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Mathematics and Logic

Hermann Weyl
<span title="">1946</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6jb2mei4hzg4vdohokley4c5om" style="color: black;">The American mathematical monthly</a> </i> &nbsp;
Logic, v. 2, 1937, pp. 65-77 and the references given there. 6. Cf. G. Cantor, Gesammelte Abhandlungen, ed. E. Zermelo, 1932, pp. 443-451 (correspond- ence Cantor-Dedekind). 7.  ...  W=Weyl py 1/ TE ae eee we Or SY B H discussed gives any hope of accomplishing (2), the subjugation of mathematics by logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00029890.1946.11991619">doi:10.1080/00029890.1946.11991619</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rmrctp3w7fbhhj5gbkmijn3jgq">fatcat:rmrctp3w7fbhhj5gbkmijn3jgq</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_american-mathematical-monthly_1946-01_53_1/page/2" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_american-mathematical-monthly_1946-01_53_1/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00029890.1946.11991619"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

How Mathematics Isn't Logic

Roger Wertheimer
<span title="">1999</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6pldu5rj5zdo3oxk5kglq2ccni" style="color: black;">Ratio</a> </i> &nbsp;
If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles.  ...  Suppose that mathematics is analytic, that all arithmetic and other mathematical truths are derivable with only a handful of definitions and logical principles.  ...  Consider: A: 7=7 7 is 7 B: 7=VII 7 is VII C: 15-7=15-VII D: 15-7=2 3 E: 15-VII=2 3 F: 15-7=12-2 2 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/1467-9329.00093">doi:10.1111/1467-9329.00093</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4hr33e52zrggjbmn3w4ogaavr4">fatcat:4hr33e52zrggjbmn3w4ogaavr4</a> </span>
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BERKELEY'S LOGIC OF MATHEMATICS

G. A. Johnston
<span title="">1918</span> <i title="The Open Court Publishing Co."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ndqe7e5h4rhf3lmcv4yrgcddom" style="color: black;">The Monist</a> </i> &nbsp;
Ed. cisms of the logical basis of the infinitesimal calculus in The Analyst ( 1734) and A Defence of Free-Thinking in Math ematics (1735) are of considerable importance in the his tory of mathematics.  ...  It is, indeed, an able treatise on the logic of mathematics.  ... 
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Concise survey of mathematical logic

John Stillwell
<span title="">1977</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qucxg3yndjaptj6krclryhveua" style="color: black;">Journal of the Australian Mathematical Society</a> </i> &nbsp;
logic and number theory, and the Godel incompleteness theorem.  ...  This paper contains proofs of the compactness, completeness and Lowenheim-Skolem theorems for predicate logic, together with their application to nonstandard numbers; proofs of undecidability in predicate  ...  ,d n eD is true, so automatically Vx x ...V x^x^...,x n ) will hold in any D'sD.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1446788700020164">doi:10.1017/s1446788700020164</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ej3k7glhandvfa6daui4fsxsyu">fatcat:ej3k7glhandvfa6daui4fsxsyu</a> </span>
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A Mathematical Setting for Fuzzy Logics

Mai Gehrke, Carol Walker, Elbert Walker
<span title="">1997</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2mchw27ezjaivoukjltsyavclq" style="color: black;">International Journal of Uncertainty Fuzziness and Knowledge-Based Systems</a> </i> &nbsp;
The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic.  ...  The propositional logic obtained when the algebra of truth values is the set f(a; b) j a b and a; b 2 [0; 1]g of subintervals of the unit interval with component-wise operations, is propositional interval-valued  ...  Introduction In this paper we spell out in detail the setup of a mathematical propositional logic in algebraic terms, describing exactly when two choices of truth value algebras give the same logic.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921224408/http://emmy.nmsu.edu/~elbert/LogicPaper.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b0/ea/b0ea7905f6efd2facf34f10c0e76ca62aeaf6144.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s021848859700021x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

