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Running Head The World is all that is the case h t t p / / w w w . h u m a n i t i e s - e b o o k s . c o . u k Philosophy Insights General Editor: Mark Addis For advice on use of this ebook please scroll to page 2 ‘What makes an argument valid?’ Formal Logic Mark Jago Publication Data © Mark Jago, 2007Te Author has asserted his right to be identifed as the author o this Work in accord-ance with the Copyright, Designs and Patents Act 1988.Published by Humanities-Ebooks.co.uk irril Hall, irril, Penrith CA10 2JE Reading Options Beore continuing, please use the command ‘View > ft to page’ and then progressby using the ‘next page’ arrows at the top or bottom right o the Viewer screen.o navigate through the contents use the ‘Bookmarks’ at the let o the screen.o search, click on the search symbol in the toolbar and select ‘show all results’.For ease o reading, use <CRL+L> to enlarge the page to ull screenUse <CRL+L> to return to the ull menu, with its bookmarks and search tool.Hyperlinks (i any) appear in Blue Underlined ext. ****** Licence and permissions Tis book is licensed or a particular computer or computers. Te fle itsel may be cop-ied, but the copy will not open until the new user obtains a licence rom the Humani-ties-Ebooks website in the usual manner. Te srcinal purchaser may license the same work or a second computer by applying to
[email protected] withproo o purchase.Permissions: it is permissible to print one (watermarked) copy o the book or your ownuse, but not to copy and paste text. ISBN 978-1-84760-041-7 Formal Logic Mark Jago Bibliographical Entry: Jago, Mark. Formal Logic . Philosophy Insights. Tirril: Humanities-Ebooks, 2007 A Note on the Author Mark Jago is a lecturer in the Department o Philosophy at the University o Notting-ham, UK and a Junior Research Associate in the Research Group on the Philosophy o Inormation at the University o Oxord. He wrote the Wittgenstein guide in thePhilosophy Insights series and has published articles on truth, belie, logic, ction andinormation.Personal website:http://www.nottingham.ac.uk/philosophy/staf/mark-jago.htm. Philosophy Insights: Formal Logic 5 Contents Introduction71 Logical Reasoning9 1.1 Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Valid Arguments. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Valid Forms of Inference. . . . . . . . . . . . . . . . . . . . . . . . 12Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Propositional Logic16 2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Logical Connectives. . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 The Logical Language. . . . . . . . . . . . . . . . . . . . . . . . . 202.4 Construction Trees. . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5 Truth Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.6 Valuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Entailment and Equivalence32 3.1 Logical Entailment. . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Equivalence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.3 Equivalence Schemes. . . . . . . . . . . . . . . . . . . . . . . . . . 36Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4 Proof Trees41 4.1 Proofs in Logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 The Proof Tree Method. . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Examples of Proof Trees. . . . . . . . . . . . . . . . . . . . . . . . 444.4 Decidability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.5 Valuations From Open Finished Trees. . . . . . . . . . . . . . . . . 464.6 Soundness and Completeness. . . . . . . . . . . . . . . . . . . . . . 48Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
