The article presents Erik Stenius' conception of logical constants and compares it with the standard approach.

The present volume collects presented at a symposium on The History of Logic held in Helsinki in June 11–13, 2000 hosted by the University of Helsinki, Finland. They bear on issues in the history of logic and foundations of mathematics and are contributions by some of the most renown scholars in the field.

The paper argues that unlike Ramsey, Frege and Russell lacked the idea of an arbitrary function and this had important consequences for their foundational programs.

În prezent, în România, ca și în toate celelalte state euro-atlantice și în cadrul organizațiilor internaționale din care facem parte (NATO de exemplu), există o cerere puternică de analiști de informații „bine pregătiți”. Pentru a funcționa într-un mod eficient, structurile de informații au nevoie de analiști de informații eficienți, sau cu alte cuvinte, de analiști de informații bine pregătiți. Acesta este cazul comunității noastre naționale de informații, precum și al componentelor și structurilor sale. Necesitatea și importanța proiectului este în consecință (...) înrădăcinată în nevoia de analiști bine pregătiți și în misiunea lor centrală în domeniul informațiilor, și anume crearea de produse (informații de securitate) care să poată prezenta o înțelegere corectă și exactă a diferitelor procese, evenimente. și fenomene pentru factorii de decizie. Selecția celor vizați pentru a fi pregătiți necesită alcătuirea inițială a profilului unui analist de informații, selecția însăși necesitând orientarea către un profil psihologic compatibil cu misiunea pe care acesta va trebui să o îndeplinească și care posedă un nivel minim de analitică. abilitățile necesare, celelalte aspecte referitoare la instruirea analistului vor fi implementate într-un program numit pentru educația și formarea analiștilor de informații. (shrink)

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...) be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)

The structural theory of metaphor (STM) uses techniques from possible worlds semantics to generate and interpret metaphors. STM is presented in detail in The Logic of Metaphor: Analogous Parts of Possible Worlds (Steinhart, 2001). STM is based on Kittay’s semantic field theory of metaphor (1987) and ultimately on Black’s interactionist theory (1962, 1979). STM uses an intensional calculus to specify truth-conditions for many grammatical forms of metaphor. The truth-conditional analysis in STM is inspired in part by Miller (1979) and Hintikka (...) & Sandu (1994). STM is by no means a toy theory. It has been successfully tested on dozens of large texts taken from real authors. Its methods can be applied in very large linguistic databases like WordNet or MindNet. (shrink)

Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by (...) means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement and exploit it to define entanglement measures in the general probabilistic framework. In addition, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted). (shrink)

