The article aims to show how the acceptance of non-monotonic logic enables arguments to be held between science and religion in a way that does not exclude either of these two spheres. The starting point of the analyses is the idea of the 13th century Danish philosopher, Boethius of Dacia, who states that it is both acceptable that: a natural scientist negates that the world had a beginning, and a Christian theologian asserts that the world had a beginning, because each (...) of them is basing their statements on the principles of their respective discipline: the first on the principles of nature, and the latter on knowledge supplemented by divine revelation. What is more, analogically: a metaphysician, when limited to his principles, cannot settle the issue, as he takes into account supranatural beings and their powers, but cannot know what God or another powerful supranatural would have decided in a such a case. The paper shows that Boethius’s approach: violates the rule of monotonicity, cannot be finally interpreted in terms of classical logic and assumes certain non-monotonic logic as its inference framework. Other presented examples of arguments between religious beliefs and the statements of natural science are resolved in the same way. Thus, it is shown how non-monotonic thinking allows us to seriously treat both scientific and religious inference as compatible. (shrink)

The 2nd World Congress on Logic and Religion, held in Warsaw, Poland, in 2017, is summarized. Then the connective “and” is analyzed; we focus on its meaning in the title of the congress and the title of the present volume. Finally, all the eleven papers included here are briefly introduced; we indicate whether logic or theology is the primary topic of the given paper.

U radu se nastoji prikazati kako se vjera i teologija mogu iskoristiti za testiranje uspješnosti velikih jezičnih modela (LLM–ova) i automatiziranih programa za čavrljanje (chatbotova) pogonjenima na takvim modelima, mjerenjem njihovih filozofskih vještina. Predstavljaju se rezultati testiranja četiriju odabranih chatbotova: ChatGPT, Bing, Bard i Llama2. Za potrebe testiranja uzeta su tri moguća izvora iz područja vjere i teologije: 1) teorija četiri smisla Svetog pisma, 2) apstraktne teološke izjave, 3) apstraktna logička formula izvedena iz vjerskog teksta kako bi se pokazalo da (...) su ovi izvori korisni u zadacima koji učinkovito mjere filozofske vještine kao što su npr. interpretacija danog isječka, kreativna dedukcija te prepoznavanje ontoloških ograničenja. Ovakav pristup omogućuje ispitivanje osjetljivosti kojom se otkrivaju razlike u uspješnosti četiriju chatbotova. Također je dan primjer kako odrediti referentne vrijednosti za ocjenu i usporedbu vještina, koristeći kriterije za procjenu te pojednostavljene skale za ocjenjivanje svakog korištenog chatbota u pogledu ispunjenja pojedinog kriterija. (shrink)

Some interesting cases of non-monotonic reasoning have already been identified in medieval theological texts. Jacob Archambault proved in 2015 that the argumentation presented by St Anselm of Canterbury in his Proslogion has non-monotonic “embeddings”. My own contribution from 2011 indicated that we can argue that a non-monotonic logic underlies some discussions provided by St Thomas Aquinas in his Summa theologiae, and showed that Boethius of Dacia used non-monotonic reasoning in his De aeternitate mundi. In this article, I would like to (...) briefly present these examples and verify whether we can speak about similar cases in medieval Biblical exegesis. My aim is to outline particular problems connected with the identification of non- monotonicity which are specific to theology, as well as assumptions that should be adopted to successfully discuss this issue. (shrink)

Does Thomas Aquinas use non-monotonical reasonings? In my recent paper Thomas Aquinas Non-monotonically I argued that he does. However Patryk Pogoda has opposed to my statement. In this paper I try to disarm his arguments. What is more this polemic became for me an occasion to develop some crucial problems concerning non-monotonicity. Before all while answering to some arguments of my opponent I had an opportunity to show that non-monotonical reasoning is a proper way of inferention in theology. The main (...) causes of this fact are: the plurality of meanings in theology, the process of deeper and deeper penetrating the revelation and the fact that information studied in theology is given not by a human, but by God. These three causes create a specific situation for the theologian who cannot translate a revealed information which looks as it was metaphorical to some simple unequivocal sentences. In the starting point he does not know the status of this information and should first trust to God’s word to became aquainted with it, so he has to accept it as it is and on this basis infere what he can. But if he (or another theologian) get some other premises he may dismiss the former correct inference – and this is exactly what we call non-monotonical reasoning. (shrink)

A non-monotonic logic is a formal calculus where the consequence relation is not monotonic. Intuitively, nonmonotonicity of the consequence relation indicates that obtaining a new piece of information can reduce the set of the accepted sentences. In particular, it allows us to draw conclusions on the basis of „the lack of evidence to the contrary”. The purpose of the paper is to present the basic notions of non-monotonic logic, which will be needed in two papers in this volume.

In this paper, the theory of necessity proposed by Robert Grosseteste is presented. After showing the wide range of various kinds of determination discussed by him (connected with: (1) one’s knowledge about the future, (2) predestination, (3) fate, (4) grace, (5) sin and temptation), a different context of Grosseteste’s use of the notion of necessity is analyzed (within logical and metaphysical approaches). At the heart of his theory lie: the definition of necessity, which is that something lacks the capacity (posse) (...) for its opposite, and the distinction between two perspectives within which we can consider necessity: (1) the one according to which the truthfulness of a dictum determines that it cannot be the opposite, (2) a pre- or atemporal one, as if something had not yet begun. On these grounds, Robert explains that God’s omniscience is compatible with contingency, including human free decisions. Robert’s theory is still relevant and useful in contemporary debates, as it can provide strong arguments and enrich discussions, thanks to the twoperspectives approach, which generates nine kinds of positions on the spectrum of determinism and indeterminism. (shrink)

Non-monotonic logics has been popular for recent 15 years. However, it occurs that they are useful to describe some reasonings presented by… Thomas Aquinas. In this paper I show four examples of reasonings where Thomas abandons the principle of monotonicity, all taken from two questions of Summa theologiae concerning God. In each of them Aquinas adds some new premises to the previous set of premises and then draws a conclusion contrary to the previous one, what is impossible under the classical (...) inference. In the next step I present some conclusions, primarily: that for sure we cannot state that these reasonings are just entimematic; that Thomas appears as a superintelligent observer having a holistic view and hence may seem to use in his reasonings rather reduction than deduction; and that we should not call his logic „default”, but rather talk about „the logic of theoria ” or „contemplative/speculative logic”. Finally, I try to find the goal (or the meaning) of using by Thomas one of non-monotonic logics, taking into account that his inferential and interpretive rules serve to organise and clarify some theses (which are very instructive from the perspective of hermeneutics). Perhaps we may find this goal in… education. Well, after all, the Summa is a textbook. As we can see — not only of theology. (shrink)