In the latter part of the fifteenth century, a Jewish translator, working together with a Slavic amanuensis, translated into the East Slavic language of the Grand Duchy of Lithuania three medieval Hebrew translations of Arabic philosophical texts: the Logical Terminology, a short work on logic attributed to Maimonides (but probably by a different medieval Jewish author); and two sections of the Muslim theologian Al-Ghazali's famous Intentions of the Philosophers. Highlighting the unexpected role played by Jewish translators as agents of cultural (...) transmission in the heady messianic atmosphere leading up to the year 1492, these texts drew the attention of the Orthodox Church authorities as being in the possession of the enlightened heretical sect known as the Judaizers, which had emerged in Novgorod and spread to Moscow. Reflecting three and even four layers of translation, Prof. Moshe Taube's new triple-language critical edition of the Logika of the Judaizers displays the Slavic texts alongside the Hebrew translations on which they are based and accompanies them with a modern English translation. In his comprehensive introduction and commentary, Taube surveys earlier scholarly efforts to identify the provenance and purport of the translations, discusses the linguistic and textological issues raised by these early Ruthenian texts, puts forward the likely dissimilar motivations of the Jewish translator and the Christians who commissioned the work, and reveals the translator's probable identity. The present publication, a long-awaited desideratum, will be of interest not only to historians of the Great Duchy of Lithuania and of the principality of Muscovy, but also to scholars of Jewish history and of the history of philosophy and science, as well as to linguists studying the history of the Belorussian, Ukrainian and Russian languages. (shrink)

The problem of logical omniscience breaks down to the problems of the closure of knowledge under implication and of the distribution of knowledge over implication. In late medieval scholasticism these two related issues were engaged in various genres, in particular in general analysis of validity, games of obligationes, solution to self-referential antinomies and semantics of terms. The present study analyses the corpus of fourteenth-century texts with some overreaches to the subsequent two centuries, attempting to cover representatives of both the “British” (...) and the “Continental” tradition. With some degree of simplification, this results in a range of four basic positions: 1. knowledge is closed under “analytic entailment” (Buridan), 2. knowledge distributes over implication (Heytesbury), 3. knowledge distributes over implication provided that its consequent’s truth is being taken into consideration (Peter of Mantua), 4. knowledge does not distribute overimplication (Wyclif). (shrink)

deel 1. Klassieke systemen.--deel 2. Niet-klassieke systemen en toegepaste logika.

Artykuł podejmuje zagadnienie relacji między językoznawstwem a logiką. Punktem wyjścia są dyskusje między logikami a językoznawcami, które miały miejsce w ostatnich kilkunastu latach. W artykule poddano analizie wzmiankowane dyskusje i wskazano, że faktycznie wkradają się w nie nieporozumienia; spróbowano również dokładniej określić domenę logiki i ukazać, że różni się ona zasadniczo od domenyjęzykoznawstwa.

Does formal logic make sense?This text is a commentary on the book Logika i argumentacja. Praktyczny kurs krytycznego myślenia Logic and Argumentation. A Practical Course In Critical Thinking by Professor Andrzej Kisielewicz. Prof. Kisielewicz argues there, among other things, that formal symbolic logic is inadequate to explain practical rational reasoning. This commentary defends formal logic in this respect. In particular, Prof. Kisielewicz proposes in his book a definition of practical logical inference. According to him, a conclusion follows from a (...) given set of premises if there is no situation, where the premises hold, while the conclusion fails. In this commentary it is pointed out that this is a well-known notion of semantic inference in formal logic. It is also well-known that semantic and syntactic inference in logic are equivalent, i.e. equally strong. (shrink)

Leibniz zamierzał stworzyć lingua characteristica universalis – język, w którym dałaby się zapisać wszelka wiedza, oraz calculus ratiocinator – metodę umożliwiającą rachunkowe określenie prawdziwości dowolnego zdania tego języka. Taka idea leży u podstaw współczesnej logiki. Taka idea w odniesieniu do poprawności sprzętu i programów leży u podstaw metod logicznych weryfikacji systemów informatycznych.Dziś widzimy, że dalszy rozwój informatyki zależy istotnie od postępu badań logicznych, a logika – ta starożytna dyscyplina – znalazła nowe bogate pole dociekań, zyskała nowe perspektywy badań. Jej (...) zastosowania mogą mieć tak znaczący wymiar praktyczny, o jakim nie śniło się filozofom. (shrink)

