Laws of Form - an Exploration in Mathematics and Foundations
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Jurisprudence--Philosophy Or Science Henry Rottschaefer
University of Minnesota Law School Scholarship Repository Minnesota Law Review 1927 Jurisprudence--Philosophy or Science Henry Rottschaefer Follow this and additional works at: https://scholarship.law.umn.edu/mlr Part of the Law Commons Recommended Citation Rottschaefer, Henry, "Jurisprudence--Philosophy or Science" (1927). Minnesota Law Review. 1465. https://scholarship.law.umn.edu/mlr/1465 This Article is brought to you for free and open access by the University of Minnesota Law School. It has been accepted for inclusion in Minnesota Law Review collection by an authorized administrator of the Scholarship Repository. For more information, please contact [email protected]. MINNESOTA LAW REVIEW Journal of the State Bar Association VOLUI%1E 11 MARCH, 1927 No. 4 JURISPRUDENCE- PHILOSOPHY OR SCIENCE By HENRY ROTTSCHAEFER* T WOULD perhaps be practically impossible to secure for any definition of the term Jurisprudence any very general accep- tance. It is doubtful whether there exists even any general agree- ment as to what subjects are within its scope. The problem of whether, and in what sense, it is to be considered philosophy or science, cannot, however, be discussed without adopting at least some tentative notion of its meaning that shall serve as the basis for the discussion. This can be more effectively done by a general description of the types of problem usually dealt with in treatises and courses on Jurisprudence than by framing a logically correct definition that secured accuracy and completeness by resort to a convenient vagueness. Investigation discloses its use to denote lines of inquiry having little in common other than a professed interest in general questions and problems concerning law and justice. -
1 Elementary Set Theory
1 Elementary Set Theory Notation: fg enclose a set. f1; 2; 3g = f3; 2; 2; 1; 3g because a set is not defined by order or multiplicity. f0; 2; 4;:::g = fxjx is an even natural numberg because two ways of writing a set are equivalent. ; is the empty set. x 2 A denotes x is an element of A. N = f0; 1; 2;:::g are the natural numbers. Z = f:::; −2; −1; 0; 1; 2;:::g are the integers. m Q = f n jm; n 2 Z and n 6= 0g are the rational numbers. R are the real numbers. Axiom 1.1. Axiom of Extensionality Let A; B be sets. If (8x)x 2 A iff x 2 B then A = B. Definition 1.1 (Subset). Let A; B be sets. Then A is a subset of B, written A ⊆ B iff (8x) if x 2 A then x 2 B. Theorem 1.1. If A ⊆ B and B ⊆ A then A = B. Proof. Let x be arbitrary. Because A ⊆ B if x 2 A then x 2 B Because B ⊆ A if x 2 B then x 2 A Hence, x 2 A iff x 2 B, thus A = B. Definition 1.2 (Union). Let A; B be sets. The Union A [ B of A and B is defined by x 2 A [ B if x 2 A or x 2 B. Theorem 1.2. A [ (B [ C) = (A [ B) [ C Proof. Let x be arbitrary. x 2 A [ (B [ C) iff x 2 A or x 2 B [ C iff x 2 A or (x 2 B or x 2 C) iff x 2 A or x 2 B or x 2 C iff (x 2 A or x 2 B) or x 2 C iff x 2 A [ B or x 2 C iff x 2 (A [ B) [ C Definition 1.3 (Intersection). -
Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur Si Muove: Biomimetic Embedding of N-Tuple Helices in Spherical Polyhedra - /
Alternative view of segmented documents via Kairos 23 October 2017 | Draft Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur si muove: Biomimetic embedding of N-tuple helices in spherical polyhedra - / - Introduction Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension? Dynamic bonding patterns in n-tuple helices engendering n-fold rotating symbols Embedding the triple helix in a spherical octahedron Embedding the quadruple helix in a spherical cube Embedding the quintuple helix in a spherical dodecahedron and a Pentagramma Mirificum Embedding six-fold, eight-fold and ten-fold helices in appropriately encircled polyhedra Embedding twelve-fold, eleven-fold, nine-fold and seven-fold helices in appropriately encircled polyhedra Neglected recognition of logical patterns -- especially of opposition Dynamic relationship between polyhedra engendered by circles -- variously implying forms of unity Symbol rotation as dynamic essential to engaging with value-inversion References Introduction The contrast to the geocentric model of the solar system was framed by the Italian mathematician, physicist and philosopher Galileo Galilei (1564-1642). His much-cited phrase, " And yet it moves" (E pur si muove or Eppur si muove) was allegedly pronounced in 1633 when he was forced to recant his claims that the Earth moves around the immovable Sun rather than the converse -- known as the Galileo affair. Such a shift in perspective might usefully inspire the recognition that the stasis attributed so widely to logos and other much-valued cultural and heraldic symbols obscures the manner in which they imply a fundamental cognitive dynamic. Cultural symbols fundamental to the identity of a group might then be understood as variously moving and transforming in ways which currently elude comprehension. -
