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Introduction to Logic

by: Eva Bosco

Introduction to Logic PHIL 201

Eva Bosco
GPA 3.54

George Knight

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George Knight
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This 2 page Class Notes was uploaded by Eva Bosco on Saturday October 3, 2015. The Class Notes belongs to PHIL 201 at Boise State University taught by George Knight in Fall. Since its upload, it has received 9 views. For similar materials see /class/218027/phil-201-boise-state-university in PHIL-Philosophy at Boise State University.


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Date Created: 10/03/15
Philosophy 103 Introduction to Logic The Language of Symbolic Logic Abstract Conventions for translating ordinary language statements into symbolic notation are outlined I We are going to set up an arti cial quotlanguagequot to avoid the dif culties of vagueness equivocation amphiboly and confusion from emotive signi cance A The rst thing we are going to do is to learn the elements of this quotnew languagequot B The second is to learn to translate ordinary language grammar into symbolic notation C The third thing is to consider arguments in this quotnew languagequot 11 Symbolic logic is by far the simplest kind of logiciit is a great timesaver in argumentation Additionally it helps prevent logical confusion when dealing with complex arguments The modern development of symbolic logic begin with George Boole in the 19th century A Symbolic logic can be thought of as a simple and exible shorthand LA 111 Consider the symbols 13 Sq q 30 31 Dr This rule was well known to the Stoics but they expressed it this way quotIf if the rst then the second and if the second then the third then if the rst then the thirdquot We will nd that all of the essential manipulations in symbolic logic are about as complex and working with numbers made up on ones and zeros We begin with the simplest part of propositional logic combining simple propositions into compound propositions and determining the truth value of the resulting compounds Propositions can be thought of as the quotatomsquot of propositional logic 1 Simple propositions are statements which cannot be broken down without a loss in meaning E g quotJohn and Charles are brothersquot cannot be broken down without a change in the meaning of the statement Note the change in meaning from quotJohn and Charles are brothersquot to the mistranslation quotJohn is a brotherquot and quotCharles is a brotherquot Fquot On the other hand quotJohn and Charles work diligently can be broken down without a change in meaning quotJohn works diligentlyquot quotCharles works diligentlyquot It is assumed contextually that the meaning of the original statement is not that John and Charles work diligently together Conventionally capital letters usually towards the beginning of the alphabet may be used as abbreViations for propositions Eg quotJohn and Charles are brothersquot can be symbolized as B and quotJohn and Charles work diligentlyquot can be symbolized as the two statements J and C The logical operator quotandquot as we will see will be symbolized in these notes as o although other symbols are often used elsewhere In addition to propositions propositional logic uses operators on propositions Propositions can be thought of like the sticks of a tinkertoy set Operators are like the connecting blocks Typical operators include quotandquot quotorquot and quotimpliesquot By adding more and more operators we get more compleX structures For evaluation of statements there is only one condition to be lea1ned quotIn order to knowtlie trutli value of tlie proposition Wliicli results from applying an opera tor to propositions all tliatneed be known is tlie definition oft1e opera tor and tlie trutli value oft1e propositions usedquot


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