Logic and Critical Thinking 007

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Logic & Critical Thinking {Reference Material} (Week No. 7 & on wards) 1

Fallacies

Concept :In our daily life we use verity of words to convey our message. But we still needs

some comprehensive supporting statements as well.A fallacy is counterfeit (fake, bogus) argument in support to conclusion, but infactdo not provide any support at all.

Definition1. A mistake in reasoning; an argument that fails to provide adequate logical

support for thetruth of its conclusion, yet appears convincing or persuasive insome other way. Common examples include both formal fallacies (structuralerrors in deductive logic) and informal fallacies (efforts to persuade by non-

rational appeals).2. An argument whose premises do not support its conclusion is one whose

conclusion could be false even if all its premises were true, in such case,reasoning is bad, and the argument is said to be fallacious.

3. Fallacy is the mistake arise commonly in ordinary discourse which in turndestroys the argument.

4. Fallacy as a type of argument that may seem to be correct, but that proves,on examination, not to be so.

Types

Fallacies of Relevance

Concept :

A type of argument which clearly fail to provide adequate reason for believing thetruth of their conclusions. Although they are often used in attempts to persuade

people by non-logical means.Definition

1. When an argument relies on premises that are not relevant to its conclusion,and that therefore cannot possibly establish its truth, the fallacy committedis on of relevance.

Lecturer : Arshad Zia Siddiqui E-mail [email protected]

.(M.Com, MCS, MA Economics)
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2. The conclusion is logically irrelevant to the premises, even if it ispsychologically or emotionally relevant. They key to spotting a fallacy ofrelevance is to distinguish genuine evidence from emotional appeal.

There are 5 types of Relevance Fallacies.

Appeal to Force

If someone "persuade" something by means of threats, without giving areason for thinking the proposition is true; by simply scaring to think, or atleast into saying, it is true.Definition1. A type of argument in which the reason to believe or follow the

recommendations of the arguer is to avoid harm or to gain some reward.It replaces REASON with FEAR or DESIRE.2. Trying to get someone to accept a proposition on the basis of a threat3. The fallacy need not involve actual physical force or violence. It is

committed whenever any sort of threat is used, and nonphysical threatsare probably more common than physical ones.

For example :Student said to examination incharge : "I deserve a good grade, wouldn'tyou agree? If you don't agree, I'm afraid about what might happen: I just

can't control hands here".Appeal to Emotion (Argumentum ad Populum)

This fallacy is the attempt to persuade someone of a conclusion by anappeal to emotion instead of evidence. A person who commits this fallacy ishoping that his listeners will adopt a belief on the basis of a feeling he hasinstilled in them--outrage, hostility, fear, pity, guilt, or whatever.DefinitionTrying to get someone to accept a proposition on the basis of an emotion it

induces.For example :Nobody have a common sense or believes that our President not politicianand truly an effective political leader. Therefore, the President is not aneffective leader.


mailto:[email protected]:[email protected]


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Appeal to PityTries to win acceptance by pointing out the unfortunate consequences thatwill otherwise fall upon the speaker and others, for whom we would thenfeel sorry.

DefinitionArguing for reason to believe; to avoid harming others, or conversely tocause them pleasure- at their request.In this form of the fallacy, REASON is replaced with PITY.(shame,crime,mercy)

For example :I am a single parent, solely responsible for the financial support of mychildren. If you give me this traffic ticket, I will lose my license and beunable to drive to work. If I cannot work, my children and I will become

homeless and may starve to death. Therefore, you should not give me thistraffic ticket.The conclusion may be false (that is, perhaps I should be given the ticket)even if the premises are all true, so the argument is fallacious.ORTrying to support a conclusion by evoking pity in the listener.I need to pass this class in order to graduate, if I don't graduate, myparents will kill me.Therefore, I should receive a passing grade in the class".

Appeal to Authority (Argumentum ad Verecundiam)Opinion of someone famous or accomplished in another area of expertise issupposed to guarantee the truth of a conclusion.DefinitionWhen appeal is made to parties having no legitimate claim to authority inthe matter at hand on the basis of :

(a) an expert in the field,(b) traditional wisdom,

(c) likeable figures (celebrities), or

(d) mass opinion.

For example :Mr. Pervez Chairman Agriculture Science Board believes that spiders are insects.Therefore, spiders are insects.




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Argument from IgnoranceSupposing that a proposition must be true because there is no proof that itis false.Definition

A proposition is true simply on the basis that it has not been proved false,or that it is false because it has not been proved true.

For example :No one has conclusively proven that there is no life on the moons ofJupiter. Therefore, there is life on the moons of Jupiter

Argument from Ad HominemThe fallacy of supposing that a proposition should be deniedbecause of

some disqualifying feature of the person who affirms (announce, verify) it.Definition1. Literary means against the person. A type of fallacy in which the

thrust is directed, not at a conclusion, but at person who asserts ordefends it.

2. This fallacy feeds off of the same psychological emotions that theappeal to authority does, but in this case the argument consists ofan attack on the person instead of the ideas or position they aredefending.

3. Attacking the source of an argument instead of the argument itself.4. Using a negative trait of a speaker as evidence that his statement isfalse or his argument is weak.

For example :Mr. Kamran sys that the legal month for annual examination should beDecember instead of March.But we all know that Mr. Kamran . . .. . . goes to his village at March or. . . never attends classes in winter or

. . . believes that the in winter we should restTherefore, the legal month for examination should be March instead ofDecember.

This fallacy can take one of three forms- Abusive- name calling: in this form the person attacks the character

of the person Mr. Javed calling Noman a Nomi, Chootoo.etc


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Circumstantial- guilt by association: this one surfaces in politicalcircles often- usually the opposition argument is characterized as`liberal' or `socialistic', etc.