Laws of Form - the Language of the Consciousness and Its Applications - ID: 58298
This PDF is for review purposes ONLY. This PDF is for review purposes ONLY. Laws of Form - the language of the consciousness and its applications - ID: 58298 Type of Funding Request: Online Funding Inquiry Status of this Funding Request: Draft/Saved Instructions: This PDF document is a read-only version of your funding request as it currently stands. You may print or save this document for your records. However, you should not attempt to edit this document. Any edits made to this PDF will not be saved in the Templeton Portal. If there are further edits that you would like to make to your funding request, please return to the request inside the Templeton Portal, select the appropriate section(s) of the form, make your edits, and save your work. After saving your work in the portal, you will be able to generate a new PDF version of the funding request that includes your recent edits. Below you will find a list of all fields that must be completed before submitting this funding request to the Foundation. To complete these fields, please return to the request inside the Templeton Portal, select the appropriate section(s) of the form, add the required content, and save your work. When all fields are completed and you are satisfied with your description of the proposed project, you may go to the Templeton Portal to submit your request. Please note that all requests must be submitted through the Templeton Portal and the Foundation will not accept this PDF as a valid application for funding. After submitting your request, it will become read-only and you will not be able to make any additional edits. -
Laws in Metaphysics
LAWS IN METAPHYSICS BY TOBIAS WILSCH A dissertation submitted to the Graduate School—New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Philosophy Written under the direction of Jonathan Schaffer and approved by ___________________________________ ___________________________________ ___________________________________ ___________________________________ New Brunswick, New Jersey May, 2015 ABSTRACT OF THE DISSERTATION Laws in Metaphysics By TOBIAS WILSCH Dissertation director: Jonathan Schaffer The first two chapters of this dissertation defend the Deductive-Nomological Account of metaphysical explanation. Chapter 1 develops the Nomological Account of ground, – p1, …, pn ground q if and only if the laws of metaphysics determine q on the basis of p1, …, pn, – and the constructional theory of the metaphysical laws, – the laws are general principles that characterize construction-operations. Chapter 2 offers an analysis of the notion of determination involved in the Nomological Account: the laws determine q based on p1, …, pn if and only if q follows from p1, …, pn and the laws in the grounding-calculus. The grounding-calculus is characterized in terms of two inference rules and a suitable notion of ‘proof’. The rules are designed to analyze the input- and output notions that are intuitively associated with laws: the laws take some facts as input and deliver some other facts as output. ii Chapters 1 and 2 also go beyond the development of the positive view. Chapter 1 shows how the Nomological Account explains general patterns among grounding-truths, the modal force of ground, and certain connections between ground and construction. Chapter 2 shows why the Deductive-Nomological Account of metaphysical explanation escapes the objections to the traditional DN-account of scientific explanation, and it also outlines two views on logical explanation that are available to the proponent of the Nomological Account. -
LAW and ENCHANTMENT: the PLACE of Belieft
University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1987 Law and Enchantment: The lP ace of Belief Joseph Vining University of Michigan Law School, [email protected] Available at: https://repository.law.umich.edu/articles/1630 Follow this and additional works at: https://repository.law.umich.edu/articles Part of the Law and Philosophy Commons, and the Legal Profession Commons Recommended Citation Vining, Joseph. "Law and Enchantment: The lP ace of Belief." Mich. L. Rev. 86 (1987): 577-97. This Essay is brought to you for free and open access by the Faculty Scholarship at University of Michigan Law School Scholarship Repository. It has been accepted for inclusion in Articles by an authorized administrator of University of Michigan Law School Scholarship Repository. For more information, please contact [email protected]. ESSAYS LAW AND ENCHANTMENT: THE PLACE OF BELIEFt Joseph Vining* I. THE QUESTION The question I wish to raise is whether one must believe what one says when one makes a statement of law. The language of belief that we know, and from which moral discourse and the moral never stray far: do judges, lawyers, law participate in it? Any such question is but an aspect of a larger question, indeed issue, of what we may call the objectivity of legal language. It is raised perhaps most acutely by the broad claims now being made for artificial intelligence and in particular for the computer programming of legal advice (as a species of what is called, in that field of applied science, an "expert system"). -
