121470934 legal technique finals reviewer

7/14/2019 121470934 Legal Technique Finals Reviewer

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LEGAL TECHNIQUES AND LOGIC

JUDGE ALGODON

I. INTRODUCTION

A. History of Logic

B. Civil Law vs. Common Law Tradition

C. The Role of Logic in Law

A. History of Logic

The founder of Logic is Aristotle of Stagira in Thrace (384-322B.C.), son of thephysician NIchomachus and became Platos student at 18 years of age andstudied with him for 20 years. Shortly afterward in 343 B.C., became a tutor for3 years to the 13- year old Alexander, who was to rule the world as Alexanderthe Great. In 335 B. C., he founded his own school, the Peripathetic School ofphilosophers.

Aristotles work on logic is found in his Organon (meaning the method or organof investigation) which consisted of a number of his writings, including thefollowing:

On Interpretation -dealt with the structure of logical proposition; Prior Analytics-the doctrine of syllogism; Posterior Analytics-the logic of science and the applications of thesyllogism; Topics-the logic of argument based on probable truths; Sophistical Test-dealt with logical fallacies.

Logical reasoning makes us certain that our conclusions are true and thisprovides us with accepted scientific proofs of universally valid propositions orstatements.


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B. Civil Law vs. Common Law Tradition

COMMON LAW:That which derives its force and authority from the universal consent andimmemorial practice of the people. The system of jurisprudence that originatedin England and which was latter adopted in the U.S. that is based on precedentinstead of statutory laws.

Traditional law of an area or region; also known as case law. The law created byjudges when deciding individual disputes or cases. The body of law whichincludes both the unwritten law of England and the statutes passed before thesettlement of the United States.


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In the common law, civil law is the area of laws and justice that affect the legal status of individuals. Civil law,in this sense, is usually referred to in comparison to criminal law, which is that body of law involving the stateagainst individuals (including incorporated organizations) where the state relies on the power given itby statutory law.

CIVIL LAW:

Civil law may also be compared to military law, administrative law and constitutional law (the laws governingthe political and law making process), and international law. Where there are legal options for causes ofaction by individuals within any of these areas of law, it is thereby civil law.

Civil law courts provide a forum for deciding disputes involving torts (such asaccidents, negligence, andlibel), contract disputes, the probate of wills, trusts, property disputes, administrative law,commercial law,and any other private matters that involve private parties and organizations including governmentdepartments. An action by an individual (or legal equivalent) against the attorney general is a civil matter, butwhen the state, being represented by the prosecutor for the attorney general, or

some other agent for thestate, takes action against an individual (or legal equivalent including a government department), thisis public law, not civil law.

The objectives of civil law are different from other types of law. In civil law:

a. there is the attempt to right a wrong,b. honor an agreement, orc. settle a dispute.

d. If there is a victim, they get compensation, and the person who is the causeof the wrong pays, thisbeing a civilized form of, or legal alternative to, revenge.e. If it is an equity matter, there is often a pie for division and it gets allocated by a process of civil law,possibly invoking the doctrines of equity.f. In public law, the objective is usually deterrence, and retribution.


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An action in criminal law does not necessarily preclude an action in civil law in common law countries, andmay provide a mechanism for compensation to the victims of crime. Such a situation occurred when O.J.Simpson was ordered to pay damages for wrongful death after being acquitted of the criminal chargeof murder.

Civil law in common law countries usually refers to both common law and the lawof equity, which while nowmerged in administration, have different traditions, and have historically operated to different doctrines,although this dualism is increasingly being set aside so there is one coherent body of law rationalized aroundcommon principles of law.

C. Role of Logic in Law

Regardless of the professions we are in, we always use logic. We use it when wemake decisions or when wetry to influence the decisions of others or when we are engaged in argumentationand debate.

A lawyer presents his arguments using the principle of logic to prove the tenability of his position, otherwise,he will send his client to jail. Everybody uses logic since everyone possesses reason.


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II. REASONING

A. Basic Concepts

1. What is Logic

2. Propositions and Sentences

3. Arguments, Premises and Conclusions

4. More Complex Arguments

5. Recognizing Arguments

6. Deduction and Induction

7. Validity and Truth

8. Arguments and Explanations

B. Analyzing and Diagramming Arguments

C. Problem Solving

1. What is Logic

1. Reasoning conducted or assessed according to strict principles of validity: "experience is a better guide to thisthan deductive logic".2. A particular system or codification of the principles of proof and inference:"Aristotelian logic".

2. Propositions and Sentences

Proposition refers to either the "content" or "meaning" of a meaningful declarative sentence. The meaningof a proposition includes having the quality or property of being either true orfalse

Propositional logic largely involves studying logical connectives such as the words and and or and therules determining the truth-values of the propositions they are used to join, as


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well as what these rules meanfor the validity of arguments, and such logical relationships between statementsas being consistent orinconsistent with one another, as well as logical properties of propositions

Sentence

. Sentence logic deals with sentences of a natural language that are either trueor false. Sentence logic ignores the internal structure of simple sentences. Sentence logic is concerned with sentences which are compounded in a certain way.. A primary goal of sentence logic is to enable the evaluation of a certain class of arguments in naturallanguage. In an argument, a sentence that is the arguments con

3. Arguments, Premises and Conclusions

Argument is a connected series of statements intended to establish a definite proposition. ...an argument isan intellectual process... contradiction is just the automatic gainsaying of anything the other person says.


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An argument is a deliberate attempt to move beyond just making an assertion. When offering an argument,you are offering a series of related statements which represent an attempt to supportthat assertion togive others good reasons to believe that what you are asserting is true rather than false.

Here are examples of assertions:

1. Shakespeare wrote the play Hamlet.2. The Civil War was caused by disagreements over slavery.3. God exists.4. Prostitution is immoral.

Sometimes you hear such statements referred to as propositions. Technically speaking, a proposition is theinformational content of any statement or assertion. To qualify as a proposition, a statement must becapable of being either true or false

3 major components of Argument:

1. Premise

2. Inference

3. Conclusion

Premises are statements of (assumed) fact which are supposed to set forth the reasons and/or evidence forbelieving a claim. The claim, in turn, is the conclusion: what you finish with at the end of an argument. Whenan argument is simple, you may just have a couple of premises and a conclusion:

1. Doctors earn a lot of money. (premise)2. I want to earn a lot of money. (premise)

3. I should become a doctor. (conclusion)

Inferences are the reasoning parts of an argument. Conclusions are a type of inference, but always the finalinference. Usually an argument will be complicated enough to require inferenceslinking the premises withthe final conclusion:

1. Doctors earn a lot of money. (premise) [FACTUAL]2. With a lot of money, a person can travel a lot. (premise) [FACTUAL]3. Doctors can travel a lot. (inference, from 1 and 2)4. I want to travel a lot. (premise)5. I should become a doctor. (from 3 and 4)

2 Types of Claims:

1. Factual Claim

2. Inferential Claim


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- it expresses the idea that some matter of fact is related to the sought-afterconclusion. This is the attemptto link the factual claim to the conclusion in such a way as to support the conclusion. The third statementabove is an inferential claim because it infers from the previous two statementsthat doctors can travel a lot.

Without an inferential claim, there would be no clear connection between the premises and the conclusion.It is rare to have an argument where inferential claims play no role. Sometimesyou will come across anargument where inferential claims are needed, but missing you wont be able to seethe connection fromfactual claims to conclusion and will have to ask for them.

5. Recognizing Arguments

we use the term "argument" to mean a set of propositions in which some propositions--the premises--areasserted as support or evidence for another--the conclusion.

The author doesn't just tell us something that he takes to be true; he also presents reasons intended to

convince us that it is true.This intention is usually signaled by certain indicator words. The following isa list of the more commonindicator words:

Premise Indicators

Conclusion Indicators

Since

Therefore

Because

Thus

As

So

For

Consequently

Given that

As a result

Assuming that

It follows that

Inasmuch as


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Hence

The reason is that

Which means that

In view of the fact that

Which implies that

6. Deduction and Induction

Deduction:

A deductive argument claims that its premises make its conclusion certain.

This deductive argument is valid because theconclusion follows with certainty if the premises aretrue. There is no possible way for the premises to betrue and yet the conclusion false

Example: All mammals have lungs.

All whales are mammals.

Therefore all whales have lungs.