The confessional work of the Church has been from the very beginning a foundation and basis for the Divine Truth. Starting from this real necessity, the Apologetic Theology claims some important research directions, grounded on the Holy Scripture and the Holy Tradition. Given this historical and doctrinal context, we can highlight the next support coordinates of the Christian Apologetics background: “the truth of God’s existence, the reality of the supernatural world and man’s immortality. All of this are, as we can (...) say, the Christian specific starting from the first ages. The truths about the divine origin of Christianism are to be found here, on the dignity of this revealed doctrine, on the divine-human character of his Founder, on the importance and necessity of Christian Church for the religious and morale life of human kind”. . Apologetics and (or) Fundamental Theology The reason why the Church must justify her teaching in the context of her missionary activity does not rise up from inner necessity. It does more from external misconceptions. In this context we can define the main concern of apologetics as a theological discipline. On the other hand, one can discover almost the same meaning in Fundamental Theology. However, as a difference between them, Fundamental Theology is interested in the direction and bears informative message, since “it aims at basic religious principles systematic presentation, both external and internal, as well as their justification before the scientific-theological conscience of believers. Thereafter, Christianity can be considered the only true religion”. On the other hand, one can claim that the name of “Apologetics” rises up from the necessity that the Christian arguments must be scientifically enforced and illustrated externally. Therefore, the mission of Christian Apologetics is to reject the anti-Christian objections through the power of the theological arguments in dialogue with philosophy, culture or science. In fact, even the object of Apologetics is "the scientific ground of Christian truths" with the purpose to "offer the Truth, reject error, and eradicate lies." In order to achieve its goal, Christian Apologetics offers us a positive method, which consists in "a logical and direct development of a certain thesis, in clarifying a certain truth, by revealing its content and the outcomes deriving from it". Therefore, we have a very dynamic field through which this discipline comes and supports the active life of the Church. Moreover, the method of the Apologetics as a theological subject is based on a conceptual struggle, very active starting with the very first centuries of the Early Church. Due to its energetic character, Fundamental Theology won its most important place among Christian doctrines. “Through struggle, Fundamental Theology imposed itself as a theological subject and became individualised. Through struggle and only through struggle, Fundamental Theology must exist and strengthen the positions of Christianity”. In its theologically mission, Christian Apologetics identifies and also prevents the alteration of the doctrinal truth. In this concern, it has the responsibility to enforce of believers’ moral conscience in their spiritual process of development. As a subject, one can say that the mission of Apologetics is “rational, objective and represents a very important basis for the Christian truths of faith”. Therefore, one can notice that the most important aspect of our subject is to enforce the Christian faith and experience through proper knowledge of the fundamental principles of the doctrine. This is the reason why we also mention Apologetics together with Fundamental Theology. However, we must highlight a few important details regarding the sensible difference between both of the denominations. Therefore, historically speaking, “they both arise from those who personally share Christian faith and act within the believing community and in its service. They both aim to respond to objections raised by critics and to offer a trustworthy account of main beliefs about matters as the existence of a personal God, the divine self-revelation in Jesus Christ, and the nature of faith”. On the other hand, we can identify almost three important differences between Apologetics and Fundamental Theology. “First, a Christian apologist can simply address a question: does the existence of horrendous evil in our world rule out the existence of almighty and all-loving God? or has science caused faith in God to be demoted in the past? … Second, good Apologetics has typically a sharply defined audience: Apologetics can seek, for example, to alert non-believers to the weakness of the case currently being against God and religion. But Fundamental Theology addresses to a wider range of readers … Third, polemics (in the good sense of this word and not as mindless ranting) belong to the exercise of Apologetics … The tone of fundamental theologians, even when rebutting objections to Christian faith, is or should be more expository and less polemically inclined to illustrate defects in opposing positions”. Moreover, we must mention that Apologetics can be considered as a particular subject. Although, it is similar in terms of content with Dogmatic and Philosophy through its method, our subject has its own research direction. Therefore, if Dogmatic is defined by an expositive and imperative character, Apologetics is demonstrative and constraining. In other words, dogmatic rationality, which has a subsidiary role, in Apologetics becomes primordial. In this case, “the faith truths become truths also for the rationality and moreover, the eternal truths of the Divine Reason become constraining for the human reason, too. Truths of natural religion, which are in fact the object of the Philosophy of Religion, are conditioned in Apologetics by the Absolute Truth completed in the Christian faith”. In all its theological and external interaction perspectives, Apologetics holds the main role to “expose, defend and justify with rational meanings the general truths of religion”. It is necessary to clear up one aspect: as subject, Apologetics is different from Apology. On the one hand, one can speak about the general research background and, on the other hand, one can describe a singular part of theological approach. Therefore, these two “theological sisters” are different depending on the type of approach. However, Apology is older than Apologetics. Among the first Christian apologists, we mention: Saint Justin the Martyr and Philosopher, Tatian, Athenagoras or Tertullien. In its current meaning, Apologetics is of a western theological origin, having its beginning in Middle Ages. Even so, its blooming age is the 18th century, when the Western Catholic Church replied to the materialist and atheistic philosophy. In the Eastern Church this type of confession had a more profound theological overview, in a theonomic perspective. “In the light of the Holy Scripture, the eastern theological thinking always shows priority to the divine Revelation in spite of the philosophical human systems and places the Creator - Logos at the basis of all creation, in the light of biblical thoughts”. -/- II. “Rational-spiritual Apologetics” Reverend Professor Dumitru Popescu, one of the most important Romanian theologians, develops the concept of “Rational-spiritual Apologetics”. In his theological approach, he illustrates the fact that one of the most essential part of the Church’s confessional work are the relations between rational arguments and spiritual purpose of the Christian life. In this case, we can identify two possibilities of argumentation: rational and spiritual, each of them in connection with the knowledge of God. This is in fact, the Orthodox specificity of the Apologetics, as theological subject, in contrast with the principles of western scholastic. Therefore, the most important argument, which Dumitru Popescu brings up in the support of his thesis, belongs to Saint Maximus the Confessor’s theology: “The Scripture provide a double knowledge of the divine things. One is relative and consists in its rationality and meanings, without the direct feeling of God. Through it we are guided in this life. The other one is in a true sense true and consists in leaving experience of divine grace, outside rationality and meanings, having the complete experience of God. Through it we will receive in the future life the deification”. On the other hand, we can understand that the purpose of human rationality is not to replace the spiritual perspective, since human mind does not own the divine mystery. In this case, rationality can be useful in discovering and demonstrating the existence of God from natural realities to a point where we must assume a spiritual understanding. Consequently, in the context of human deification, the orthodox theology cannot conceive the gnoseological process in rational terms. Therefore, Rev. Dumitru Popescu carries out a dual argumentation: 1. since God is not a solitary power, but descends and interacts with man providentially (through His divine grace and energies); 2. because the created world doesn’t have an independent rationality through which man can receive the possibility to reach God. Therefore, Father Professor Dumitru Popescu concludes that “the deification process is here, on the earth, a foretaste of immortality, which springs from the personal meeting of man with God”. One of the most recent Romanian Apologetics academically approach is the book of professor Adrian Lemeni: “Truth and Demonstration”. Except his very complex analysis on the interaction between theology and science, Professor Lemeni goes further and perfects Dumitru Popescu’s theological view, on the “Rational-spiritual” character of Orthodox Apologetics. Therefore, he offers a very important example, starting from Saint Gregory Palamas’ theological view. In his work “the authority of Patristic gnoseology” is illustrated, which is offered by the “Eternal Truth, God’s Word, incarnated in the Person of Jesus Christ”. “The authority of patristic gnoseology” – notes down Adrian Lemeni – “is expressed along the process for searching the truth of knowledge illustrated by deeds and life. In his debate with Varlaam from Calabria, Saint Gregory Palamas insists on the power of persuasion which arises from the Church’s Tradition, biblical and patristic fundamentally. In an ultra-confident argument, based on the autonomic logical power, we believe that one word has power over another. But Saint Gregory Palamas shows that the truth is based and validated through spiritual and ecclesiastical experience. Truth is validated by the words and deeds of the Holy Fathers, in direct connection with apostolic Tradition. Any argument can be fought against by another argument. Nevertheless, the apologetic concession based on the deeds of the saints is unbookable. This is the thesis which Saint Gregory Palamas develops in complete harmony with the patristic gnoseological Tradition”. Therefore, we can consider that the position of the subject of Apologetics (of Fundamental Theology) is one of interactions. It has connections with all domains external to Theology. In this case, we can consider it sets up a dialogue or debate with philosophy, culture or science. Starting from the historical argument, this interaction between theology and other sciences has existed from the very first Christian century. Therefore, we have an apologetic literary genre starting with the first patristic writings. Including the Early Church, we can identify three important stages in terms of historical apologetics development: 1. The Christian apologists struggle age with Judaism and paganism; 2. From the issue of Islam to the Middle Eve; 3. From the period of the Renaissance of Western sciences to the present day. (shrink)

