LEGAL TECHNIQUES AND LOGIC
 Methods in reasoning
 Logical organization of the legal language
LOGIC - study of reasoning; deals with language
- limits of your language is the limit of yourself
DIFFERENT MEANINGS:
1.
2.
3.
4.
Intuitive – result of direct observation
Abstractive – result of your thinking / judgment
Contrary – opposite side of the spectrum (happy – sad)
Contradictory – exact meaning of the opposite (true – false)
DEFINITION – ideas / concept
- It expresses what the thing is
1.
2.
3.
4.
5.
Real – use to identify what the thing really is; exact meaning / definite meaning
Stipulative – a definition as a result of deliberately assigning a meaning
Precising – makes the meaning scientific; totally eliminates biases
Persuasive – seek to spare emotions or influence; strives to convince people
Theoretical – express theological ; generalization about reality
Chapter 1
BASIC LOGICAL CONCEPTS
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LOGIC – is the study of the methods and principles used to distinguish correct reasoning from
incorrect reasoning
PROPOSITION – building blocks of every argument which is something that may be asserted or
denied
-
Refers to what declarative sentences are typically used to assert
Not peculiar to any language, but may be asserted in many languages
COMPOUND PROPOSITIONS – containing other propositions within themselves.
 Conjunctive Propositions – asserting the conjunction of two propositions is equivalent
to asserting each of the component propositions themselves; both propositions asserted
are equivalent
-
“The British were at the gates of Hamburg and Bremen” – conjunction of two
propositions namely: “The British were at the gates of Hamburg” and “The British
were at the gates of Bremen”
 Alternative or Disjunctive Propositions – one proposition is true, the other is false
-
Only compound “either-or” disjunctive proposition is asserted
“Circuit Courts are useful, or they are not useful.”
 Hypothetical or Conditional – only the “if-then” proposition is asserted by the
hypothetical or conditional statement, and the conditional statement might be true even
though both of its components were false.
-
“If God did not exist, it would be necessary to invent him.”
INFERENCE – refers to the process by which one proposition is arrived at and affirmed on the
basis of one or more other proposition accepted as the starting point of the process.
 To determine whether an inference is correct, the logician will examine the propositions
with which that process begins and ends; and the relations between them. This cluster of
propositions constitutes an argument, and therefore, there is an argument corresponding
to every possible inference.
ARGUMENT – any group of propositions of which one is claimed to follow from the others,
which are regarded as providing support or grounds for the truth of that one.
 An argument is not a mere collection of propositions; a passage may contain several
related propositions and yet contain no argument at all.
 For an argument to be present, the cluster of propositions must have a structure (by
using “premiss” and “conclusion”
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CONCLUSION – is the proposition that is affirmed on the basis of the other propositions of the
argument, and these other propositions, which are affirmed as providing support or reasons for
accepting the conclusion, are the PREMISSES of that argument.
 “No one was present when life first appeared on earth. Therefore any statement about
life’s origins should be considered as theory, not fact.”
-
Premiss – no one was present……
Conclusion – therefore any statement ……
TECHNIQUES IN ANALYZING ARGUMENTS
1. PARAPHRASE – setting forth its propositions in clear language and logical order
 Often assists our understanding of it because in doing so, we must bring to the
surface what is assumed in the argument but is not fully or explicitly stated
 “Archimedes will be remembered when Aeschylus is forgotten, because
languages die and mathematical ideas do not.”
-
To paraphrase:
1. Languages die.
2. The great plays of Aeschylus are in a language.
3. So the work of Aeschylus will eventually die.
4. Mathematical ideas do not die.
5. The great work of Archimedes was with mathematical ideas.
6. So the work of Archimedes will not die.
Therefore Archimedes will be remembered when Aeschylus is forgotten.
2. DIAGRAMMING – exhibiting its structure using spatial relations in two dimensions.
 Avoids the need to restate the premisses
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 Because (1) the greatest mitochondrial variations occurred in African people, scientists
concluded that (2) they had the longest evolutionary history, indicating (3) a probable
African origin for modern humans.
 To paraphrase:
1. The more mitochondrial variation in a people the longer its evolutionary
history;
2. The greatest mitochondrial variations occurred in African people.
Therefore African people have had the longest evolutionary history.
 To diagram
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 Conclusion-indicators:
Therefore
Hence
Thus
So
Accordingly
In consequence
Consequently
Proves that
As a result
For this reason
for these reasons
shows that
it follows that
entails that
we may infer
demonstrates that
I conclude that
ergo
which shows that
then
which means that
which entails that
which implies that
which allow us to infer that
which points to the conclusion that
 Premiss-indicators:
Since
Because
For
As
Follows from
As shown by
inasmuch as
as indicated by
the reason is that
for the reason that
may be inferred from
may be derived from
may be deduced from
in view of the fact that
can be shown by
is implied by
due to
assuming that
is proved by
can be concluded from
RHETORICAL – a question may suggest or assume a premiss when the question is one whose
answer the author believes to be obvious or inescapable.
 Arguments in which one of the premises is a question whose answer is assumed to be
evident are very common
 “If there is no one who desires to be miserable, there is no one, Meno, who desires evil;
for what is misery but the desire and possession of evil?”
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 The conclusions of arguments that depend on rhetorical questions are suspect. To avoid
responsibility for the forthright assertion of their premises, authors sometimes ask a
question whose answer is supposed to be obvious when that assumed answer actually
is dubious or even false.
UNSTATED PROPOSITIONS – when one or more of its constituent propositions is not stated
but is assumed to be understood; assumed; presumed
 “If the Miranda decision is reversed, police will no longer be compelled to give those
warnings [of the right to remain silent, etc.]; and if they aren’t compelled to give them,
they won’t give them. But because police interrogations take place out of public view, the
integrity of such interrogations can be safeguarded only if those Miranda warnings are
invariably given.”
-
The conclusion of their argument – that those warnings must always be given and
that the Supreme Court should not reverse the Miranda decision – did not need to
be stated in that context.
 Americans don’t like Asians; so Americans don’t like me.
-
The unstated proposition - “I am an Asian” – did not need to be stated in that
context.
ENTHYMEMES – arguments in everyday discourse often rely on some proposition that is not
stated.
 Sometimes it may not be obvious just how one would formulate the proposition on which
the speaker relies, even though, once formulated, it is readily accepted.
 “If one doesn’t believe that moral arguments make any difference, then one doesn’t
believe in republican government.”
-
In this enthymeme, the unstated premise is the claim that “believing in republican
government entails that one does believe that moral arguments make a difference”
– a claim that most of us would grant.
 On the other hand, the unstated proposition on which an enthymeme relies may not be
obvious, but disputable – and the absence of an explicit statement of that proposition
may serve to shield it from attack
 “This research [involving the use of embryonic stem cells] is illegal, for this reason: The
deliberate killing of a human embryo is an essential component of the contemplated
research.”
-
The stated premiss is true; if the embryo were not destroyed, research of that kind
would be impossible. But the conclusion that such research is illegal depends on
the unstated premiss that the killing of a human embryo is illegal – a claim that is
very much in dispute.
TWO MAJOR CLASSES OF ARGUMENTS
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1. DEDUCTIVE – makes the claim that its conclusion is supported by its premises
conclusively
 If a claim for conclusiveness is being made
 If the premises provides conclusive grounds for the conclusion
 A deductive argument is valid when, if its premisses are true, its conclusion must
be true
 Is one whose conclusion is claimed to follow from its premisses with absolute
necessity, this necessity not being a matter of degree and not depending in any
way on whatever else may be the case.
 Valid – if the claim that its premisses provide irrefutable grounds for the truth of
its conclusion, if it is a correct argument; conclusiveness of the relationship of
premiss and conclusion
 Invalid – if it is not correct, or that if the premisses when true fail to establish the
conclusion irrefutably; there are other basis for the conclusion
 Validity – applicable only to deductive arguments
-
refers to relation between propositions – between he set of propositions
that serve as the premisses of a deductive argument, and the one
proposition that serves as the conclusion of that argument
 Examples:

If all humans are mortal and Socrates is human, we may conclude that
Socrates is mortal.

All traditional politicians are power brokers and some local executives are
traditional politicians. Then it follows that some local executives are power
brokers.
2. INDUCTIVE – do not claim that their premises, even if true, support their conclusions
with certainty.
 Such claim is not being made
 The premisses merely supports the conclusion; based on supportive grounds
 Is one whose conclusion is claimed to follow from its premisses only with
probability, this probably being a matter of degree and dependent upon what else
may be the case
 The premises merely supports the conclusion (based on supportive ground)
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 Example:

Most corporation lawyers are conservatives.
Angela Palmieri is a corporation lawyer.
Therefore Angela Palmieri is probably a conservative.
TRUTH – is the attribute of a proposition that asserts what really is the case
TRUTH AND FALSITY – are attributes of individual propositions or statements
VALIDITY AND INVALIDITY – are attributes of arguments
ILLUSTRATIONS OF ARGUMENTS:
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Legal Techniques & Logic
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Chapter 4
FALLACIES
FALLACY – is a type of argument that may seem to be correct, but proves on examination not
to be so; in a very general sense, it is any error in reasoning
GROUPS OF FALLACIES
1. FALLACIES OF RELEVANCE – when an argument relies on premisses that are not relevant
to its conclusion, and that therefore cannot possibly establish its truth; the premises of the
argument are simply not relevant to the conclusion.
1.1 Appeal to Emotion / to the Populace (Ad Populum) – is fallacious because it
replaces the laborious task of presenting evidence and rational argument with
expressive language and other devices calculated to excite enthusiasm, excitement,
anger, or hate.
 When careful reasoning is replaced with devices calculated to elicit enthusiasm
and emotional support for the conclusion advanced.
 Everyone is selfish; everyone is doing what he believes will make himself
happier. The recognition of that can take most of the sting out of accusations that
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you're being "selfish." Why should you feel guilty for seeking your own happiness
when that's what everyone else is doing, too?
 “Band-Wagon Fallacy” from the known phenomenon that, in an exciting
campaign, many will be anxious to “jump on the bandwagon” to do what others
do because so many others are doing it.

