8 Rules of Syllogism - Arguments and Validity - PHILO-notes Whiteboard Edition

what is an argument and how do we determine its validity an argument consists of two or more propositions offered as evidence for another proposition in logic and critical thinking the propositions that are offered as evidence in the argument are called the premises while the proposition for which the evidence is offered is called the conclusion thus when one gives an argument one is providing a set of premises as reasons for accepting his or her conclusion it is important to note that when one gives an argument one does not necessarily attacks or criticizes the other in this way an argument can also be viewed as a support of someone's viewpoint now arguments can either be inductive or deductive on the one hand an inductive argument is one in which it is claimed that if the premises are true then it is probable that the conclusion is true hence even if all the premises are true inductive argument or reasoning allows the conclusion to be false it is also important to note that inductive arguments go from the specific or particular to the general in other words inductive arguments make broad generalizations from specific observations let's consider this example 90% of the mungo seeds germinate in day one and in day two 90% of the [ __ ] seeds germinate therefore 90% of the [ __ ] seeds germinate based in this example we can also say that inductive arguments are based on observations or experiments deductive arguments on the other hand is one in which it is claimed that if the premises are true then the conclusion is necessarily true and unlike inductive arguments deductive arguments proceed from the general to the particular thus a deductive argument or reasoning begins with a general statement or hypothesis and then examines the possibilities to reach a specific logical conclusion here is an example of a deductive argument anybody who kills a person is guilty of a felony Jim kills jack therefore Jim is guilty of a felony now that we already have a basic understanding of what arguments are let's talk about syllogisms syllogisms are arguments that consists of three propositions which are so related so that when the first two propositions that is the premises are posited as true the third proposition that is the conclusion must also be true in other words a syllogism is an argument arranged in a specific manner in such a way that it contains a major premise minor premise and a conclusion here is a classic example of a categorical syllogism all men are mortal Socrates is a man therefore Socrates is mortal now how do we determine the major premise minor premise and the conclusion the major premise is the premise that contains the major term while the minor premise is the premise that contains the minor term the conclusion is the third proposition whose meaning and truths are implied in the premises and how do we determine the major term minor term and the middle term the major term is the predicate of the conclusion while the minor term is the subject of the conclusion the middle term is the remaining term which does not and cannot appear in the conclusion looking back at the example then we know that the major term is mortal because it is the predicate of the conclusion and the minor term is Socrates because it is the subject of the conclusion the middle term is men or men because it is the remaining term and which does not appear in the conclusion as we can see the major term is in red color the minor term in blue and the middle term in purple now that we have presented the key concepts in arguments or syllogisms let us proceed to the determination of their validity logicians have formulated eight rules of syllogisms but of course they can be expanded to ten or reduce to six but let us follow what logicians commonly used that is the eight rules of syllogism it must be noted that all of the a thrills of syllogism must be met or satisfied for the argument or syllogism to be valid if at least one of the eight rules of syllogism is violated then the argument or syllogism is invalid here are the eighth rules of syllogism one there should only be three terms in the syllogism namely the major term the minor term and the middle term and the meaning of the middle term in the first premise should not be changed in the second premise otherwise the syllogism will have four terms to the major and the minor terms should only be universal in the conclusion if they are universal in the premises in other words if the major and the minor terms are universal in the conclusion then they must also be universal in the premises for the argument to be valid hence if the major and minor terms are particular in the conclusion then rule number two is not applicable three the middle term must be universal at least once or at least one of the middle terms must be universal for if the premises are affirmative then the conclusion must be affirmative five if one premise is affirmative and the other negative then the conclusion must be negative six the argument is invalid whenever the premises are both negative this is because we cannot draw a valid conclusion from two negative premises seven one premise at least must be Universal and eight if one premise is particular then the conclusion must be particular now let us examine some example of arguments and apply the eight rules of syllogisms to determine their validity let us color the terms to avoid confusion so let us assign the color red for the major term blue for the minor term and purple for the middle term rule number one of the eighth rules of syllogism States there should only be three terms in the syllogism mainly the major term the minor term and the middle term let us validate this example all stars are heavenly bodies Angelina Jolie is a star therefore Angelina Jolie is a heavenly body if we analyze this syllogism it would appear that the argument is invalid because it violates rule number one as we can see the syllogism now contains four terms because the meaning of the middle term stars in the first premise is changed in the second premise the term stars in the first premise refers to astronomic all bodies or objects while the term star in the second premise refers to celebrities let us consider another example every police officer is brave Mike is a police officer therefore Mike is brave as we can see this syllogism contains only three terms hence this syllogism is valid in the context of rule number one rule number two of the eighth rules of syllogism states the major and the minor terms should only be universal in the conclusion if they are universal in the premises example every philosopher is brilliant but no terrorist is a philosopher therefore no terrorist is brilliant before we proceed in determining the validity of this argument in the context of rule number two let me emphasize the importance of a basic knowledge about terms and propositions especially their quantity and quality for an easier analysis and application of the rule since Allah jism in determining the validity of arguments so check out our separate discussion on terms and propositions link is on the card on the upper right