The Ad Hominem Fallacy of Tu Quoque

Suppose that someone criticizes you for telling a white lie. If yourcritic is a infamous liar, you would probably be tempted to say, "Lookwho's talking!"This response is certainly understandable--no one enjoys beingcensured by a moral inferior--but it is fallacious.It's a species of ad hominemknown as the tu quoque("you're another")argument. The fact that someone else is guilty of blame doesn't provethat you are innocent. A related version of the ad hominem fallacyoccurs when we attack someone's position by claiming that it is

inconsistent with his or her practice or other positions

Appeal to Irrelevant ConclusionThe fallacy of the irrelevant conclusion tries to establish the truth of aproposition by offering an argument that actually provides support for anentirely different conclusionDefinitionProcess of defending the truth of a proposition by appeal to an argument

that is actually concerned with something elseFor example :1. Parents with large incomes can buy lots of things for their children.

Therefore, the children of wealthy parents are happy.2. All children requires attention from their parents. Parents who work

full-time cannot give attention to their children. Therefore, mothersshould not work full-time.(truth of a conclusion focussed on women alone and not on men)


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Fallacies of AmbiguityThe presence of two or more distinct meanings for a single word orexpression. In itself, ambiguity is a common, harmless, and often amusing(funny) feature of ordinary language. When unnoticed in the context of

otherwise careful reasoning leads to fallacy.DefinitionWhen the meaning of words or phrase may shift as a result of inattentionIt is called Fallacy of AmbiguityFor example :"I'll give you a ring tomorrow." could signify either the promise of a gift ofjewelry or merely an intention to telephone. If says to girl friend.

EquivocationAn equivocation trades upon the use of an ambiguous word or phrase in oneof its meanings in one of the propositions of an argument but also inanother of its meanings in a second proposition.For example :

Really exciting novels are rare.But rare books are expensive.Therefore, Really exciting novels are expensive.

Or

Where the conclusion of the argument depends on the fact that a word isbeing used in two different senses due too semantic ambiguity.For example :Everyone wants to do what is right. Therefore, you have the right to dowhat you want.

Amphiboly

Where the conclusion of the argument depends on the fact that a sentenceis syntactically ambiguous.

For example :Norris said he operates a small car repair shop. Therefore, you can't takeyour Corolla to him. This can be a real problem in legal documents.A sentence is syntactically ambiguous when the grammar of the sentenceallows for more than one interpretation of its meaning.Example: John attacked the man with a knife.


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Accent

The fallacy of accent arises from an ambiguity produced by a shift ofspoken or written emphasis.

For example :

"Joan said that she never wants to see another Demi Moore movie, sowe won't show her another one; we'll just play this same one over andover again."

Composition

The fallacy of composition involves an inference from the attribution of

some feature to every individual member of a class (or part of a greaterwhole) to the possession of the same feature by the entire class (orwhole).For example :

Every course I took in college was well-organized.Therefore, my college education was well-organized.

Division

Similarly, the fallacy of division involves an inference from the attributionof some feature to an entire class (or whole) to the possession of the samefeature by each of its individual members (or parts).For example :

Ocelots are now dying out. (name of sea animal)Sparky is an ocelot.Therefore, Sparky is now dying out

The essential point in the fallacy of division is that even when something

can be truly said of a whole class, it does not follow that the same can betruly said of each of its individual parts


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Comprehension Questions1. Identify the fallacy committed by the following argument. That is the best movieever. Why? Because I really liked it.

a) subjectivism b) appeal to majorityc) appeal to emotion d) appeal to force

2. Identify the fallacy committed by the following argument. This is the right way todo it because I am the boss.


3. Identify the fallacy committed by the following argument. One million computer

users can't be wrong.a) subjectivism b) appeal to majorityc) appeal to emotion d) appeal to force

4. Identify the fallacy committed by the following argument.It is easy to see that abortion using the new abortion pill is wrong. What could be

more horrible that munching donuts while you flush the remains of your fetus down the

toilet?


5. Identify the fallacy committed by the following argument.Dont criticize my country for having the KGB. Your country has the CIA.

a) appeal to authority b) tu quoque c) poisoning the well

6. Identify the fallacy committed by the following argument.Of course, the generals want a higher military budget. It's their jobs that are on the

line.a) appeal to authority b) tu quoque c) poisoning the well

7. Identify the fallacy committed by the following argument.




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Categorical Propositions

Now that we've taken notice of many of the difficulties that can be caused bysloppy use of ordinary language in argumentation, we're ready to begin the more

precise study of deductive reasoning. Here we'll achieve the greater precision byeliminating ambiguous words and phrases from ordinary language and carefullydefining those that remain. The basic strategy is to create a narrowly restrictedformal systeman artificial, rigidly structured logical language within which thevalidity of deductive arguments can be discerned with ease. Only after we'vebecome familiar with this limited range of cases will we consider to what extent ourordinary-language argumentation can be made to conform to its structure.

Our initial effort to pursue this strategy is the ancient but worthy method of

categorical logic. This approach was originally developed by Aristotle, codified ingreater detail by medieval logicians, and then interpreted mathematically by GeorgeBoole and John Venn in the nineteenth century. Respected by many generations ofphilosophers as the the chief embodiment of deductive reasoning, this logical systemcontinues to be useful in a broad range of ordinary circumstances.

Terms and Propositions

We'll start very simply, then work our way toward a higher level. The basic unit ofmeaning or content in our new deductive system is the categorical term. Usually

expressed grammatically as a noun or noun phrase, each categorical term designatesa class of things. Notice that these are (deliberately) very broad notions: acategorical term may designate any classwhether it's a natural species or merelyan arbitrary collectionof things of any variety, real or imaginary. Thus, "cows,""unicorns," "square circles," "philosophical concepts," "things weighing more than fifty kilograms,"and "times when the earth is nearer than 75 million miles from the sun," are all categoricalterms.

Notice also that each categorical term cleaves the world into exactly two mutually

exclusive and jointly exhaustive parts: those things to which the term applies andthose things to which it does not apply. For every class designated by a categoricalterm, there is another class, its complement, that includes everything excluded fromthe original class, and this complementary class can of course be designated by itsown categorical term. Thus, "cows" and "non-cows" are complementary classes, as are"things weighing more than fifty kilograms" and "things weighing fifty kilograms or less."


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Everything in the world (in fact, everything we can talk or think about) belongseither to the class designated by a categorical term or to its complement; nothing isomitted.

