PHIL1005 Lecture Notes - Lecture 3: Logical Biconditional, Material Conditional, Active Voice

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20 Jun 2018
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L3.1%PROPOSITIONS:%COMPOUND%AND%ATOMIC%
!"#$%"&'%()#*)$"%+'(%(,)"%-./-0/123)(.$$"%(('#/))
Connectives%
4 56%)7'/-)'()-2'/8)0/-)6'()6%'")'()+'(('/8)90&#+'1)(&0&%+%/&(:)
4 56%)"0/(#+);'<<)1#+%)#")2#.");'<<)/%=%")>%)"%<%0(%-)
4 ?5#-02)'()not%+2)>'"&6-02@A)9It%is%not%the%case%that%&#-02)'()+2)>'"&6-02:)
4 ?If%B%"#)>%1#+%()%+$%"#"3)then%Rome%;'<<)*0<<@A)à)&;#)0&#+'1)(&0&%+%/&()
4 )
Propositions:%Atomic%and%Compound%
4 !"#$#('&'#/();'&6#.&)1#//%1&'=%()0"%)10<<%-)atomic'$"#$#('&'#/()
4 C&#+'1)$"#$#('&'#/()>#./-)&#8%&6%")>2)1#//%1&'=%()0"%)10<<%-)compound'#")complex'
$"#$#('&'#/(A))
4 D#+$#./-)0/-)0&#+'1)$"#$#('&'#/()0"%)&".&6)0$&A))
Truth-functionality%
4 56%)&".&6)#*)0)1#+$#./-)$"#$#('&'#/)'()-%&%"+'/%-)>2))
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Some%Notation%
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4 I)J)&".%3)K)J)*0<(%%
4 H"017%&()"%$"%(%/&)&6%)>#./-0"'%()#*)1#+$#./-)$"#$#('&'#/(%
Conjunction%(and)%%
4 L%&)M)(&0/-)*#")1#/N./1&'#/)
4 F56%)7'/-)'()-2'/8)and%6'()6%'")'()+'(('/8G)
4 C)M)H)
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Disjunction%(or)%
4 L%&)v'(&0/-)*#")-'(N./1&'#/)
4 56%)"0/(#+)+;'<<)1#+%)or%2#.);'<<)/%=%")>%)"%<%0(%-)
4 C)v'H))
Negation%(not)%
4 L%&)Q)(&0/-)*#")/%80&'#/%
4 ?5#-02)'()not%+2)>'"&6-02%
4 QC%
Material%Conditional%(if,%then)%
4 L%&)É)(&0/-)*#")+0&%"'0<)1#/-'&'#/0<)
4 ?If%B%"#)>%1#+%()%+$%"#"3)then%R#+%);'<<)*0<<@)
4 CÉH)
Biconditional%(If,%and%only%if)%
4 L%&)º)(&0/-)*#")>'41#/-'&'#/0<%
4 ?S'<<)'()0)('(&%"3)if,%and%only%if,%S'<<)'()0)*%+0<%)('><'/8@%
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Document Summary

The kind is dying and his heir is missing (atomic statements) The ransom will come or your will never be released. Today is not my birthday". (it is not the case that today is my birthday) Propositions without connectives are called atomic propositions. Atomic propositions bound together by connectives are called compound or complex propositions. Compound and atomic propositions are truth apt. The truth of a compound proposition is determined by. Truth value of its constituent atomic propositions and. The ransom will come or you will never be released. Capital (a,b,c) will stand for atomic propositions. Brackets represent the boundaries of compound propositions. The kind is dying and his heir is missing . From a&b two different atomic propositions. Truth of compound propositions (a&b) depends on truth of. 0 atomic propositions that make it up (whether a is true and whether b is true) The ransom mwill come or you will never be released.

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