“Why are so many people attracted to the Pontiac Grand Prix? It could be
that so many people are attracted to the Grand Prix because – so many
people are attracted to the Grand Prix! (bandwagon fallacy)
 Appeal to Pity (Argument ad misericordiam – literally means ‘merciful heart’) –
generosity and mercy of the audience are the special emotions appealed to.

When careful reasoning is replaced with devices calculated to elicit sympathy
on the part of the hearer for the objects of the speaker’s concern.

I, who am probably in danger of my life, will do none of these things. The
contrast may occur to [each juror’s] mind, and he may be set against me, and
vote in anger because he is displeased at me on this account. Now if there be
such a person among you – mind, I do not say that there is – to him I may
fairly reply: My friend, I am a man, and like other men, a creature of flesh and
blood, and not “of wood or stone” as Homer says; and I have a family, yes,
and sons, O Athenians, three in number, one almost a man, and the two
others who are still young; and yet I will not bring any of them here to petition
you for acquittal.
1.2 The Red Herring – an informal fallacy committed when some distraction is used to
mislead and confuse; deliberately misleading trail

One legislator, apparently speaking to protect his corporate donors, entered the
debate with the irrelevant point that there is a serious need for the provision of
better advice to retired persons on the investment of their pensions. No doubt
there is. But one commentator absolutely observed, “What does this have to do
with employers squandering their worker’s retirement?”

At Duke University in 2006, three student athletes were indicted for rape; the
indictments were plainly unfounded and soon withdrawn. When the prosecutor
was charged with misconduct in office, feelings at the university grew intense.
One member of the Duke faculty, writing in the local newspaper, defended the
prosecutor and some other faculty members who had supported him. In the
course of this defense, she argued that the real “social disaster” in the Duke rape
case was that “18 percent of the American population lives below the poverty
line” and that we do not have “national health care or affordable childcare.”
1.3 The Straw Man – may view this fallacy as a variety of the red herring, because it also
introduces a distraction from the real dispute. In this case, however, the distraction is
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of particular kind: it is an effort to shift the conflict from its original complexity into
different conflict, between parties other than those originally in dispute.
 In general, straw man often take the form of supposing that the position under
attack adopts the most extreme view possible – that every act or policy of a
certain kind is to be rejected. Its premises are not relevant to the conclusion that
was originally proposed.
 Often presents a genuine objection or criticism, and the objection may be sound,
but it is aimed at a new and irrelevant target.
 Every fallacious argument presents some risk of this kind; the fallacy of the straw
man invites it with special force.
 “You say that the New Testament teaches that we are not under law, and that we
are saved by grace through faith alone. Therefore, what you teach is that we can
sin all we want after we are saved.”
1.4 Argument Ad Hominem (Argument Against the Person) – a fallacious attack in
which the thrust is directed, not at a conclusion, but at the person who asserts or
defends it.
Ad Hominem arguments are fallacious (and often unfair to the adversary) because an
attack against some person is generally not relevant to the objective merits of the
argument that person has put forward.
 Abusive – participants in strenuous argument sometimes disparage the character
of their opponents, deny their intelligence or reasonableness, question their
integrity, and so on.
-
“Who cares what you think about movies? You're just an ignorant American
who doesn't know anything about real culture.”
-
“One dishonest and unworthy tactic used by several of my detractors is to
attribute to me complaints I never made and then to dismiss the
“complaints” as “irresponsible and evidence of my reckless unfairness.”
 Circumstantial – it is the irrelevance of the connection between the belief held
and the circumstances of those holding it that gives rise to the mistake. The
circumstances of one who makes (or rejects) some claim have no bearing on the
truth of that claim
-
Hunters, accused of the needless slaughter of unoffending animals,
sometimes reply by noting that “their critics eat the flesh of harmless cattle.”
1.5 Appeal to Force (Argument Ad Baculum) – literally means appeal to the stick; when
careful reasoning is replaced with direct or insinuated threats in order to bring about
the acceptance of some conclusion; abandonment of reason.
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 What is put forward may be a veiled threat, or a proposition that suggest some
danger if the proposition in question is not given full assent.

The President continues to have confidence in the Attorney General and I
have confidence in the Attorney General and you ought to have confidence in
the Attorney General, because we work for the President and because that’s
the way things are. And if anyone has a different view of that, or any different
motive, ambition, or intention, he can tell me about it because we’re going to
have to discuss your status.
1.6 Missing the Point (Ignoratio Elenchi) – when the premisses miss the point,
purporting to support one conclusion while in fact supporting or establishing another
 It arises when the argument goes awry – when, on close examination, there is a
“disconnect” between the premises and the conclusion.
 Deliberate deception
 Product of sloppy thinking, a confusion in reasoning that the author of the
argument herself does not fully recognize, or grasp.
 A mistake that is made in seeking to refute another’s argument.

One person emphasizes how important it is to increase funding for the public
schools. His opponent responds by insisting that a child’s education involves
much more than schooling and gets underway long before her formal
schooling begins.
-
That assertion is entirely reasonable, of course, but it misses the point of
what was said earlier. One party presents an argument for P, to alleviate
the need for funds; his interlocutor counters with an irrelevant Q, about
the importance of preschool education.
 Non sequitur (does not follow) – an argument in which the conclusion simply
does not follow from the premises; most commonly applied when the failure of
the argument is obvious, when the gap between the premises and the conclusion
is painfully wide.