Now let's use these simple building blocks to assemble something more interesting.A categorical proposition joins together exactly two categorical terms and assertsthat some relationship holds between the classes they designate. (For our ownconvenience, we'll call the term that occurs first in each categorical proposition itssubject term and other its predicate term.) Thus, for example, "All cows are mammals"and "Some philosophy teachers are young mothers" are categorical propositions whosesubject terms are "cows" and "philosophy teachers" and whose predicate terms are"mammals" and "young mothers" respectively.

Each categorical proposition states that there is some logical relationship that holdsbetween its two terms. In this context, a categorical term is said to be distributedif that proposition provides some information about every member of the classdesignated by that term. Thus, in our first example above, "cows" is distributedbecause the proposition in which it occurs affirms that each and every cow is also amammal, but "mammals" is undistributed because the proposition does not stateanything about each and every member of that class. In the second example, neitherof the terms is distributed, since this proposition tells us only that the two classesoverlap to some (unstated) extent.

Quality and Quantity

Since we can always invent new categorical terms and consider the possiblerelationship of the classes they designate, there are indefinitely many differentindividual categorical propositions. But if we disregard the content of thesepropositions, what classes of things they're about, and concentrate on their form,the general manner in which they conjoin their subject and predicate terms, then weneed only four distinct kinds of categorical proposition, distinguished from eachother only by their quality and quantity, in order to assert anything we like about the

relationship between two classes.

The quality of a categorical proposition indicates the nature of the relationship itaffirms between its subject and predicate terms: it is an affirmative proposition ifit states that the class designated by its subject term is included, either as a wholeor only in part, within the class designated by its predicate term, and it is a negative


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proposition if it wholly or partially excludes members of the subject class from thepredicate class. Notice that the predicate term is distributed in every negativeproposition but undistributed in all affirmative propositions.

The quantity of a categorical proposition, on the other hand, is a measure of thedegree to which the relationship between its subject and predicate terms holds: it isa universal proposition if the asserted inclusion or exclusion holds for every memberof the class designated by its subject term, and it is a particular proposition if itmerely asserts that the relationship holds for one or more members of the subjectclass. Thus, you'll see that the subject term is distributed in all universalpropositions but undistributed in every particular proposition.

Combining these two distinctions and representing the subject and predicate terms

respectively by the letters "S" and "P," we can uniquely identify the four possibleforms of categorical proposition:

A universal affirmative proposition (to which, following the practice ofmedieval logicians, we will refer by the letter "A") is of the form

All S are P.

Such a proposition asserts that every member of the class designated by the

subject term is also included in the class designated by the predicate term.Thus, it

distributes its subject term but not its predicate term.

A universal negative proposition (or "E") is of the form

No S are P.

This proposition asserts that nothing is a member both of the class

designated bythe subject term and of the class designated by the predicate terms. Since itreports that every member of each class is excluded from the other, thisproposition distributes both its subject term and its predicate term.

A particular affirmative proposition ("I") is of the form


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Some S are P.

A proposition of this form asserts that there is at least one thing which is a

member both of the class designated by the subject term and of the classdesignated by the predicate term. Both terms are undistributed inpropositions of this form.

Finally, a particular negative proposition ("O") is of the form

Some S are not P.

Such a proposition asserts that there is at least one thing which is a member of theclass designated by the subject term but not a member of the class designated by

the predicate term. Since it affirms that the one or more crucial things that theyare distinct from each and every member of the predicate class, a proposition ofthis form distributes its predicate term but not its subject term.

Although the specific content of any actual categorical proposition depends upon thecategorical terms which occur as its subject and predicate, the logical form of thecategorical proposition must always be one of these four types.

The Square of Opposition

When two categorical propositions are of different forms but share exactly thesame subject and predicate terms, their truth is logically interdependent in a varietyof interesting ways, all of which are conveniently represented in the traditional"square of opposition."

"All S are P." (A)- - - - - - -(E) "No S are P."| * * |

* *

| * * |

*

| * * |* *

| * * |

"Some S are P." (I)--- --- ---(O) "Some S are not P."

Propositions that appear diagonally across from each other in this diagram (A and Oon the one hand and E and I on the other) are contradictories. No matter what their


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subject and predicate terms happen to be (so long as they are the same in both) andno matter how the classes they designate happen to be related to each other in fact,one of the propositions in each contradictory pair must be true and the other false.Thus, for example, "No squirrels are predators" and "Some squirrels are predators" are

contradictories because either the classes designated by the terms "squirrel" and"predator" have at least one common member (in which case the I proposition is trueand the E proposition is false) or they do not (in which case the E is true and the I isfalse). In exactly the same sense, the A and O propositions, "All senators are politicians"and "Some senators are not politicians" are also contradictories.

The universal propositions that appear across from each other at the top of thesquare (A and E) are contraries. Assuming that there is at least one member of theclass designated by their shared subject term, it is impossible for both of these

propositions to be true, although both could be false. Thus, for example, "All flowersare colorful objects" and "No flowers are colorful objects" are contraries: if there are anyflowers, then either all of them are colorful (making the A true and the E false) ornone of them are (making the E true and the A false) or some of them are colorfuland some are not (making both the A and the E false).

Particular propositions across from each other at the bottom of the square (I andO), on the other hand, are the subcontraries. Again assuming that the classdesignated by their subject term has at least one member, it is impossible for bothof these propositions to be false, but possible for both to be true. " Some logicians areprofessors" and "Some logicians are not professors" are subcontraries, for example, since ifthere any logicians, then either at least one of them is a professor (making the Iproposition true) or at least one is not a professor (making the O true) or some areand some are not professors (making both the I and the O true).

Finally, the universal and particular propositions on either side of the square ofopposition (A and I on the one left and E and O on the right) exhibit a relationshipknown as subalternation. Provided that there is at least one member of the classdesignated by the subject term they have in common, it is impossible for the

universal proposition of either quality to be true while the particular proposition ofthe same quality is false. Thus, for example, if it is universally true that "All sheep areruminants", then it must also hold for each particular case, so that "Some sheep areruminants" is true, and if "Some sheep are ruminants" is false, then "All sheep are ruminants"must also be false, always on the assumption that there is at least one sheep. Thesame relationships hold for corresponding E and O propositions.