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tree.jpgA valid deductive argument with true premises is a sound argument. A sound argument is often called aproof, but this term can be misleading. If the premises themselves are absolutelycertain, then a soundargument does indeed offer proof, as in the below example:

1. All bachelors are unmarried.2. All bachelors are male.3. Therefore all bachelors are unmarried males.

The premises are certain here because they are true by definition, and the argument is sound, so theconclusion is proven

Inductive:

Inductive arguments do not try to establish their conclusions with certainty. Instead, an inductive argumentclaims that its premises make the conclusion probable. Inductive arguments canno

t be valid or invalid.Instead, they are weak or strong, better or worse. And even when the premises are true and provide verystrong support for the conclusion, the conclusion cannot be certain. The strongest inductive argument is notas conclusive as a sound deductive argument.

Example: Most corporation lawyers are conservatives.

Betty Morse is a corporation lawyer.

Therefore Betty Morse is a conservative.

7. Validity and Truth

Validity:

Deductive arguments may be either valid or invalid. If an argument is valid, and

its premises are true, theconclusion must be true: a valid argument cannot have true premises and a falseconclusion.


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The validity of an argument depends, however, not on the actual truth or falsityof its premises andconclusions, but solely on whether or not the argument has a valid logical form.The validity of an argument isnot a guarantee of the truth of its conclusion. A valid argument may have falsepremises and a falseconclusion.

The corresponding conditional of a valid argument is a necessary truth (true inall possible worlds) and so theconclusion necessarily follows from the premises, or follows of logical necessity. The conclusion of a validargument is not necessarily true, it depends on whether the premises are true. The conclusion of a validargument need not be a necessary truth: if it were so, it would be so independently of the premises.

For example:

Some Greeks are logicians; therefore, some logicians are Greeks.

Valid argument; it would be self-contradictory to admit that some Greeks are logicians but deny

that some (any) logicians are Greeks.

All Greeks are human and all humans are mortal; therefore, all Greeks are mortal. :

Valid argument; if the premises are true the conclusion must be true.

Some Greeks are logicians and some logicians are tiresome; therefore, some Greeks are tiresome.

Invalid argument: the tiresome logicians might all be Romans (for example).

Either we are all doomed or we are all saved; we are not all saved; therefore, we are all doomed.

Valid argument; the premises entail the conclusion. (Remember that this does notmean theconclusion has to be true; it is only true if the premises are true, which theymay not be!)

Premise 1: Some men are hawkers. Premise 2: Some hawkers are rich. Conclusion: Somemen are rich.

This argument is invalid. There is a way where you can determine whether an argument isvalid, give a counter-example with the same argument form.


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Counter-Example: Premise 1: Some people are herbivores. Premise 2: Some herbivores arezebras. Conclusion: Some people are zebras. (This is obviously false.)

Note that the counter-example follows the P1. Some x are y. P2. Some y are z. C.Some xare z. format. We can now conclude that the hawker argument is invalid.

Arguments can be invalid for a variety of reasons. There are well-established patterns ofreasoning that render arguments that follow them invalid; these patterns are knownas logical fallacies.

Truth:

1. Coherence - Is a statement true when it aligns with, is consistent with and doesn't contradict other truestatements?2. Correspondence - Is a statement true when it corresponds to something in thereal world?3. Foundationalism - Can certain statements be asserted as true in and of themse

lves, self-evidently? Willtruth then deductively follow from these assumptions?4. Pragmatic accounts - Is a statement true when it proves to be useful or practical? ()5. Consensus - Is a statement true when enough people argue or believe that it is true? ()


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6. Deflationism - Is truth not an actual property of a statement at all, but something else? Can 'true' or'the truth' ever be predicated in a meaningful, non-redundant way? ()

8. Argument and Explanation

Argument Types:

1. Deductive Argument

- asserts that the truth of the conclusion is a logical consequence of the premises

2. Inductive Argument

- asserts that the truth of the conclusion is supported by the premises

Argument is an attempt to persuade someone of something, by giving reasons or ev

idence for accepting aparticular conclusion. The general structure of an argument in a natural language is that of premises (typicallyin the form of propositions, statements or sentences) in support of a claim: theconclusion. Many argumentscan also be formulated in a formal language. An argument in a formal language shows the logical form of thenatural language arguments obtained by its interpretations.*

arguments obtained by its interpretations.*

Distinguish arguments from explanations.

Argument

Explanation

(1) expresses an


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inference

does not usuallyexpress aninference

(2) offersevidence, groundsor reasons

offers an accountwhy

(3) goes from wellknown statementsto statements lesswell known

gives less wellknownstatements whya better knownstatement is true

(4) draws a logicalconnectionbetweenstatements

describes a


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causalconnection

(5) has thepurpose toestablish the truthof a statement

has the purposeto give anaccount ofsomething


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Definition of an Argument and an ExplanationArgument has a number of different definitions. Essentially, it is a line of logic that is presented in order tosupport the veracity of a statement. Argument has combative connotations, but anargument does not haveto be belligerent.

Explanation is used to clarify and explicate a statement. Its aim is to make thelistener understand thestatement rather than persuade him to accept a certain point of view.Example of an Argument and an ExplanationArgument one person wants to convince the other person that it is going to snow tomorrow. He will citepredictions from the weather station, as well as the clouds visible on the horizon, the damp chill in the air,and the squirrels furiously hiding their nuts.

Explanation one both people agree is it going to snow tomorrow because, they say,there is a cold frontcoming in and the air feels damp.In both cases, the example of snow is used, but note that the argument is trying

to convince someone of thetruth of their statement, whereas with the explanation, it is not a matter of ifthe statement is true, but whyit is true.Uses of Arguments and ExplanationsArguments arguments are used in a variety of professional and academic applications. For instance, adebate club will take on both sides of an argument and strive to prove each oneis right. Arguments are alsoused by lawyers to convince the jury of the defendants guilt or innocence. Diplomats will approach anegotiating table with a certain argument in mind. Entrepreneurs will present potential backers with an

argument in support of their business model.

Explanations are used all the time in the classroom to put across new items to students. Giving directions isa form of explanation. You will also find explanations included with most new purchases, especially thosewith some assembly required. When the aforementioned entrepreneur is presentingan argument about hisbusiness model, he may be asked to explain how it all works.

Summary:1.Arguments and explanations are both used to get the point across when speakingor writing.2.Arguments are persuasive and seek to make people understand that something istrue, whereasexplanations start with the assumption of truthfulness and tell why or how the statement has come intobeing.3.Both arguments and explanations have wide application in education and business, but arguments are used


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for persuasion and explanations are used for clarification.

Explanation:

An explanation is a set of statements constructed to describe a set of facts which clarifiesthe causes, context, and consequences of those facts.

In scientific research, explanation is one of the purposes of research, e.g., exploration and description.Explanation is a way to uncover new knowledge, and to report relationships amongdifferent aspects ofstudied phenomena.

4 Types of Explanation:


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1. A thing's material cause is the material of which it consists. (For a table,that might be wood; fora statue, that might be bronze or marble.)2. A thing's formal cause is its form, i.e. the arrangement of that matter.3. A thing's efficient or moving cause[4] is "the primary source of the change or rest." An efficientcause of x can be present even if x is never actually produced and so should notbe confusedwith a sufficient cause.[5] (Aristotle argues that, for a table, this would be the art of table-making,which is the principle guiding its creation.)[2]4. A thing's final cause is its aim or purpose. That for the sake of which a thing is what it is. (For aseed, it might be an adult plant. For a sailboat, it might be sailing. For a ball at the top of a ramp,it might be coming to rest at the bottom.)

III. LANGUAGE

A. Uses of Language

1. Three Basic Functions of Language

2. Discourse Serving Multiple Functions

3. Forms of Discourse

4. Emotive Words

5. Kinds of Agreement and Disagreement

6. Emotively Neutral Language

1. Three Basic Functions of Language

1. Informative language function: essentially, the communication of information.


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a. The informative function affirms or denies propositions, as in science or thestatement ofa fact.

b. It is used to describe the world or reason about it (e.g.., whether a state of affairs hasoccurred or not or what might have led to it).

c. These sentences have a truth value; that is, the sentences are either true orfalse(recognizing, of course, that we might not know what that truth value is). Hence, they areimportant for logic.

