1 Rereading Russell and Wittgenstein
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David Suchoff Family Resemblances: Ludwig Wittgenstein As a Jewish Philosopher the Admonition to Silence with Which Wittgenstein
David Suchoff Family Resemblances: Ludwig Wittgenstein as a Jewish Philosopher The admonition to silence with which Wittgenstein ended the Tractatus Logico-Philosophicus (1922) also marks the starting point for the emer- gence of his Jewish philosophical voice. Karl Kraus provides an instructive contrast: as a writer well known to Wittgenstein, Kraus’s outspoken and aggressive ridicule of “jüdeln” or “mauscheln” –the actual or alleged pronunciation of German with a Jewish or Yiddish accent – defined a “self-fashioning” of Jewish identity – from German and Hebrew in this case – that modeled false alternatives in philosophic terms.1 Kraus pre- sented Wittgenstein with an either-or choice between German and Jewish identity, while engaging in a witty but also unwitting illumination of the interplay between apparently exclusive alternatives that were linguistically influenced by the other’s voice. As Kraus became a touchstone for Ger- man Jewish writers from Franz Kafka to Walter Benjamin and Gershom Scholem, he also shed light on the situation that allowed Wittgenstein to develop his own non-essentialist notion of identity, as the term “family resemblance” emerged from his revaluation of the discourse around Judaism. This transition from The False Prison, as David Pears calls Wittgenstein’s move from the Tractatus to the Philosophical Investiga- tions, was also a transformation of the opposition between German and Jewish “identities,” and a recovery of the multiple differences from which such apparently stable entities continually draw in their interconnected forms of life.2 “I’ll teach you differences,” the line from King Lear that Wittgenstein mentioned to M. O’C. Drury as “not bad” as a “motto” for the Philo- sophical Investigations, in this way represents Wittgenstein’s assertion of a German Jewish philosophic position. -
Application: Digital Logic Circuits
SECTION 2.4 Application: Digital Logic Circuits Copyright © Cengage Learning. All rights reserved. Application: Digital Logic Circuits Switches “in series” Switches “in parallel” Change closed and on are replaced by T, open and off are replaced by F? Application: Digital Logic Circuits • More complicated circuits correspond to more complicated logical expressions. • This correspondence has been used extensively in design and study of circuits. • Electrical engineers use language of logic when refer to values of signals produced by an electronic switch as being “true” or “false.” • Only that symbols 1 and 0 are used • symbols 0 and 1 are called bits, short for binary digits. • This terminology was introduced in 1946 by the statistician John Tukey. Black Boxes and Gates Black Boxes and Gates • Circuits: transform combinations of signal bits (1’s and 0’s) into other combinations of signal bits (1’s and 0’s). • Computer engineers and digital system designers treat basic circuits as black boxes. • Ignore inside of a black box (detailed implementation of circuit) • focused on the relation between the input and the output signals. • Operation of a black box is completely specified by constructing an input/output table that lists all its possible input signals together with their corresponding output signals. Black Boxes and Gates One possible correspondence of input to output signals is as follows: An Input/Output Table Black Boxes and Gates An efficient method for designing more complicated circuits is to build them by connecting less complicated black box circuits. Gates can be combined into circuits in a variety of ways. If the rules shown on the next page are obeyed, the result is a combinational circuit, one whose output at any time is determined entirely by its input at that time without regard to previous inputs. -
Shalack V.I. Semiotic Foundations of Logic
Semiotic foundations of logic Vladimir I. Shalack abstract. The article offers a look at the combinatorial logic as the logic of signs operating in the most general sense. For this it is proposed slightly reformulate it in terms of introducing and replacement of the definitions. Keywords: combinatory logic, semiotics, definition, logic founda- tions 1 Language selection Let’s imagine for a moment what would be like the classical logic, if we had not studied it in the language of negation, conjunction, dis- junction and implication, but in the language of the Sheffer stroke. I recall that it can be defined with help of negation and conjunction as follows A j B =Df :(A ^ B): In turn, all connectives can be defined with help of the Sheffer stroke in following manner :A =Df (A j A) A ^ B =Df (A j B) j (A j B) A _ B =Df (A j A) j (B j B) A ⊃ B =Df A j (B j B): Modus ponens rule takes the following form A; A j (B j B) . B 226 Vladimir I. Shalack We can go further and following the ideas of M. Sch¨onfinkel to define two-argument infix quantifier ‘jx’ x A j B =Df 8x(A j B): Now we can use it to define Sheffer stroke and quantifiers. x A j B =Df A j B where the variable x is not free in the formulas A and B; y x y 8xA =Df (A j A) j (A j A) where the variable y is not free in the formula A; x y x 9xA =Df (A j A) j (A j A) where the variable y is not free in the formula A. -
