DOCSLIB.ORG

Author's Name in Vita Is: Gwendolyn Ethel Duell Bowne. University Microfilms, Inc., Ann Arbor, Michigan Copyright By

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Author's Name in Vita Is: Gwendolyn Ethel Duell Bowne. University Microfilms, Inc., Ann Arbor, Michigan Copyright By This dissertation has been 63—6231 microfilmed exactly as received BOWNE, Gwendolyn Duell, 1925— THE DEVELOPMENT OF THE PHILOSOPHY OF LOGIC FROM 1880 TO 1908. The Ohio State University, Ph.D., 1963 Philosophy Please Note: Author's name in vita is: Gwendolyn Ethel Duell Bowne. University Microfilms, Inc., Ann Arbor, Michigan Copyright by Gwendolyn Duell Bowne TIB DEVKLOTMDfT OP TBB PHILOSOPHT OP LOGIC FROM I860 TO 1906 DISaSRTUIOW Presented in Fhrtial Fulfillment of the Requirmeirts for the Degree Doctor of Philosophy in the Graduate Sohool of The Ohio State Bbirersity Gwendolyn Duell Bowne, B. A., M, i. ****** The Ohio State Uhirersity 19 6 } Approved bp Department of Philosophy AcaouuDoram I should like to thsnk Professor Morris Welts sad Professor Stsphsa Barker for thsir helpful suggestions end for the interest they here shown in this dissertation. The instruction in the philosophy of Kant and in eons as­ pects of neo-Kantian philosophy which I received fron Professor Marvin Foac was of great value in this study. It is inpossible to express adequately the extent of m y Indebtedness to Professor Everett J. Kelson, who has been my teacher in philosophy for nany years. I hope he will continue in the endeavor as long as his patience endures. ii TABLE OF COSTENTS Page ACKNOWLEDGMENTS ........................................ it INTRODUCTION ....................... 1 Chapter I. BRADLST’S L O G I C .......................... 3 H . BERTRAND RUSSELL: FOUNDATIONS- OF GEOMETRY . 16 m . oouturat *s PS MiTBHMKPE? METAPHYSICS ............................ 29 IV. COUTURAT-S DtE L*INFIMI MATgatATIQUE: INFINITE NUMBERS ........................ k2 V. A. N. WHITEHEAD: A TREATISE ON UNIVERSAL ALGEBRA AND LtoXciSM ........ ... 55 VI. THE LOGIC OF G. E. M O O R E ................... 68 VII. THE FIRST CONGRESS OF PHILOSOPHY SUBJECTS, PREDICATES, AND RELATIONS. .. 98 VIII. LOGICISM AND LOGISTIC ....................... 123 IX. LOGISTIC AND INTUITION THE SECOND CONGRESS OF PHILOSOPHY...... 1^9 X. THE LOGISTIC REFUTATION OF KANT ........ 171 XI. LOGICAL INTUITION: POINCARE, RUSSELL, AND BROUWER ............................ 182 XII. CONCLUSIONS . .............................212 BIBLIOGRAPHY ............................................ 221 AUTOBIOGRAPHY ..................... 23I ill IHtSODO^IOH The development of mathematical logic In the late nine­ teenth end early twentieth centurlee involved both the construction of new symbolic "languages* of logic, and the preeentatlon of various interpretations of the philosophical importance of these constructs* In this study I have avoided the technical development of mathematical logic, which can reasonably be regarded as a chapter in the history of mathe­ matics rather than of philosophy* The,metaphysical and eplstsmologloal views which were associated with the mathe­ matical techniques are a complex and fascinating toplo in themselves) and this study is devoted primarily to tracing out the arguments which were carried on among the "mathematical philosophers" between 1885 and In this interval the original "logistic" philosophy was proposed, criticized, and finally abandoned by its leading proponents, Louis Oouturat in France and Bertrand Russell in England. Most of the interest in mathematical philosophy in this period appears to have been In France* The discussions on which this study is based are primarily taken from the Revue da Mdtaphyslque at des Morales and from other French journals of the period— Translations given are ay own, but where the passages involved are lengthy or complex, the original is included. 1 Although mm discussion is included where it seems necessary to clarity the issues, I have concentrated upon following the course of the argunent as It took place and presenting the views which were actually advanced. There are of course, value judgments involved In the selection of im- portant arguments and of central figures. I have decided to use the contemporary estimates as a guide rather than those of later periods. "Unconscious influences" are not philo­ sophically interesting to any one who distinguishes philo­ sophy from psychology; and a philosopher's actual state­ ment of his reasons for holding a view and of the arguments which have influenced his thought deserves to be taken seriously. From this point of view, the central figures in the early development of the philosophy of logic were Louis Couturat, Pierre Boutroux, and Henri PoincarS in France; and Bertrand Russell and G. E. Moore in England. The other major party to the argument was Immanuel Kant, who had died in 1S0H but still exercised a powerful influence upon philosophy. CHAPTER X BRADSJEF'S LOGIC In 1683 the Absolut* Id sol 1st philosophy dominated philo­ sophical thought* as reflected In ths professional journals of ths tins* As a leading representative of that viewpoint, F. H. Bradley had a oharaeterlstio approaoh not only to prob­ lems of ethios and aataphyslos, but also to loglo. Hie The Ptlnolnles of Loxio.