This book is an introduction to elementary logic (classical propositional and first-order logic), comprising brief summaries of the basics of elementary logic, with the emphasis on typical questions and procedure descriptions and with a large number of corresponding exercises and problems. Solutions are given for each problem and exercise, often with commentaries. The first part, Basics of Logic, deals with (a) formal language, models, Venn diagrams for sentences, and translation from natural into formal language and vice versa, (b) deduction and (...) refutation methods in the format of natural deduction (Fitch and Suppes-Lemmon styles), tableau system and Venn diagrams, and (c) basic logical properties and relations (consistency, validity, consequence, equivalence, various types of opposition, logical completeness and independency, relationship between syntax and semantics). The second part, Logic in Understanding and Analysis, introduces into (a) logical approach to problem solving in concrete situations and events as presented in brief tales and anecdotes, (b) discovering the meaning, and reconstruction of logical interconnections, in ordinary, scholarly and philosophical texts, (c) application of already mastered logical tools in examining and defining further theoretical (logical, scientific) concepts and in building formal languages. The shorter third part, From the Traditional Logic, is dedicated to the traditional logic of concepts, judgements and syllogisms, largely with the use of Venn diagrams. (shrink)

Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are elaborated, (...) and examples of cyclic and convergent causation are given. Soundness and completeness proofs are sketched. (shrink)

On the ground of Kant’s reformulation of the principle of con- tradiction, a non-classical logic KC and its extension KC+ are constructed. In KC and KC+, \neg(\phi \wedge \neg\phi),  \phi \rightarrow (\neg\phi \rightarrow \phi), and  \phi \vee \neg\phi are not valid due to specific changes in the meaning of connectives and quantifiers, although there is the explosion of derivable consequences from {\phi, ¬\phi} (the deduc- tion theorem lacking). KC and KC+ are interpreted as fragments of an S5-based first-order (...) modal logic M. The quantification in M is combined with a “subject abstraction” device, which excepts predicate letters from the scope of modal operators. Derivability is defined by an appropriate labelled tableau system rules. Informally, KC is mainly ontologically motivated (in contrast, for example, to Jaśkowski’s discussive logic), relativizing state of affairs with respect to conditions such as time. (shrink)

The square of opposition (as part of a lattice) is used as a natural way to represent different and opposite ways of who makes decisions, and in what way, in/for a group or a society. Majority logic is characterized by multiple logical squares (one for each possible majority), with the “discursive dilemma” as a consequence. Three-valued logics of majority decisions with discursive dilemma undecided, of veto, consensus, and sequential voting are analyzed from the semantic point of view. For instance, the (...) paraconsistent and paracomplete logics M3, M3veto and C3 are described. The distinction of designated and non-designated values is not used, and instead, the consequence relation is defined as a preservation of the minimum truth-value of the implying set of sentences. The consequence and opposition relations of the logics described are compared, and an ordering of the logics with respect to their opposition relations is established. (shrink)

After delineating the corpus of Croatian philosophy, the historical and conceptual identity and continuity of Croatian philosophy are analysed with respect to several aspects: (1) the historical space and time of Croatian philosophy; (2) its socio-cultural role and character (educational, linguistic and national-political); (3) its traditions and interconnections; and (4) the idea of Croatian philosophy. Special attention is paid to the difference between Franjo pl. Marković’s views on Croatian philosophy and the present state-of-the-art. Finally, the roots of Croatian philosophy are (...) considered at the moment of transition from myth to Christianity and in the introductory reflections of the Charter of Duke Trpimir. (shrink)

Bishop Nicholai Velimirovich (1881–1956) spent WWII in Nazi captivity. After the war, in 1946, he left for the United States, where he lived for the rest of his life. During his life, he enjoyed great spiritual and moral authority, both in Eastern Orthodox Church as well as in a wider international and ecumenical context. However, his public image was significantly changed 30 years after his death, i.e. after the publication of several pieces attributed to him posthumously, and especially after the (...) book entitled To the Serbian People Through the Dungeon Window was published. In the present paper, we will consider some aspects of this book, with special reference to the questions of the authenticity of this work. (shrink)

U članku se promatraju osnovne karakteristike razvojne dinamike hrvatskoga logičkoga nazivlja od izlazka Pacelove Logike za gimnazije, prve sustavne logike na hrvatskome jeziku, 1868. godine, pa sve do Petrovićeve Logike, također za srednja učilišta, iz 1964., koja je još uviek u uporabi. Nazivlje je u tu svrhu razvrstano u nekoliko tipičih skupina. Općenito, uočava se porast zastupljenosti latinizama (i grecizama) na štetu hrvatskih naziva. U analizi nazivlja autor se ograničuje na knjige namienjene nastavi logike bilo na srednjim učilištima, bilo na (...) sveučilištu, i to na nazivlje tradicionalne logike. Mjestimice su pridodane i napomene o nazivlju moderne (matematičke) logike. (shrink)