The prisoner pleaded guilty. He then said he had made a mistake, and the
judge allowed him to change his plea to not guilty. The case was tried. The
jury acquitted. “Prisoner”, said Mr. Justice Hawkins, “a few minutes ago you
said you were a thief. Now the jury say you are a liar. Consequently, you are
discharged.”
2. FALLACIES OF DEFECTIVE INDUCTION – the premises may be relevant to the conclusion,
but they are far too weak to support the conclusion and wholly inadequate; what are asserted
as premises simply do not serve as good reasons to reach the conclusion drawn.
2.1 Appeal to Ignorance (Ad Ignorantiam) - The mistake that is committed when it is
argued that 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.
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Appeal to ignorance succeeds only when innocence must be assumed in the absence
of proof to the contrary; in other contexts, such an appeal is indeed an argument ad
ignoratiam.
 “No there isn’t. There really isn’t, but there is no evidence to the contrary, either.”
 The moon is not a perfect sphere, he replied, because there are surely crystal
mountains – invisible! – rising high from its surface. Because my theological
critics cannot prove the claim false, we cannot conclude that such mountains are
not there!
2.2 Appeal to Inappropriate Authority (Ad Verecundiam) – when the premises of an
argument appeal to the judgment of some person or persons who have no legitimate
claim to authority in the matter at hand.
Our mistake becomes one of reasoning (a fallacy) when our conclusion is based on
the verdict of an authority who has no rational claim to expertise in that matter.
 Advertising ‘testimonials’ – we are urged to drink a beverage of a certain brand
because some movie star or football coach expresses enthusiasm about it.
2.3
False Cause – when one treats as the cause of a thing what is not really the cause of
that thing, often relying (as in the subtype post hoc ergo propter hoc) merely on the
close temporal succession of two events.

When mistakenly presume that one event is caused by another because it
follows that other closely in time. (fallacy of post hoc ergo propter hoc)


Committed when one mistakenly argues against some proposal on the ground
that any change in a given direction is sure to lead to further changes in the
same direction – and thus to grave consequences (fallacy of slippery slope)


2.4
The sun would invariably reappear after an eclipse if the drums had been
beaten in the darkness.
One common objection to the legalization of assisted suicide is that once
formal permission has been given to medical doctors to act in a way that is
of disputable morality, doctors will be led to engage in more and greater
immorality of the same or similar type.
The slippery slope is indeed a fallacy – but the mere allegation that the fallacy
has been committed does not prove the argument in question faulty.
Hasty Generalization (converse accident) – when one moves carelessly or too
quickly from one or a very few instances to a broad or universal claim.
Committed when we draw conclusions about all the persons or things in a given class
on the basis of our knowledge about only one of the members of that class.
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
Take my son, Martyn. He’s been eating fish and chips his whole life, and he just
had a cholesterol test, and his level is below the national average. What better
proof could there be than a fryer’s son?
3. FALLACIES OF PRESUMPTION – the mistaken arguments arise from reliance upon some
proposition that is assumed to be true, but is in fact false, or dubious, or without warrant;
arguments that depend on unwarranted leaps
3.1 Accident – when one applies a generalization to an individual case that it does not
properly govern
It arises when we move carelessly or unjustifiably from a generalization to some
particulars that it does not in fact cover.

Birds can fly.
Tweety the Penguin is a bird.
Therefore, Tweety can fly.
3.2 Complex Question – when a question is asked in such a way as to presuppose the
truth of some assumption buried in that question.

"Have you stopped beating your wife?" presupposes that you have beaten your
wife prior to its asking, as well as that you have a wife. If you are unmarried, or
have never beaten your wife, then the question is loaded.

“Does the distinguish senator believe that the American public is really so
naïve that they will endorse just any stopgap measure?” it conceals several
unchallenged assumptions: that what is proposed is a “stopgap” measure, that
is inadequate, and that the American public would reject it.
3.3 Begging the Question (Petitio Principii) – when one assumes in the premises of an
argument the truth of what one seeks to establish in the conclusion of that argument;
the conclusion of an argument is stated or assumed in one of the premises.
The arguments are circular – every petitio is a circular argument – but the circle that
has been constructed may be large and confusing, and thus the logical mistake goes
unseen.
To “beg the question” is not to raise the issue, but to assume the truth of the
conclusion sought.
Circular arguments are certainly fallacious, but the premises are not irrelevant to the
conclusions drawn. They are relevant; indeed, they prove the conclusion, but they do
so trivially – they end where they began. A petition principia is always technically valid,
but always worthless.

“To cast abortion as a solely private moral question,…is to lose touch with
common sense: How human beings treat one another is practically the
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definition of a public moral matter. Of course, there are many private aspects of
human relations, but the question whether one human being should be allowed
fatally to harm another is not one of them. Abortion is an inescapably public
matter.”