Hilbert, logicism, and mathematical existence

José Ferreirós
<span title="2008-06-07">2008</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/munzfrczajgrfktmdt7fobcory" style="color: black;">Synthese</a> </i> &nbsp;
Logicism defends two key theses, the conceptual thesis (1) that the basic concepts of mathematics can be defined by logical concepts alone, and the doctrinal thesis (2) that the basic complete adherence  ...  In his view, all of arithmetic and pure mathematics can be "divest[ed] … of [its] specifically arithmetic character" so as to be "subsumed under more general notions and under activities of the understanding  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11229-008-9347-1">doi:10.1007/s11229-008-9347-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sv4oamhkdvhlzfno7vf55ahlo4">fatcat:sv4oamhkdvhlzfno7vf55ahlo4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923012955/https://idus.us.es/xmlui/bitstream/handle/11441/40316/Hilbert%20logicism%20postprint.pdf?sequence=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/93/94933aa0050e4036b1f9bfca6574d3fd30d822c8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11229-008-9347-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

TENDENCIES IN THE LOGIC OF MATHEMATICS

E. R. HEDRICK
<span title="1933-04-07">1933</span> <i title="American Association for the Advancement of Science (AAAS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qirzh7firjdsjhg4tutxtir6ey" style="color: black;">Science</a> </i> &nbsp;
SCIENCE 341 by Whitehead and Russell (2d ed., 1925-27), to which reference has been made above.  ...  Brouwer contends that logic is not a sure guide toward the building-up of mathematical thought, an! that the existence of a variety of possible logical sys 16 Bull. Amer. Math.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1126/science.77.1997.335">doi:10.1126/science.77.1997.335</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/17794280">pmid:17794280</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a4xjjavwlfbcfjj3mu4hh6lbpi">fatcat:a4xjjavwlfbcfjj3mu4hh6lbpi</a> </span>
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Book Review: The elements of mathematical logic

I. L. Novak
<span title="1952-03-01">1952</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjoli2j6qffdpaalkszryuidk4" style="color: black;">Bulletin of the American Mathematical Society</a> </i> &nbsp;
(Compare for instance Quine, Mathematical logic, p. 27.)  ...  WHYBURN The elements of mathematical logic. By P. C. Rosenbloom. New York, Dover, 1950. 4+214 pp. $2.95.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1952-09603-8">doi:10.1090/s0002-9904-1952-09603-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2ei5k4yafjgilcmf2u6icodcf4">fatcat:2ei5k4yafjgilcmf2u6icodcf4</a> </span>
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I.—THE LOGICAL FOUNDATIONS OF MATHEMATICS

R. B. HALDANE
<span title="">1909</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/om4uzvbarjcblp7jjfed4ili74" style="color: black;">Mind</a> </i> &nbsp;
If we put x = 2, the synthesis of the function is easy.  ...  LogikundMetaphysik (4th ed., p. 44), observes: "Das sehr merkwiirdige Problem, wie ganz bestimmte Zusammengehorige Quanta (z. b.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/mind/xviii.1.1">doi:10.1093/mind/xviii.1.1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xwajwd46njhpzavnjqx2tcwvbi">fatcat:xwajwd46njhpzavnjqx2tcwvbi</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/crossref-pre-1923-scholarly-works/10.1093%252Fmind%252Fxix.1.422.zip/10.1093%252Fmind%252Fxviii.1.1.pdf" title="fulltext access" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/54/7d/547d01e79a0342f35d392897107dd3987d33711c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/mind/xviii.1.1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

"Mathematics is the Logic of the Infinite": Zermelo's Project of Infinitary Logic

Jerzy Pogonowski
<span title="2021-12-01">2021</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qwzusus4sbb45ib6ar7bifd6ie" style="color: black;">Studies in Logic, Grammar and Rhetoric</a> </i> &nbsp;
In this paper I discuss Ernst Zermelo's ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences.  ...  The presentation of Zermelo's ideas is accompanied with some remarks concerning the development of infinitary logic.  ...  Prace Ernsta Zermela z podstaw matematyki (Mathematics is the logic of the Infinite. Ernst Zermelo’s works on the foundations of mathematics) remains unpub- lished. 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2478/slgr-2021-0042">doi:10.2478/slgr-2021-0042</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nnowhogl3bhklm234xa7dion7u">fatcat:nnowhogl3bhklm234xa7dion7u</a> </span>
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Killeen's (2005) prep coefficient: Logical and mathematical problems