2. Expressive language function: reports feelings or attitudes of the writer (orspeaker), or of thesubject, or evokes feelings in the reader (or listener).

a. Poetry and literature are among the best examples, but much of, perhaps mostof,ordinary language discourse is the expression of emotions, feelings or attitudes.

b. Two main aspects of this function are generally noted: (1) evoking certain feelings and (2)expressing feelings.

c. Expressive discourse, qua expressive discourse, is best regarded as neither true orfalse. E.g., Shakespeare's King Lear's lament, "Ripeness is all!" or Dickens' "I

t was the best of


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times, it was the worst of times; it was the age of wisdom; it was the age of foolishness"Even so, the "logic" of "fictional statements" is an interesting area of inquiry.

3. Directive language function: language used for the purpose of causing (or preventing) overt action.

a. The directive function is most commonly found in commands and requests.b. Directive language is not normally considered true or false (although variouslogics ofcommands have been developed).

c. Example of this function: "Close the windows." The sentence "You're smoking in anonsmoking area, although declarative, can be used to mean "Do not smoke in thisarea."

2. Discourse Serving Multiple Functions

Almost any ordinary communication will probably exhibit all three uses of language. Thus a poem, which maybe primarily expressive, also may have a moral and thus also be directive. And,of course, a poem may containa certain amount of information as well. Effective communication often demands that language servemultiple functions.

3. Forms of Discourse

. Sentences are commonly divided into four grammatical forms:a. declarative,b. interrogative,c. imperative, andd. exclamatory.

. Much discourse is intended to serve two or possibly all three functions of languageinformative,expressive, directiveat once. In such cases each aspect or function of a given passage is subject toits own proper criteria.


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. Logicians are most concerned with truth and falsehood and the related notionsof the correctnessand incorrectness of arguments. Thus, to study logic we must be able to differentiate discourse thatfunctions informatively from discourse that does not.

. argumentation/ persuasion one of the four forms of discourse which uses logic,ethics, andemotional appeals (logos, ethos, pathos) to develop an effective means to convince the reader tothink or act in a certain way

. persuasion relies more on emotional appeals than on facts

. argument form of persuasion that appeals to reason instead of emotion to convince an audience tothink or act in a certain way

. description a form of discourse that uses language to create a mood or emotionexposition one ofthe four major forms of discourse, in which something is explained or "set forth" narrative the formof discourse that tells about a series of events.


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4. Emotive Words

. Emotive words are words that carry emotional overtones. These words are said to have emotivesignificance or emotive meaning or emotional impact.

1. Two different words or phrases can have literal (or denotative) meanings which are similar, but differsignificantly in their emotive significance.2. Often, we speak of "slanting" as emotive significance; i.e., a word or phrasecan be positively slanted,neutral, or negatively slanted.

. The informative function derives from the literal meaning of the words in thesentencethe objects,

events, or attributes they refer toand the relationship among them asserted by the sentence. Theexpressive content emerges because some of the words in the sentence may also have emotionalsuggestiveness or impact. Words, then, can have both a literal meaning and an emotive meaning.The literal meanings and the emotive meanings of a word are largely independentof one another.. Language has a life of its own, independent of the facts it is used to describe.

. The game confirms what common experience teaches: One and the same thing can be referred to bywords that have very different emotive impacts.

5. Kinds of Agreement and Disagreement

. Aexcessive reliance on emotively charged language can create the appearance ofdisagreementbetween parties who do not differ on the facts at all, and it can just as easilydisguise substantivedisputes under a veneer of emotive agreement. Since the degrees of agreement inbelief andattitude are independent of each other, there are four possible combinations atwork here:1. Agreement in Belief and Agreement in Attitude;


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2. Agreement in Belief but Disagreement in Attitude;3. Disagreement in Belief but Agreement in Attitude;4. Disagreement in Belief and Agreement in Attitude.

. Agreement in belief and agreement in attitude: There aren't any problems in this instance, sinceboth parties hold the same positions and have the same feelings about them.. Ex. Mr. Recto: The sun is very far since its 90 million miles away.. Ms. Grace: Yes that is very far, indeed.

. Agreement in belief but disagreement in attitude: This case, if unnoticed, maybecome the cause ofendless (but pointless) shouting between people whose feelings differ sharply about some fact upon

which they are in total agreement.. Ex.Mr. Abella: The sun is not so far; its only 93 million miles away.. Ms. Tiffany: The sun is, indeed, very far since its 93 million miles away.

. Disagreement in belief but agreement in attitude: In this situation, parties may never recognize,

much less resolve, their fundamental difference of opinion, since they are lulled by their sharedfeelings into supposing themselves allied.. Ex. Mr. Magarin: The sun is incredibly far from the earth; its 60 million milesaway.. Ms. Smith: Yes, the sun is extremely far from the earth, but its 90 million milesaway.


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. Disagreement in belief and disagreement in attitude: Here the parties have solittle in common thatcommunication between them often breaks down entirely.. Ex. Mr. Cade: The sun is really very close to earth, only 60 million miles.. Ms. Cade: No, the sun is incredibly far away; its over 93 million miles from earth.

. It is often valuable, then, to recognize the levels of agreement or disagreement at work in anyexchange of views. That won't always resolve the dispute between two parties, ofcourse, but it willensure that they don't waste their time on an inappropriate method of argument or persuasion.

5. Emotively Neutral Language

. Neutral language is to be preferred when factual truth is our objective. Whenwe are trying to learnwhat really is the case, or trying to follow an argument, distractions will be frustrating; and emotionis a powerful distraction. Therefore, when we are trying to reason about facts,

referring to them inemotive language is a hindrance.

. Language that is altogether neutral may not be available when we deal with some very controversialmatters. Language that is heavily charged with emotional meaning is unlikely toadvance the questfor truth.

. If our aim is to communicate information, and if we wish to avoid being misunderstood, we shoulduse language with the least possible emotive impact.


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B. Definition

1. Disputes, Verbal Disputes and Definitions

2. Kinds of Definition and the Resolution of Disputes

3. Denotation (Extension) and Connotation (Intension)

4. Extension, and Denotative Definitions

5. Intension, and Connotative Definition

6. Rules for Definition by Genus and Difference

1. Disputes, Verbal Disputes and Definitions

Disputes:Disputes have their origins in disagreements between individuals.

The disagreement only becomes a dispute when one or other party cannot live withtheconsequences of the disagreement, and insists on having it resolved.

Disputes mostly arise either from a genuine difference of opinion or from dising

enuous self-interest.

2. Kinds of Definition and the Resolution of Disputes

Dispute Resolution:

Generally refers to one of several different processes used to resolve disputesbetween parties, includingnegotiation, mediation, arbitration, collaborative law, and litigation. Dispute

resolution is the process of


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resolving a dispute or a conflict by meeting at least some of each sides needs and addressing their interests.Dispute resolution, or conflict resolution to use another common term, is a relatively new field, emergingafter World War II. Scholars from the Program on Negotiation were leaders in establishing the field.

. Adjudicative processes, such as litigation or arbitration, in which a judge, jury or arbitratordetermines the outcome.. Consensual processes, such as collaborative law, mediation, conciliation, or negotiation, in which theparties attempt to reach agreement.. Not all disputes, even those in which skilled intervention occurs, end in resolution. Such intractabledisputes form a special area in dispute resolution studies.

Theoretical definitions:

Are special cases of stipulative or precising definition, distinguished by theirattempt to establish the use ofthis term within the context of a broader intellectual framework. Since the adoption of any theoreticaldefinition commits us to the acceptance of the theory of which it is an integralpart, we are rightly cautious inagreeing to it

Persuasive definition:

Is an attempt to attach emotive 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.

The most common way of preventing or eliminating differences in the use of languages is by agreeing on thedefinition of our terms. Since these explicit accounts of the meaning of a wordor phrase can be offered indistinct contexts and employed in the service of different goals, it's useful todistinguish definitions of severalkinds:

Kinds of Definition:

1. Stipulative Definition2. Lexical Definition


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Stipulative Definition:

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

Lexical Definition:

A lexical definition simply reports the way in which a term is already used within a language community.

