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Eduction and Infe

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What is inference?

It is the way by which the mindacquires new knowledge from aset of facts that is already known

The knowledge gained frominference is called insight and itis arrived at by way of judgment

To judge is to arm whateveris true, and truth is arrived atwhen we infer from a set of

known facts

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Judgment is rendered when themind sees new information

Inference, thus, is a result of theminds way of connecting a new

set of data with a !reviouslyknown truth"Inference is either mediate or imme

There are two ty!es of immediateinference# EDUCTION and

OPPOSITION

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Immediate inference - springs directly from asingle premise to a conclusion without the mediationof any other premise.

e.g. No saint is a sinner.

No sinner is a saint.

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Mediate inference derivation of a conclusionfrom at least two identified related facts as premises.

e. g. All men of integrity are not morally offensive.

But all morally offensive people are enviouspeople.

Hence, a number of envious people are not menof integrity.

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$s forms of immediate inference,they allow the human mind to derivesome meaning from a given!ro!osition said to be im!lied in the

formerIt e%!resses not a new truth orfact but sim!ly shows by way of a

new !ro!osition a meaningalready im!lied in the given!ro!osition

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EDUCTIONEDUCTION

It is a !rocess of creating a new!ro!osition from a given !ro!ositionby interchanging the subject and the

!redicate of the given !ro!ositionand&or the use or removal ofnegatives

$lso called as equipollence, or givingequal value, it is the method of statingthe same truth in another way

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Types of EductionTypes of Eduction

1.1. ConversionConversion' it deals with thecreation of a new !ro!osition byinterchanging the subject and

!redicate of a given !ro!osition butleaving its quality unchanged"(e)!hrases the truth of a given!ro!osition called convertendconvertend by

interchanging the subject and the!redicate, without over)e%tending thequality of either of them" The resulting

statement is called converse"

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Method:Method:

$" Interchange subject (S)subject (S) andpredicte (!) without over)e%tending their quality" *ver)e%tension is the mirror of taking a

!articular term as a universal term"To avoid this mistake, determine +rstthe res!ective e%tension of subject

and !redicate before interchangingtheir !osition in the sentence"

" (etain the "u#it$of the copu#ofthe convertend, that is, thearmative remains armative, or

the negative remains negative"

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The given !ro!osition is called the

convertendconvertendwhile the new !ro!osition

is called the converseconverse"

-%am!les#Convertend# .o man is in+nite" /0u

1 2!3Converse .o in+nite being is a

man" /0u 1 2!3

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-%am!le#Convertend -very man is an animal"

Converse 0ome animals are men" /The universal subject !Every man"ofthe convertend becomes a particularterm when it becomes the !redicate ofthe converse which is an armativeand because the convertendis ana#rmative, the !redicate !animal" is a

particular term and remains so, asindicated by the quanti+er 4some5 when itbecomes the subject)term of the converse"

This shows how the $ is convertin% to I

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Convertend $ll birds arenotchines" /0e ' 2u3Converse $ll machines arenot birds"

)2u3In the e%am!le above, theconvertend being a negative -!ro!osition, the su&'ectand thepredicate are both universal terms6ence, interchanging their !osition

in the converse does not alter theirres!ective e%tension"Thus, the - !ro!osition converts to

- !ro!osition"

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T$pes of Conversion%& Si'p#e Conversion !reserves the

quantity of the convertend to converse"This is only !ossible with the!ro!ositions - and I since these

!ro!ositions both subject /03 and!redicate /23 have the same quantity ore%tension" Thus, - converts to - and Iconverts to I as in these e%am!les#E(ample of E)E

convert

E $ do% is not acat.

$ cat is not a do%.* *

E(ample of I)I

convert

I Some men areteac+ers.

Some teac+ers are

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& !rti# or ccident# conversion has thequantity of the converse di7erent from thatof the convertend, such as the conversion of

$ !ro!osition to I !ro!osition#

$ ) I Every student is dili%ent.Some dili%ent are students.

Sa , Pp ) Si , Pp8onversion is not a!!licable to the *!ro!osition since this would result to over)e%tension when its !articular subject /0o3

becomes a universal term as the !redicate /2u3of a negative !ro!osition, as shown#

0ome students are not diligent )

particular)

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:" Obversion' re!hrases the truth of agiven !ro!osition called overtend, by

changing the quality of the co!ula andthat of the !redicate" The resulting!ro!osition is called obverse" ;ollowthese ste!s#

" astly, use the contradictory of the

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This method a!!lies to all four categorical!ro!ositions" $ obverts toE and vice versa"I obverts to Oand vice versa" -ither whichway the truth e%!ressed remains the same"

-a$)E O&vertend -very man is rational"Sa , Pu

O&verse -very man is not irrational"Se / Pu

-& E)$ O&vertend -very chemical is notsafe" Se / Pu

O&verse -very chemical is unsafe"Sa , Pu

-c I)O O&vertend 0ome fruits are green"

Si , Pp O&verse 0ome fruits are not non)

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Give the obversion of the following:

1. None of the boys is absent. se !u

All of the boys is present. sa"!p

#. $ome boo%s are novel. si"!p

$ome boo%s are not nonnovel . so!p&. $ome flowers are not red. so!p

$ome flowers are nonred. si"!p

'. (very creature is mortal. sa"pu

(very creature is not immortal. sepu

). $ome candies are not sweet. sopp

$ome candies are nonsweet. si"pp

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*. $ome + programs are funny. $i"!p$ome + programs are not non funny. $o!p

-. (very product is priced. $a"!u.

