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. Intuitive result of direct observation2.
Abstractive result of your thinking / judgment3. Contrary opposite
side of the spectrum (happy sad)4. Contradictory exact meaning of
the opposite (true false)
DEFINITION ideas / concept It expresses what the thing is
1. Real use to identify what the thing really is; exact meaning
/ definite meaning2. Stipulative a definition as a result of
deliberately assigning a meaning3. Precising makes the meaning
scientific; totally eliminates biases4. Persuasive seek to spare
emotions or influence; strives to convince people5. Theoretical
express theological ; generalization about reality
Chapter 1BASIC LOGICAL CONCEPTS
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
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 lifes 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
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
Conclusion-indicators:
Thereforefor these reasonsshows thatHenceit follows thatentails
thatThuswe may inferdemonstrates thatSoI conclude
thatergoAccordinglywhich shows thatthenIn consequencewhich means
thatConsequentlywhich entails thatProves thatwhich implies thatAs a
resultwhich allow us to infer thatFor this reasonwhich points to
the conclusion that
Premiss-indicators:
Sinceas indicated bycan be shown byBecausethe reason is thatis
implied byForfor the reason thatdue toAsmay be inferred
fromassuming thatFollows frommay be derived fromis proved byAs
shown bymay be deduced fromcan be concluded from inasmuch asin view
of the fact that
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?
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 arent compelled to give them, they wont 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 dont like Asians; so Americans dont 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 doesnt believe that moral arguments make any difference,
then one doesnt 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
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)
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:
Chapter 4FALLACIES
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 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
speakers concern.
I, who am probably in danger of my life, will do none of these
things. The contrast may occur to [each jurors] 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 workers 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 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.
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 thats 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 were 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 anothers
argument.
One person emphasizes how important it is to increase funding
for the public schools. His opponent responds by insisting that a
childs 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.
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 isnt. There really isnt, 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)
The sun would invariably reappear after an eclipse if the drums
had been beaten in the darkness.
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)
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.
2.4Hasty 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.
Take my son, Martyn. Hes 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
fryers 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 youhavea
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 nave 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 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,
thepremissis 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.
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 it4.4 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.
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 3LANGUAGE and DEFINITIONS
MAJOR FUNCTIONS OF LANGUAGE
1. Informative (or logical) without the intention to inform, we
may express ourselves using language.
Thats 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.
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. Declarative when we are reasoning (We will discuss.)2.
Exclamatory when we are expressing emotion (Thats fantastic!)3.
Imperative when we are seeking to direct conduct; command (Take off
your pants!)4. Interrogative attitudes may also be expressed (What
can you possibly mean by that?)
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.
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 prcising 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 abody
mass index over 27 for women and 28 for men5. 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 DefinitionTypeDefinitionExample
Stipulative A definition in which a new symbol is introduced to
which some meaning is arbitrarily assigned. As 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 or not the
term has already got a meaning
OMG oh my gosh
murder is the premeditated killing of a human being
Lexical A definition which report the meaning that the term
already has
Dictionary meaning bird means any warm-blooded vertebrate with
feathers
alienate to convey or transfer
Precising A definition devised to eliminate vagueness by
delineating a concept more sharply. 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.
Theoretical A definition of a term that attempts to formulate a
theoretically adequate or scientifically useful description of the
objects to which the term applies. evolution of man man came from
apes
overweight - having abody mass index over 27 for women and 28
for men
Persuasive A definition formulated and used to resolve a dispute
by influencing attitudes or stirring emotions, often relying upon
the use of emotive language. fetus unborn person
abortion murder of a fetus
Chapter 5CATEGORICAL 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.
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.
All S is P All politicians are liars. S 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
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 A: All S is P E: No S is P predicate term term
undistributed distributed I: Some S is P.O: Some S is not P.
Subject term undistributed
Illustration:
NameStatementQuantityQualityDistribution
SubjectPredicate
AAll S is Puniversalaffirmativedistributedundistributed
ENo S is Puniversalnegativedistributeddistributed
ISome S is Pparticularaffirmativeundistributedundistributed
OSome S is not Pparticularnegativeundistributeddistributed
Traditional Square of Opposition
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.
A and O propositionsAll judges are lawyers.Some judges are not
lawyers.
E and I propositionsNo politicians are idealists.Some
politicians are idealists.
B. 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
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)
Square of Opposition
(All S is P.)A contraries E(No. S is
P.)superalternsuperaltern
subalternationsubalternation
contradictories
subalternsubaltern(Some S is P.) I subcontraries O(Some S is not
P)
A E I O
1. T F T FA being given as true -falsetruefalse2. F T F TE being
given as truefalse -falsetrue3. U F T UI being given as
trueundeterminedfalse -undetermined4. F U U TO being given as
truefalseundeterminedundetermined -5. F U U TA being given as false
-undeterminedundeterminedtrue6. U F T UE being given as
falseundetermined -trueundetermined7. F T F TI being given as
falsefalsetrue -true8. T F T FO being given as falsetruefalsetrue
-
Immediate Inferences
A. Conversion interchanging the subject and predicate terms of
the propositions
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. A proposition, has as its obverse
theNo residents are nonvoters.E proposition
No umpires are partisans.E proposition, has its obverse the
logically equivalentAll umpires are nonpartisans.A proposition
Some metals are conductors.I propositionSome metals are not
nonconductors.O proposition (obverse)
Some nations were not belligerents.O propositionSome nations
were nonbelligerents.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 CONVERSIONCONVERTENDCONVERSE
A: All S is PI: Some P is S (by limitation)E: No S is PE: No. P
is S.I: Some S is P.I:Some P is S.O:Some S is not P(conversion not
valid)
OBVERSION
OBVERTENDOBVERSE
A: All S is PE: No S is non-P. E: No S is PA:All S is non-P. I:
Some S is P.O:Some S is not non-P. O:Some S is not PI:Some S is
non-P.
CONTRAPOSITION
PREMISSCONTRAPOSITIVE
A: All S is PA: All non-P is non-S. E: No S is PO:Some non-P is
not non-S (by lim.) I: Some S is P.(contraposition not valid)
O:Some S is not PO:Some non-P is not non-S.
SYMBOLIC REPRESENTATION OF CATEGORICAL PROPOSITION
Form PropositionSymbolic Rep.Explanation
AAll S is P.SP = 0The class of things that are both S and non-P
is emptyENo S is P.SP = 0The class of things that are bothS and P
is emptyISome S is P.SP 0The class of things that are bothS and P
is not empty (SP has atleast one member)OSome S is not P.SP 0The
class of things that are both S and non-P is not empty. (SPhas at
least one member)Chapter 6CATEGORICAL SYLLOGISMSSyllogism 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)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.
ENo heroes are cowards. ISome soldiers are cowards. OTherefore,
some soldiers are not heroes.
Mood : EIO Figure:
First FigureSecond FigureThird FigureFourth Figure
M PP MM PP MS MS MM SM
S-----------------------------------------------------------------------S
PS PS PS - P
Valid Forms of the Standard-Form Categorical Syllogism
First Figure Second Figure Third FigureFourth Figure
bArbArA
AAA-1cAmEstrEsAEE-2dAtIsIAII-3cAmEnEsAEE-4cELArEntEAE-1cEsArEEAE-2dIsAmIsIAI-3dImArIsIAI-4dArIIAII-1bArOkOAOO-2fErIsOnEI0-3frEsIsOnEIO-4fErIOEIO-1fEstInOEIO-2bOkArdOOAO-3
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Rowena B. Gallego Legal Techniques & LogicAtty. Freedom
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