Kinds of Resolutions of Disputes:

1. Judicial Dispute Resolution2. Extrajudicial Dispute Resolution

3. Online Dispute Resolution4. Genuine and Verbal Resolution

Judicial Dispute Resolution:

. The legal system provides a necessary structure for the resolution of many dis

putes. However, somedisputants will not reach agreement through a collaborative processes. Some disputes need the


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coercive power of the state to enforce a resolution. Perhaps more importantly, many people want aprofessional advocate when they become involved in a dispute, particularly if the dispute involvesperceived legal rights, legal wrongdoing, or threat of legal action against them.

. The most common form of judicial dispute resolution is litigation. programs annexed to the courts, tofacilitate settlement of lawsuits.

Extrajudicial Dispute Resolution

. Some use the term dispute resolution to refer only to alternative dispute resolution (ADR), that is,

extrajudicial processes such as arbitration, collaborative law, and mediation used to resolve conflictand potential conflict between and among individuals, business entities, governmental agencies, and(in the public international law context) states.

Online Dispute Resolution

. Dispute resolution can also take place on-line or by using technology in certain cases. Online disputeresolution, a growing field of dispute resolution, uses new technologies to solve disputes. OnlineDispute Resolution is also called "ODR". Online Dispute Resolution or ODR also involves theapplication of traditional dispute resolution methods to disputes which arise online

Genuine and Verbal Resolution

. Genuine disputes involve disagreement about whether or not some specific proposition is true. Sincethe people engaged in a genuine dispute agree on the meaning of the words by means of which theyconvey their respective positions, each of them can propose and assess logical a


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rguments that mighteventually lead to a resolution of their differences.

. Merely verbal disputes, on the other hand, arise entirely from ambiguities inthe language used toexpress the positions of the disputants. A verbal dispute disappears entirely once the peopleinvolved arrive at an agreement on the meaning of their terms, since doing so reveals theirunderlying agreement in belief.

3. Denotation (Extension) and Connotation (Intension)

4. Extension, and Denotative Definitions

A denotative definition tries to identify the extension of the term in question.Thus, wecould provide a denotative definition of the phrase "this logic class" simply bylisting allof our names.

The extension of a general term is just the collection of individual things to which it is correctly applied. Thus,the extension of the word "chair" includes every chair that is (or ever has beenor ever will be) in the world.

5. Intension, and Connotative Definition


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The intension of a general term, on the other hand, is the set of features whichare shared by everything towhich it applies. Thus, the intension of the word "chair" is (something like) "apiece of furniture designed tobe sat upon by one person at a time."

A connotative definition tries to identify the intension of a term by providingasynonymous linguistic expression or an operational procedure for determining theapplicability of the term.

6. Rules for Definition by Genus and Difference

Classical logicians developed an especially effective method of constructing connotative definitions forgeneral terms, by stating their genus and differentia.

Five rules by means of which to evaluate the success of connotative definitionsby genus and differentia:

1. Focus on essential features. Although the things to which a term applies mayshare manydistinctive properties, not all of them equally indicate its true nature.

2. Avoid circularity. Since a circular definition uses the term being defined aspart of its owndefinition, it can't provide any useful information; either the audience alreadyunderstands themeaning of the term, or it cannot understand the explanation that includes thatterm. Thus, for

example, there isn't much point in defining "cordless 'phone" as "a telephone that has no cord."

3. Capture the correct extension. A good definition will apply to exactly the same things as theterm being defined, no more and no less. There are several ways to go wrong. Consider


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alternative definitions of "bird":

"warm-blooded animal" is too broad, since that would include horses, dogs, and aardvarks alongwith birds.

"feathered egg-laying animal" is too narrow, since it excludes those birds who happen to bemale, and

"small flying animal" is both too broad and too narrow, since it includes bats (which aren't birds)and excludes ostriches (which are).

Successful intensional definitions must be satisfied by all and only those things that are includedin the extension of the term they define.

4. Avoid figurative or obscure language. Since the point of a definition is to explain the meaning ofa term to someone who is unfamiliar with its proper application, the use of lang

uage thatdoesn't help such a person learn how to apply the term is pointless. Thus, "happiness is a warmpuppy" may be a lovely thought, but it is a lousy definition.

5. Be affirmative rather than negative. It is always possible in principle to explain the applicationof a term by identifying literally everything to which it does not apply. In a few instances, thismay be the only way to go: a proper definition of the mathematical term "infinit

e" might well benegative, for example. But in ordinary circumstances, a good definition uses positivedesignations whenever it is possible to do so. Defining "honest person" as "someone who rarelylies" is a poor definition.


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IV. DEDUCTIVE REASONING

A. Categorical Propositions

1. Categorical Propositions and Classes

2. Quality, Quantity and Distribution

3.The Traditional Square of Opposition

4. Further Immediate Inferences

5 Existential Import

6. Symbolism and Diagrams for Categorical Propositions

1. Categorical Propositions and Classes:

. Propositions are Statements or sentences where the content or meaning of a meaningfuldeclarative sentence. Statements or sentences that posses a quality or propertyof beingeither TRUE or FALSE. External manifestation of the mental product of Judgement

. Categorical Propositions are IS THE KIND OF PROPOSITION WHEREIN THE JUDGEMENTISDONE IN ABSOLUTE MANNER, i.e., The agreement or disagreement between the subjectand the predicate, is done in an absolute manner and MAKES A DIRECT ASSERTION OFAGREEMENT BETWEEN THE SUBJECT AND THE PREDICATE.

. Examples:a) HONEST FILIPINOS AVOID CHEATERS.

(asserts that the entire class of honest Filipinos is included in the class of peoplewho avoid liars.)

b) PEDICABS DO NOT BELONG TO EXPRESSWAYS.


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(asserts that the entire class of Pedicabs is excluded from the class of vehicles thatbeling to expressways.)

c) MANY STUDENTS HAVE CELLPHONES.d) NOT ALL LONG DISTANCE RELATIONSHIPS HAVE HAPPY ENDINGS.e) ANN CURTIS IS A FAMOUS SHOWBIZ PERSONALITY.

Classes of Categorical Propositions:

1. THOSE THAT ASSERT THAT THE WHOLE SUBJECT CLASS IS INCLUDED IN THE PREDICATECLASS.

2. THOSE THAT ASSERT THAT PART OF THE SUBJECT CLASS IS INCLUDED IN THE PREDICATECLASS.

3. THOSE THAT ASSERT THAT THE WHOLE SUBJECT CLASS IS EXCLUDED FROM THEPREDICATE CLASS

4. THOSE THAT ASSERT THAT PART OF THE SUBJECT CLASS IS EXCLUDED FROM THEPREDICATE CLASS.

3 Elements of a Proposition:

1. Subject This man..2. Coupla is...


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3. Predicate a doctor.

2. Quantity, Quality and Distribution

Quantity of a Proposition: Is equivalent of a quantity of a subject.

1. SINGULAR

- Stands for a single definite individual group

- Example: Aristotle is the father of logic.

2. PARTICULAR

- The subject designates an indefinite part of its total extension.

- Example: Some philosophers are atheists.

3. UNIVERSAL

- subject can apply to every portion of the term being indicated.

- Example: Love is not selfish.

Quantity of a Predicate:

1. Singular

- The predicate indicates any signs of singularity

- Ex. The new Dean of the College of Law of LDCU is Atty.Adel Tamano.


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2. Particular

- The predicate of a categorical is not singular and the copula is affirmative.

- A truly happy life is a life of goodness

3. Universal

- The predicate is not singular, and the copula is negative, then the predicateis universal.

- Most politicians are not moral persons.

A Proposition E Proposition

UNIVERSAL / SINGULAR

QUANTITY

UNIVERSAL / SINGULAR

QUANTITY


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AFFIRMATIVE

QUALITY

NEGATIVE

QUALITY

PARTICULAR

QUANTITY

PARTIcULAR

QUANTITY

AFFIRMATIVE

QUALITY

NEGATIVE

QUALITY

I Proposition O Proposition

A Proposition:

EXAMPLES:

1. ALL SOLDIERS ARE PATRIOTIC.

2. EVERY PHILOSOPHER IS A LOVER OF WISDOM.

3. AN ORANGUTAN IS AN APE.

*Quantity is UNIVERSAL/SINGULAR Quality is AFFIRMATIVE

E Proposition:

EXAMPLES:

1. NO SINNERS ARE SAINTS.

2. A GREEN MANGO IS NOT SWEET.

3. NEITHER DIAMONDS NOR GOLD IS EXPENSIVE.


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*Quantity is UNIVERSAL/SINGULAR Quality is NEGATIVE

I Proposition:

EXAMPLES:

1. SOME PHILOSOPHERS ARE ATHEISTS.

2.FILIPINOS ARE NATURE-LOVERS.