“There is no such thing as knowledge which cannot be carried into practice, for
such knowledge is really no knowledge at all.”
4. FALLACIES OF AMBIGUITY (sometimes “sophisms”) – the mistaken arguments are
formulated in such a way as to rely on shifts in the meaning of words or phrases, from their
use in the premises to their use in the conclusion; a term may have one sense in a premise
but quite a different sense in the conclusion.
4.1 Equivocation – when the same word or phrase is used with two or more meanings,
deliberately or accidentally, in the formulation of an argument; misuse of relative terms,
which have different meanings in different contexts.

All banks are beside rivers.
Therefore, the financial institution where I deposit my money is beside a
river.
In this argument, there are two unrelated meanings of the word "bank":


A riverside: In this sense, the premiss is true but the argument is invalid,
so it's unsound.

A type of financial institution: On this meaning, the argument is valid, but
the premise is false, thus the argument is again unsound.
Someone is a good scholar and is therefore likely to be a good teacher.
4.2 Amphiboly - when one of the statements in an argument has more than one plausible
meaning, because of the loose or awkward way in which the words in that statement
have been combined. (arrangement of words)
The fallacy of amphiboly occurs when one is arguing from premises whose
formulations are ambiguous because of their grammatical construction.

“The anthropologists went to a remote area and took photographs of some
native women, but they weren't developed.” - “they” is ambiguous between the
photographs and the native women, though presumably it was intended to refer
to the former.
4.3 Accent – when a shift of meaning arises within an argument as a consequence of
changes in the emphasis given to its words or parts. (manner of delivering the words)
The various arguments that emerge are plainly the outcome of the deliberate
manipulation of emphasis; the sentence can be used to achieve assorted fallacious
ambiguities.
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The fallacy of accent may be construed broadly to include the distortion produced by
pulling a quoted passage out of its context, putting it in another context, and there
drawing a conclusion that could never have been drawn in the original context.
Physical manipulation of print or pictures is commonly used to mislead deliberately
through accent.

“I resent that letter.” This sentence could mean either that one sent the letter
again, or that one has a feeling of resentment towards it
4.4 Composition – this fallacy is committed:
a. When one reasons mistakenly from the attributes of the parts of a whole to
the attributes of the whole itself.

Every part of a certain machine is light in weight, the machine “as a
whole” is light in weight.

Each scene of a certain play is a model of artistic perfection, the play
as a whole is artistically perfect.

Every ship is ready for battle, the whole fleet must be ready for battle.
b. When one reasons mistakenly from the attributes of the individual elements
or members of a collection to attributes of the collection or totality of those
elements. – invalid inference that what may truly be predicated of a term
distributively may also be truly predicated of the term collectively.

A bus uses more gasoline than an automobile, all buses use more
gasoline than all automobiles.

The atomic bombs dropped during World War II did more damages
than did the ordinary bombs dropped – but only distributively.

Should we not assume that just as the eye, hand, the foot, and in
general each part of the body clearly has its own proper function, so
man too has some function over and above the function of his parts?
4.5 Division – simply the reverse of the fallacy of composition. This fallacy is committed:
a. When one argues fallaciously that what is true of a whole must also be true
of its parts.

A certain corporation is very important and Mr. Doe is an official of that
corporation, therefore, Mr. Doe is very important.
b. When one argues from the attributes of a collection of elements to the
attributes of the elements themselves.
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
Because university students study medicine, law, engineering,
dentistry, and architecture, therefore, each, or even any, university
student studies medicine, law, engineering, dentistry, and architecture.

The universe has existed for fifteen billion years.
The universe is made out of molecules.
Therefore, each of the molecules in the universe has existed for
fifteen billion years.
Chapter 3
LANGUAGE and DEFINITIONS
 MAJOR FUNCTIONS OF LANGUAGE
1. Informative (or logical) – without the intention to inform, we may express ourselves
using language.
“That’s really great!”
Match me such marvel, save in Eastern clime –
A rose-red city – “half as old as time.

We distinguish between facts a sentence formulates and facts about the speaker who
formulates them.

“War is always the wrong solution to international conflict.” - evidence of beliefs
of the person who utters that remark.
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

“I strongly oppose our involvement in this war on moral grounds.” –statement
about the speaker, but it also serves to express judgment about the morality of
the war under discussion.
Some expressive discourse also has informative content, and may express attitudes
as well as beliefs.

Grow old along with me!
The best is yet to be,
The last of life for which the first was made.
2. Directive – with or without expressive or informative elements. It seeks to guide or to
command.


“Step on the scale, please.”
“Drive defensively. The cemetery is full of law-abiding citizens who had the right
of way.”
3. Emotive – may be used to advance our purposes in directing others; expressing an
attitude, seeking to direct behavior, and probably reporting a fact.

“That conduct is utterly disgusting!”
 LESS COMMON TYPES OF USE:
4. Ceremonial – words may combine expressive and other functions; proforma / template

“How do you do?”
5. Performative – words themselves serve, when spoken or written, to perform the
function they announce.