CS 173: Discrete Structures, Spring 2012 Homework 1 Solutions
CS 173: Discrete Structures, Spring 2012 Homework 1 Solutions This homework contains 3 problems worth a total of 25 points. 1. [1 point] Finding information on Piazza How many pet rats does Margaret’s family have? (Hint: see Piazza.) Solution: Margaret’s family has six pet rats. 2. [4 points] Demographic Survey 3. [20 points] Logic operators The late 19th century philosopher Charles Peirce (rhymes with ‘hearse,’ not ‘fierce’) wrote about a set of logically dual operators and, in his writings, coined the term ‘Ampheck’ to describe them. The two most common Ampheck operators, the Peirce arrow (written ↓ or ⊥ or ∨ by different people) and the Sheffer stroke (written ↑ or | or ∧ by different people), are defined by the following truth table: p q p ↑ q p ↓ q T T F F T F T F F T T F F F T T (a) (4 points) The set of operators {∧, ∨, ¬} is functionally complete, which means that every logical statement can be expressed using only these three operators. Is the smaller set of operators {∨, ¬} also functionally complete? Explain why or why not. Solution: By De Morgan’s laws, ¬(¬p∨¬q) ≡ ¬¬p∧¬¬q ≡ p∧q So every logical statement using the ∧ operator can be rewritten in terms of the ∨ and ¬ operators. Since every logical statement can be expressed in terms of the ∧, ∨, and ¬ operators, this implies that every logical statement can be expressed in terms of the ∨ and ¬ operators, and so {∨, ¬} is functionally complete. (b) (4 points) Express ¬p using only the Sheffer stroke operation ↑. Solution: Note that ¬p is true if and only if p is false. -
6 X 10.5 Long Title.P65
Cambridge University Press 978-0-521-83843-6 - Seeing Wittgenstein Anew Edited by William Day and Victor J. Krebs Excerpt More information Introduction Seeing Aspects in Wittgenstein William Day and Victor J. Krebs To see and describe aspects in Wittgenstein (aspects of insight, of perspicuity, of profundity, etc.) is what any discussion of his writings, and in particular of the enigmatic Philosophical Investigations, attempts to do. It would be a cute pun, but a sad excuse for a book, if this vol- ume of new essays offered simply the promise of “seeing” and describ- ing “aspects” in Wittgenstein’s discussion of aspect-seeing. Having invited and then discussed the essays in the present volume with our contributors over a handful of years, we find that they offer more than that simple promise. At a minimum, they bring out a range of connections between Parts I and II of the Investigations that should interest Wittgensteinian scholars whose central concerns would oth- erwise seem untouched by the discussions of aspect-seeing in the Investigations and elsewhere. More than occasionally these essays open up novel paths across familiar fields of thought to anyone for whom, for example, the objectivity of interpretation, the fixity of the past, the acquisition of language, or the nature of human consciousness remain live issues. But a recurring discovery in the chapters that fol- low is that there is something to be found in his remarks on aspect- seeing that is crucial to, yet all but overlooked in, the reception of the later Wittgenstein. And since the fate of the reception of the later Wittgenstein remains tied to one’s reading of the Investigations, however broadened by the publication of subsequent volumes of his later writings, it matters that these essays also have something to con- tribute to that perennial, and perhaps most pressing, question in 1 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83843-6 - Seeing Wittgenstein Anew Edited by William Day and Victor J. -
The History of Russell's Pythagorean Mysticism
Reviews 175 THE HISTORY OF RUSSELeS PYTHAGOREAN MYSTICISM STEFAN ANDERSSON Theology and Religious Studies I University of Lund 5-223 62, Lund, Sweden [email protected] Ray Monk. Russell: Mathematics: Dreams and Nightmares. (The Great Philos ophers.) London: Phoenix, 1997. Paperbound. Pp. vi, 58. £2.00. CDN$4·99· ay Monk's short book on Russell is number seven in a series of books R called The Great Philosophers. Since there is neither a publisher's fore word nor an author's preface, the only suggestion concerning the content is the subtitle Mathematics: Dreams and Nightmares. For those familiar with Monk's earlier work on Wittgenstein and Russell and his understanding of the relationship between them, it will corne as no surprise that Monk has chosen this theme for his little book. His essay has two parts: 'The Pythagorean Dream" and "The Mathema tician's Nightmare". In the first part Monk describes the content, origin, and development of the Pythagorean dream up to Russell's discovery of his para dox. The second part is devoted to showing how the dream turned into a nightmare, mainly due to Wittgenstein's influence. Monk traces the origin of the dream back to an experience that Russell had at the age of eleven, when his older brother Frank gave him lessons in geometry. Russell described the experience as being "as dazzling as first love" and went on to say that from that moment until he finished Principia Mathe matica, written with his former teacher Alfred North Whitehead, "mathemat ics was my chief interest, and my chief source of happiness." What made geometry so attractive to Russell was that it purported to provide him and everyone else with knowledge that was so certain that no reasonable man could question its truth. -