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CATEGORICAL PROPOSITIONS (2nd Options)

We make claims about certain classes or categories and their relations. These claimsilluminate the structure of thought. There are certain rules with a precise structure

that enable us to tell if an argument is valid or not.A proposition is a sentence that is either true of false. A proposition is a categoricalproposition when it states or express a relationship between categories.

Propositions can be in standard and non-standard form. If you are a proposition instandard form, you will be expressed in one of the A,E,I,O forms (more on thatlater).

Standard categorical form is a form that propositions can be in or out of.

Propositions that are in this form have the following:

Quantifiers: all, no, some

Subject terms: s

Copula: the very linking the subject and predicate terms.

Predicate term: P

For example:




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The Four Kinds of Categorical Propositions A,E,I,O:

Letter Name Quantity Quality

A universal affirmative

E universal negative

I particular affirmative

O particular negative

A, E, I, O propositions are pictured by the following Venn diagrams:

THE TRADITIONAL SQUARE OF OPPOSITION




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At least one must be true. Both are not false, but both could be true.

Aristotelian Principles:

1) If one knows that A or E are true, then we can infer the value of every other

claim or proposition.

2) If one knows that I or O is false, then we can infer the value of every other claim

or proposition.

If A or E is false, only the corresponding I or O claim is true.

If I or O is false, we con only infer the values of A and E.

When drawing Venn Diagrams for categorical syllogisms, use the following form:

The middle term "M" goes on top. The subject or minor term "S" goes on the left.The predicate or major term "P" goes on the right.

We diagram the argument above as follows:




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This argument is valid (AAA-1). The diagram show that indeed all S's are P's.

Ordinary Language Arguments - How to turn our ordinary speech into standard-form categorical syllogisms.

Step 1: Identify the conclusion. Remember conclusion indicators.Step 2: Translate the conclusion/statements into standard-form propositions

Step 3: Test for validity.




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Remember to eliminate synonyms. For example:

No wealthy persons are vagrants.All lawyers are rich people.

Therefore no attorneys are traps.

How many synonymous words here? Wealthy persons = rich people; vagrants =tramps; lawyers = attorneys. Once the synonyms are eliminated, we have:

No wealthy persons are vagrants. No W are V.All lawyers are wealthy persons. All L are W.Therefore no lawyers are vagrants. No L are V.

This argument is valid: EAE-1Remember to eliminate compliments.

All mammals are warm-blooded animals. All M are W.No lizards are warm-blooded animals. No L are W.Therefore, all lizards are non-mammals. No L are M.

obverse = No lizards are mammals.

AEE-2 Valid




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Definition

An explanation of the meaning of a word is called definition whareas meaningis The customary significance attached to the use of a word, phrase, or

sentence, including both its literal sense and its emotive associations.The five major kinds of definition (distinguished by the functions they may beused to perform) include:

Stipulative definitionThe arbitrary assignment of meaning to a term not previously in use. Althoughit may be relatively inconvenient or useless, such a definition can never bemistaken or incorrect.

Lexical definitionA faithful report of the way in which a term is used within a particularlanguage-community.

Precising definitionA careful effort to reduce the vagueness of a term by stipulating featuresnot included in its lexical definition

Theoretical definitionA proposal for understanding the meaning of a term in relation to a set ofscientificaly useful hypotheses

Persuasive definitionAn effort to influence attitudes by surreptitiously attachingemotive significance tothe meaning of a term. According to stevenson, the most common instance isan effort to change the descriptive meaning of an emotionally-chargedevaluative term.

Kinds/Types of definition

A lexical definition simply reports the way in which a term is already used withina language community. The goal here is to inform someone else of the accepted

meaning of the term, so the definition is more or less correct depending upon theaccuracy with which it captures that usage. In these pages, my definitions oftechnical terms of logic are lexical because they are intended to inform you aboutthe way in which these terms are actually employed within the discipline of logic.

At the other extreme, a stipulative definition freely assigns meaning to acompletely new term, creating a usage that had never previously existed. Since the


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goal in this case is to propose the adoption of shared use of a novel term, there areno existing standards against which to compare it, and the definition is alwayscorrect (though it might fail to win acceptance if it turns out to be inapt or useless).If i now decree that we will henceforth refer to presidential speeches delivered in

french as "glorsherfs," i have made a (probably pointless) stipulative definition.

Combining these two techniques is often an effective way to reduce thevagueness of a word or phrase. These precising definitions begin with the lexicaldefinition of a term but then propose to sharpen it by stipulating more narrow limitson its use. Here, the lexical part must be correct and the stipulative portion shouldappropriately reduce the troublesome vagueness. If the usps announces that "propernotification of a change of address" means that an official form containing therelevant information must be received by the local post office no later than four

days prior to the effective date of the change, it has offered a (possibly useful)precising definition.

T heoretical definitions are special cases of stipulative or precising definition,distinguished by their attempt to establish the use of this term within the contextof a broader intellectual framework. Since the adoption of any theoretical definitioncommits us to the acceptance of the theory of which it is an integral part, we arerightly cautious in agreeing to it. Newton's definition of the terms "mass" and"inertia" carried with them a commitment to (at least part of) his theories about theconditions in which physical objects move.

Finally, what some logicians call a persuasive definition is an attempt to attachemotive meaning to the use of a term. Since this can only serve to confuse the literalmeaning of the term, persuasive definitions have no legitimate use.


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Categorical Statements

Concept

Categorical statements express ideas in absolute terms, usually referring to orimplying "all," "none," "never," or "always." For example, the following are categoricalstatements:

You can always count on your friends. Everybody loves a good joke. Cats can never be trained. All indigenous people need protection.

It's a good idea to avoid categorical statements unless we have proof that what weare saying applies to a whole class or category. Of course, some categoricalstatements are universally true of the category, therefore acceptable, such as "Allliving people must eat and drink to stay alive."

Some categorical statements are less obvious than the ones above. English grammarincludes some hidden categorical elements, just in the implications of certain formsand verb tenses. Think about these:

Human beings are social animals. Time is money. Dogs love people. Men don't cry. Women must take care of children.

