We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix $${\mathbb {A}}$$ with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i,j =?. The method allows us to decide whether to declare a i,j = 0 or a i,j = 1 or a i,j =? (...) undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences. (shrink)

Haḳdamah. Masekhet Taʻanit -- shel avotenu ṿe-shalanu -- Shaʻar 1. Ketsad medabrim ʻal birkat ha-ḥayim -- Shaʻar 2. Adam ṿe-adamah, ʻananim ṿe-heʻanut -- Shaʻar 3. ha-Homer ḥai u-medaber -- ha-ḥoḳ, ha-pele ṿeha-ʻanṿah -- Shaʻar 4. "Ka-mayim ha-panim la-panim ken lev ha-adam la-adam" -- normot ḥevratiyon u-reṿaḥat ha-adam -- Shaʻar 5. "Tefilah la-ʻani ki yaʻaṭof" -- ha-kisufim le-magaʻ -- Shaʻar 6. Nispaḥ ḥaṿayah ṿe-tiḳṿah.

During the 2016 election, Donald Trump won conservative support by promising that he would, if elected, nominate “pro‐life” justices to the U.S. Supreme Court. Whether President Trump makes good on his campaign promise to restrict abortion rights may come down to competing impulses of the chief justice, John Roberts. These dueling dispositions—from the man whom many see as the new “swing justice”—hold the key to a blockbuster new case that legal historians call “the most unpredictable the Supreme Court has been (...) on abortion in decades.” The case, June Medical Services v. Russo, turns on arduous new requirements that Louisiana has imposed on facilities and clinicians that provide abortion. But the case is not just about abortion access. The Court will have to decide whether a clinic has a right to challenge the law in the first place. (shrink)

ḥeleḳ 1. Liḳuṭ ʻinyanim niflaʼim ʻal godel ḳedushat ha-Shabat -- ḥeleḳ 2. Liḳuṭ ʻinyanim niflaʼim ʻal tefilot u-seʻudot Shabat.

This article deals with a set-theoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP).

Ḥeshbonot -- ʻEtsot maʻásiyot -- Harḥaḳot.

kerekh 1-2. Maʼamarim rishon ṿe-sheni -- kerekh 3-4. Maʼamarim shelishi u-reviʻi -- kerekh 5. Maʼamar ḥamishi u-firḳe mavo.

This Article examines the influence of the Americans with Disabilities Act (ADA) on affective attitudes toward children with disabilities and on the incidence of disability-selective abortion. Applying regression analysis to U.S. natality data, we find that the birthrate of children with Down syndrome declined significantly in the years following the ADA's passage. Controlling for technological, demographic, and cultural variables suggests that the ADA may have encouraged prospective parents to prevent the existence of the very class of people the Act was (...) designed to protect. We explain this paradox by showing how specific ADA provisions could have given rise to demeaning media depictions and social conditions that reinforced negative understandings and expectations among prospective parents about what it means to have a child with a disability. We discuss implications for reproduction law and antidiscrimination policy. (shrink)

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' (...) uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation"--Publisher. (shrink)

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive (...) Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. (shrink)

If we arrange in chronological order the various statements Darwin made about God, creation, design, plan, law, and so forth, that I have discussed, there emerges a picture of a consistent development in Darwin's religious views from the orthodoxy of his youth to the agnosticism of his later years. Numerous sources attest that at the beginning of the Beagle voyage Darwin was more or less orthodox in religion and science alike.78 After he became a transmutationist early in 1837, he concluded (...) that the doctrine of secondary causes must be extented even to the history of life and that after the first forms of life were created, there was no further need for divine intervention, except where man was concerned. Man's body, he thought, was produced by the process of transmutation, but he believed for a time that man's soul was “superadded.” By mid-1838 he had become convinced that nothing, after the creation of life, was due to miracles. God works only through laws, which are capable of producing “every effect of evey kind which surrounds us.” The existence of man, the idea of God in man's mind, and the harmony of the whole system were in his eyes prearranged goals of deterministic laws imposed by God. Such a conception excludes the miracles on which Christianity depends; but it is not possible to say whether Darwin's loss of Christian faith, which occurred at about this same time, preceded and made possible his “materialism” or was rather caused or hastened by it.79 In the weeks after his reading of Malthus, Darwin's belief in a plan of creation gave way to the belief that God created matter and life and designed their laws, leaving the details, however, to the workings of chance. This remained his view until the 1860s.There is no exact parallel between this development of Darwin's religious views and the development of his ideas on evolution, but there is a general correspondence. When he believed in a plan of creation, Darwin's theory of transmutation did not depend on struggle or the selection of chance variations. Adaptation was, for him, an automatic response to environmental chance. From late 1838 to 1859 he believed in designed laws and chance, and this belief, too, has its parallel in his theory. The element of chance in natural selection meant that there could be no detailed plan,in which even man's idea of God would be a necessary outcome of nature's laws (man himself is not a necessary outcome of the working of natural selection).80 But Darwin still believed nature was programmed to achieve certain general ends. We might say that he believed in a general, though not a special, teleology. Natural selection was for him a law to maximize utility, creating useful organs, retaining vestiges for future use. For many years it was a law designed to produce organisms perfectly adapted to their environments. Only later did Darwin come to doubt even this sort of design in nature.81 One way of describing the development of Darwin's evolutionary thought is to say that it shows a gradual abandoning of his “theistic” assumptions, so that by the late 1860s his theory was informed to a slighter extent by notions of purpose and design than it was in 1838 or 1844 or 1859. (shrink)