* published In 1883, was extremely in^ fluential among philosophers, although there were even at . this time several other sohools of logician* who refused to aoeept the Hegelian ideal of loglo. The old tradition of formal loglo still claimed ths allegianoe of soma students; and ths induotive logic of J. 3. Mill was a new contender in the field. There was also some very new work in the field of formal loglo being carried on, in Bradley's opinion, as a variety of mathematics. As suoh, he believed, it was incapable of acquiring any philosophical significance. Most of the questions which were at Issue between the idealist logic and a suddenly revitalised formal logio during the subsequent twenty-five years are, X believe, still open. *F. H. Bradley, The Principles of Logic (London* Regan Paul, Trench, & Oo., 1883). 5 Indeed, they eeem to here once again aroueed the interest of philosophical logioiane. In the earlier debates on these queetions, Bertrand Russell took a particularly active part. Hie writings are also of special interest, since he began as a partisan of the idealistic logic and became for a time the leading defender of the new formal logic. Russell's reasons for such a reactionary procedure are to be found in the de­ bates of this transition period between the dominance of the idealistic logic and the dominance of mathematical logic. Bradley's reasons for his own views appear in his Logic. Although Bradley expressed his views in a vocabulary which is alien to most English-speaking readers of 196?, the views he held are apparently as modern now as then.* His rejection of the old tradition of formal logic was on the p basis of its philosophical inadequacy, a defect which he thought also appeared in such newer formal logics as the "Equational Logic" of Professor Jevons^ which he regarded as the best example of that mathematical approach. Bradley believed that the business of logic uas to give an account of "reasoning in general," which no formal logic, ^Consider P. 7. Strawson's writings on Logic. p ^Bradley also dismissed J. S. Hill's inductive logic for similar reasons. R. Jsvons, a contemporary of George Boole. Bradley refers to his Principles of Science In a number of dieoussions In the Logic. 5 whether syllogistic or equational could ever do* Formal loglo, Bradley argued, had the fatal defect of being unable to preeent an accurate picture of actual reasoning processes* Equational logic was, he believed, United by its nathenatieal nature to dealing with "those problems which acooaodate themselves to numerical reasoning, and could not include other obviously valid inferences which did not fit the subject-attribute pattern*2 Bradley* s examples of recalcitrant inferences were such relational arguments as: A is to the right of B, and B is to the right of C, so A is to the right of C* The inadequacy of equational logic could, Bradley said, only be even more striking in mathematical logic* Therefore, the mathematicians* variants on the work of Jevons could safely be dismissed by philosophical logicians without study* At least, this was the course Bradley proposed for himself, since he lacked, he said, the mathematical training which would have made it possible for him to follow the work of the math­ ematicians* He stated that, given the proper training, he would have found it "a pleasure to have seen how the defects of the Equational Theory appeared in mathematical form*" In a passage that hints at philosophical claims made by the math­ ematical logicians, he oontinued: "If I knew perhaps what mathematics were, I would see bow there is nothing special ^Bradley, Bk* U , Pt* II, ohap* iv, par. 1, p* 3U3. ^Bradley, Bk* II, Pt* II, chap* iv, par. 23, p* 360. 6 or United about them, and how they are the soul of logic in general and (for all I know) of metaphysics too.But such a logic, Bradley stated, would not provide "any account (adequate or inadequate) of reasoning in general" and there­ fore could not properly claijn to be logic at all. Bradley was convinced that whatever account of reasoning in general a logic might manage to give could not, at any rate, be a set of formal rules of inference* He argued that formal logicians, whether they were "friends of the syllogism" or preferred the equational logic, emphasised the importance of perceived identities in reasoning. •They reasoned on the basis of universal connections between attributes such that "given one in a subject, you must have the other also."