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Arguments and Necessary and Sufficient Conditions

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    Matheson

    ARGUMENTS &NECESSARY ANDSUFFICIENTCONDITIONS

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    Project of Philoso h!

    here are t"o central rojects inhiloso h!#

    $%To analyze concepts. hat is free will ' hat "o(l) God *e li+e'

    ,% To evaluate arguments % Is this ar-(.ent that "e )on/t +no"

    an!thin- a -oo) ar-(.ent' Is this ar-(.ent that a*ortion is

    er.issi*le a -oo) ar-(.ent'

    e "ill loo+ at ho" to )o *oth to)a!%

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    Necessar! an) S(0cient con)itions 1

    is a necessary condition of *ein- a Y j(st in case nothin- can *e a Y"itho(t also *ein- an 1% 2ein- Cana)ian is a necessar! con)ition for 3otin- in a Cana)a national

    election%

    1is a sufcient condition for *ein- a Y j(st in case *ein- an 1 iseno(-h for *ein- a Y% 2ein- *orn in Cana)a is a s(0cient con)ition for *ein- a Cana)ian citi4en%

    1an) Y are individually necessary and jointly sufcient con)itionsfor *ein- a 5 j(st in case 1 an) Y are each necessar! con)itions for*ein- a 56 an) *ein- a 71 an) Y8 is a s(0cient con)ition for *ein- a 5%

    So.ethin- is a trian-le j(st in case it is a three9si)e) :-(re%

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    E3al(atin- Anal!ses of conce ts T

    he clai. ;1 is a trian-le j(st in case 1 is a three9si)e):-(re/ is correct j(st in case an! an) e3er! trian-le "o(l)*e a three9si)e) :-(re6 an) an! an) e3er! three9si)e):-(re "o(l) *e a trian-le%

    So6 to e3al(ate the anal!sis of a conce t !o( loo+ for aCOUNTERE1AMP(are j(st in case it is a fo(r9si)e) :-(re% So.ethin- is a *achelor j(st in case it is an (n.arrie)

    .ale%

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    hat is an Ar-(.ent'

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    Ar-(.ents

    rgument # a se>(ence of sentences "here so.e 7there.ises8 cite) in fa3or of another 7the concl(sion8%

    tandard Form: e "ill t! icall! e=a.ine ar-(.ent instan)ar) for. ? "here each line of the ar-(.ent is -i3en an(.*er6 an) the re.ises are )i3i)e) fro. the concl(sion"ith a line% 7analo-! "ith .ath ro*le.s8

    $% Philoso h! is the *est%,% If Philoso h! is the *est6 then this class roc+s%@% This class roc+s%

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    Goo) Ar-(.ents

    hat is the (r ose of an ar-(.ent' , co..on ans"ers# 7a8 to convince someone or 7*8

    to make the conclusion reasonable % These ans"ers are )istinct an) can co.e a art 7!o(

    can )o 7a8 "itho(t 7*86 an) !o( can )o 7*8 "itho(t 7a88% O(r foc(s "ill *e on 7*8%

    i3en that6 there are t"o -eneral "a!s that an ar-(.entcan -o *a)# 7$8 it/s concl(sion )oesn/t follo"6 or 7,8 ithas *a) re.ises%

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    ali)it!r-(.ents a3oi) the :rst error *! *ein- 3ali)%

    $% The rin-s of Sat(rn are *ri-ht this !ear%

    ,% There "ill *e ros erit! this !ear%

    n ar-(.ent is valid j(st in case it is i. ossi*le for it toha3e all tr(e re.ises an) a false concl(sion 7if the

    re.ises "ere all tr(e6 the concl(sion "o(l) *e tr(e8

    n ar-(.ent is invalid j(st in case it is not 3ali)%

    $% The rin-s of Sat(rn are *ri-ht this !ear%

    ,% If the rin-s of Sat(rn are *ri-ht this !ear6 thenthere "ill *e ros erit! this !ear%

    ,% There "ill *e ros erit! this !ear%

    ali) ar-(.ents can still *e >(ite *a) since 3ali)it! )eals

    onl! "ith its lo-ical for.% e r(le o(t both errors "ithso(n) ar-(.ents%

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    So(n)ness An ar-(.ent is sound j(st incase it is 3ali) an) all of its

    re.ises are tr(e% An ar-(.ent is unsound j(st incase it is not so(n)%

    Sound Arguments must havea true conclusion.

