Eighteen articles concerning modern logic by Ackermann, Carnap, Curry, Gödel, Heyting, among others, reprinted from the double issue of the review Dialectica for 1958.--L. S. F.

In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.

There is an error in the completeness proof for the {λ, =} part of FOIL-K. The error occurs in Section 4, in the text following the proof of Corollary 4.7, and concerns the definition of the interpretation I on relation symbols. Before this point in the paper, for each object variable v an equivalence class v has been defined, and for each intension variable f a function f has been defined. Then the following definition is given for a relation symbol (...) P : v1, v2, . . . , f1, f2, . . . ∈ I(P )(Γ) just in case there are w1, w2, . . . in d(Γ) with wi ∈ vi such that P (w1, w2, . . . , f1, f2, . . .) ∈ Γ. It was pointed out by Torben Brauner that we could have f1 and g1 being the same function, but also have P (w1, w2, . . . , f1, f2, . . .) ∈ Γ without having P (w1, w2, . . . , g1, f2, . . .) ∈ Γ. Our solution is to modify the definition of the model, rather artificially, so that if f and g are the same function, then f and g are syntactically the same intension variable. This is done as follows. First, arbitrarily choose some object variable w, and its corresponding equivalence class w. For each intension variable f we define a disambiguation world ˆ. (shrink)

El primer apartado del trabajo considera cómo el pensar es privado de su carácter primario cuando la lógica originaria y el lenguaje de las señas son sustituidos por la lógica del enunciado y el lenguaje de los signos. En segundo lugar, se muestra que la elucidación de las señas del Ser conduce a un examen del peligro que enfrenta el pensar en presencia de la filosofía. El tercer apartado se ocupa del ulterior peligro que surge cuando se intenta derivar el (...) pensar a partir del poetizar. El pensador aguarda señas porque ya no cuenta con sistemas de pensamiento, y en este proceso ha de estar dispuesto para la verdad del ser. Mientras que el poeta instituye de una manera originaria el Ser en una comunidad, el pensador concibe y ensambla, y de ese modo abre por primera vez lo que ha sido desvelado por el poeta. Finalmente, se ofrece un análisis de la relación de la lógica originaria con la hermenéutica y la fenomenología. (shrink)

Come migliore introduzione ad un manuale di logica deduttiva pensato per le scienze psicologiche, crediamo sia necessario definire i seguenti termini: logica, logica deduttiva e logica come arte. Crediamo, infatti, che la chiara conoscenza di tali concetti predisponga e prepari allo studio di una materia complessa come la logica e allo studio delle relazioni, forse ancor più complesse, tra logica e psicologia. Possiamo dare della logica almeno due definizioni, una più ampia ed una (...) più ristretta. Secondo un’accezione estesa, possiamo allora definire la logica come lo studio dei processi inferenziali del ragionamento umano. La logica studia, cioè, la struttura e le funzioni della ragione nel momento in cui essa produce giudizi o argomentazioni sul mondo. Invece, secondo un’accezione ristretta del termine, possiamo definire la logica come lo studio della validità dei ragionamenti umani, così come essi sono espressi linguisticamente. La logica studia, cioè, le forme corrette della ragione distinguendole dalle forme scorrette, o fallaci. La logica, infine, deve essere distinta da tutte le scienze che, come la psicologia, possono condivide- re il medesimo oggetto di studio, il ragionamento umano. Esiste, infatti, una parte cospicua della psicologia che studia proprio il ragionamento. Mentre, però, la psicologia considera quest’ultimo nella sua complessità psichica e mentale, la logica considera, invece, solo i suoi prodotti finali e formali, senza occuparsi dei suoi contenuti. La logica deduttiva è, invece, una branca della logica focalizzata sullo studio delle inferenze certe che, a partire da premesse vere e note, conducono a conclusioni, prima ignote, che sono altrettanto vere. Il senso della deduzione è, infatti, proprio il movimento che la ragione umana svolge quando cerca conferma alle proprie conoscenze acquisite e alle proprie generalizzazioni. La deduzione procede, cioè, dal generale, espresso nelle premesse, al particolare, espresso invece nella conclusione. In senso ri- stretto, perciò, la logica deduttiva studia la validità di tali forme di ragionamento e argomentazione. Deduzione e logica deduttiva devono, infine, essere distinte da induzione e logica induttiva, da un lato, e da abduzione e logica abduttiva, d’altro lato. L’induzione, infatti, procede dal particolare al generale, in senso contrario rispetto alla deduzione, da premesse parziali e non certe a conclusioni sempre incerte ma generali. L’abduzione, invece, è una modalità di ragionamento del tutto ipotetica, lontana dalle certezze conoscitive della deduzione o dalle certezze agognate dall’induzione. Concludiamo con il concetto di logica come arte. L’arte è, qui, da intendersi come sublime saper fare e produrre, estetica che diviene pragmatica. L’arte è, però, anche uno straordinario strumento di massima espressività estetica al servizio dell’artista che ne fa uso per rappresentare il mondo, la vita e se stessi. La logica come arte è, allora, da intender- si come sublime ragionare, pensiero forte che diviene pratica. La logica come arte è, inoltre, un potente strumento di massima espressività razionale al servizio dello scienziato o dello studioso che ne fa uso per spiegare come funzionano il mondo, la vita e se stessi. In questo manuale, useremo pertanto la logica come strumento di massima espressività razionale al servizio dello psicologo, che è lo scienziato e studioso della psiche. La logica come scienza, invece, è concentrata su se stessa, sulle proprie conoscenze esclusive, tutte legate al tema della dimostrazione, e sui propri progressi, così incurante di ogni altra scienza, se non collateralmente. La logica come arte deriva dalla logica come scienza ma se ne distacca nelle finalità ultime, privilegiando e potenziando le sue qualità applicative e strumentali. (shrink)