- Bradley agreed that this was one extremely important type of reasoning. But, he argued, not all inferences were of this subject- attribute t y p e . 3 Formal logic had once claimed, he said, using the past tense as is appropriate in speaking of the dead, to provide us with "not merely principles of reasoning, but actual canons and tests of inference. Within the pale we were secure of salvation, and on the outside it was heresy to doubt that you were lost." Pherefore Bradley argued, the existence of valid relational inference is a fatal blow ^-Bradley, Bk.
Load more

Recommended publications
  • The Constituents of the Propositions of Logic Kevin C
    10 The Constituents of the Propositions of Logic Kevin C. Klement 1 Introduction Many founders of modern logic—Frege and Russell among them—bemoan- ed the tendency, still found in most textbook treatments, to define the subject matter of logic as “the laws of thought” or “the principles of inference”. Such descriptions fail to capture logic’s objective nature; they make it too dependent on human psychology or linguistic practices. It is one thing to identify what logic is not about. It is another to say what it is about. I tell my students that logic studies relationships between the truth-values of propositions that hold in virtue of their form. But even this characterization leaves me uneasy. I don’t really know what a “form” is, and even worse perhaps, I don’t really know what these “propositions” are that have these forms. If propositions are considered merely as sentences or linguistic assertions, the definition does not seem like much of an improvement over the psychological definitions. Language is a human invention, but logic is more than that, or so it seems. It is perhaps forgiveable then that at certain times Russell would not have been prepared to give a very good answer to the question “What is Logic?”, such as when he attempted, but failed, to compose a paper with that title in October 1912. Given that Russell had recently completed Principia Mathematica, a work alleging to establish the reducibility of mathematics to logic, one might think this overly generous. What does the claim that mathematics reduces to logic come to if we cannot independently speci- Published in Acquaintance, Knowledge and Logic: New Essays on Bertrand Russell’s Problems of Philosophy, edited by Donovan Wishon and Bernard Linsky.
    [Show full text]
  • The Philosophical Importance of Mathematical Logic Bertrand Russell in SPEAKING of "Mathematical Logic", I Use This Word in a Very Broad Sense
    The Philosophical Importance of Mathematical Logic Bertrand Russell IN SPEAKING OF "Mathematical logic", I use this word in a very broad sense. By it I understand the works of Cantor on transfinite numbers as well as the logical work of Frege and Peano. Weierstrass and his successors have "arithmetised" mathematics; that is to say, they have reduced the whole of analysis to the study of integer numbers. The accomplishment of this reduction indicated the completion of a very important stage, at the end of which the spirit of dissection might well be allowed a short rest. However, the theory of integer numbers cannot be constituted in an autonomous manner, especially when we take into account the likeness in properties of the finite and infinite numbers. It was, then, necessary to go farther and reduce arithmetic, and above all the definition of numbers, to logic. By the name "mathematical logic", then, I will denote any logical theory whose object is the analysis and deduction of arithmetic and geometry by means of concepts which belong evidently to logic. It is this modern tendency that I intend to discuss here. In an examination of the work done by mathematical logic, we may consider either the mathematical results, the method of mathematical reasoning as revealed by modern work, or the intrinsic nature of mathematical propositions according to the analysis which mathematical logic makes of them. It is impossible to distinguish exactly these three aspects of the subject, but there is enough of a distinction to serve the purpose of a framework for discussion. It might be thought that the inverse order would be the best; that we ought first to consider what a mathematical proposition is, then the method by which such propositions are demonstrated, and finally the results to which this method leads us.