    So(n) ar-(.ents are 3ali) alltr(e re.ises -(arantees a tr(econcl(sion%

    So(n) ar-(.ents ha3e all tr(ere.ises%

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    Co..on Si. le ali) Ar-(.ents

    ODUS PONENS

    $% If P then % ,% P @% So6 %

    No .atter "hat ro ositions

    !o( (t in for ;P/ an) ; /6!o( cannot ha3e all tr(e

    re.ises an) a falseconcl(sion%

    ODUS TO

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    Ar-(.ent E= lanation

    o explain an ar-(.ent fro. the te=t#

    De:ne all technical terms that a ear in the ar-(.ent% Gi3e reasons to thin+ that each re.ise 7not s(*9concl(sions

    or concl(sion8 is tr(e% The te=t "ill often ro3i)e thesereasons6 or !o( .a! nee) to co.e ( "ith "h! a reasona*le

    erson .i-ht acce t each re.ise% Sell each re.ise7ar-(.ent sales erson8%

    For each s(*9concl(sion an) concl(sion6 e= lain ho" the! are-(arantee) to *e tr(e if the re.ises "hich s( ort the. aretr(e 7*! sho"in- ho" the! are a concl(sion of a 3ali) si. lear-(.ent8% If !o( can6 state "hich +in) of 3ali) si. lear-(.ent%

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    Ar-(.ent E3al(ation T

    o evaluate an ar-(.ent fro. the te=t#

    State "hether the ar-(.ent 3ali) 7for co. le= ar-(.ents6 state"hether e3er! si. le ar-(.ent it is co. ose) of is 3ali)8% Na.e the3ali) for. if !o( can%

    State "hether the co. le= ar-(.ent is so(n) 7"hether all its

    re.ises are tr(e6 if it is 3ali)8% If

    the ar-(.ent is not so(n)6 or it has a contro3ersial re.ise6 oint o(tthis premise an) critici4e it% 7!o( cannot si. l! critici4e a s(*9concl(sion or concl(sion8 If !o( thin+ it is so(n)6 )efen) this re.ise a-ainst the reasona*le criti>(e !o(

    ha3e raise)% If !o( thin+ it is (nso(n)6 state ho" !o( thin+ the a(thor .i-ht res on) to !o(r

    criti>(e%

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    Practice

    % If the a-(ars "in the AFC So(th this !ear6 then the! "ill.a+e the la!o s this !ear%

    % The a-(ars "ill "in the AFC So(th this !ear%

    % The a-(ars "ill .a+e the la!o s this !ear%

    E= lain% E3al(ate%

    ali)' So(n)'

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    Necessar! Con)itions

    $% 2ein- ali3e is a necessar! con)ition of *ein-h(.an%

    9 False

    ,% 2ein- .a)e of o(r is a necessar! con)ition of*ein- *rea)%9 False

    @% 2ein- o3er H feet tall is a necessar! con)ition of*ein- an N2A la!er%

    9 FalseH% 2ein- a .ale is a necessar! con)ition of *ein- a*rother%

    9 Tr(e

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    S(0cient Con)itions

    $% 2ein- feet tall is a s(0cient con)ition forla!in- in the N2A%

    9 False,% 2ein- a .ale si*lin- is a s(0cient con)ition for*ein- a *rother% 9 Tr(e@% 2ein- .a)e of -lass is a s(0cient con)ition for*ein- fra-ile%

    9 FalseH% Ja3in- a st()ent ID is a s(0cient con)ition for*ein- a st()ent%

    9 False

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    Ar-(.ent $

    $% If Socrates is a .an6 then Socrates is .ortal%

    ,% Socrates is a .an% KKKKKKKKKKKKKKKKKKKKKKKKK @% Therefore6 Socrates is .ortal%

    A

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    Ar-(.ent ,

    $% If Geor-e 2(sh is the resi)ent6 then the resi)ent isfro. Te=as%

    ,% The resi)ent is fro. Te=as% KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK @% Therefore6 Geor-e 2(sh is resi)ent%

    IN A

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    Ar-(.ent H

    % If -rass is re)6 then i-s can !%

    % Grass is re)% KKKKKKKKKKKKKKKKKKKKKKKKKKKK

    % Therefore6 i-s can !%

    A


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