Obszerna antologia Logika i język z analitycznej filozofii języka, do której J. Pelc wybrał i przełożył teksty, była przez wiele lat wykorzystywana w nauczaniu i badaniach w Polsce. W udany sposób przedstawia niektóre dyskusje toczone w ramach filozofii analitycznej. Jednakże obok tekstów kluczowych, które weszły do kanonu tej tradycji, zawiera także prace marginalne i mało znaczące. Zaskakujące jest pominięcie przez Pelca kilku bardzo ważnych filozofów i ich dorobku, a podane we wstępie do antologii uzasadnienie tych braków jest niekompletne i (...) mało przekonujące. (shrink)

U ovome radu zagovaram stajalište koje uključni pozitivisti dijele s Ronaldom Dworkinom. Prema tezi o uključenosti morala , logički je moguće da pravni sustav uključuje moralne kriterije pravnosti . Do ovoga trenutka rasprava je uvijek imala oblik napada na koherentnost TUM-a, pri čemu su branitelji TUM-a samo pokušavali osporiti napadajući argument. Ja u prilog TUM-u iznosim pozitivan argument, koji započinjem objašnjenjem logike dokazivanja mogućnosnih tvrdnji kao što je to TUM. Pritome na samom početku vrijedi istaknuti da se logika dokazivanja (...) mogućnosnih tvrdnji umnogome razlikuje od logike dokazivanja kontingentnih deskriptivnih tvrdnji ili nužnih tvrdnji. Zbog toga će ovdje biti potrebno dati neka pojašnjenja važnih obilježja semantike modalne logike. Nakon prikladne razrade strukturnog okvira, argument u prilog TUM-a bit će zasnovan na iznenađujuće jednostavnom mislenom eksperimentu. Zapravo, argument pronalazi svoje nadahnuće u Razovom argumentu u prilog mogućnosti postojanja pravnog sustava koji se ne temelji na prisilnoj mašineriji izvršavanja prava; prema njemu, društvo anđela i dalje bi imalo sustav prava, iako u tom sustavu ne bi postojala prisilna mašinerija. Moj argument sadržavat će dvije teorijski važne značajke koje sadrži i Razov snažno jednostavan, ali u konačnici neuspješan argument. (shrink)

Existuje obrovské množství definic logiky; avšak je tu jistá jednotící myšlenka, která se proplétá většinou z nich, a to je ta, že logika nám má pomoci klasifikovat úsudky, způsoby argumentace či důkazy na „správné“ a „nesprávné“, a tímto způsobem nám má pomoci lépe „usuzovat“. A protože úsudek či argumentační schéma je věcí kroku od nějakých premis k nějakému závěru a jeho správnost můžeme vyjadřovat také tak, je jeho závěr odvoditelný z jeho premis či z nich vyplývá . Toto úzké (...) pojetí logiky nás vede přímo k jejímu modernímu chápání jakožto zkoumání vyplývání či odvoditelnosti. Nazvěme takové kritické zkoumání argumentací, úsudků či odvození základní agendou logiky. (shrink)

Fourteenth-century logic gave rise, among others, to the genre De scire et dubitare, which offered a unified framework for discussing different forms of epistemic sophisms by utilising the underlying systems of epistemic logic. One of the problems introduced in this context already by the founding father of this genre, William Heytesbury, was the so-called axiom of positive introspection, i.e., the principle that an agent who knows that something is the case, knows that she knows that it is the case. Owing (...) to Heytesbury’s enormous popularity in the subsequent centuries, discussion of this problem became relatively widespread. This debate was addressed already in Boh’s seminal Epistemic Logic in the Later Middle Ages, which, despite its limitations acknowledged by its author, is a standard source. The present study elaborates on Boh by extending the corpus of his works and drawing new connections based on that. The core of the survey consists of an analysis of the positions of William Heytesbury and John Wyclif, their Italian reception by Peter of Mantua, and the “continental” reception of Heytesbury by John of Holland. The main goals of this study are to formalise the key arguments, which makes it possible to address the underlying systems of epistemic logic and their respective “strength”, and to articulate the conceptual background of those arguments and systems. The gist of the debate is, on one of the sides, an attempt to prove that it is impossible to doubt whether one knows that something is the case by employing whether the principles of positive introspection and of distribution of knowledge over implication, or the principles of positive and negative introspection combined. (shrink)