corner on your screen now let's continue as we can see the minor term terrorists in the conclusion is universal because of the universal signifier no and since the minor term terrorists in the second premise is universal because of the universal signifier no then the syllogism does not violate rule number two in the context of the minor term however the major term brilliant in the conclusion is universal because the proposition is negative as we already know the predicate terms of all negative propositions are universal but if we look at the major term in the first premise it is particular because as we already know the predicate terms of all affirmative propositions are particular in the end this syllogism is invalid because it violates rule number two this is what logicians call the fallacy of illicit major let us consider another example all artists are creative however all artists are weird people therefore all weird people are creative because the major term creative in the conclusion is particular as it is a predicate term of an affirmative preposition then it does not violate rule number two because the rule is not applicable here as we can see rule number two is applicable only to universal minor and major terms but if we check the minor term weird people in the conclusion we learn that it is universal because of the universal signifier all since the minor term weird people is universal in the conclusion then it must also be universal in the second premise for the syllogism to be valid now we look at the minor term in the second premise it is particular because it is a predicate term of an affirmative proposition therefore in the end the syllogism is invalid because it violates rule number two this is what logicians call the fallacy of illicit minor let us consider a valid argument in the context of rule number two of the eight rules of syllogism no lawyers are liars Greg is a lawyer therefore Greg is not liar this syllogism is valid in the context of rule number two of the eighth rules of syllogism because rule number two is not violated as we can see the minor term Greg in the conclusion is particular hence rule number two is not applicable of course if a rule is not applicable then it cannot be violated and if no rule or law is violated then the argument is automatically valid now if we look at the major term liar in the conclusion it is the universal because it is a predicate term of a negative proposition but because the minor term liar is also universal in the first premise because again it is a predicate term of a negative preposition then this argument satisfies rule number two here's another example of a valid argument in the context of rule number two of the eight rules of syllogism some lunatic easily gets irritated but some insecure teachers easily get irritated therefore some insecure teachers are lunatic both the minor and major terms in the conclusion of this syllogism are particular for this reason rule number two of the eight rules of syllogism is not applicable hence the syllogism is automatically valid in the context of rule number two of the eight rules of syllogism rule number three of the eight rules of syllogism states the middle term must be universal at least once let's consider this example all beings are Li giving us mango seeds our beans therefore [ __ ] seeds are leguminous this syllogism is valid in the context of rule number three of the eight rules of syllogism because the middle term beings in the first premise is universal in fact rule number three of the eight rules of syllogism asks that at least one of the middle terms must be universal here's another example some lawyers are not studious marco is a lawyer therefore Marco is not studious as we can see both middle terms in the first and second premise are particular but because rule number three of the eight rules of syllogism asks that at least one of the middle terms must be universal then the syllogism is invalid rule number four of the eight rules of syllogism states if the premises are affirmative then the conclusion must be affirmative let's consider this all bodily beings are corporeal plants are bodily beings therefore plants are corporeal this syllogism is valid because it satisfies rule number four of the eight rules of syllogism as we can see both premises are affirmative and the conclusion is affirmative here's another example some students are lazy but some Asians are students therefore some Asians are not lazy this syllogism is invalid because it does not satisfy rule number four of the eight rules of syllogism as we can see both premises are affirmative but the conclusion is negative now rule number five of the eight rules of syllogism states if one premise is affirmative and the other negative then the conclusion must be negative example most Filipinos are Fiesta lovers Diego is not a Filipino therefore Diego is not a fiesta lover this syllogism is valid in the context of rule number five of the eight rules of syllogism as we can see the first premise is affirmative the second premise is negative and the conclusion is negative let's consider another example some students are cheaters but some students are not lazy therefore some cheaters are lazy now this syllogism is invalid in the context of rule number five of the H rules of syllogism as we can see the first premise is affirmative the second premise is negative but the conclusion is affirmative hence it violates rule number five of the H rules of syllogism rule number six of the eight rules of syllogism States the argument is invalid whenever the premises are both negative example no idiot is rational Kurt is not an idiot therefore Kurt is rational obviously this syllogism is invalid because both premises are negative rule number seven of the eight rules of syllogism states one premise at least must be universal example all rich individuals are hardworking but some fishermen are hardworking therefore some fishermen are rich individuals this syllogism is valid in the context of rule number seven of the eight rules of syllogism because it qualifies the rule as we can see the first premise is universal lastly rule number eight of the eight rules of syllogism states if one premise is particular then they conclude must be particular example some lawyers are professionals but no criminals are professionals therefore some criminals are lawyers the first premise of this syllogism is particular and the conclusion is particular to therefore this syllogism is valid in the context of rule number eight of the each rules of syllogism that's it for now thanks for visiting us today for another whiteboard discussion here at filo notes full transcript of this video is available at Fila notes calm and to keep you updated of our newest videos simply 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Keywords: Rules of Syllogism, Validity of Arguments, What Is an Argument, Premises, Conclusion, Inductive Argument, Deductive Argument, Types of Arguments, Syllogism, Major Premise, Minor Premise, Fallacy of Illicit Minor, Fallacy of Illicit Major, Valid Argument, Invalid Argument

Id: U4ig5uHOy4w

Length: 24min 27sec (1467 seconds)

Published: Sat Mar 16 2019