The paper sets out from Göodel's question about primitive concepts, in connection with Gödel's proposal of the employment of phenomenological method. The author assumes that the answer that can be found in Kant is relevant as a starting point. In a modification of the approach by K. Reich, a reconstruction of Kant's "deduction'' of logical forms of judgment is presented, which serve Kant as the basis for his "metaphysical deduction of categories'' including substantiality and causality. It is proposed that different (...) aspects of Kant's "original unity of self-consciousness'' as applied and attached to concrete representations step by step yield different forms of concepts, judgments, and inferences. Categorical, hypothetical and disjunctive judgments are shown to be gradually strengthening the conditions of bringing our representations under the "objective unity of consciousness", and in this way gradually implementing logical laws. The corresponding concepts of substantiality, causality, and mutual influence appear to be grounded in the primitive forms of our thinking. (shrink)

Obituary for Marijan Cipra, a most prominent Croatian philosopher. In his essential book "Metamorfoze metafizike" ("Metamorphoses of Metaphysics", 1978), he proposed a metaphysical foundations of the historical development of philosophy, based particularly on his in-depth study of Greek philosophy.

U tekstu se obrađuju Stadlerovo i Bauerovo shvaćanje i zasnivanje formalne logike. Formalna je logika u oba slučaja postavljena u duhu novoskolastičke filozofije druge polovice 19. stoljeća. Subjektivna je strana mišljenja (samosviest, djelatba) spojena s njegovom objektivnom stranom (objektivna vriednost), a logička se načela temelje na ontologijskim. Stadler se i Bauer oddvajaju od onodobnoga formalizma i logicizma, kao i od psihologizma i voluntarizma. Pritom je Bauer izrazitije ušao u razpravljanje s drugačijim shvaćanjima (psihologizam i voluntarizam u Wundta).

A first-order logic of belief with identity is proposed, primarily to give an account of possible de re contradictory beliefs, which sometimes occur as consequences of de dicto non-contradictory beliefs. A model has two separate, though interconnected domains: the domain of objects and the domain of appearances. The satisfaction of atomic formulas is defined by a particular S-accessibility relation between worlds. Identity is non-classical, and is conceived as an equivalence relation having the classical identity relation as a subset. A tableau (...) system with labels, signs, and suffixes is defined, extending the basic language $\mathscr{L}_{\mathbf{QB}}$ by quasiformulas (to express the denotations of predicates). The proposed logical system is paraconsistent since $\phi \wedge \neg\phi$ does not ``explode'' with arbitrary syntactic consequences. (shrink)

Logic has a fundamental role in the philosophy of Franjo Marković (1845-1914). His theory of concepts and reasoning is analyzed, especially with respect to the essential role of the principle of sufficient reason and in connection with the concept of causality. The interplay of various types of evidence in Marković's inductive-deductive logic is analysed by means of contemporary justification logic tools.

Gödel's ontological argument is related to Gödel's view that causality is the fundamental concept in philosophy. This explicit philosophical intention is developed in the form of an onto-theological Gödelian system based on justification logic. An essentially richer language, so extended, offers the possibility to express new philosophical content. In particular, theorems on the existence of a universal cause on a causal "slingshot" are formulated.

Logical reasoning is not only a component of religious faith (cf., for instance, the "Golden rule"), but, in addition, the religious faith itself can be conceived as a logical pragmatic function applied to sentences and their meanings. Pragmatic role of religious faith is shown on the examples of the analogy of seed and spoken word (e.g., Mt 13:3-23) and on the degrees of faith described in the episode about Nicodemus (John 3). Pragmatics adds (different grades of) perseverance to the correctness (...) of reasoning and to the truth-preservation of the consequence relation. Correspondingly, religious faith is described by formally defined model and satisfaction relation, which are applied to and examined on the text of John 3. (shrink)

We show how some model-theoretical devices (local reasoning, modes of presentation, an additional accessibility relation) can be combined in first-order modal logic to formalize the consequence relation that includes de dicto and de re contradictory beliefs. Instead of special ``sense objects'', appearances of objects in an agent's belief are introduced and presented as ordered pairs consisting of an object and an individual constant. A non-classical identity relation is applied. A relation S on the set of possible worlds is introduced, which (...) models possible distortions in an agent's picture of a (real) world. The application of such models in deontic logic is illustrated by a characteristic example. (shrink)