“I apologize for my foolish remark”
“I congratulate you”
“I accept your offer”
“I promise you that”
 FORMS OF LANGUAGE
1.
2.
3.
4.
Declarative – when we are reasoning (“We will discuss.”)
Exclamatory – when we are expressing emotion (“That’s fantastic!”)
Imperative – when we are seeking to direct conduct; command (“Take off your pants!”)
Interrogative – attitudes may also be expressed (“What can you possibly mean by
that?”)
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 DEFINITION – are definitions of symbols (not of objects), because only symbols have the
meanings that definition may explain; it expresses what the thing is; states the meaning of a
term
Definiendum – the symbol being defined
Definiens – symbol or group of symbols used to explain the meaning of the definiendum

Definiendum is the term to be defined, while definiens is the definition of it.
 KINDS OF DEFINITION
1. Stipulative – a definition that has a meaning that is deliberately assigned to some
symbol; sometimes called nominal; a meaning is assigned to a term (and hence which
cannot be true or false)
-
May simply be convenient, one word may stand for many words in a message
May protect secrecy, if the sender and the receiver are the only persons who
understand the stipulation
May advance economy of expression
In science, to mean what has been meant by a long sequence of familiar word,
thus saving time and increasing clarity
a definition as a result of deliberately assigning a meaning
It is used to assign a new meaning to a term, whether or not the term has already
got a meaning
-
A stipulative definition is a proposal (or a resolution or a request or an instruction) to
use definiendum to mean what is meant by the definiens. Such definition is therefore
directive rather than informative.


“OMG” – oh my gosh
“murder” – the premeditated killing of a human being
2. Lexical or Real – which report the meaning that the term already has (and hence can
be true or false). That report may be correct, or incorrect – and therefore it is clear that a
lexical definition may be either true or false.
When the purpose of the definition is to explain that use, or to eliminate ambiguity, the
definition is lexical.


“bird” – means any warm-blooded vertebrate with feathers is true
“alienate” – to convey or transfer
“Real definition” – to indicate that the definiendum really does have the meaning
identified.
In essence, it may be true or false, in the sense that they may be true to actual usage, or
may fail to be true to it.
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3. Precising – which aim to eliminate vagueness or ambiguity
Ambiguous – when it has more than one distinct meaning and the context does not
make clear which meaning is intended.
Vague – when there are borderline cases to which the term might or might not apply.
Borderline cases can be resolved only by going beyond the report of normal usage with
the definition given.
It differs from stipulative definitions in that its definiendum is not a new term, but one
whose usage is known, although unhappily vague. In constructing a précising definition,
therefore, we are not free to assign to the definiendum any meaning we please.


“Obligation” – under the Civil Code, is the juridical necessity to give, to do or not
to do.
“Marriage” - is a special contract of permanent union between a man and a
woman entered into in accordance with law for the establishment of conjugal and
family life.
4. Theoretical – aim is to encapsulate our understanding of some intellectual sphere;
products of our comprehensive understanding in some sphere.


“evolution of man” – man came from apes
“overweight” - having a body mass index over 27 for women and 28 for men
5. Persuasive – aims to influence conduct; a definition put forward to resolve a dispute by
influencing attitudes or stirring emotions


“fetus” – unborn person
“abortion” – murder of a fetus
Kinds of Definition
Type
Stipulative
Definition
Example
 A definition in which a new  “OMG” – oh my gosh
symbol is introduced to
which some meaning is  “murder” – is the premeditated
arbitrarily assigned. As
killing of a human being
opposed
to
a lexical
definition,
a
stipulative
definition cannot be correct
or incorrect.
 It is used to assign a new
meaning to a term, whether
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or not the term has already
got a meaning
 A definition which report the “bird” – means any warmmeaning that the term
blooded vertebrate with
already has
feathers
Lexical
 Dictionary meaning
Precising
Theoretical
Persuasive

A definition devised to
eliminate vagueness by
delineating a concept more
sharply.
 A definition of a term that
attempts to formulate a
theoretically adequate or
scientifically
useful
description of the objects to
which the term applies.
 “alienate” – to convey or
transfer

“Obligation” – under the
Civil Code, is the juridical
necessity to give, to do or
not to do.

“Marriage” - is a special
contract of permanent
union between a man and
a woman entered into in
accordance with law for
the establishment of
conjugal and family life.

“evolution of man” – man
came from apes

“overweight” - having
a body mass index over 27
for women and 28 for men
 A definition formulated and  “fetus” – unborn person
used to resolve a dispute by
influencing
attitudes
or  “abortion” – murder of a fetus
stirring emotions, often
relying upon the use of
emotive language.
Chapter 5
CATEGORICAL PROPOSITIONS
Classical logic – deals mainly with arguments based on the relations of classes of objects to one
another. By a class, we mean a collection of all objects that have some specified characteristic in
common. Everyone can see immediately that two classes can be related in at least the following three
ways:
1.
All of one class may be included in all of another class. Thus, the class of all dogs is wholly
included (or wholly contained) in the class of all mammals.
2. Some, but not all, of the members of one class may be included in another class. Thus, the
class of all athletes is partially included (or partially contained) in the class of all females.
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3. Two classes may have no members in common. Thus, the class of all triangles and the class
of all circles may be said to exclude one another.
Categorical Proposition- is a part of deductive reasoning that contains two categorical terms,
the subject and the predicate, and affirms or denies the latter of the former.