V članku skušam opredeliti vlogo pojma protislovnosti v zgodovini metafizike. Podrobnejši vpogled v Aristotelovo mišljenje o tem pojmu pokaže, v kolikšni meri je načelo neprotislovnosti zakoreninjeno v metafiziki. V nadaljevanju se osredotočam na Kantovo razvijanje transcendentalne logike in Heglovo izenačenje logike z metafiziko. V zaključku razmišljam o možnosti drugačne logike – logike preobilja – onkraj heglovske afirmacije protislovnosti, ki razkriva mejo principa protislovnosti znotraj določenih struktur ali elementov.This paper traces the role that the concept of contradiction plays in the history (...) of metaphysics. By investigating the way that this concept was taken up by Aristotle, it shows how thoroughly the principle of non-contradiction belongs to metaphysics. The paper then traces Kant's development of a transcendental logic and Hegel's identification of logic and metaphysics. The paper explores, finally, the possibility that even beyond Hegelian affirmation of contradiction another logic--an exorbitant logic--can be conceived that exposes the limits of the principle of non-contradiction and accordingly affirms contradiction whithin certain domains of structures or elements. (shrink)

Autor przedstawia i poddaje analizie, stworzoną przez Ch. Perelmana koncepcję logiki prawniczej. Rozpatrując ten problem autor odwołuje się do teoretycznego modelu stosowania prawa. Analizy Perelmana doprowadziły go, jak wiadomo, do wniosku, iż logika prawnicza odwołuje się nie tyle do technik formalnologicznych ile raczej do technik znanych z teorii argumentacji. Koncepcję tę uznać należy za antyformalistyczną, wiążącą się z przekonaniem, że błędne jest traktowanie logiki prawniczej jako zastosowania logiki ogólnej w domenie prawa. Stanowisko Perelmana poddane zostaje krytyce. Nie negując bowiem (...) znaczenia argumentacji, odrzucić należy pogląd kwestionujący użyteczność szeroko rozumianej logiki w sferze prawa. (shrink)

Further development of the research on the fourteenth-century logic of iterated modalities leads to further exploration in fifteenth- and sixteenth-century Italian scholasticism, in particular, the contributions of Paul of Venice and his followers. The research confirms the well-established notion of “British logic in Italy”, as the major logical strategies used in the analysed works can be traced back to earlier British authors. Logically speaking, the problem of iterated epistemic modalities was framed as debate on the consistency of the hypothesis that (...) an agent doubts whether she knows φ and the hypothesis that an agent knows φ and doubts whether she knows φ, in which the principles of positive and negative introspection play a major part. Philosophically speaking, the debate on the possibility of doubting one’s own knowledge utilised theories of evidence and scientific proof and philosophy of the mind. (shrink)

Logic in the second scholastic era canbe characterised as a decline of interest in purelogic combined with a flourishing of attentiondevoted to applied logic. In epistemic logic, thistendency translates to the disappearance of theoriginal medieval genres and the migration ofcertain topic to different disciplines, such as psychology, epistemology, and theology. The presentstudy addresses three topics of epistemic logic inthe post-medieval era. First, the problem of theveridicality of knowledge, insofar as it took theform of analysing the logical structure of statementssuch as (...) “Peter knows that φ, therefore φ”.This analysis resulted into introducing the logic ofa weak implication called “moral implication” (relatedto the scholastic probability debate). Second, the problem of logical omniscience, which turnedinto an important psychological topic related toissues such as cognitive capacity and the (acquired)automatization of inferential behaviour. Third, the problem of (positive) introspection, which becamepart of the theory of evidence and its self-manifesting character. (shrink)

Traditional theism (in Christianity, Judaism and Islam) understands God as possessing certain attributes including omnipotence. God is omnipotent in the sense that God possesses unlimited (maximal) power. For some classical philosophers and theologians (PetrusDamiani, René Descartes) God’s omnipotence requires his being able to do absolutely anything, including the logically impossible. But in Thomas Aquinas’ opinion, to do what is logically impossible is not an act of power but is self-contradictory action. For Aquinas, a logically impossible action is not an action. (...) The contemporary British philosopher of religion, Richard Swinburne, considers omnipotence from an analytic perspective and, partially,within Aquinas’ tradition. For Swinburne, omnipotence includes the power to perform only logically possible and consistent tasks. In this paper, I discuss systematically (§§ 3-6) the philosophical and logical problems of omnipotence and the relation between God and logic from the perspective of Jan Łukasiewicz’s logical investigations. Keywords: Omnipotence, God, logic, rationality, Richard Swinburne, Jan Łukasiewicz. (shrink)

Audiozáznam přednášky proslovené 17. 10. 2011 na FF MU.

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.