Faust Vrančić's (Faustus Verantius, 1551-1617) logic is analyzed in comparison to Renaissance Aristotelianism in logic with regard to the problem of determining logic, the subject of logic, and understanding the method. Vrančić's logic is compared to Markantun de Dominis' understanding of logic and to the understanding of logic in Jacopo Zabarella and in the Jesuit Renaissance tradition (P. Fonseca, F. Toletus, F. Suárez). In addition, the concept of science is discussed. "Censura logicae" published at the end of Vrančić's "Logica nova" (...) (1616) is attributed to de Dominis. -- German version: 'Faust Vrančić and der Aristotelismus in der Logik', Studia historiae philosophiae Croaticae 2 (1993), 229-252). (shrink)

It is shown in what sense essential characteristics of formalism, which is normative for exact knowledge, can be found already in Aristotle. It is described how exactness and formalism are pre-conditioned by sensible intuition. The machine character (Turing machine) of a formalism is considered. The general concept of provability leads to an expanding and dynamic understanding of a formalism, with the final source of logical patterns in the "forms of life" (Wittgenstein).

Quine rejects intensional Platonism and, with it, also rejects attributes (properties) as designations of predicates. He pragmatically accepts extensional Platonism, but conceives of classes as merely auxiliary entities needed to express some laws of set theory. At the elementary logical level, Quine develops an “ontologically innocent” logic of predicates. What in standard quantification theory is the work of variables is in the logic of predicates the work of a few functors that operate on predicates themselves: variables are eliminated. This “predicate (...) functor logic” may be conceived as a peculiar sort of Platonism - ontologically neutral, reduced to schematized linguistic forms. (shrink)

Zlatko Posavac is one of the most thorough and deepest experts on Croatian cultural history, with a focus on aesthetics both as a theory and as realized in artistic practice. On the basis of his improved factography, he examines aesthetic phenomena through the model of meaningful-stylistic structures and epochal change. As one of the fundamental phenomena, he highlights the "prevention of free transmission of tradition" (silencing, falsifying, expulsion of truth). He introduces significant structural shifts in cultural-historical periodization.

The Zagreb Royal Academy, the successor of the former Jesuit Neoacademy, was founded in 1776 as the central institution of higher education in Croatia as part of the educational reform in the Austro-Hungarian Empire. After presenting the basic characteristics of the reform concept, the paper deals with the teaching of theoretical philosophy at the Zagreb Academy. Philosophy was taught by E. Raffay, A. Minković, G. Valičić, S. Čučić, S. Pogledić, S. Moyses, and S. Muzler until the abolition of the Academy (...) in 1850. In the transitional period of 1773-1776, theoretical philosophy was taught by V. Kalafatić (ethics by F. Sebastijanović). Philosophy, along with other subjects (primarily mathematics, physics, and history), was studied for two years, including logic, metaphysics, moral philosophy, and empirical psychology. Textual documentation of theoretical (as well as practical) philosophy is represented by printed examination theses that were publicly defended at the Academy. The most significant systematic work of theoretical philosophy, however, is Čučić's "Philosophia critice elaborata". A new, updated bibliography of these theses is also presented in the supplement. [Zagrebačka kraljevska akademija, nasljednica prijašnje isusovačke Neoacademije, osnovana je, u sklopu školske reforme u Austrijskoj Monarhiji, 1776. godine kao središnja visokoškolska ustanova u Hrvatskoj. Nakon izlaganja osnovnih karakteristika reformske koncepcije, rad se bavi nastavom teorijske filozofije na zagrebačkoj akademiji. Filozofiju su do ukinuća Akademije 1850. godine predavali E. Raffay, A. Minković, G. Valičić, S. Čučić, S. Pogledić, S. Moyses i S. Muzler. U prijelaznom razdoblju 1773-76. god. teorijsku je filozofiju predavao V. Kalafatić (etiku F. Sebastijanović). Filozofija se, uz ostale predmete (prvenstveno matematiku, fiziku i povijest), slušala dvije godine i to logika, metafizika i moralna filozofija i empirijska psihologija. Tekstovnu dokumentaciju teorijske (kao i praktičke) filozofije predstavljaju tiskane ispitne teze koje su se na Akademiji javno branile. U dodatku ,se donosi i nova, dopunjena bibliografija tih tezarija. Teorijski je međutim najznačajnije Čučićevo sustavno djelo "Philosophia critice elaborata«.]. (shrink)