3. ALMOST ALL PEOPLE ARE GOD-FEARERS.

* Quantity PARTICULAR Quality -AFFIRMATIVE


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images.jpg

O Proposition:

EXAMPLES:

1. NOT ALL SENATORS ARE HONEST POLITICIANS.

2.NOT EVERYONE WHO CALLS TO ME LORD, LORD ARE PERSONS TO BE SAVED.

3. SOME FILIPINOS ARE NOT PATRIOTIC.

*Quantity PARTICULAR Quality - NEGATIVE

Quality of a Proposition:

1. AFFIRMATIVE

affirms class membership.

- connotes that all, or some, of the members indicated by the subject are contained in

the class indicated by the predicate.

2. NEGATIVE denies class membership. If all, or some of the members indicated bythesubject are not contained in the class indicated by the predicate

3.The Traditional Square of Opposition

. CONTRARIES CANNOT BOTH BE TRUE, BUT BOTH CAN BE FALSE.

. SUBCONTRARIES CANNOT BOTH BE FALSE, BUT BOTH CAN BE TRUE.. SUBALTERN PAIRS CAN BOTH BE TRUE OR BOTH BE FALSE.

. CONTRADICTORIES CANNOT BE TRU AND CANNOT BE FALSE.


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4. Further Immediate Inferences

1. Conversion

- is the new categorical proposition that results from putting the PREDICATEterm of the original proposition in the SUBJECT place of the NEW PROPOSITIONand the SUBJECT term of the original in the PREDICATE place of the new.

. Example. No cats are canines. Some snakes are poisonous animals

No canines are cats. Some poisonous Animals are snakes

- The converse of any E or I propositions are true only if the original proposition wastrue. From either pair of examples above, both propositions are true or both arefalse.That is why conversion grounds an immediate inference for both E and I propositions.

2. Subalternation

- if we first perform a subalternation and then convert our result, then the truth of an Aproposition may be said, in "conversion by limitation," to entail the truth of an Iproposition with subject and predicate terms reversed

. Example: All dogs are mammals" to be true while "All mammals are dogs" is false

"Some females are not mothers" to be true while "Some mothers are not females" isfalse. Thus, conversion does not warrant a reliable immediate inference with respect toA and O propositions.

3. Obversion

- In order to form the obverse of a categorical proposition, we replace the predicateterm of the proposition with its complement and reverse the quality of the proposition,either from affirmative to negative or from negative to affirmative


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. Example: "All ants are insects" is "No ants are non-insects"

"No fish are mammals" is "All fish are non-mammals"

- Obversion is the only immediate inference that is valid for categorical propositions ofevery form. In each of the instances cited above, the original proposition and its obversemust have exactly the same truth-value, whether it turns out to be true or false.

4. Contrapositions

- The contrapositive of any categorical proposition is the new categorical propositionthat results from putting the complement of the predicate term of the originalproposition in the subject place of the new proposition and the complement of the

subject term of the original in the predicate place of the new

. Examples: "Some carnivores are not mammals" is "Some non-mammals are not non-carnivores."


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- the contrapositive of any A or O proposition is true if and only if the original proposition

was true. If we form the contrapositive of our result after performing subalternation,

then an E proposition, in "contraposition by limitation," entails the truth ofa related O

proposition

. If "No bandits are biologists" then "Some non-biologists are not non-bandits,"

(Provided that there is at least 1 member of the class designated by bandits)

- contraposition is not valid for E and I propositions.. Example: "No birds are plants" and "No non-plants are non-birds" need not havethesame truth-value

5. Existential Import

. A term, whether subject or predicate, is said to have existentialimport if the term implies the actual existence of members of thatcategory. Aristotelian logic inferred affirmative propositions suchas "All cats are felines" include that there are such entities ascats. Aristotelian logic also inferred the existence of members of Ipropositions. "Some diesel engines are engines powered bycoconut oil," also implied the existence of such diesel engines

6. Symbolism and Diagrams for Categorical Propositions

. The modern interepretation of categorical logic also permits a moreconvenient way of assessing the truth-conditions of categoricalpropositions, by drawing Venn diagrams, topological representationsof the logical relationships among the classes designated bycategorical terms. The basic idea is fairly straightforward:


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Each categorical term is represented by a labelledcircle. The area inside the circle represents theextension of the categorical term, and the areaoutside the circle its complement. Thus, members ofthe class designated by the categorical term would belocated within the circle, and everything else in theworld would be located outside it.


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We indicate that there is at least one member of aspecific class by placing an inside the circle; an outside the circle would indicate that there is at leastone member of the complementary class.

To show that there are no members of a specificclass, we shade the entire area inside the circle;shading everything outside the circle wouldindicate that there are no members of thecomplementary class.

In order to represent a categorical proposition, we must draw two overlapping circles,creating four distinct areas corresponding to four kinds of things:

1. those that are members of the class designated by the subject term but not of thatdesignated by the predicate term;

2. those that are members of both classes;

3. those that are members of the class designated by the predicate term but notofthat designated by the subject term;

4. and those that are not members of either class.

The universal negative (E) proposition asserts thatnothing is a member of both classes designated by itsterms, so its diagram shades the area in which the twocircles overlap.


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The particular affirmative (I) proposition asserts thatthere is at least one thing that is a member of bothclasses, so its diagram places an in the area wherethe two circles overlap.


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two diagrams models the contradictory relationshipbetween E and I propositions; one of them must betrue and the other false, since either there is at leastone member that the two classes have in common orthere are none.

The particular negative (O) proposition asserts that there isat least one thing that is a member of the class designatedby its subject term but not of the class designated by itspredicate term, so its diagram places an in the area insidethe circle that represents the subject term but outside thecircle that represents the predicate term.

Finally, the universal affirmative (A) proposition asserts thatevery member of the subject class is also a member of thepredicate class. Since this entails that there is nothing that isa member of the subject class that is not a member of thepredicate class, an A proposition can be diagrammed byshading the area inside the subject circle but outside thepredicate circle.

B. Categorical Syllogisms

1. Standard-Form Categorical Syllogisms

2. The Formal Nature of Syllogistic Argument

3. Venn Diagram: Technique for Testing Syllogisms

4. Six Rules of Categorical Syllogisms

1. Standard-Form Categorical Syllogism

- A categorical syllogism is a verbal expression of an inference. It is an oral orwritten discourseshowing the agreement or disagreement between two terms on the basis of their respective relationto a common third term


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- Is any argumentation in which, from two prepositions called the premise, we conclude a thirdproposition called the conclusion, which is so related to the premise taken jointly that if thepremises are true, the conclusion must also be true

- The logical form is the structure of a categorical syllogism indicated by itsfigures and moods.

. Figure is the arrangement of the terms. major, minor, middleterms of the argument.

a. Major term is found in the major premise, used either as subjector predicate, or as predicate of the conclusion. Since the major termhas the greatest extension, it has the greatest concept compared tothe other terms.

b. Minor term is the term whose function is to mediate between theother two terms. In an affirmative syllogism. The middle term unitesthe major term and the minor term. In a negative syllogism, itseparates the two. thus, the quality of the syllogism depends on therole of the middle term toward the other two terms. The middleterm is never to be found in the conclusion. It is used either assubject or predicate in the premises.

. Mood is the arrangement of the preposition by quantity orquality.

2. The Formal Nature of Syllogistic Argument

A categorical syllogism must always have that SEQUENTIAL RELATION as adifferentiating mark of a true and valid syllogism from what is not.

SEQUENTIAL RELATION refers to the interdependence of the premise upon oneanother. The sure sign of the sequential relation is the presence of a middleterm in the premise.

NOT A VALID SYLLOGISM.

. No sequential relation between the firstand second premise because there is no


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middle term to connect or disconnect thetwo terms.. There is no relation between the twopremise in which to derive a validconclusion.. The above supposed conclusion is noconclusion at all.

EXAMPLE: Every man is biped.

But every cow is quadruped.

Therefore, every cow is not a man.

. VALID AND TRUE SYLLOGISM

. There exist a sequential flow of thoughtfrom the first premise to the secondpremise, and then from the premise to theconclusion.. The propositions are connected to oneanother through the middle term creaturewhich connects the major term mortal and

the minor term person.