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic formulas provided it (...) can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)

Con el fin de cuestionar la primacía del contrato sobre la lógica del don en la modernidad, se contrastan tres arquetipos de relación social a la luz de los radicales polianos, así como los tipos de reciprocidad que se derivan de cada uno de ellos. A la reciprocidad cerrada-dual moderna se opone la reciprocidad abierta-triádica, que es la que caracteriza a las relaciones de don, tanto en su versión clásica como cristiana. Se concluye que sólo el radical cristiano de la (...) persona integra la lógica del don con el sentido radical de la libertad, desde una antropología que complementa la práctica de virtudes como camino de perfección moral con la apertura a la trascendencia y la ayuda al más necesitado. (shrink)

The paper wishes to investigate the way Giles of Rome thought about logic: as a discipline, as a method, through an examination of the powers of logic, but also as a teaching subject. It tries to illuminate his views on logical education, and how he may have acted in favour of the latter as an Augustinian leader. It first offers a general presentation of the logical productions, from the 1270s to 1291. It then addresses the topic of logical education from (...) two viewpoints: by a look taken at Giles’ views on logic in the De regimine principum, and by a quick survey of the history of the teaching of logic in the studia of the Augustinian order from the mid-1280s on. The last section is dedicated to the philosophy and anthropology of logic. It tries to enlighten the originality of Giles’ s position, as a new departure taken from traditional theories regarding the absolute necessity of logic as a science, as an art, and as the underlying logic of all sciences, itself included. Rather than essentially necessary for any kind of philosophical endeavour, logic is presented a need for men, due to the fallible nature of his potential intellect. Rather than a science, it is described as a method for science which doesn’t use its more powerful instrument, i.e. the theory of scientific syllogism, since it proceeds in a non-demonstrative manner in the theory of demonstration. Logic and metaphysics are compared as respectively under and above special sciences. The last paragraph deals with the problem of the powers of logic in the context of metaphysical knowledge. (shrink)

The paper wishes to investigate the way Giles of Rome thought about logic: as a discipline, as a method, through an examination of the powers of logic, but also as a teaching subject. It tries to illuminate his views on logical education, and how he may have acted in favour of the latter as an Augustinian leader. It first offers a general presentation of the logical productions, from the 1270s to 1291. It then addresses the topic of logical education from (...) two viewpoints: by a look taken at Giles’ views on logic in the De regimine principum, and by a quick survey of the history of the teaching of logic in the studia of the Augustinian order from the mid-1280s on. The last section is dedicated to the philosophy and anthropology of logic. It tries to enlighten the originality of Giles’ s position, as a new departure taken from traditional theories regarding the absolute necessity of logic as a science, as an art, and as the underlying logic of all sciences, itself included. Rather than essentially necessary for any kind of philosophical endeavour, logic is presented a need for men, due to the fallible nature of his potential intellect. Rather than a science, it is described as a method for science which doesn’t use its more powerful instrument, i.e. the theory of scientific syllogism, since it proceeds in a non-demonstrative manner in the theory of demonstration. Logic and metaphysics are compared as respectively under and above special sciences. The last paragraph deals with the problem of the powers of logic in the context of metaphysical knowledge. (shrink)

Christian Ethics and Contemporary Philosophy. Edited by Ian T. Ramsey.Evil and the God of Love. By John Hick.Blondel et Teilhard de Chardin, Correspondance Commentée. By Henri de Lubac.The Structure of Behaviour. By Maurice Merleau-Ponty.New Testament Essays. By Raymond E. Brown, S.S.Ideologies. By Patrick Corbett.Worship in Israel. By Hans-Joachim Kraus. Translated by Geoffrey Boswell.The Theology of St John. By Joseph Crehan, S.J.Jesus and the Kingdom. By George Eldon Ladd.Finding the Historical. By James Peter.The Shape of Christology By John Mcntyre.Christology. By Dietrich (...) Bonhoeffer. Translated by John Bowden, with an introduction by Edwin H. Robertson.Theology of the English Reformers. By Philip Edgcumbe Hughes.The Execution of Justice in England: A True, Sincere, and Modest Defense of English Catholics. By William Cecil and William Allen. Edited by Robert M. Kingdon.The Revolution of the Saints. By Michael Walzer.L'Église au temps du Grand Schisme et de la crise conciliaire. By E. Delaruelle, E.-R. Labande and P. Ourliac.John Hus at the Council of Constance. Translated and introduced by M. Spinka.Mission to France 1944–1953, Angelo Giuseppe Roncalli, Pope John XXIII. Edited by Don Loris Capovilla. Translated by Dorothy White.The Vatican Council and Christian Unity. A commentary on the Decree on Ecumenism of the Second Vatican Council. By Bernard Leeming, S.J.The Documents of Vatican II. Edited by Walter M. Abbott, S.J. Translations edited by Mgr Joseph Gallagher. (shrink)