Definition

The basic unit of meaning or content in deductive system is the categorical term.Usually expressed grammatically as a noun or noun phrase, each categorical termdesignates a class of things such as COWS

Examples

Look at the following statements and decide which are categorical and why. Remember

-- a categorical statement can be true, but it's still categorical. If it's a categorical

statement, add modifiers to make it acceptable.


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Statement Categorical or not and why Suggested alternatives

All men are created equal.Categorical - it uses 'all' and

the simple present.

All men may be created equal. Mo

people believe that all men are

created equal. All men are believed

be created equal.

Animals will stop eating

when they get full.

Categorical - it uses future

and no modifiers.

Most animals will stop eating when

they get full. Animals normally sto

eating when they get full.

Computers are a wonderful

aid for teaching.

Not clearly categorical - it

uses 'a' - but 'wonderful' is

strong

Better: Computers can be a wonde

aid for teaching.

Comics in the newspapers

are just to make you laugh.

Categorical - it uses 'just' and

the simple present.

Most comics in the newspapers are

designed to make you laugh. Comi

in the newspapers are often just to

make you laugh.

Americans prefer action

movies.

Categorical - it uses simple

present and no modifiers.

Most Americans prefer action

movies. Americans tend to prefer

action movies.

Sustainable development of

the rainforest is necessary.


present and 'necessary.'

Sustainable development of the

rainforest is probably necessary.

Sustainable development has been

recommended.

Everyone deserves accessto health care.

Categorical - it uses

'everyone' and simplepresent.

Many people believe that everyonedeserves access to health care.

Students learn more when

they study in groups.



Students seem to learn more when

they study in groups. In many case

students learn more when they stud

in groups.

Countries with more guns

have more gun crime.



It appears that countries with more

guns have more gun crime. There i

link between more guns in a count

and more gun crime.

Poverty is related to

violence.

Not categorical - it uses the

mild 'is related to' rather than

a strong connector.

Milder: Poverty seems to be related

violence.

A categorical syllogism is a deductive argument with two premises, in which the premisesand the conclusion are categorical propositions.




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A categorical proposition, in turn, is a statement that makes a straightforward assertionwith no "ifs," "ands," or "buts." Categorical propositions are typically expressed by simplystructured sentences containing a subject and a predicate, but not conjunctions or the othergrammatical devices involved in more complex sentences.

1. Is the following a categorical proposition? A dog is a mammal, if it has hair.

a) yes b) no

2. Is the following a categorical proposition? Either that is a dog, or it is a funnylooking cat.

a) yes b) no

3. Is the following a categorical proposition? Amphibians breathe from their mouth,except when they are under water.

a) yes b) no

4. Is the following a categorical proposition? Those who have the courage to dare willsucceed.

a) yes b) no

Components of Categorical PropositionsThe parts of the proposition that refer to classes are called the terms of the proposition,and there are two terms: the subject and the predicate, symbolized by S and P. Subjectsand predicates are not always single words.

In addition to the subject and predicate, there is a second component of categoricalpropositions, indicated by the words "is" or "are." This is called the copula because it linkssubject and predicate.

In terms of classes, we can make both the affirmative statement that S is included in P and

the negative statement that S is excluded from P. The affirmative or negative character ofa proposition is called its quality.

The fourth component of a proposition is called its quantity. A proposition with the form"All S are P" is universal, as is the proposition "No S are P." A proposition with the form"Some S are P" is particular. A proposition with the form "Some S are not P" is alsoparticular.




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Summary

The quality of a categorical proposition indicates the nature of the relationship it affirmsbetween its subject and predicate terms. (From Square consider the relashionships if A ifTrueThe quantity of a categorical proposition, on the other hand, is a measure of the degree towhich the relationship between its subject and predicate terms holds. It must consist thewords

All , Some, No, Not

Combining these two distinctions and representing the subject and predicate termsrespectively by the letters "S" and "P," we can uniquely identify the four possibleforms of categorical proposition:

A universal affirmative proposition (to which, following the practice of medievallogicians, we will refer by the letter "A") is of the formAll S are P.

Such a proposition asserts that every member of the class designated by thesubject term is also included in the class designated by the predicate term. Thus, itdistributes its subject term but not its predicate term.A universal negative proposition (or "E") is of the form

No S are P.This proposition asserts that nothing is a member both of the class designated bythe subject term and of the class designated by the predicate terms. Since itreports that every member of each class is excluded from the other, thisproposition distributes both its subject term and its predicate term.A particular affirmative proposition ("I") is of the form

Some S are P.A proposition of this form asserts that there is at least one thing which is a memberboth of the class designated by the subject term and of the class designated by thepredicate term. Both terms are undistributed in propositions of this form.Finally, a particular negative proposition ("O") is of the form

Some S are not P.Such a proposition asserts that there is at least one thing which is a member of theclass designated by the subject term but not a member of the class designated bythe predicate term. Since it affirms that the one or more crucial things that theyare distinct from each and every member of the predicate class, a proposition ofthis form distributes its predicate term but not its subject term


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CATEGORICAL PROPOSITIONS

We make claims about certain classes or categories and their relations. These claimsilluminate the structure of thought. There are certain rules with a precise structure

that enable us to tell if an argument is valid or not.A proposition is a sentence that is either true of false. A proposition is a categoricalproposition when it states or express a relationship between categories. Propositionscan be in standard and non-standard form. If you are aproposition in standard form, youwill be expressed in one of theA,E,I,O forms (more on that

later). Standard categoricalform is a form that propositionscan be in or out of. Propositionsthat are in this form have thefollowing:

Quantifiers: all, no, someSubject terms: s Copula: thevery linking the subject andpredicate terms. Predicate term: P

The Four Kinds of Categorical Propositions A,E,I,O:

Letter Name Quantity Quality

A universal affirmative

E universal negative

I Particular affirmative

O Particular negative

A, E, I, O propositions are pictured by the following Venn diagrams:




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THE TRADITIONAL SQUARE OF OPPOSITION




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Contraries:

At least one must be false (both are not true, but both could be false for Aand E propositions.

Both A and E could be false (e.g., All animals are dogs).