EXAMPLE: All creatures are mortal.But a person is a creature.Therefore, a person is mortal.


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21.jpgminor.jpg20.jpg

A syllogism is called categorical if the premise and the conclusion composing itarecategorical propositions expressed in a declarative form like women are beautiful.not allFilipinos are poor. Or every creature is good.

3. Venn Diagram: Technique for Testing Syllogisms

In order to test a categorical syllogism by the method of Venn diagrams, one must first represent both of itspremises in one diagram. That will require drawing three overlapping circles, for the two premises of astandard-form syllogism contain three different terms-minor term, major term, and middle term.

How to draw Venn Diagram:

STEP 1:

First draw three overlapping circles and label them to represent the

major, minor, and middle terms of the syllogism.

No M are P.

Some M are S.

Therefore, Some S are not P.

STEP 2:

Since the major premise is a universal proposition, we may begin withit. The diagram for "No M are P" must shade in the entire area in whichthe M and P circles overlap. (Notice that we ignore the S circle by


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shading on both sides of it.)


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22.jpg23.jpg24.jpg

Now we add the minor premise to our drawing. The diagram for "SomeM are S" puts an inside the area where the M and S circles overlap.But part of that area (the portion also inside the P circle) has alreadybeen shaded, so our must be placed in the remaining portion.

Next, on this framework, draw the diagrams of both of the syllogism's premises.

a. Always begin with a universal proposition, no matter whether it is the majoror the minorpremise.b. Remember that in each case you will be using only two of the circles in eachcase; ignore the

third circle by making sure that your drawing (shading or ) straddles it.

STEP 3:

Ignoring the M circle entirely, we need only ask whether the drawing ofthe conclusion "Some S are not P" has already been drawn.

Finally, without drawing anything else, look for the drawing of the conclusion.If the syllogism is valid, thenthat drawing will already be done.

Since it perfectly models the relationships between classes that are at work incategorical logic, thisprocedure always provides a demonstration of the validity or invalidity of any categorical syllogism.

Here is a diagram of a syllogistic form. In such case, both of thepremises have already been drawn in the appropriate way, so if thedrawing of the conclusion is already drawn, the syllogism must be valid,and if it is not, the syllogism must be invalid.


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AAA-1 (valid)All M are P.All S are M.Therefore, All S are P.


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4. Six Rules of Categorical Syllogisms

Rule 1: A syllogism must contain exactly three terms, each of which is used in the same sense.

- The use of exactly three categorical terms is part of the definition of a categorical syllogism, and we sawearlier that the use of an ambiguous term in more than one of its senses amountsto the use of two distinctterms. In categorical syllogisms, using more than three terms commits the fallacy of four terms.

This syllogism appears to have only threeterms, but there are really four since oneof them, the middle term power is usedin different senses in the two premises.

Example of INVALID SYLLOGISM: Power tends to corrupt.Knowledge is power.

Knowledge tends to corrupt

Rule 2: In a valid categorical syllogism the middle term must be distributed inat least one of the premises.

- In order to effectively establish the presence of a genuine connection betweenthe major and minor terms,the premises of a syllogism must provide some information about the entire classdesignated by the middleterm. If the middle term were undistributed in both premises, then the two portions of the designated classof which they speak might be completely unrelated to each other. Syllogisms thatviolate this rule are said tocommit the fallacy of the undistributed middle.

The middle term is what connects themajor and the minor term. If the middleterm is never distributed, then the major

and minor terms might be related todifferent parts of the M class, thus giving nocommon ground to relate S and P.

Example of INVALID SYLLOGISM: All sharks are fishAll salmon are fish


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All salmon are sharks

Rule 3: In a valid categorical syllogism if a term is distributed in the conclusion, it must be distributed inthe premises.

- A premise that refers only to some members of the class designated by the major or minor term of asyllogism cannot be used to support a conclusion that claims to tell us about every member of that class.Depending which of the terms is misused in this way, syllogisms in violation commit either the fallacy of theillicit major or the fallacy of the illicit minor.

When a term is distributed in the conclusion,lets say that P is distributed, then that term issaying something about every member of theP class. If that same term is NOT distributed inthe major premise, then the major premise issaying something about only some membersof the P class.

Example of INVALID SYLLOGISM: All horses are animalsSome dogs are not horsesSome dogs are not animals


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Rule 4: No syllogism can have two negative premises.

- The purpose of the middle term in an argument is to tie the major and minor terms together in such a waythat an inference can be drawn, but negative propositions state that the terms of the propositions areexclusive of one another. In an argument consisting of two negative propositionsthe middle term is excludedfrom both the major term and the minor term, and thus there is no connection between the two and noinference can be drawn. A violation of this rule is called the fallacy of exclusive premises.

If the premises are both negative, then therelationship between S and P is denied. Theconclusion cannot, therefore, say anything in apositive fashion. That information goesbeyond what is contained in the premises.

Example of INVALID SYLLOGISM: No fish are mammalsSome dogs are not fishSome dogs are not mammals

Rule 5: If either premise of a valid categorical syllogism is negative, the conclusion must be negative.

- An affirmative proposition asserts that one class is included in some way in another class, but a negativeproposition that asserts exclusion cannot imply anything about inclusion. For this reason an argument with a

negative proposition cannot have an affirmative conclusion. An argument that violates this rule is said tocommit the fallacy of drawing an affirmative conclusion from a negative premise.

Example of INVALID SYLLOGISM: All crows are birdsSome wolves are not crowsSome wolves are birds

Rule 6. In valid categorical syllogisms particular propositions cannot be drawnproperly from universalpremises.

- Because we do not assume the existential import of universal propositions, they cannot be used as premisesto establish the existential import that is part of any particular proposition.The existential fallacy violates thisrule. Although it is possible to identify additional features shared by all valid categorical syllogisms (none ofthem, for example, have two particular premises), these six rules are jointly sufficient to distinguish betweenvalid and invalid syllogisms.


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Thus, if the syllogism has universal premises, theynecessarily say nothing about existence. Yet if theconclusion is particular, then it does saysomething about existence. In which case, theconclusion contains more information than thepremises do, thereby making it invalid.

Example of INVALID SYLLOGISM: All mammals are animalsAll tigers are mammalsSome tigers are animals


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C. Arguments in Ordinary Language

1. Reducing the Number of Terms in a Syllogistic Argument

2. Translating Categorical Propositions into Standard Form

3.Uniform Translation

4.Enthymemes

5 Sorites

6. Disjunctive and Hypothetical Syllogisms

7.The Dilemma

1. Reducing the Number of Terms in a Syllogistic Argument

In slightly more complicated instances, an ordinary argument may deal with more

than three terms, but itmay still be possible to restate it as a categorical syllogism. Two kinds of tools will be helpful in making such atransformation:

STEP 1: First, it is always legitimate to replace one expression with another that means the same thing. Ofcourse, we need to be perfectly certain in each case that the expressions are genuinely synonymous. But inmany contexts, this is possible: in ordinary language, "husbands" and "married males" almost always meanthe same thing.

STEP 2: Second, if two of the terms of the argument are complementary, then appropriate application of theimmediate inferences to one of the propositions in which they occur will enableus to reduce the two to asingle term.

Consider, for example, "No dogs are non-mammals, and some non-canines are not non-pets, so some non-mammals are pets." Replacing the first proposition with its (logically equivalent) obverse, substituting "dogs"for the synonymous "canines" and taking the contrapositive of the second, and applying first conversion andthen obversion to the conclusion, we get the equivalent standard-form categorica

l syllogism:

All dogs are mammals.

The invalidity of this syllogism is more readilyapparent than that of the argument from which itwas derived.

Some pets are not dogs.


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Therefore, Some pets are not mammals.

2. Translating Categorical Propositions into Standard Form

We may need only to re-arrange the propositions of the argument in order to translate itinto a standard-form categorical syllogism.

Thus, for example, "Some birds are geese, so some birds are not felines, since no geese arefelines" is just a categorical syllogism stated in the non-standard order minorpremise,conclusion, major premise; all we need to do is put the propositions in the right order, andwe have the standard-form syllogism: No geese are felines.

Some birds are geese.

Therefore, Some birds are not felines.

