SYLLOGISM Greeks give the word “syllogism”, which means 'inference' or 'deduction'. Aristotle Aristotle introduced it. Now let us see how to solve syllogism by method.. PROPOSITION A proposition proposition is a sentence that makes a statement and gives a relation between two or more terms. n logic, any statement is termed a proposition.
!g " i# All windows are rods ii# No cloth is a bay iii# $ome students are members iv# $ome green are not white %he parts of proposition are given below. b elow. i# $ub&ect" A sub&ect is the part of the reposition about which something is being said. ii# redicate" redicate is the part of the proposition denoting, that which is affirmed or denied about the sub&ect. eg " n the proposition All novels are songs, something is being said about novels. $o novels are the sub&ect. $ongs is the predicate here because it affirmed about the sub&ect. CLASSIFICATION OF PROPOSITIONS CLASSIFICATION i# (nive (nivers rsal al pos posit itiv ivee propo proposi siti tion on"" A propo proposi siti tion on of of the the form form All $ are are is cal calle led d a universal positive proposition. A universal positive proposition is denoted by A. eg " All girls are disciplined. All bulbs are lions.
ii# (niversal negative proposition "A proposition proposition of the form No $ is is called a universal negative proposition. t is usually denoted by !. eg " No professors is la)y. No bo*es are baskets. iii# articular positive roposition " A proposition of the form $ome $ are is called a particular positive proposition. t is usually denoted by . eg " $ome boys are smarts. $ome boys are cats. iv# articular negative proposition " A proposition proposition of the form $ome $ are not is called particular negative proposition. t is denoted by the letter +. eg " $ome flowers are not grapes. g rapes.
$ome fans are not black. n syllogism, there are two types of inferences. # Mediate inference "-ere conclusion is drawn from two propositions. or e*ample, if you are given All cats are dogs and All dogs are animals, then a conclusion of the form All cats are animals could be drawn from it. /) Immediate inference : -ere conclusion is drawn from only one given proposition. or e*ample if a given statement is All gates are blue, then based on this a conclusion could be drawn that.. $ome blue are gates. %his is a case of immediate inference. %wo important cases of immediate inference is given below. a) Implications : f a given proposition is A 0 type, then it also implies that the 0 type conclusion must be true. 1et us verify it by considering the proposition, All elephants are big. %his statement naturally implies that the conclusion $ome elephants a re big must be true. $imilarly we can prove that an ! 0 type proposition also implies an + 0 type conclusion. ) Con!ersion %wo steps are to be followed in conversion. %he first step is to change the sub&ect as the predicate and the predicate as the sub&ect. %he second step is to change the type of the given proposition to the pattern given in the following table. %ype of the given %ype of the proposition. proposition after conversion A !! + 2annot be converted 1et us consider the statement $ome posters are good looking. %his can be converted by using the above table as $ome good looking are posters. n the same way, No books are pencils can be converted as No pencils are books. -33!N 4++$%+N 5ou may find it difficult to categorise some propositions of the form 4ahim is brilliant, !very man talks !nglish, Not a single student passed the e*am, No student e*cept rem was present, etc. 6e shall know, how to find the hidden propositions in such sentences. A 0 type hidden propositions " 7 All positive propositions beginning with 'each', 'every' and 'any'. 7 A positive sentence with a particular person as its sub&ect. 7 A positive sentence with a very definite e*ception.
eg " !ach of them plays football. -e should be awarded. All members e*cept 8avitha have a share of profit. ! 0 type hidden proposition 7 All negative sentences beginning with 'no one', 'none' and 'not a single' 7 A sentence with a particular person as its sub&ect but a negative sense. 7 A negative sentence with a very definite e*ception. 7 An interrogative sentence which is used to make an assertion. eg " None can escape from death. $wathi is not an A$ officer. No student e*cept $alim has attend the party. s there any person who can cheat himself 9 0 type hidden propositions " 7 ositive propositions beginning with words such as 'most', 'a few', 'mostly', 'generally', 'almost', :fre;uently', and ne gative propositions beginning with words such as 'few', 'seldom', :hardly', 'scarcely', 'rarely' and 'little'. 7 A positive sentence with an e*ception which is not definite.eg " 21($
proposition. $uch propositions can be reduced to A or ! or type. +nly brave men are pilots. %his sentence means that ?No coward man is a pilot? and ?All pilots are brave men?. SOL"TION OF SYLLOGISM #Y ANALYTICAL M$T%O& %here are two steps to be followed for solving syllogism by analytical method. A problem of syllogism consists of two propositions which have one common term. %his common term will be the predicate of the first proposition and the sub&ect of the second. f this condition is not satisfied in the given propositions, they should be aligned accordingly. eg " $tatement " All birds are trees. $ome trees are cows. -ere the common term is 'trees'. Also it satisfies the above said condition. -ence the $tatements are properly aligned. 1et us consider another e*ample. eg " $tatement " All pencils are bottles All bricks are pencils. -ere the common term is 'pencil'. @ut it does not satisfy the given condition. $o we have to align this pair. %his can be aligned easily by changing the order of the statements. %he aligned pair will be All bricks are pencils. All pencils are bottles. eg " $tatements " No watch is hat All pins are hats. n this pair, the common term is 'hat' and it is the predicate of both the sentences. $o we have to align the sentences by converting any of the sentences and changing the order if needed. After alignment, the above e*ample will become All pins are hats No hat is watch. 6hile aligning a given pair of statements, the priority should be given while converting, to 0 type statements to !0type statements and then to A 0 type statement, in that order. %hat is, the rule of !A should be followed. After aligning the given pair of statements, the conclusion can be easily drawn by using the following table.
$tatement $tatement 0 2onclusion ABACA AB!C! ! B A C +D ! B C +D BAC
B!C+ No definite conclusion can be drawn for other combinations like AB, +BA etc.. or the above given combinations which are aligned properly, the conclusion is a proposition whose sub&ect is the sub&ect of the first statement and whose predicate is the predicate of the second statements. %he common terms disappears. n the above table, +D implies that the conclusion is of type 0 +, whose sub&ect is the predicate of the second statement and the predicate of the conclusion is the sub&ect of the first statement. 0by 8+=A1 E!! +E-A..