The Movement of the „Burning Bush” in Apologetically Context -/- Following the historical context of a very hard period in the Romanian Orthodox Church, the communist period, our research has some important directions regarding the apologetically specific of the Movement of the “Burning Bush”. Starting with the Christian journalism of Nichifor Crainic, who phonated the Periodic “Gândirea”, the passion for the dialogue between theology and culture had grown up. Therefore, we remember here the direct implication of Sandu Tudor, a (...) very important cultural presence in Bucharest. After two or three visits in the Holly Mont Athos, Sandu Tudor decided to enter in monasticism. From this point he created the Movement of the “Burning Bush” at “Saint Antim” Monastery from Bucharest. The program was based on discussions and prayer. In this concern we can remember here the presence of the Father Ioan Kulaghin. Anoter very important member of the Movement was Alexandru Mironescu. His entire work was confiscated and burned by the communists. His implication denotes that we can speak about the dialogue between theology and science. (shrink)

O sintagmă revine recurent, cel puţin în prima parte a cărţii, „conștiinţă feministă”. Legat de aceasta, constatările Lilianei Popescu, conferenţiară universitară și prorectoră la Școala Naţională de Studii Politice și Administrative (SNSPA), mi-au confirmat câteva intuiţii despre felul în care s-a produs transformarea politică a societăţii românești în ultimele trei decenii. „Coagularea conștiinţei feministe în ţara noastră după anul 1990 – susţine autoarea – s-a făcut mai ales prin adoptarea tradiţiei feminismului occidental. În același timp, trebuie remarcat faptul că, (...) înainte de anul 1990, în societatea socialistă existau elemente implicite și explicite de afirmare a egalităţii de gen: educaţia era deschisă atât tinerilor, cât și tinerelor; oportunităţile de muncă erau accesibile atât bărbaţilor, cât și femeilor; statul socialist oferea facilităţi tinerelor mame, concedii maternale, creșe, grădiniţe, iar la întoarcerea din concediul de creștere a copilului, serviciul era asigurat. Multe dintre societăţile occidentale au luptat din greu pentru obţinerea acestor drepturi. (…) Consider că în conștiinţa feministă de după 1990 s-a pus un accent supradimensionat pe principiile și pe practicile feministe venite dinspre Vest și s-a subestimat propria noastră moștenire din perioada socialistă, care era valoroasă și merita preţuită. Este suficient să ne gândim la scăderea dramatică a cifrei de reprezentare a femeilor în parlamentele formate începând cu 1990. Practic, reprezentarea femeilor a scăzut de aproape 10 ori – de la peste 30% la 4%” (p. 52-53). (shrink)