3.Uniform Translation


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In order to achieve the uniform translation of all three propositions containedin a categorical syllogism, it issometimes useful to modify each of the terms employed in an ordinary-language argument by stating it interms of a general domain or parameter.

The goal here, as always, is faithfully to represent the intended meaning of each of the offered propositions,while at the same time bringing it into conformity with the others, making it possible to restate the whole asa standard-form syllogism.

Thus, for example, in the argument, "The attic must be on fire, since it's fullof smoke, and where there'ssmoke, there's fire," the crucial parameter is location or place. If we supposethe terms of this argument tobe "places where fire is," "places where smoke is," and "places that are the attic," then by applying our othertechniques of restatement and re-arrangement, we can arrive at the syllogism:

This standard-form categorical syllogismof the form AAA-1 is clearly valid.

All places where smoke is are places where fire is.

All places that are the attic are places where smoke is.

Therefore, All places that are the attic are places where fire is.

4.Enthymemes

- Another special case occurs when one or more of the propositions in a categori

cal syllogism is left unstated.Incomplete arguments of this sort, called enthymemes are said to be "first-," "second-," or "third-order,"depending upon whether they are missing their major premise, minor premise, or conclusion respectively.

In order to show that an enthymeme corresponds to a valid categorical syllogism,we need only supply themissing premise in each case.

Thus, for example, "Since some hawks have sharp beaks, some birds have sharp beaks" is a second-orderenthymeme, and once a plausible substitute is provided for its missing minor pre

mise ("All hawks are birds"),it will become the valid IAI-3 syllogism:

Some hawks are sharp-beaked animals.

All hawks are birds.

Therefore, Some birds are sharp-beaked animals.


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5.Sorites

Finally, the pattern of ordinary-language argumentation known as sorites involves several categoricalsyllogisms linked together. The conclusion of one syllogism serves as one of thepremises for anothersyllogism, whose conclusion may serve as one of the premises for another, and soon. In any such case, ofcourse, the whole procedure will comprise a valid inference so long as each of the connected syllogisms isitself valid.

6. Disjunctive and Hypothetical Syllogisms (KINDS OF COMPOUND PROPOSITION)

DISJUNCTIVE:


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The disjunctive holds that at least one of the two components are true, allowingfor the possibility that bothare true. If we have a disjunction as one premise, and a denial of one of the disjuncts as a second premise, wecan validly infer that the other disjunct component is true

P1 Either that's a gun in your pocket, or you're happy to see me

P2 You don't have a gun in your pocket (This is implied - implied premises are called "enthymemes")

C: You must be happy to see me

This argument is valid, because it eliminates one of the disjuncts. Take a lookat this argument:

P1 Either that's a gun in your pocket, or you're happy to see me

P2 You have a gun in your pocket

C: Therefore you're not happy to see me

This argument is invalid. It bears a superficial similiarty to the above argument, but rather than eliminate oneof the disjuncts, it merely affirms one of them.

HYPOTHETICAL SYLLOGISMS:

We can call these statements If/Then statements, where the "If" part is the antecedant and the partfollowing after "Then" is the consequent.

A conditional that contains conditional statements exclusively is called a purehypothetical syllogism:

Example: P1: If you study (antecedent), then you will become a good student (consequent).

P2: If you become a good student, then you will go to college

Therefore, If you study, then you will go to college.

Notice that the first premise and the conclusion have the same antecedent, and t

he second premise and theconclusion have the same consequent.

There are two valid and two invalid forms of a mixed hypothetical syllogism:

a) modus ponens (From the Latin "ponere", "to affirm")b) modus tollens (Latin: "To deny")


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The next form, Affirming the consequent, is invalid: Affirming theconsequent

. If P is true then Q is true

. Q is true

. Therefore, P is true

MODUS PONENS:

If P is true, then Q is true

P is true

Therefore, Q is true

MODUS TOLLENS:

If P is true, then Q is true

Here the syllogism denies the consequent of the conditional premise, andthe conclusion denies the antecedant.


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Q is not true

Therefore, P is not true

7.The Dilemma

It is a form of argument that is composed of a conjunction of two conditional hypothetical statements as itsmajor premise.

KINDS:

1. Simple Dilemma

. A form wherein the conclusion is a categorical proposition.

Example:

The security officer of a certain university was called into the office of the chief security on the issue

of allowing students to enter the school premises without wearing their IDs. Thechief security saidto the guard:

Either you were playing favorites or you were not; if you were playing favorites,then you should bepunished for being incompetent. If you were not playing favorites, you deserve punishment fordereliction of duty. Therefore, in either case, you should be punished.

2. Complex Dilemma

. It is a form of dilemma wherein the conlusion is a disjunctive proposition offering alternatives.

Example:

If the next president of the Phil. Is a re-electionist, then he has nothing newto offer. If the nextpresident of the Phil. Is not a re-electionist, then he is not yet equipped in the countrys political andeconomic matters. Therefore, in either case, the next president of the Philippines has nothing new to

offer or he is not yet equipped in the countrys political and economic matters.

D. Symbolic Logic


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1. The Value of Special Symbols

2. The Symbols for Conjunction, Negation, and Disjunction

3. Conditional Statements and Material Implication

4. Argument Forms and Arguments

5. Statement Forms, Material Equivalence, Logical Equivalence

6. The Paradoxes of Material Implication

7. The Three Laws of Thought

2. The Symbols for Conjunction, Negation, and Disjunction

Conjunction:

In logic, a conjunction is a compound sentence formed by using the word and to join two simplesentences. The symbol for this is .. (whenever you see . read 'and') When two simple sentences, pand q, are joined in a conjunction statement, the conjunction is expressed symbollically as p . q.


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Simple Sentences

Compound Sentence : conjunction

p: Joe eats fries.q: Maria drinks soda.

p . q : Joe eats fries, and maria drinks soda.

Conjunction = and =

Conjunction is only true if both conjuncts are true

Negation:

Indicates the opposite, usually employing the word not. The symbol to indicate negation is : ~

Original Statement

Negation of statment

Today is monday.

Today is not monday.

That was fun.

That was not fun.

Negation = not = ~

Negation of a statement is true if statement is falseNegation of a statement is false if statement is true

Disjunction:

. In logic, a disjunction is a compound sentence formed by using the word or tojoin twosimple sentences. The symbol for this is .. (whenever you see . read 'or') Whentwo simplesentences, p and q, are joined in a disjunction statement, the disjunction is expressedsymbollically as p . q.


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Pneumonic: the way to remember the symbol for disjuntion is that, this symbol .lookslike the 'r' in or, the keyword of disjunction statements.

Simple Sentences

Compound Sentence : disjunction

p: The clock is slow.q: The time is correct.

p . q : The clock is slow, or the time is correct.

Warning and caveat: The only way for a disjunction to be a false statement is ifBOTH halves arefalse. A disjunction is true if either statement is true or if both statements are true! In other words,the statement 'The clock is slow or the time is correct' is a false statement on

ly if both parts arefalse! Likewise, the statement 'Mr. G teaches Math or Mr. G teaches Science' istrue if Mr. G isteaches science classes as well as math classes!

Disjunction = or = v

Disjunction is true if either disjunct is true

Examples:


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1. It is not true that evil spirits exist.

First step: Make a dictionary (define statements)

Second step: Look at the sentence, symbolize statements correctly (using , ~, orv)

(Third step: Determine truth values)

Answer: It is not true that evil spirits exist.

~E

E=Evil spirits exist.

If evil spirits do exist (E is True), then ~E is false.

If evil spirits do not exist (E is False), then ~E is true.

2. Determine whether the following is true:

~(A v C) v ~(X ~Y) Given: A, B, and C are True X, Y, and Z are False

~(A v C) v ~(X ~Y)

. The main connective = the middle wedge (v) (disjunction)

. Therefore we have two disjuncts

. Left disjunct= ~(A v C)

. Right disjunct = ~(X ~Y)

. Strategy: determine truth values of each disjunct, then we know if at least one disjunct is true, thiswill make the whole statement true. ~(A v C) v ~(X ~Y). Left disjunct: ~(A v C). Both A and C are true. This makes (A v C) true.. But (A v C) is negated, so ~(A v C) is false.. Right disjunct: ~(X ~Y). X is false.. Y is false, so this means ~Y is true.