[English in PhilArchive, unpublished]. Ruđer Bošković's (Rogerius Joseph Boscovich, 1711-1787) induction is described as a reasoning procedure that combines abductive, generalizing and deductive forms of inference. According to Bošković, the application of inductive reasoning extends beyond natural science. Bošković's critique of the use of the principle of sufficient reason is discussed, and constructive rules of Bošković's inductive logic are proposed from the standpoint of contemporary justification logic. To that end, justification logic could be extended with Bošković's typology of reasons. Hunter's (...) result (1965) is conceived as a confirmation that the inference from the constructive defectus rationis is a necessary component of Bošković's induction. - English version in _PhilArchive_. (shrink)

In the book, the decisive, foundational role of transcendental apperception for logic and transcendental philosophy in Kant is corroborated. The book contains many implicit connections with modern logic that could help a logician with a philosophical interest to gain a deeper insight into the origins and foundations of concepts such as object, truth, analyticity, identity, contradiction, judgment, existence, reference, quantification and others, as well as into the foundations and possible general features of logic. In distinction to the book, this review (...) emphasizes the objective validity of analytic judgements and the foundational role of hypthetical and disjunctive forms of a judgment in Kant. (shrink)

The publication of Gödel’s Max IV contributes to better understanding of the complex development of Gödel’s philosophical thought, and, alongside the other published notebooks, it is a further contribution to modifying a conventional view on the 20th-century philosophy, where Gödel should be recognized as one of the most important and profound philosophers. Moreover, his questions, problem formulations, and ideas, particularly as presented in his philosophical notebooks, transcend the historical distance and can immediately resonate with and inspire the current philosophical research.

No es frecuente encontrarse con personas que en estos tiempos se dediquen a la discusión teórica y sobre todo que asuman con tanta seriedad la tarea de pensar procesos en los que todos estamos inmersos. El libro se presenta como un desafío a la reflexión, una fuerte provocación cuando muchos tenemos la sensación diaria de que la contingencia llena la mayor parte de las horas del día, y en este sentido creo que es justo en primer lugar valorar el aporte (...) que este ensayo representa para repensar.. (shrink)

Faust Vrančić's (Faustus Verantius, 1551-1617) logic is analyzed in comparison to Renaissance Aristotelianism in logic with regard to the problem of determining logic, the subject of logic, and understanding the method. Vrančić's logic is compared to Markantun de Dominis' understanding of logic and to the understanding of logic in Jacopo Zabarella and in the Jesuit Renaissance tradition (P. Fonseca, F. Toletus, F. Suárez). In addition, the concept of science is discussed. "Censura logicae" published at the end of Vrančić's "Logica nova" (...) (1616) is attributed to de Dominis. (shrink)

The book is a collection of papers addressing the role of logic in forming and developing philosophy. In particular, on the ground of modern development of logic, it is shown that philosophy can be established (and, in fact, to a large extent is established) as a modern science. The following problems are addressed: general relationship between philosophy and science (especially from a logical viewpoint); the use of logic in ordinary language; names and descriptions; Quine's pragmatic extensional Platonism and predicate-functor logic; (...) philosophical and logical aspects of Gödel's onto-theological system. In the last two chapters, an early critique and emendement of algebraic logic by Croatian philosophers Franjo Marković and Mate Meršić, respectively, is examined. (shrink)

The content for an advanced logic course is presented, which includes the properties of first-order logic language, soundness and completeness of the first-order logic deductive system, Peano arithmetic, Gödel's incompleteness theorems, higher-order logic and its properties. As a reminder, a brief description of first-order logic is included.

The Aristotelian origins of formal systems are outlined, together with Aristotle's use of causal terms in describing syllogisms. The precision and exactness of a formalism, based on the projection of logical forms into perceptive signs, is contrasted with foundational, abstract concepts, independent of any formalism, which are presupposed for the understanding of a formal language. The definition of a formal system by means of a Turing machine is put in the context of Wittgenstein's general considerations of a machine understood as (...) a sign. A modification of Łukasiewicz's logic Ł3 with the inclusion of justification terms is proposed in order to formally analyse some features of formalistic reasoning as a mechanical, causal affair within a wider context of "indeterminacy". (shrink)

There is a long tradition of logic, from Aristotle to Gödel, of understanding a proof from the concepts of necessity and causality. Gödel's attempts to define provability in terms of necessity led him to the distinction of formal and absolute (abstract) provability. Turing's definition of mechanical procedure by means of a Turing machine (TM) and Gödel's definition of a formal system as a mechanical procedure for producing formulas prompt us to understand formal provability as a mechanical causality. We propose a (...) formalism which makes explicit the mechanical causal nature of a TM's work. We claim that Gödel's axiomatised ontotheology and his ontological proof give a clue for the understanding of the concept of absolute provability and the pattern of the corresponding absolute completeness proof, respectively. (shrink)