Boolean Logic
Boolean logic Lecture 12 Contents . Propositions . Logical connectives and truth tables . Compound propositions . Disjunctive normal form (DNF) . Logical equivalence . Laws of logic . Predicate logic . Post's Functional Completeness Theorem Propositions . A proposition is a statement that is either true or false. Whichever of these (true or false) is the case is called the truth value of the proposition. ‘Canberra is the capital of Australia’ ‘There are 8 day in a week.’ . The first and third of these propositions are true, and the second and fourth are false. The following sentences are not propositions: ‘Where are you going?’ ‘Come here.’ ‘This sentence is false.’ Propositions . Propositions are conventionally symbolized using the letters Any of these may be used to symbolize specific propositions, e.g. :, Manchester, , … . is in Scotland, : Mammoths are extinct. The previous propositions are simple propositions since they make only a single statement. Logical connectives and truth tables . Simple propositions can be combined to form more complicated propositions called compound propositions. .The devices which are used to link pairs of propositions are called logical connectives and the truth value of any compound proposition is completely determined by the truth values of its component simple propositions, and the particular connective, or connectives, used to link them. ‘If Brian and Angela are not both happy, then either Brian is not happy or Angela is not happy.’ .The sentence about Brian and Angela is an example of a compound proposition. It is built up from the atomic propositions ‘Brian is happy’ and ‘Angela is happy’ using the words and, or, not and if-then. -
Propositional Logic
Mathematical Logic (Based on lecture slides by Stan Burris) George Voutsadakis1 1Mathematics and Computer Science Lake Superior State University LSSU Math 300 George Voutsadakis (LSSU) Logic January 2013 1 / 86 Outline 1 Propositional Logic Connectives, Formulas and Truth Tables Equivalences, Tautologies and Contradictions Substitution Replacement Adequate Sets of Connectives Disjunctive and Conjunctive Forms Valid Arguments, Tautologies and Satisfiability Compactness Epilogue: Other Propositional Logics George Voutsadakis (LSSU) Logic January 2013 2 / 86 Propositional Logic Connectives, Formulas and Truth Tables Subsection 1 Connectives, Formulas and Truth Tables George Voutsadakis (LSSU) Logic January 2013 3 / 86 Propositional Logic Connectives, Formulas and Truth Tables The Alphabet: Connectives and Variables The following are the basic logical connectives that we use to connect logical statements: Symbol Name Symbol Name 1 true ∧ and 0 false ∨ or ¬ not → implies ↔ iff In the same way that in algebra we use x, y, z,... to stand for unknown or varying numbers, in logic we use the propositional variables P, Q, R,... to stand for unknown or varying propositions or statements; Using the connectives and variables we can construct propositional formulas like ((P → (Q ∨ R)) ∧ ((¬Q) ↔ (1 ∨ P))). George Voutsadakis (LSSU) Logic January 2013 4 / 86 Propositional Logic Connectives, Formulas and Truth Tables Inductive (Recursive) Definition of Propositional Formulas Propositional formulas are formally built as follows: Every propositional variable P is a propositional formula; the constants 0 and 1 are propositional formulas; if F is a propositional formula, then (¬F ) is a propositional formula; if F and G are propositional formulas, then (F ∧ G), (F ∨ G), (F → G) and (F ↔ G) are propositional formulas. -
Combinational Circuits
Combinational Circuits Jason Filippou CMSC250 @ UMCP 06-02-2016 Jason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 1 / 1 Outline Jason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 2 / 1 Hardware design levels Hardware design levels Jason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 3 / 1 Hardware design levels Levels of abstraction for ICs Small Scale Integration: ≈ 10 boolean gates Medium Scale Integration: > 10; ≤ 100 Large Scale Integration: Anywhere between 100 and 30; 000. Very Large Scale Integration: Up to 150; 000. Very Very Large Scale Integration: > 150; 000. Jason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 4 / 1 Hardware design levels Example schematic Figure 1: VLSI schematic for a professional USB interface for Macintosh PCs. Jason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 5 / 1 Hardware design levels SSI Consists of circuits that contain about 10 gates. 16-bit adders. Encoders / Decoders. MUX/DEMUX. ::: All our examples will be at an SSI level. Logic Design is the branch of Computer Science that essentially analyzes the kinds of circuits and optimizations done at an SSI/MSI level. We do not have such a course in the curriculum, but you can expect to be exposed to it if you ever take 411. Jason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 6 / 1 Combinational Circuit Design Combinational Circuit Design Jason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 7 / 1 A sequential circuit is one where this constraint can be violated. Example: Flip-flops (yes, seriously). In this course, we will only touch upon combinational circuits. Combinational Circuit Design Combinational vs Sequential circuits A combinational circuit is one where the output of a gate is never used as an input into it. -