Subcontraries:

At least one must be true. Both are not false, but both could be true.




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SubAlternation

1) If one knows that A or E are true, then we can infer the value of every otherclaim or proposition.

2) If one knows that I or O is false, then we can infer the value of every other claimor proposition.

If A or E is false, only the corresponding I or O claim is true. If I or O is false, we con only infer the values of A and E.

Square of Opposition

Classical logicians described the various logical relations among the four standard forms in

terms of what they called the square of opposition, and identified four relations among thefour standard forms when placed in the square of opposition:

ContrariesAn A proposition and an E proposition that have the same subject and predicate termscannot both be true, but they could both be false. We identify this relationship in logic bycalling A and E contrary propositions. "All S is P" and "No S is P" are contraries.

Example:

"All bread is nutritious" and "No bread is nutritious" are opposing statements. They cannotboth be true. However, they could both be false. If some types of bread are nutritious andothers are not, then both statements would be false

ContradictoriesIn some cases, there are propositions that cannot both be true and both be false.Propositions that have this relationship are called contradictories.

Example: A and O:

If you accept the O proposition "Some bread is not nutritious," then you cannot also acceptthe A proposition, "All bread is nutritious," and vice versa. They cannot both be true.

O and A cannot both be false. The only way for A to be false is for there to be at least oneS that is not P (some bread that is not nutritious), and in that case O is true. Similarly, theonly way for O to be false is for there to be not even one S that is not P (not even some




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bread that is not nutritious), and in that case all S are P (all bread is nutritious) -- the Aproposition is true.

Example: E and I:

E and I are also contradictories. They cannot both be true and they cannot both be false. Ifit is false that no bread is nutritious, that could only be because at least some bread isnutritious, in which case I is true. On the other hand, if I is false, that means not even oneS is P, and thus it would be true to say that no S is P -- E would be true.

SubalternatesBoth A and I are affirmative propositions; they differ only in quantity. A is the moresweeping statement, because it makes a claim about all Ss -- that they are P.

I is more cautious. When we say that some S are P, we are not committing ourselves to anyclaim about the whole class of Ss.

Example:

We can see that if A is true, I must be true as well. If all Ss are P, then it is safe to saythat some Ss are P -- though we usually wouldn't bother to say it.

For exactly the same reasons, the O proposition is subalternate to the E proposition. In thiscase, both propositions are negative; still, the universal one always implies the particular.

This illustrates the concept of subalternates with true universals.

When we consider false statements, the tables are turned. If the I proposition is false,then the A must be false as well. If not even one S is P, then it is certainly false that all Sare P.

In the same way, on the negative side of the square, if not even one S is not P, then it iscertainly false that no S is P; if O is false, E is false as well.

Example:

Suppose that A is false, Does that mean I must be false as well? No. Even if it isn't truethat all politicians are honest, it might still be true that some are. Similarly, the falsity ofan E proposition leaves the truth or falsity of the O undetermined. It would be false, forexample, to say that no natural substances cause cancer, but it is still possible that some donot.




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This illustrates the concept of subalternates with false particulars

SubcontrariesLet's look at the propositions, "Some S are P" (I) and "Some S are not P" (O). Propositions I

and O cannot both be false. This relationship is called subcontrary.Can I and O both be true? Yes--that happens quite often. For instance, some animals aremammals, some are not.

However, I and O can never both be false. Any given object in the class of Ss must eitherbe P or not be P. If it is P, that makes the I proposition true. If it is not P, that makes the Oproposition true. For instance, any given animal either is a mammal or is not.

1. In which relationship from the square of opposition is it true that both propositionscannot be true and both cannot be false?a) contradictory b) contraryc) subcontrary d) subalternation

2. In which relationship from the square of opposition is it true that both propositionscannot be false, but they can both be true?a) contradictory b) contraryc) subcontrary d) subalternation

3. In which relationship from the square of opposition is it true that both propositionscannot be true, but they can both be false?

a) contradictory b) contraryc) subcontrary d) subalternation

4. In which relationship from the square of opposition is it true that when the universalis true the particular one of the same quality is true and when the particular is falsethe universal one of the same quality is false?

a) contradictory b) contraryc) subcontrary d) subalternation

5. Which propositions in the square of opposition are contradictories?a) A and I b) A and E c) I and O d) A and O e) E and O




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6. Which propositions in the square of opposition are subalternates?a) A and I b) A and E c) I and O d) A and O e) E and I

7. Which propositions in the square of opposition are contradictories?

a) A and I b) A and E c) I and O d) E and I e) E and O8. Which propositions in the square of opposition are subalternates?

a) A and E b) I and O c) A and O d) E and I e) E and O

Standard Form

Because there are two possible qualities and two possible quantities, there are just fourstandard logical forms for categorical propositions, no matter how complex their subjectand predicate terms may be. These four forms are:

AFFIRMATIVE NEGATIVE

UNIVERSAL A: All S are P E: No S is P

PARTICULAR I: Some S are P O: Some S are not P

The letters A, E, I, and O are the traditional labels for the four standard forms.Comprehension Questions

1. Is the following proposition universal or particular? Not any of you came to myassistance.a) universal b) particular

2. Is the following proposition universal or particular? Not every cow is brown.a) universal b) particular

3. Is the following proposition universal or particular? Three out of four dogs preferDogTime Treats.a) universal b) particular

4. Is the following proposition affirmative or negative? All noble deeds are rare.a) affirmative b) negative

5. Is the following proposition affirmative or negative? Some nondogs are cats.a) affirmative b) negative

6. Is the following proposition affirmative or negative? Some living things arenonplants.a) affirmative b) negative




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7. What kind of proposition is the following? No man is an island.a) universal affirmative (A) b) universal negative (E)c) particular affirmative (I) d) particular negative (O)

8. What kind of proposition is the following?Every general is fighting the previous war.a) universal affirmative (A) b) universal negative (E)c) particular affirmative (I) d) particular negative (O)

9. What kind of proposition is the following? Some liars can fool all of the people.a) universal affirmative (A) b) universal negative (E)c) particular affirmative (I) d) particular negative (O)

10. What kind of proposition is the following? Some who are famous are not infamous.a) universal affirmative (A) b) universal negative (E)

c) particular affirmative (I) d) particular negative (O)

A categorical syllogism is an argument consisting of exactly three categoricalpropositions (two premises and a conclusion) in which there appear a total of exactlythree categorical terms, each of which is used exactly twice.