    [Show full text]
  • Mathematics, Reason & Religion
    05_JavierLEACH.qxd:Maqueta.qxd 26/6/08 11:54 Página 639 MATHEMATICS, REASON & RELIGION JAVIER LEACH Universidad Complutense de Madrid ABSTRACT: This paper will study the relationship between mathematics and religion from the perspective of reason and the role played by reason in human knowledge. Firstly, I will study the relationship between reason, logic and mathematics. From this starting point, I will study the relationship between reason and natural science and finally, I will draw some conclusions on the relationship between reason, philosophy and theology. The relationship between mathematics, reason and religion will be studied within the context of the global unity of human knowledge. This paper intends to explain how the ‘pure deductive reason’ is present in all human thinking. Mathematics and natural science share this universal presence with metaphysics and religion. Pure deductive reasoning is somehow an absolute value that transcends all aspects and levels of human knowledge, including metaphysical and religious knowledge. Metaphysical and theological arguments need to be able to span different cultural communities. Pure deductive reasoning is a kind of reasoning that can fully span communities and it forms a basis for inter- disciplinary, inter-cultural and inter-religious communication. KEY WORDS: mathematics, reason, pure deductive reason, logic, natural science, metaphysics, religión, revelation. Matemática, Razón y Religión RESUMEN: En este artículo voy a estudiar la interrelación entre matemática y religión desde el punto de vista de la razón y del papel de ésta en el conocimiento humano. En primer lugar estudiaré la rela- ción entre la razón, la lógica y la matemática. Partiendo de ahí estudiaré la relación entre la razón y las ciencias de la naturaleza y por último sacaré conclusiones acerca de la relación entre la razón, la filo- sofía y la teología.
    [Show full text]
  • Otto Hölder's Interpretation of David Hilbert's Axiomatic Method*
    Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences 17-1 | 2013 The Epistemological Thought of Otto Hölder Otto Hölder’s Interpretation of David Hilbert’s Axiomatic Method Mircea Radu Electronic version URL: http://journals.openedition.org/philosophiascientiae/831 DOI: 10.4000/philosophiascientiae.831 ISSN: 1775-4283 Publisher Éditions Kimé Printed version Date of publication: 1 March 2013 Number of pages: 117-129 ISBN: 978-2-84174-620-0 ISSN: 1281-2463 Electronic reference Mircea Radu, « Otto Hölder’s Interpretation of David Hilbert’s Axiomatic Method », Philosophia Scientiæ [Online], 17-1 | 2013, Online since 01 March 2016, connection on 03 November 2020. URL : http:// journals.openedition.org/philosophiascientiae/831 ; DOI : https://doi.org/10.4000/ philosophiascientiae.831 Tous droits réservés Otto Hölder’s Interpretation of David Hilbert’s Axiomatic Method ∗ Mircea Radu Universität Bielefeld (Germany) Résumé : L’article présente une reconstruction brève de la conception de preuve développée par Otto Hölder. La reconstruction se concentre sur la critique de la conception axiomatique de David Hilbert en général et sur sa conception des métamathématiques en particulier. On affirme que l’analyse faite par Hölder des idées méthodologiques générales de Hilbert et surtout de la structure logique des preuves fournie par Hilbert dans les Grundlagen der Geometrie (1899) est très utile pour comprendre plus clairement la thèse de van der Waerden affirmant le lien entre la conception de la preuve développée par Hölder et la tradition établie par Kurt Gödel. Abstract: In this paper I provide a brief reconstruction of Otto Hölder’s conception of proof. My reconstruction focuses on Hölder’s critical assess- ment of David Hilbert’s account of axiomatics in general, and of Hilbert’s conception of metamathematics in particular.