The propositions with which such arguments are formulated
The subject and the predicate are called the terms of the proposition. The subject is what the proposition
is about, while the predicate is what the proposition affirms or denies about the subject.
Four Kinds of Standard-Form Categorical Propositions
1. Universal affirmative propositions (A propositions) – the whole of one class is included or
contained in another class

Such a proposition affirms that the relation of class inclusion holds between two classes
and says that the inclusion is complete, or universal.

S
All S is P – All politicians are liars.
P
2. Universal negative propositions (E propositions) – it asserts that the subject class, S, is
wholly excluded from the predicate class P

This kind of proposition denies the relation of inclusion between the two terms, and denies it
universally.

No S is P – No politicians are liars.
S
P
3. Particular affirmative propositions (I propositions) – this proposition does not affirm or deny
anything about that entire class

The proposition affirms that the relation of class inclusion holds, but does not affirm it of the
first class universally but only partially, that is, it is affirmed of some particular member, or
members, of the first class.

Some S is P – Some politicians are liars.
S
P
x
4. Particular negative propositions (O propositions) – it does not affirm the inclusion of some
member or members of the first class in the second class, this is precisely what is denied.

The denial is not universal
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
Some S is not P. – Some politicians are not liars.
S
P
X
Categorical propositions can be categorized into four types on the basis of their quality, quantity, and
distribution. These four types are A, E, I and O. This is based on the Latin word affirmo (I affirm),
referring to affirmative propositions A and I, and nego (I deny), referring to the negative propositions E
and O.
Quality
– refers to whether the proposition affirms or denies the inclusion of a subject within the class
of the predicate. The two qualities are affirmative and negative.
Quantity
– refers to the amount of members of the subject class that are used in the proposition. If
the proposition refers to all members of the subject class, it is universal. If the proposition does not
employ all members of the subject class, it is particular.
Distribution
– refers to whether all or some members of a class are affected by a proposition. Both
subjects and predicates have distribution. If all members of a class are affected by a proposition, that
class is distributed, otherwise, it is undistributed.
Subject term distributed
predicate
term
undistributed
A: All S is P
E: No S is P
predicate
term
distributed
I: Some S is P.O: Some S is not P.
Subject term undistributed
Illustration:
Name
Statement
Quantity
Quality
Distribution
Subject
Predicate
A
All S is P
universal affirmative distributed
undistributed
E
No S is P
universal negative
distributed
I
Some S is P
particular affirmative undistributed undistributed
O
Some S is not P particular negative
distributed
undistributed distributed
Traditional Square of Opposition
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A. Contradictories – two propositions are contradictories if one is the denial or negation of the
other; that is, if they cannot both be true and cannot both be false. A and O are contradictories, as
are E and I.
B.
A and O propositions
All judges are lawyers.
Some judges are not lawyers.
E and I propositions
No politicians are idealists.
Some politicians are idealists.
Contraries – two propositions are said to be contraries if they cannot both be true; that is, if the
truth of one entails the falsity of the other. The traditional account held that universal propositions
having the same subject and predicate terms, but differing in quality, were contraries. A and E
propositions can be regarded as contraries.
Texas will win the coming game with Oklahoma.
Oklahoma will win the coming game with Texas.
*If either of these propositions is true, then the other must be false.
All poets are idlers. and No poets are idlers.

cannot be both true but can be both false ( ≠ True; = False)

Same subject and predicate, both universal, differs in quality
C. Subcontraries
– two propositions are said to be subcontraries if they cannot both be false,
although they both may be true. The traditional account held that particular propositions having the
same subject and predicate terms differing in quality were subcontraries. I and O propositions can
be regarded as subcontraries.
Some diamonds are precious stones.
Some diamonds are not precious stones.
 Cannot be both false but both can be true ( ≠ False, = True)
 Same subject and predicate, both particular, differs in quality
D. Subalternation
– whenever two propositions have the same subject and the same predicate
terms and agree in quality (both are affirmative or both are negative) but differ only in quantity, they
are called corresponding propositions. A proposition has a corresponding I proposition, and the E
proposition has a corresponding O proposition.
All spiders are eight-legged animals. (A)
Some spiders are eight-legged. (I)
No whales are fishes. (E)
Some whales are not fishes. (O)