One of those terms must be used as the subject term of the conclusion of thesyllogism, and we call it the minor term of the syllogism as a whole. The major term

of the syllogism is whatever is employed as the predicate term of its conclusion. Thethird term in the syllogism doesn't occur in the conclusion at all, but must beemployed in somewhere in each of its premises; hence, we call it the middle term.

Since one of the premises of the syllogism must be a categorical proposition thataffirms some relation between its middle and major terms, we call that the majorpremise of the syllogism. The other premise, which links the middle and minor terms,we call the minor premise.

Consider, for example, the categorical syllogism:

No geese are felines.Some birds are geese.

Therefore, Some birds are not felines.


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Clearly, "Some birds are not felines" is the conclusion of this syllogism. The majorterm of the syllogism is "felines" (the predicate term of its conclusion), so "Nogeese are felines" (the premise in which "felines" appears) is its major premise.Simlarly, the minor term of the syllogism is "birds," and "Some birds are geese" is

its minor premise. "geese" is the middle term of the syllogism.

Categorical Syllogisms

If an argument has two categorical premises and a categorical conclusion, and thetwo categorical premises jointly support the conclusion, then this argument is acategorical syllogism.

Example:

All mammals are animals that breathe by means of lungs.All whales are mammals.

Therefore, all whales are animals that breathe by means of lungs.1.What kind of propositions are the premises of a categorical syllogism?

a) hypothetical and categorical b) disjunctive and categoricalc) categorical only d) all of the above

2. A categorical proposition is

a) a proposition that makes an assertion about the relations of classesb) a proposition that asserts that the truth of one proposition is sufficient for

the truth of another c) a proposition which asserts that either one or another of two propositions is

true

3. How do the premises support the conclusion in a categorical syllogism?a) jointly b) independently c) either jointly or independently

4. Is the following argument a categorical syllogism?If you play with fire, you will get burned. You played with fire.You got burned.

a) Yes b) No

5. Is the following a categorical syllogism?




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No horned animal is a carnivore.All moose are horned animals.No moose is a carnivore.

a) Yes b) No

6. Is the following argument a categorical syllogism?Either my book is in my bag or I left it in the library.My book is not in my bag.I left my book in the library.

a) Yes b) No

7. Is the following argument a categorical syllogism?All supporters of the nuclear freeze want to preserve peace.

No conservatives support the nuclear freeze.No conservatives want to preserve peace.a) Yes b) No

Each syllogism has three propositions. Because every proposition has two terms,there could be six distinct terms here. However, there are only three--the majorterm, the minor term, and the middle term.

Example:

All whales are animals that breathe by means of lungs.All whales are mammals.All whales are animals that breath by means of lungs.

The major term of this argument is "animals that breathe by means of lungs."

The major premise is the premise that contains the major term-- "All mammals areanimals that breathe by means of lungs."

The minor term is the term that occurs in the subject of the conclusion.

Example:

All mammals are animals that breathe by means of lungs.All whales are mammals.All whales are animals that breathe by means of lungs.




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The minor term of this argument is "whales." The minor premise is the premise thatcontains the minor term-- "All whales are mammals."

The middle term occurs once in each of the premises, and it serves to link togetherthe major and minor terms. In this case, the middle term is "mammals."

Example:


The minor term of this argument is "whales."

The minor premise is the premise that contains the minor term-- "All whales aremammals."

The middle term occurs once in each of the premises, and it serves to link togetherthe major and minor terms.

Example:


In this case, the middle term is "mammals."

1. How many terms are there in a categorical syllogism?

a) 6 b) 2 c) 3 d) 4

2. Which term in a categorical syllogism occurs in the subject of theconclusion?a) the major term b) the minor term c) the middle term




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3. Which term in a categorical syllogism occurs in the predicate of theconclusion?a) the major term b) the minor term c) the middle term

4. Which term in a categorical syllogism occurs in each premise and serves tolink together the other two terms?a) the major term b) the minor term c) the middle term5. What is the major term of the following categorical syllogism?

No horned animal is a predatorAll moose are horned animalsNo moose is a predator

a) horned animal b) predator c) moose

6. What is the minor term of the following categorical syllogism?No Marxist advocates private propertyAll conservatives advocate private propertyNo conservative is a Marxist.

a) Marxist b) advocates private property c) conservatives

7.What is the major term of the following categorical syllogism?All mammals are animals that breathe by means of lungsAll whales are mammalsAll whales are animals that breathe by means of lungs

a) mammals b) animals that breathe by means of lungs c) whales

8. What is the middle term of the following categorical syllogism?No horned animal is a predatorAll moose are horned animalsNo moose is a predator

a) horned animal b) predator c) moose

- The Mood -The premises and conclusion of a categorical syllogism can have any of the standardforms: A, E, I, or O. A categorical syllogism is identified, in part, by reference tothis fact. We list the letters that identify the forms of the propositions in thesyllogism in the following order: major premise, minor premise, conclusion. This list iscalled the mood of the syllogism.




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Example:The mood of the following argument is AAA:

All mammals are animals that breathe by means of lungs.

All whales are mammals.

Therefore, all whales are animals that breathe by means of lungs.