Michael Maraun, Stephanie Gabriel
<span title="">2010</span> <i title="American Psychological Association (APA)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/n6e74shnbfdrhh6piebhycvvy4" style="color: black;">Psychological methods</a> </i> &nbsp;
It follows directly from Killeen's Assumptions 1 through 3 that the mean of dЈ 2 is not equal to dЈ 1 but rather to ␦: E͑dЈ 2 ͒ ϭ E͓͑dЈ 1 Ϫ ⌬ 1 ͔ ϩ ⌬ 2 ͒ ϭ E͑dЈ 1 ͒ Ϫ E͑⌬ 1 ͒ ϩ E͑⌬ 2 ͒ ϭ ␦ ϩ 0 ϩ 0 ϭ ␦  ...  andcovariance matrix ͩ d 2 0 0 d 2ͪ: E͑dЈ 2 ͒ ϭ E͓͑dЈ 1 Ϫ ⌬ 1 ͔ ϩ ⌬ 2 ͒ ϭ E͑dЈ 1 ͒ Ϫ E͑⌬ 1 ͒ ϩ E͑⌬ 2 ͒ ͑linearity property of expectation operator) ϭ dЈ 1 ϩ 0 ϩ 0 ͑mean of constant is constant; ϭ dЈ 1  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1037/a0016955">doi:10.1037/a0016955</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/20515239">pmid:20515239</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ambxfti4ajakzhzwiwkht3spqq">fatcat:ambxfti4ajakzhzwiwkht3spqq</a> </span>
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On Certain Mathematical Terms in Aristotle's Logic: Part II

Benedict Einarson
<span title="">1936</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ot4wjesgffecld24ovlfexgthy" style="color: black;">American Journal of Philology</a> </i> &nbsp;
(for music) Theo Smyrnaeus, ed. Hiller, p. 57, 64; for mathematics the scholia on Euclid, pp. 320f. (Euclidis, Opera, vol. V, Heiberg) ; and for logic Olympiodorus, in Platonis Phaed. Comm. ed.  ...  ON CERTAIN MATHEMATICAL TERMS IN ARISTOTLE’S LOGIC. Part 11 (Cont. from p. 54).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/290473">doi:10.2307/290473</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u56abteodzdgpmloxz7ral7gry">fatcat:u56abteodzdgpmloxz7ral7gry</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_american-journal-of-philology_1936-04_57_2/page/151" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_american-journal-of-philology_1936-04_57_2/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/290473"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>

Russell's Two Lectures in China on Mathematical Logic

Lianghua Zhou, Bernard Linsky
<span title="2018-07-16">2018</span> <i title="McMaster University Library Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o3kr23cysvdhvghf572n4oiej4" style="color: black;">Russell: the Journal of Bertrand Russell Studies</a> </i> &nbsp;
In 1921 Bertrand Russell delivered two lectures on mathematical logic at Peking University.  ...  An introduc­tion and notes with a glossary discuss the background and content of the lectures as well as the linguistic difficulties in translating logical terms.  ...  Moreover, (1) is associated with (2) and (3): if (2) and (3) exist, then (1) exists as well. "Equivalence" in mathematical logic is comparable to "equality" [ ̌] 50 in ordinary mathematics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15173/russell.v38i1.3643">doi:10.15173/russell.v38i1.3643</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u6xpil7kqjguzmjnnxa7ep5yxm">fatcat:u6xpil7kqjguzmjnnxa7ep5yxm</a> </span>
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Some interconnections between modern algebra and mathematical logic

Leon Henkin
<span title="1953-03-01">1953</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w3g32txdvneltemssag5nwfxcy" style="color: black;">Transactions of the American Mathematical Society</a> </i> &nbsp;
Mathematical logic originated when mathematical methods were brought to bear on traditional questions of logic, especially the problem of what constitutes a valid proof.  ...  This possibility is illustrated in the present paper, which presupposes no knowledge of mathematical logic.  ...  Mathematical logic originated when mathematical methods were brought to bear on traditional questions of logic, especially the problem of what constitutes a valid proof.  ... 
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Some Interconnections Between Modern Algebra and Mathematical Logic

Leon Henkin
<span title="">1953</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w3g32txdvneltemssag5nwfxcy" style="color: black;">Transactions of the American Mathematical Society</a> </i> &nbsp;
Mathematical logic originated when mathematical methods were brought to bear on traditional questions of logic, especially the problem of what constitutes a valid proof.  ...  This possibility is illustrated in the present paper, which presupposes no knowledge of mathematical logic. 1. Some concepts of logic.  ...  In the sequel we shall refer to this corollary as "our basic result from logic." 2. Applications to algebra.  ... 
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