Law and the Metaethics of Discord
Katja Maria Vogt, katjavogt.com, Columbia University 1 Law and the Metaethics of Discord, NYU Colloquium in Legal, Political, and Social Philosophy, Draft 08-2020 For: Special issue on the Normativity of Law, Ancient Philosophy Today: Dialogoi Law and the Metaethics of Discord Plato’s Euthyphro, I argue, lays out a metaethics that responds to persistent and unresolved value disagreement, and that is a genuine contender for us today. With this proposal, I reject centuries of scholarship, not to speak of countless anthologies and syllabi in ethics and the philosophy of law.1 The Euthyphro begins with three cases of unresolved value disagreement. These cases are to be adjudicated by the law, which turns out to be difficult. Today if an author starts with three examples, we expect that the subsequent text is going to address them. This, I submit, is the structure of the Euthyphro. Against my reading, discussions of the Euthyphro tend to focus almost exclusively on a brief section in which Plato discusses what is now known as the Euthyphro Problem. Socrates asks whether the gods love the pious because it is pious, or whether the pious is pious because it is loved by the gods. In the idiom of contemporary metaethics, the puzzle may seem to be this: is value attitude-independent or is value conferred by attitudes?2 Alternatively, in the idiom of traditional Divine Command Theory, do the gods —or, does God, since Divine Command Theory tends to be monotheistic—recognize value, or is value conferred by divine approval?3 1 Much of the literature on the Euthyphro focuses on two out of fifteen pages of the dialogue, where the so- called Euthyphro Problem is discussed. -
Theory of Forms 1 Theory of Forms
Theory of Forms 1 Theory of Forms Plato's theory of Forms or theory of Ideas[1] [2] [3] asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality.[4] When used in this sense, the word form is often capitalized.[5] Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt.[6] Plato spoke of Forms in formulating a possible solution to the problem of universals. Forms Terminology: the Forms and the forms The English word "form" may be used to translate two distinct concepts that concerned Plato—the outward "form" or appearance of something, and "Form" in a new, technical nature, that never ...assumes a form like that of any of the things which enter into her; ... But the forms which enter into and go out of her are the likenesses of real existences modelled after their patterns in a wonderful and inexplicable manner.... The objects that are seen, according to Plato, are not real, but literally mimic the real Forms. In the allegory of the cave expressed in Republic, the things that are ordinarily perceived in the world are characterized as shadows of the real things, which are not perceived directly. That which the observer understands when he views the world mimics the archetypes of the many types and properties (that is, of universals) of things observed. -
LAWS of FORM Alphabetum
LAWS OF FORM Alphabetum III LAWS OF ALPHABETUM III ▶ — George Spencer-Brown of Form Laws FORM 2019 � � LAWS OF FORM GEORGE SPENCER-BROWN In collaboration with the Liverpool University and the Laws of Form 50th Anniversary Conference. Alphabetum III September 28 — December 31, 2019 West Den Haag, The Netherlands The Yin and Yang of G. Spencer Brown’s Laws of Form R. John Williams I. Changing Consciousness One evening in the fall of 1969, along the picturesque cliffs of Big Sur, California, media gadfly and Whole Earth Catalog editor, Stewart Brand, approached the neuro- physiologist and dolphin researcher, John C. Lilly, with a copy of a strange little book called Laws of Form. They had spent the weekend attending panels, meditating, and dropping acid at a recently established center named Esalen — one of several burgeoning hotspots of what had come to be known as the ‘human potential movement’. Brand needed somebody to review the book, but thus far had had difficulty finding anyone who would dare take on the project. Brand didn’t claim to really understand the book, but he did sense that it was more than a mere exercise in logic. Indeed, as he puzzled over its pages, it seemed to have some kind of occult power — a key, per- haps, for unlocking the doors of perception and entering the incandescent realms that he and so many others were seeking at Esalen and other centers for new age spiritual- ity. 5 For the previous issue of The Whole Earth Catalog, Brand of consciousness dictating our realities. Only by ‘being had asked solar-energy guru and eco-warrior Steve Baer here now’ in the sensory deprivation tank, he thought, to review it, but what Baer turned in was less than helpful could we enter those transcendent realms outside of (even as it confirmed Brand’s intuition that the book time. -
Why Does Plato's Laws Exist?