Time stands at the heart of human experience. In this book, new investigations illuminate the gamut of human engagement with time in antiquity.

Logics are like shadows on a wall; to understand why they dance as they do, and how they can be made to move differently, one needs to look at the mathematical structures from which they can be projected. That is a methodology that has long proven its value for classical and other forms of deductive inference; this book manifests its pertinence to logics of uncertain qualitative reasoning. It draws together and refines work from the literature on preferential and other quite (...) different semantics for such reasoning and then, in its central chapter, integrates the leading ideas from them into a single multi-dimensional semantics. It enters new territory with investigations of interpolation and qualitative independence in non-monotonic contexts as well as connections between non-monotonic logic and neuroscience, specifically with Edelman's theory of organization of the brain. Finally, it proposes novel applications such as equational modellings for contrary-to-duty normative reasoning and mathematical analyses of some kinds of casuistic reasoning in the Talmudic tradition. Profusely signposted at every turn, the volume is accessible to readers equipped with a modicum of set theory and abstract algebra. Visitors to the area can come in by the front gate and work their way, in various orders, through as much of the garden as strikes their fancy; specialists will enter at Chap. 11 or at whatever special topic interests them, well assured that they can easily backtrack to whatever bits and pieces are needed from what they skipped. A volume with a clear vision, a book to return to many times." (David Makinson). (shrink)

Judaism is often described as a religion that tolerates, even celebrates arguments with God. In Pious Irreverence, Dov Weiss has written the first scholarly study of the premodern roots of this distinctively Jewish theology of protest, examining its origins and development in the rabbinic age (70 CE-800 CE).

-- volume 2. The philosophy of Rabbi Joseph B. Soloveitchik.

How did medieval Jewish scholars, from Saadia Gaon to Yitzhak Abravanel, imagine a world that has experienced salvation? What is the nature of reality in the days of the Messiah? This work explores reactions to the seductive promises of apocalyptic teachings, tracing their fluctuations between intellect and imagination. The volume extensively surveys the tension between naturalistic and apocalyptic approaches to the history of the messianic idea so fundamental to the history of Jewish philosophy in the Middle Ages and reveals the (...) scope and challenges of medieval thought. (shrink)

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive (...) Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. (shrink)

מאבק הפרדיגמות מציג פרשנות עקיבה להגות היהודית בימי הביניים על פי תפיסת המדע. הוא משתמש במושג "פרדיגמה" כדי לעקוב אחר ההתפתחות הרעיונית של ההגות היהודית בת הזמן. החיבור פורש לפני הקורא שלוש פרדיגמות: הכלאם, האריסטוטליות (עם או בלי לבושה הנאו-אפלטוני) והניסיוניות (הכוללת תופעות שלא היה להן הסבר בפרדיגמה הקודמת, כמו אסטרולוגיה, מאגיה ואלכימיה). הטענה המרכזית בספר היא שעד לשלהי המאה השתים-עשרה התעמתו שתי הפרדיגמות הראשונות, כלאם ואריסטוטליות, ולאחריה - שתי האחרונות, האריסטוטליות והניסיוניות. החיבור מאיר באור חדש את הגותם של רב (...) סעדיה גאון, ר' יהודה הלוי, רמב"ם ואחרים. (shrink)