    [Show full text]
  • Abductive Inference, 98 Abstractness, Platonic Vs. Nonplatonic
    Index Abductive inference, 98 Availability theory, 140 Abstractness, platonic vs. nonplatonic, Avenarius, R., 4 192 Acknowledging the predicament, 55, Basic Laws of Arithmetic (Frege), 32 69–71 Begriffsschrift (Frege), xii, 32, 120, 207, AI 229 strong, 102–106, 108 Belnap, N., 252n18 weak, 103, 105, 108 Benacerraf, P., xxi, 2, 22–25, 71, Analytic inferences, 225 155–156, 182–191, 193, 199–200 Analyticity, 36–37 Benacerraf dilemma Analytic necessity, 197 extended, 184 Analytic philosophy, xx, 1, 3 original, 182–184 Alice, 158–159, 185 Block, N., 93 Antinaturalism, 14–21 Bolzano, B., 5 Antiperceptualism, 186, 189, 191–200 Bonjour, L., 188 Antipsychologism, 14–21 Boole, G., xi–xiii, 25, 31–32, 115–116, Antirealism, 185, 188–189 131, 204–205, 216 Anti-supernaturalism, 9 Braine, M., 130 Aphasias, 86, 106–107 Brentano, F., 1, 4 A priori–a posteriori, xii, 272n20, Broca’s area, 106 273n24 Byrne, R., 135 Apriority of protologic, 29, 44–45, 109, 201 Carnap, R., 36–37, 54, 59–61, 65, 186, Aristotle, xi, xiii–xv, 31–32, 124 210–211, 226–227 Arnaud, P., xii, 204–205 Carroll, L. (Charles Dodgson), 54–59, Artificial intelligence. See AI 61–62, 65, 69, 78, 158, 223 Art of Thinking (Arnaud and Nicole), Carruthers, P., 111 xii Categorical normativity. See Aspects of the Theory of Syntax Normativity, categorical (Chomsky), 86 Causation, 23, 189–190, 242n62 Autism, 112 Central processes, 89, 100–102, 109 310 Index Chalmers, D., 12, 98, 277–278n78 Darwinian evolution, 97, 142–143 Cheng, P., 141 Davidson, D., 110, 173 Cherniak, C., 146, 270n88 Dedekind, R., 36 Chinese brain argument, 106–107 Dedicated cognitive capacity, 88, 101 Chinese nation argument, 93 Deduction, intuitive vs.
    [Show full text]
  • To Prove Or Disprove: the Use of Intuition and Analysis by Undergraduate Students to Decide on the Truth Value of Mathematical Statements and Construct Proofs and Counterexamples
    To Prove or Disprove: The Use of Intuition and Analysis by Undergraduate Students to Decide on the Truth Value of Mathematical Statements and Construct Proofs and Counterexamples A dissertation presented to the faculty of The Patton College of Education of Ohio University In partial fulfillment of the requirements for the degree Doctor of Philosophy Kelly M. Bubp December 2014 © 2014 Kelly M. Bubp. All Rights Reserved. 2 This dissertation titled To Prove or Disprove: The Use of Intuition and Analysis by Undergraduate Students to Decide on the Truth Value of Mathematical Statements and Construct Proofs and Counterexamples by KELLY M. BUBP has been approved for the Department of Teacher Education and The Patton College of Education by Robert M. Klein Associate Professor of Mathematics Renée A. Middleton Dean, The Patton College of Education 3 Abstract BUBP, KELLY M., Ph.D., December 2014, Mathematics Education To Prove or Disprove: The Use of Intuition and Analysis by Undergraduate Students to Decide on the Truth Value of Mathematical Statements and Construct Proofs and Counterexamples Director of Dissertation: Robert M. Klein Deciding on the truth value of mathematical statements is an essential aspect of mathematical practice in which students are rarely engaged. This study explored undergraduate students’ approaches to mathematical statements with unknown truth values. The research questions were 1. In what ways and to what extent do students use intuition and analysis to decide on the truth value of mathematical statements? 2. What are the connections between students’ process of deciding on the truth value of mathematical statements and their ability to construct associated proofs and counterexamples? 3.