(very product is not unpriced. $e!u

. No bird is cat. $epuAll bird are not non cat . $a"pu

/. $ome toys are not mechanical. $opp

$ome toys are nonmechanical. $i"pp

10. $ome ilipinos are authors. $i"!p

$ome ilipinos are not non authors. $o !p

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& Contrposition ' re!hrases thetruth of a given !ro!osition called

contrponend by combining the!rocedures of obversion and conversion"The resulting !ro!osition is called

contrposit" 8ontra!osition may eitherbe !artial or com!lete"

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This method contra!oses $ to -, - to I, and * toI" 6owever, the I !ro!osition cannot becontra!osed because it obverts to * and *

cannot be converted# -%am!les#/a3 $9-#

8ontra!onend# $ll men are rational" 0a 1 2u*bverse# .o man is irrational" 0e ' 2u8ontra!osit# .o irrational is man" 0e '

2u/b3 -9I#

8ontra!onend# .o crime is tolerable" 0e ' 2u

*bverse# $ll crimes are intolerable" 0a 12u

8ontra!osit# 0ome intolerable are crimes"0i 12!

/e3 *9I#

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3. Complete contraposition makes it!ossible to change $ to $, - to *, and * to

*" ;ollow these ste!s#/3 *bvert the converse"

-a$)$-$ctivity Complete t+e sym&olic

presentation

8ontra!onend# -very T)re% is e%tinct" Sa , Pu*bverse# -very T)re% is not a non)e%tinct

creature"

8onverse# -very non)e%tinct creature is not aT)re%""

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-& E)O8ontra!onend# $ dog is not a cat"*bverse# -very dog is non)cat"8onverse# 0ome non)cats are dogs"8ontra!osit# 0ome non)cats are

non)dogs"-c O)O8ontra!onend# 0ome students are not

scholars"

*bverse# 0ome students are non)scholars"

8onverse# 0ome non)scholars arestudents"

*bverse# 0ome non)scholars are

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.ote that in contraposition, thecontraposithas a su&'ectthat serves as

the contradictoryof the predicateof thegiven !ro!osition" Thus the original!redicate 4e%tinct5 is transformed into itscontradictory 4non)e%tinct5 and becomesthe subject of the contra!osit"$n I proposition does not have anycontra!osit"

0ince the +rst ste! in contra!osition isobversion, obverting an I propositionyields an O proposition, however, youcan not convert an * !ro!ositionThe rocess of contra osition cannot be

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2ontrapose the following propositions

1. (very p is a non3. sa"pu

(very p is not a 3 4 sepu

(very 3 is not a p 4 sepu

#. (very nonp is a non3. sa"pu(very nonp is not a 3. sepu

(very 3 is not a nonp. sepu

&. All dinosaurs are e5tinct. sa"pu

All dinosaurs are not none5tinct. $epu

All none5tinct are not dinosaurs. $epu

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'.$ome stones are billions of years old .$i"!p

).$ome A! planes are not combat. $opp

$ome A! planes are noncombat. $i"pp

$ome noncombat are A! planes. $i"pp

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*& Inversion re!hrases a given!ro!osition called invertend resultingto its inverse"Thisis done through aseries of conversion and obversion"

Inversion can only be a!!lied to$ and E

propositions I and O propositions cannotbe inverted

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Invertin% $ to O and E to Ipropositions

Invertin% an $ proposition follo4st+ese steps

O&version*conversion*o&version*

conversion*o&version or -O*C*O*C*O-%am!le#

!Every 5 is a 6" is o&vertedto !Every

5 is not a non*60" convertedto !Everynon*6 is not an 50" o&verted to !Everynon*6 is a non*50" convertedto !Some

non*5 is a non*60" and lastly, o&verted! "

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Invertin% an E proposition follo4st+ese steps conversion)obversion)

conversion)obversionor /8)*)8)*3

-%am!le#

!No man is immortal"is convertedto !No immortal &ein% is a man0"o&vertedto !Every immortal &ein%is a non*man0" converted to !Somenon*man is an immortal &ein%" andlastly, o&vertedto !Some non*man is

not a mortal &ein%."

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$ctivity Complete t+e follo4in

Conversion# 8onvert of the following

!ro!ositions#".o kid is a wi@ard"A"0ome beings are unreal"

B"Whatever is true is of greatvalue"C"0ome engineers are

;ili!inos"D";lorence is a nurse"

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O&version# *bvert the following !ro!osi

" ove is not a thing"A" 0ome moments are

irrelevant"

B" 0ome o!inions areoutdated"

C" $ll non)! is not a non)q"

D" 0ome games are violent"

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Contraposition# 8ontra!ose the following!ro!ositions

" 0ome $;2 !lanes are not combat"

A" ;ree s!eech is loved by the masses"B" 0ome !rovince is rich in natural resourC" 0ome athletes are women"

D" -very crime is !unishable"E" $ll !oems are meaningful"

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Inversion# Invert the following !ro!ositi

" .o man is beyond the laws of !hysic

A" .o man is eternal"B" -very s!irit is not material"C" -very non)! is not a non)q"

D" -very human being is free"E" .o !erson is non)rational"

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