1. What kind of proposition is an A proposition?

a) universal affirmative b) universal negativec) particular affirmative d) particular negative

2. What kind of proposition is an E proposition?a) universal affirmative b) universal negativec) particular affirmative d) particular negative

3. What kind of proposition is an I proposition?a) universal affirmative b) universal negativec) particular affirmative d) particular negative

4. What kind of proposition is an O proposition?

a) universal affirmative b) universal negativec) particular affirmative d) particular negative

5. The letters that identify the forms of a proposition in a categoricalsyllogism are arranged in what order?

a) conclusion, major premise, minor premiseb) major premise, conclusion, minor premisec) minor premise, major premise, conclusiond) major premise, minor premise, conclusion

6. What is the mood of the following categorical syllogism?No horned animal is a predatorAll moose are horned animalsNo moose is a predator

a) AAE b) EAE c) AEE d) AEO e) none of the above

7. What is the mood of the following categorical syllogism?Lecturer : Arshad Zia Siddiqui E-mail [email protected]



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No Marxist advocates private propertyAll conservatives advocate private propertyNo conservative is a Marxist

a) EAE b) AEE c) IOE d) EOO e) none of the above

8. What is the mood of the following categorical syllogism?Some crimes against property are fraudAll frauds are feloniesSome felonies are crimes against property

a) AII b) IAI c) IEI d) OEO e) none of the above

- The Figure -

The position of the middle term in the premises is called the figure of the syllogism.Because there are two premises, and two possible positions in each premise, thereare four figures. They are identified by number as follows:

1st 2nd 3rd 4th

Major M P P M M P P M

Minor S M S M M S M S

Conclusion S P S P S P S P

Within each figure, the premises and the conclusion can have any of the standardforms for categorical propositions. That is, within each figure, a syllogism can haveany mood.

Comprehension Questions1. The figure of a categorical syllogism is determined by the position of whichterm?a) the major term b) the minor term c) the middle term

2. In which figure of a categorical syllogism is the middle term the subject ofthe major and the predicate of the minor?

a) first figure b)second figure c) third figure d) fourth figure




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3. In which figure of a categorical syllogism is the middle term the subject ofboth the major and the minor premises?

a) first figure b) second figure c) third figure d) fourth figure4. In which figure of a categorical syllogism is the middle term the predicateof both the major and the minor premises?

a) first figure b) second figure c) third figure d) fourth figure

5. In which figure of a categorical syllogism is the middle term the predicateof the major and the subject of the minor?

a) first figure b) second figure c) third figure d) fourth figure

Venn Diagrams for Categorical Syllogisms

The technique of Venn diagrams for categorical syllogisms is based on the fact that

in a valid syllogism, the conclusion asserts no more than what is already contained,implicitly, in the premises. If the conclusion asserts more than that, it does notfollow from the premises, and the syllogism is invalid. The technique is to diagramthe premises, and then see whether anything would have to be added in order todiagram what the conclusion asserts. If so, the syllogism is invalid; if not, it is valid.

Example:




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No M is P No horned animal is a carnivoreAll S is M All moose are horned animals

No S is P No moose is a carnivore

The first step is to diagram the major premise, using the circles representing M(horned animals) and P (carnivores). So we shade out the area of overlap between Mand P.

The second step is to add the minor premise to our diagram, using the circlesrepresenting S and M. Since this is an A proposition, we shade out the region of Soutside M.

The final step is to examine the completed diagram of the premises and determinewhether it contains the information asserted by the conclusion. The conclusionasserts that no S is P. Thus it requires that the overlap between S and P be shadedout, and the premises taken together do shade out that region. So the syllogism isvalid.

For a syllogism to be valid, the combined diagram must contain all the informationasserted by the conclusion. It may contain more information, but it cannot omitanything.

Now let's try a syllogism with a particular premise.

Example:




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No M is PSome M are S___________Some S are not P

First we diagram the major premise.

Second we diagram the minor premise.

Notice that we diagrammed the major premise first. This is not required logically,but whenever there is a particular and a universal premise, it is best to diagram theuniversal one first. By diagramming the universal premise first, we have shaded outone of the subregions, so now we know that the X for the other premise must gooutside the P circle. And that's useful information, it means that at least one S isnot P. Since that is what the conclusion asserts, the argument is valid.

If a syllogism is invalid, a Venn diagram will reveal that fact in one of two ways. The

combined diagram for the premises will either fail to shade out an area excluded bythe conclusion, or it will fail to put an X where the conclusion requires one.

Example:

All P are MAll S are M




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All S are P

The Venn diagram reveals the invalidity by failing to shade out the right areas.

In the combined diagram, the area of P outside M has been shaded to represent the

major premise, and the area of S outside M has been shaded to represent the minor.But one area in the region of S outside P--the one indicated by the arrow--has notbeen shaded. Thus, the premises leave open the possibility that some S are not P;they do not guarantee that all S are P. So the conclusion does not follow; thesyllogism is invalid.

Now let's examine another case in which the invalidity is revealed by the placementof Xs.

All P are MSome S are M

Some S are P

Notice that the X is on the line between two subregions of the overlap between Sand M. Locating the X on the line means: I know something is both an S and an M, butI don't know whether it is also a P or not. But the conclusion does assert that some




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S are P. For the premises to justify this assertion, they would have to give us an X inthe area of overlap between S and P. But all they tell us is: there's an S that may ormay not be a P. The conclusion doesn't follow.

Comprehension Questions1. The technique of Venn diagrams is based on the fact that in a validsyllogism the conclusiona) asserts no more than what is already contained, implicitly, in the premisesb) asserts more than what is contained in the premises

2. For a syllogism to be valid, the combined diagram musta) contain all information asserted by the conclusionb) either fail to shade out an area excluded by the conclusion, or fail to put an x

where the conclusion requires one.3. For a syllogism to be invalid, the combined diagram must

a) contain all information asserted by the conclusionb) either fail to shade out an area excluded by the conclusion, or fail to put an x

where the conclusion requires one.

4. Which of the choices represent the Venn diagrams of the given categoricalsyllogism?

All of Shakespeare's dramas are in blank verseSome great plays are in blank verseSome greatplays are Shakespeare's dramas

a) c)




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b) d)5. According to the Venn diagrams, the previous syllogism is valid or invalid?

a) valid b) invalid6. Which of the choices represent the Venn diagrams of the givencategorical syllogism?

All vertebrates reproduce sexually

All vertebrates are animalsAll animals reproduce sexually

a) c)

b) d)

7. According to the Venn diagrams the previous syllogism is valid or invalid?

a) valid b) invalid

8. Which of the choices represent the Venn diagrams of the given categoricalsyllogism?




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No A is BSome A are not CSome C are not B

a) c)

b) d)

Summary

categorical syllogism may occur by stating its mood and figure. The mood of asyllogism is simply a statement