    [Show full text]
  • Frege's Critical Arguments for Axioms
    Frege’s Critical Arguments for Axioms Abstract There is a traditional and substantive philosophical question about how we can be justied in accepting logical axioms and other basic truths. We can discover an interesting answer by considering an outstanding interpre- tive puzzle about Frege’s approach to logical axioms. The puzzle is: having claimed that logical axioms are “self-evident,” to be recognized as true “in- dependently of other truths,” why does he then oer arguments for those axioms? The answer, I argue, is that he thinks the arguments give us justi- cation for accepting the axioms, and that this does not in fact conict with anything he says about axioms. This resolution of the puzzle makes good sense in the light of historical and philosophical considerations when we read Frege’s procedure in the light of the “critical method”: an approach to the justication of axioms endorsed by leading philosophers at the time. 1 The Puzzle about Frege’s Arguments There is something puzzling about Frege’s introduction of his “Basic Laws” or “axioms” of logic. On the one hand, he thinks that “it is part of the concept of an axiom that it can be recognized as true independently of other truths,”1 and he oers a regress argument to show that there must be truths with that feature: The grounds which justify the recognition of a truth often reside in other truths which have already been recognized. But if there are any truths recognized by us at all, this cannot be the only form that justication takes.
    [Show full text]
  • A Classical Defense Against Mathematical Empiricism
    The Crucial Role of Proof: A Classical Defense Against Mathematical Empiricism by Catherine Allen Womack Submitted to the Department of Linguistics and Philosophy in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 1993 @ Massachust•Os Institute of Technology 1993. All rights reserved. Author ... ................................... ............ ......... Department of Linguistics and Philosophy March 10, 1993 Certified by .............. .......................................... James Higginbotham Professor Thesis Supervisor Read by ...... .... , .... ....... ....................................... George Boolos Professor Thesis Reader Accepted by ..-. ,. ... ..................................... - . George Boolos Chairman, Departmental Committee on Graduate Students ARCHIVES MACSACHUSETTS INSTITUTE OF TECHNOLOGY rJUN 03 1993 The Crucial Role of Proof: A Classical Defense Against Mathematical Empiricism by Catherine Allen Womack Submitted to the Department of Linguistics and Philosophy on March 10, 1993, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Mathematical knowledge seems to enjoy special status not accorded to scientific knowledge: it is considered a priori and necessary. We attribute this status to math- ematics largely' because of the way we come to know it-through following proofs. Mathematics has come under attack from sceptics who reject the idea that mathe- matical knowledge is a priori. Many sceptics consider it to be a posteriori knowledge, subject to possible empirical refutation. In a series of three papers I defend the a priori status of mathematical knowledge by showing that rigorous methods of proof are sufficient to convey a priori knowledge of the theorem proved. My first paper addresses Philip Kitcher's argument in his book The Natuire of Mathematical Knowledge that mathematics is empirical. Kitcher develops a view of a priori knowledge according to which mathematics is not a priori.
    [Show full text]
  • Frege on Knowing the Foundation Author(S): Tyler Burge Source: Mind, Vol
    Mind Association Frege on Knowing the Foundation Author(s): Tyler Burge Source: Mind, Vol. 107, No. 426 (Apr., 1998), pp. 305-347 Published by: Oxford University Press on behalf of the Mind Association Stable URL: http://www.jstor.org/stable/2659879 Accessed: 11-04-2017 02:10 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms Mind Association, Oxford University Press are collaborating with JSTOR to digitize, preserve and extend access to Mind This content downloaded from 128.97.244.236 on Tue, 11 Apr 2017 02:10:28 UTC All use subject to http://about.jstor.org/terms Frege on Knowing the Foundation TYLER BURGE The paper scrutinizes Frege's Euclideanism-his view of arithmetic and ge- ometry as resting on a small number of self-evident axioms from which non- self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered-his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential abilities.