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2017 Why Does Plato's Laws Exist? Harold Parker University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Philosophy Commons Recommended Citation Parker, Harold, "Why Does Plato's Laws Exist?" (2017). Publicly Accessible Penn Dissertations. 2515. https://repository.upenn.edu/edissertations/2515 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2515 For more information, please contact [email protected]. Why Does Plato's Laws Exist? Abstract If the ideal city described at length in Plato’s Republic is a perfect and philosophically attractive encapsulation of Plato’s political philosophy, why does Plato go on to write the Laws – which also describes an ideal city, albeit one very different from the Republic? The fundamental challenge of scholarship concerning the Laws is to supply a comprehensive account of the dialogue that explains all aspects of it while also distinguishing the Laws from the Republic in a way that does not devalue the Laws as a mere afterthought to the Republic. Past attempts at meeting this challenge, I argue, can be classified under the headings of the democratic, legal, and demiurgic approaches. Although each is prima facie plausible, each also faces its own set of problems. Furthermore, none are truly capable of explaining the Laws in its full specificity; the intricate array of customs, regulations, and practices making up the life of the city described form a complex totality not reducible to the concept of democracy, the rule of law, or demiurgy. -
George Spencer-Brown's Laws of Form Fifty Years On
MATHEMATICS TEACHING RESEARCH JOURNAL 161 Special Issue on Philosophy of Mathematics Education Summer 2020 Vol 12 no 2 George Spencer-Brown’s laws of form fifty years on: why we should be giving it more attention in mathematics education Steven Watson University of Cambridge Abstract: George Spencer-Brown’s Laws of Forms was first published in 1969. In the fifty years since its publication, it has influenced mathematicians, scientists, philosophers, and sociologists. Its influence on mathematics education has been negligible. In this paper, I present a brief introduction to the theory and its philosophical underpinnings. And I set out an argument why Laws of Form should be given more attention in mathematics education. Introduction Last year (2019) marked the 50th anniversary of the publication of Laws of Form (LoF), written by George Spencer-Brown (1969). Bertrand Russell described Laws of Form as, “a calculus of great power and simplicity. Not since Euclid’s Elements have we seen anything like it” (Homes, 2016). Heinz von Foerster, pioneer of second order cybernetics, offered no reserve in his praise for Spencer-Brown’s Laws of Form. The laws of form have finally been written! With a "Spencer-Brown" transistorized power razor (a Twentieth Century model of Occam's razor) G. Spencer-Brown cuts smoothly through two millennia of growth of the most prolific and persistent of semantic weeds, presenting us with his superbly written Laws of Form. This Herculean task which now, in retrospect, is of profound simplicity rests on his discovery of the form of laws. Laws are not descriptions, they are commands, injunctions: "Do!" Thus the first constructive proposition in this book (page 3) is the injunction: "Draw a distinction!" an exhortation to perform the primordial creative act (von Foerster, 1971, p. -
Cabineta Quarterly of Art and Culture
A QUARTERLY OF ART AND CULTURE ISSUE 18 FICTIONAL STATES CABINET US $10 CANADA $15 UK £6 inside this issue THERMIDOR 2005 Sasha Archibald • John Bear • Robert Blackson • William Bryk • Sasha Chavchavadze • Mark Dery • Allen Ezell • Charles Green • Invertebrate • Craig Kalpakjian • Peter Lamborn Wilson • David Levi Strauss • Brian McMullen • Glexis Novoa • George Pendle • Elizabeth Pilliod • Patrick Pound • Bonnie and Roger Riga • Lynne Roberts-Goodwin • Tal Schori • Cecilia Sjöholm • Frances Stark • Michael Taussig • Christopher Turner • Jonathan Ward • Christine Wertheim • Tony Wood • Shea Zellweger cabinet Cabinet is a non-profit 501 (c) (3) magazine published by Immaterial Incorporated. 181 Wyckoff Street Contributions to Cabinet are fully tax-deductible. Our survival is dependent on Brooklyn NY 11217 USA such contributions; please consider supporting us at whatever level you can. tel + 1 718 222 8434 Donations of $25 or more will be acknowledged in the next possible issue. Dona- fax + 1 718 222 3700 tions above $250 will be acknowledged for four issues. Checks should be made email [email protected] out to “Cabinet.” Please mark the envelope, “Rub your eyes before opening.” www.cabinetmagazine.org Cabinet wishes to thank the following visionary foundations and individuals Summer 2005, issue 18 for their support of our activities during 2005. Additionally, we will forever be indebted to the extraordinary contribution of the Flora Family Foundation from Editor-in-chief Sina Najafi 1999 to 2004; without their generous support, this publication would not exist. Senior editor Jeffrey Kastner Thanks also to the Andy Warhol Foundation for the Visual Arts for their two-year Editors Jennifer Liese, Christopher Turner grant in 2003-2004.