. This makes the inner conjunction false (to be true, both conjuncts (X and ~Y)must both be true)

. Because the whole statement (X ~Y) is false, this makes its negated form ~(X ~Y) true. Since the left disjunct is false, and the right disjunct is true, this means ~(A v C) v ~(X ~Y) is true(since at least one disjunct is true)


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3. Conditional Statements and Material Implication

Conditional statement: when two statements are combined by placing the word if before the first andthen before the second

. Ifthen

. We use the arrow . or horseshoe to represent the if-then phrase

. Also called a hypothetical, an implication, or an implicative statement

The component statement that follows the if is called the antecedent The component statement that follows the then is called the consequent If (antecedent), then (consequent) A conditional statement asserts that if its antecedent is true, then its consequ

ent is also true But as in disjunction, there are a few different senses in which a conditional can be interpreted


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4 Types of Implications:

Logical Implication: the consequent follows logically from its antecedent

Example: If all humans are mortal and Socrates is a human, then Socrates is mortal.

Definitional Implication: the consequent follows the antecedent by definition

Example: If Leslie is a bachelor, then Leslie is unmarried.

Causal Implication: The connection between antecedent and consequent is discovered empirically

Example: If I put X in acid, then X will turn red.

Decisional Implication: no logical connection nor one by definition between theconsequent and antecedent.This is a decision of the speaker to behave in the specified way under the specified circumstances

Example: Is we lose the game, then Ill eat my hat.Understanding the Implication:

No matter what type of implication is asserted by a conditional statement, partof its meaning is the negationof the conjunction of its antecedent with the negation of its consequent

For a conditional to be true (e.g. If p then q), ~(p ~q) must be true:

Think p=A piece of blue litmus paper is placed in that solution.

q=The piece of blue litmus paper will turn red.

If p then q = false if paper is placed in solution, but doesnt turn red

The horseshoe symbol does not stand, therefore, for all the meanings of if-then there are severalmeanings. p q abbreviates ~(p ~q), whose meaning is included in the meanings ofeach kind of implication


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Material Implication:

. represents the material implication. A fifth type of implication

E.g. If Hitler was a military genius, then Im a monkeys uncle.

No real connection between antecedent and consequent

. This kind of relationship is what is meant by material implication

. It just asserts that it is not the case that the antecedent is true when theconsequent is false.

. Many arguments contain conditional statements of various kinds of implication,but the validity of all

valid arguments (of the general type with which we will be concerned) is preserved, even if theadditional meanings of their conditional statements are ignored.

If can be replaced by such phrases as:

. in case

. provided that

. given that

. on condition that

Some indicator words for then include:

. implies...

. entails

4. Argument Forms and Arguments


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Substitution-Instances

Since the statements of the propositional calculus are propositions, they can becombined to formlogicalarguments, complete with one or more premises and a single conclusion that may follow validly fromthem. Thus, for example, each of the following is an argument expressed in the language of symbolic logic:

A . B (D B) . ~E (A . E) . (D = B)

A D B A . E

_______ _______________ ________________________

B ~E D = B

What is more, notice that all three of these arguments share a common structure:the first premise of each is

a . statement; the second premise is the antecedent of that statement; and the conclusion is its consequent.We can exhibit this common structure more clearly by using statement variables to express the argumentforminvolved:

p . q

p

________

q

Each of the three arguments above is a substitution instance of this argument form, since each of themresults from the substitution of an appropriate (simple or compound) statement for each of the statementvariables in the argument form. Notice that these substitutions must be consistent in each application; oncewe've put D B in the place of p in the first premise of the second argument, forexample, we must also put

it in the place of p in the second premise. In the same way, the first and thirdarguments abovealong withindefinitely many otherscan be shown to be substitution-instances of the same argument form. Mostarguments are substitution-instances of several distinct argument forms, each ofwhich can be no morecomplex in structure than the argument itself.

Testing for Validity


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Recognizing individual arguments as substitution-instances of more general argument forms is animportant skill because, as we've already seen, the validity of any argument depends solely upon its logicalform. An argument in the propositional calculus is valid whenever it is a substitution-instance of an argumentform in which it is impossible for the premises to be true and the conclusion false. Since the argument formreliably leads from premises of a certain general structure to a conclusion of adifferent structure, everysubstitution-instance of that argument form must express a valid argument.

Thus, the same truth-tables we used to define the statement connectives providean effective decisionprocedure for determining the validity of arguments in the propositional calculus. We simply chart the truth-values of each premise and the conclusion of an argument form for every possiblecombination of truth-values for the statement variables involved, and look to see what happens on those lines of the truth-table inwhich all of the premises are true. If the conclusion is also true on each of these lines, then the inferencecaptured by the argument form is a valid one, and arguments of this form must all be valid. If, however, there

is even a single line on which all of the premises are true but the conclusion is false, then the inference is


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invalid, and we cannot be sure whether arguments of this form are valid or invalid. (They certainly are notvalid because of this form, but of course some of them may happen to be substitution-instances of otherargument forms whose inferences are valid.)

Modus Ponens

Consider, for example, what happens when we construct a truth-table that lists each of the fourcombinations of truth-values that the component statements could exhibit in thesimple argument form thatwe identified at the top of this page.

1st Premise

2nd Premise

Conclusion

p

q

p . q

p

q

T

T

T

T

T

T

F

F

T

F

F

T

T


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F

T

F

F

T

F

F

p . q

p

_______

q

This truth-table shows that (no matter what statements wesubstitute for p and q ) both of the premises of the argumentwill be true only on the first line (when both componentstatements are true). But on that line, the conclusion is alsotrue, so the inference is valid. Whenever we come across anargument that shares this basic structure, we can be perfectlycertain of its logical validity. In fact, arguments of this form areso common that the form itself has a name, Modus Ponens, which we will usually a

bbreviate as M.P.

On the other hand, consider what happens when we construct a truth-table for testing the validity of adistinct, though superficially similar, argument form:

1st Premise

2nd Premise

Conclusion

p

q

p . q


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q

p

T

T

T

T

T

T

F

F

F

T

FT

T

T

F

F

F

T

F

F

p . q

q

_______

p

In arguments of this form, both premises are true on the firstand on the third lines of the truth-table. While the conclusion is


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true on the first line, on the third line it is false. Since it istherefore possible for the premises to be true while theconclusion is false, the inference is invalid. This unreliableargument form is called the fallacy of affirming the consequent.Although it might be mistaken for M.P. at a casual glance, thefallacyunlike its valid cousindoes not guarantee the truth of its conclusion.


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Modus Tollens

Another common argument form with a valid inference is Modus Tollens (abbreviated as M.T.), whichhas the form:

1st Premise

2nd Premise

Conclusion

p

q

p . q

~ q

~ p

T

T

T

F

F

T

F

F

T

F

F

T

T

F

T

F

F


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T

T

T

p . q

~ q

_______

~ p

As the truth-table shows, the premises are true only when bothof the component statements are false, in which case theconclusion is also true. There is no line on which both premises

are true and the conclusion false, so the inference is valid, asare all substitution-instances of this argument form.

As with M.P., there is an argument form superficiallysimilar to M.T. that yields entirely different results.

1st Premise

2nd Premise

Conclusion

p

q

p . q

~ p

~ q

T

T

T

F

F


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T

F

F

F

T

F

T

T

T

F

F

F

T

T

T

p . q

~ p

_______

~ q

This is the fallacy of denying the antecedent. As the truth-tableto the right clearly shows, it is an unreliable inference, since it ispossible (on the third line) for both of its premises to be truewhile its conclusion is false. Substitution-instances of thisargument form may not be valid.

Hypothetical Syllogism


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1st Premise

2nd Premise

Conclusion

p

q

r

p . q

q . r

p . r

T

T

T

TT

T

T

T

F

T

F

F


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T

F

T

F

T

T

T

F

F

F

T

F

F

T

T

T

T

T

F

T

F

T

F

T

F

F

T

T

T

T


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F

F

F

T

T

T

A larger truth-table is required to demonstrate thevalidity of the argument form called HypotheticalSyllogism (H.S.), since it involves three statement variablesinstead of two, and we must consider all eight of thepossible combinations of their truth-values:

p . q

q . r

_______

p . r

Despite its greater size, this truth-table establishes validity inexactly the same way as its more compact predecessors:both premises are true only on the first, fifth, seventh, and eighth lines, andthe conclusion is also true on

each

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