    [Show full text]
  • Four Challenges to the a Priori—A Posteriori Distinction
    Four challenges to the a priori—a posteriori distinction Albert Casullo Synthese An International Journal for Epistemology, Methodology and Philosophy of Science ISSN 0039-7857 Volume 192 Number 9 Synthese (2015) 192:2701-2724 DOI 10.1007/s11229-013-0341-x 1 23 Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media Dordrecht. This e-offprint is for personal use only and shall not be self- archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”. 1 23 Author's personal copy Synthese (2015) 192:2701–2724 DOI 10.1007/s11229-013-0341-x Four challenges to the a priori—a posteriori distinction Albert Casullo Received: 14 April 2013 / Accepted: 19 August 2013 / Published online: 14 September 2013 © Springer Science+Business Media Dordrecht 2013 Abstract During the past decade a new twist in the debate regarding the a priori has unfolded. A number of prominent epistemologists have challenged the coherence or importance of the a priori—a posteriori distinction or, alternatively, of the concept of a priori knowledge. My focus in this paper is on these new challenges to the a priori.
    [Show full text]
  • Uncontrolled Logic: Intuitive Sensitivity to Logical Structure in Random Responding
    Thinking & Reasoning ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/ptar20 Uncontrolled logic: intuitive sensitivity to logical structure in random responding Stephanie Howarth, Simon Handley & Vince Polito To cite this article: Stephanie Howarth, Simon Handley & Vince Polito (2021): Uncontrolled logic: intuitivesensitivitytologicalstructureinrandomresponding, Thinking & Reasoning, DOI: 10.1080/13546783.2021.1934119 To link to this article: https://doi.org/10.1080/13546783.2021.1934119 Published online: 22 Jun 2021. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=ptar20 THINKING & REASONING https://doi.org/10.1080/13546783.2021.1934119 Uncontrolled logic: intuitive sensitivity to logical structure in random responding Stephanie Howarth , Simon Handley and Vince Polito Department of Cognitive Science, Macquarie University, Sydney, Australia ABSTRACT It is well established that beliefs provide powerful cues that influence reason- ing. Over the last decade research has revealed that judgments based upon logical structure may also pre-empt deliberative reasoning. Evidence for ‘intuitive logic’ has been claimed using a range of measures (i.e. confidence ratings or latency of response on conflict problems). However, it is unclear how well such measures genuinely reflect logical intuition. In this paper we introduce a new method designed to test for evidence of intuitive logic. In two experiments participants were asked to make random judgments about the logical validity of a series of simple and complex syllogistic arguments. For simple arguments there was an effect of logical validity on random respond- ing, which was absent for complex arguments.
    [Show full text]
  • Ergostuctures, Ergologic and the Universal Learning Problem: Chapters 1, 2
    Ergostuctures, Ergologic and the Universal Learning Problem: Chapters 1, 2. Misha Gromov March 14, 2013 Contents 1 Structures and Metaphors. 1 1.1 Universality, Freedom and Curiosity . .2 1.2 Ego and Ergo. .4 1.3 Ergo-Ideas and Common Sense. .5 1.4 Ergo Perspective on Chess . .7 1.5 Learning, Communicating, Understanding. 11 2 Mathematics and its Limits. 13 2.1 Logic and Rigor. 14 2.2 Computations, Equations, Iterations, Simulations. 18 2.3 Numbers and Symmetries. 28 2.4 Languages, Probabilities and the Problems with Definitions. 30 3 Libraries, Dictionaries and language Understanding 36 4 Bibliography. 36 1 Structures and Metaphors. Every sentence I utter must be understood not as an affirmation, but as a question. Niels Bohr.1 Our ultimate aim is to develop mathematical means for describing/designing learning systems L that would be similar in their essential properties to the minds of humans and certain animals. Learning and Structures. We want to understand the process(es) of learning, e.g. of mother tongue or of a mathematical theory, in the context of what we call ergostructures. Such structures, as we see them, are present in the depth of the human (some animal?) minds, in natural languages, in logical/combinatorial organizations of branches of mathematics and, in a less 1I could not find on the web when and where Bohr said/wrote it. Maybe he never did. But here and everywhere, a quote is not an appeal to an authority but an acknowledgment of something having been already said. 1 mature form, in biological systems – from regulatory networks of living cells up to, possibly, ecological networks.2 Learning from this perspective is a dynamical process of building the internal ergostructure of an L from the raw structures in the incoming flows S of signals, where S may or may not itself contain an ergostructure or its ingredients.
    [Show full text]