Same subject, predicate and quality, differs in quantity
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The opposition between a universal proposition and its corresponding particular is known as
subalternation. In any pair of corresponding propositions, the universal proposition is called the
“superaltern”, and the particular proposition is called the “subaltern”.
All birds have feathers. (superaltern)
Some birds have feathers. (subaltern)
No whales are fishes. (superaltern)
Some whales are not fishes. (subaltern)
subaltern
(Some S is P.)
A
contraries
E
contradictories
subalternation
(All S is P.)
superaltern
subalternation
Square of Opposition
I
subcontraries
A
1.
2.
3.
4.
5.
6.
7.
8.
T F
F T
U F
F U
F U
U F
F T
T F
T F
F T
T U
U T
U T
T U
F T
T F
A being given as true
E being given as true
I being given as true
O being given as true
A being given as false
E being given as false
I being given as false
O being given as false
false
undetermined
false
undetermined
false
true
O
(No. S is P.)
superaltern
subaltern
(Some S is not P)
E
false
false
undetermined
undetermined
true
false
I
true
false
undetermined
undetermined
true
true
O
false
true
undetermined
true
undetermined
true
-
Immediate Inferences
A. Conversion – interchanging the subject and predicate terms of the propositions
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One standard-form categorical proposition is said to be the CONVERSE of another when it is
formed by simply interchanging the subject and the predicated terms of that other proposition.
“No idealists are politicians.” is the converse of “No politicians are idealists.”
CONVERTEND is used to refer to the premiss of an immediate inference by conversion, and the
conclusion of that inference is called the CONVERSE.
B. Obversion
– the subject term remains unchanged, and so does the quantity of the proposition
being obverted. To obvert a proposition, we change its quality and replace the predicate term by its
complement.
CLASS – is the collection of all objects having a certain common attribute that we refer to as the
”class-defining characteristic”.
COMPLEMENT – a collection of all things that do not belong the original class. The complement
of the class designated by the term S is then designated by the term non-S, and we may speak
of the term non-S being the complement of the term S. (winner – nonwinner)
All residents are voters.
No residents are nonvoters.
A proposition, has as its obverse the
E proposition
No umpires are partisans.
All umpires are nonpartisans.
E proposition, has its obverse the logically equivalent
A proposition
Some metals are conductors.
Some metals are not nonconductors.
I proposition
O proposition (obverse)
Some nations were not belligerents.
Some nations were nonbelligerents.
O proposition
I proposition (obverse)
The term OBVERTEND is used to refer to the premiss of an immediate inference by obversion,
and the conclusion is called OBVERSE.
C. Contraposition
– to form the contrapositive of a given proposition, we replace its subject
term by the complement of its predicate term and replace its predicate term by the complement of its
subject term.
All members are voters. is the contrapositive of All nonvoters are nonmembers.
Some students are not idealists. is somewhat cumbersome of
Some nonidealists are not nonstudents.
IMMEDIATE INFERENCES:
CONVERSION, OBVERSION, CONTRAPOSITION
VALID CONVERSION
CONVERTEND
A: All S is P
E: No S is P
I: Some S is P.
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CONVERSE
I: Some P is S (by limitation)
E: No. P is S.
I: Some P is S.
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O: Some S is not P
(conversion not valid)
OBVERSION
OBVERTEND
A:
E:
I:
O:
OBVERSE
All S is P
No S is P
Some S is P.
Some S is not P
E:
A:
O:
I:
No S is non-P.
All S is non-P.
Some S is not non-P.
Some S is non-P.
CONTRAPOSITION
PREMISS
A:
E:
I:
O:
CONTRAPOSITIVE
All S is P
No S is P
Some S is P.
Some S is not P
A: All non-P is non-S.
O: Some non-P is not non-S (by lim.)
(contraposition not valid)
O: Some non-P is not non-S.
SYMBOLIC REPRESENTATION OF CATEGORICAL PROPOSITION
Form
Proposition
Symbolic Rep.
A
All S is P.
SP = 0
E
No S is P.
SP = 0
I
Some S is P.
SP ≠ 0
O
Some S is not P.
SP ≠ 0
Explanation
The class of things that are both
S and non-P is empty
The class of things that are both
S and P is empty
The class of things that are both
S and P is not empty (SP has at
least one member)
The class of things that are both
S and non-P is not empty. (SP
has at least one member)
Chapter 6
CATEGORICAL SYLLOGISMS
Syllogism – is a deductive argument in which a conclusion is inferred from two premises.
Categorical Syllogism
– is a deductive argument consisting of three categorical propositions
that together contain exactly three terms, each of which occurs in exactly two of the constituent
propositions. It is said to be in standard form when its premises and conclusion are all standard-form
categorical propositions (A, E, I or O) and are arranged in a specified standard order.
Arrangement : major premiss, minor premiss and conclusion
Major term – predicate of the conclusion (major premiss)
Minor term – subject of the conclusion (minor premiss)
Middle term – does not occur in the conclusion, appearing instead in both premises
No heroes are cowards. (major premiss)
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Some soldiers are cowards. (minor premiss)
Therefore, some soldiers are not heroes. (conclusion)
 Middle term – cowards (does not appear in the conclusion)
Mood
– determined by the types (identified by A, E, I or O) of the standard-form categorical
propositions it contains.
E
I
O
No heroes are cowards.
Some soldiers are cowards.
Therefore, some soldiers are not heroes.

Mood : EIO
Figure:
First Figure
Second Figure
Third Figure
Fourth Figure
M–P
S–M
-------------S–P
P–M
S–M
------------------S–P
M–P
M–S
------------------S–P
P–M
M–S
------------------S-P
Valid Forms of the Standard-Form Categorical Syllogism
First Figure
bArbArA
cELArEnt
dArII
fErIO
AAA-1
EAE-1
AII-1
EIO-1
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Second Figure
cAmEstrEs
cEsArE
bArOkO
fEstInO
AEE-2
EAE-2
AOO-2
EIO-2
Third Figure
dAtIsI
dIsAmIs
fErIsOn
bOkArdO
AII-3
IAI-3
EI0-3
OAO-3
Fourth Figure
cAmEnEs
dImArIs
frEsIsOn
AEE-4
IAI-4
EIO-4
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http://www.slideshare.net/3842/categorical-syllogism
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