Logic and Bit Operations
Logic and bit operations • Computers represent information by bits. • A bit has two possible values, namely zero and one. This meaning of the word comes from binary digit, since zeroes and ones are the digits used in binary representations of numbers. The well-known statistician John Tuley introduced this terminology in 1946. (There were several other suggested words for a binary digit, including binit and bigit, that never were widely accepted.) • A bit can be used to represent a truth value, since there are two truth values, true and false. • A variable is called a Boolean variable if its values are either true or false. • Computer bit operations correspond to the logical connectives. We will also use the notation OR, AND and XOR for _ , ^ and exclusive _. • A bit string is a sequence of zero or more bits. The length of the string is the number of bits in the string. 1 • We can extend bit operations to bit strings. We define bitwise OR, bitwise AND and bitwise XOR of two strings of the same length to be the strings that have as their bits the OR, AND and XOR of the corresponding bits in the two strings. • Example: Find the bitwise OR, bitwise AND and bitwise XOR of the bit strings 01101 10110 11000 11101 Solution: The bitwise OR is 11101 11111 The bitwise AND is 01000 10100 and the bitwise XOR is 10101 01011 2 Boolean algebra • The circuits in computers and other electronic devices have inputs, each of which is either a 0 or a 1, and produce outputs that are also 0s and 1s. -
Else M. Barth What Has Happened to the Science of Logic, to Logic As An
Else M. Barth properties in the individual).' To say that Maritain's book, Petite logique, was influential is an understatement. By 1933 it had been reprinted ten times. At his death in 1973 it was made c1ear that his Introduction influence on the very highest echelons of the Catholic church had been direct and monumental, the then Pope c1aiming him as his own philosophical inspiration. However, some time after completing (with A.N. Whitehead) the Principia mathematica, Russell, the most widely influential of the logical revisionists in the first part of the century, had abandoned What has happened to the science of fundamental logica I research and had left logic, to logic as an academie discipline the scene to a younger man, the Austrian and pursuit? Though the diagnoses do not Ludwig Wittgenstein. It is known that this coincide, many agree that something has was preceded by Wittgenstein's gone seriously wrong. Some blame the philosophy of logical truth as 'tautologi technique and goal of formalization, or of eal'. algebraization and 'model theory'. Some And the logic-politics combination blame the take-over by mathematicians as disappeared - for a long time. Post hoc, such. Others blame the period of logica I ergo propter hoc? I believe the explanation positivism, or a background in Protestant is more involved. A full explanation also or Jewish religion. Quite a few regard it as has to cover other eminent politically a purely psychological question, blaming oriented logicians. For example, why did those who are drawn to logic as a profes the impact of the brilliant logical analyses sion as lacking in ordinary linguistic of German idealism by the author of proficiency, or in social and com Progress and Regress in Ph ilosophy , the municative skills, and hence in cultural German philosopher-mathematician consciousness. -
Russell-Autobiography.Pdf
Autobiography ‘Witty, invigorating, marvellously candid and generous in spirit’ Times Literary Supplement Bertrand Russell Autobiography First published in 1975 by George Allen & Unwin Ltd, London First published in the Routledge Classics in 2010 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Avenue, New York, NY 10016 Routledge is an imprint of the Taylor and Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2009. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. © 2009 The Bertrand Russell Peace Foundation Ltd Introduction © 1998 Michael Foot All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book has been requested ISBN 0-203-86499-9 Master e-book ISBN ISBN10: 0–415–47373–X ISBN10: 0–203–86499–9 (ebk) ISBN13: 978–0–415–47373–6 ISBN13: 978–0–203–86499–9 (ebk) To Edith Through the long years I sought peace, I found ecstasy, I found anguish, I found madness, I found loneliness, I found the solitary pain that gnaws the heart, But peace I did not find.