A brief overview of all the concepts relating to Syllogism generally, e.g. Categorical Proposition,Standard Form Categorical Proposition, Subject, Predicate, Copula, Quantifiers, Quality of Categorical Propositions Existential Import of Categorical Propositions, Syllogism, Categorical Syllogism, Standard Form Categorical Syllogism Terms, Modes and Figures of Categorical Syllogism

1. 2017
IHSAN ULLAH
ROLL NO. 11
7/12/2017
LOGIC & REASONING
IHSAN ULLAH
Roll No. 11
B.A/LL.B. 2nd
Year Semester 3rd
Subject Logic & Reasoning
Submitted to: Sir Asmat Ullah
Date: Wednesday, July 12, 2017

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Table of Contents
Abstract ................................................................................................... 2
Definition of syllogism........................................................................... 2
Categorical Propositions....................................................................... 2
Standard Form....................................................................................... 2
Properties of categorical propositions ................................................ 3
Quantity and quality .............................................................................. 3
Qualifier .................................................................................................. 3
Subject..................................................................................................... 3
Copula...................................................................................................... 4
Distributive............................................................................................. 4
Existential Import ................................................................................. 5
Syllogistic Rules and Fallacies............................................................. 6
The Four Figures................................................................................... 6
AEA-2 ...................................................................................................... 9
AEE-2...................................................................................................... 9
AEI-2 ...................................................................................................... 11
AEO-2.................................................................................................... 12
OIE-1 ..................................................................................................... 13
Conclusion............................................................................................. 13

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Abstract
Here in the following lines I will discuss syllogism, categorical proposition, existential import,
diagraming and standard form of categorical proposition on five assigned syllogism and will show
them on Venn diagram and will also apply six rules on them and I will also check validity of that
syllogism.
Definition of syllogism
 A deductive scheme of a formal argument consisting of a major and a minor premise and
a conclusion (as in “every virtue is laudable; kindness is a virtue; therefore kindness is
laudable”)
 A subtle, specious, or crafty argument
 Deductive reasoning
Categorical Propositions
Now that we've taken notice of many of the difficulties that can be caused by sloppy use of ordinary
language in argumentation, we're ready to begin the more precise study of deductive reasoning.
Here we'll achieve the greater precision by eliminating ambiguous words and phrases from
ordinary language and carefully defining those that remain. The basic strategy is to create a
narrowly restricted formal system—an artificial, rigidly structured logical language within which
the validity of deductive arguments can be discerned with ease. Only after we've become familiar
with this limited range of cases will we consider to what extent our ordinary-language
argumentation can be made to conform to its structure.
Our initial effort to pursue this strategy is the ancient but worthy method of categorical logic. This
approach was originally developed by Aristotle, codified in greater detail by medieval logicians,
and then interpreted mathematically by George Boole and John Venn in the nineteenth century.
Respected by many generations of philosophers as the chief embodiment of deductive reasoning,
this logical system continues to be useful in a broad range of ordinary circumstances.
Standard Form
In order to make obvious the similarities of structure shared by different syllogisms, we will always
present each of them in the same fashion. A categorical syllogism in standard form always begins
with the premises, major first and then minor, and then finishes with the conclusion. Thus, the
example above is already in standard form. Although arguments in ordinary language may be
offered in a different arrangement, it is never difficult to restate them in standard form. Once we've
identified the conclusion which is to be placed in the final position, whichever premise contains
its predicate term must be the major premise that should be stated first.

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Medieval logicians devised a simple way of labelling the various forms in which a categorical
syllogism may occur by stating its mood and figure. The mood of a syllogism is simply a statement
of which categorical propositions (A, E, I, or O) it comprises, listed in the order in which they
appear in standard form. Thus, a syllogism with a mood of OAO has an O proposition as its major
premise, an A proposition as its minor premise, and another O proposition as its conclusion; and
EIO syllogism has an E major premise, and I minor premise, and an O conclusion; etc.
Properties of categorical propositions
Categorical propositions can be categorized into four types on the basis of their "quality" and
"quantity", or their "distribution of terms". These four types have long been named A, E, I, and O.
This is based on the Latin affirmo (I affirm), referring to the affirmative propositions A and I, and
nego (I deny), referring to the negative propositions E and O.
Quantity and quality
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. For instance, an I-proposition ("Some S
is P") is particular since it only refers to some of the members of the subject class.
Qualifier
It shows the measurements, quantity of the member of a group
It is of two types
i) Universal
ii) Particular
 A type singular is counted in universal.
 Universal is extended to the whole member of the group.
 A particular qualifier is a word which is extended to certain member of the group.
 Particular qualifier are some, few, most, majority, usually, maximum, minimum
 Universal is all, total, whole
Subject
It is the part of proposition about which something is either affirmed or denied.

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Copula
Copula is connecting subject and predicate
Quality refers to whether the proposition affirms or denies the inclusion of a subject within the
class of the predicate. The two possible qualities are called affirmative and negative. For instance,
an A-proposition ("All S is P") is affirmative since it states that the subject is contained within the
predicate. On the other hand, an O-proposition ("Some S is not P") is negative since it excludes
the subject from the predicate.
Name Statement Quantity Quality
A All S is P. Universal Affirmative
E No S is P. Universal Negative
I Some S is P. Particular Affirmative
O Some S is not P. Particular Negative
An important consideration is the definition of the word some. In logic, some refers to "one or
more", which could mean "all". Therefore, the statement "Some S is P" does not guarantee that the
statement "Some S is not P" is also true.
Distributive
The two terms (subject and predicate) in a categorical proposition may each be classified as
distributed or undistributed? If all members of the term's class are affected by the proposition, that
class is distributed; otherwise it is undistributed. Every proposition therefore has one of four
possible distribution of terms.
Each of the four canonical forms will be examined in turn regarding its distribution of terms.
Although not developed here, Venn diagrams are sometimes helpful when trying to understand the
distribution of terms for the four forms.
A form
An A-proposition distributes the subject to the predicate, but not the reverse. Consider the
following categorical proposition: "All dogs are mammals". All dogs are indeed mammals, but it
would be false to say all mammals are dogs. Since all dogs are included in the class of mammals,
"dogs" is said to be distributed to "mammals". Since all mammals are not necessarily dogs,
"mammals" is undistributed to "dogs".
E form
An E-proposition distributes bidirectionally between the subject and predicate. From the
categorical proposition "No beetles are mammals", we can infer that no mammals are beetles.
Since all beetles are defined not to be mammals, and all mammals are defined not to be beetles,
both classes are distributed.

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I form
Both terms in an I-proposition are undistributed. For example, "Some Americans are
conservatives". Neither term can be entirely distributed to the other. From this proposition, it is
not possible to say that all Americans are conservatives or that all conservatives are Americans.
O form
In an O-proposition, only the predicate is distributed. Consider the following: "Some politicians
are not corrupt". Since not all politicians are defined by this rule, the subject is undistributed. The
predicate, though, is distributed because all the members of "corrupt people" will not match the
group of people defined as "some politicians". Since the rule applies to every member of the
corrupt people group, namely, "All corrupt people are not some politicians", the predicate is
distributed.
The distribution of the predicate in an O-proposition is often confusing due to its ambiguity. When
a statement like "Some politicians are not corrupt" is said to distribute the "corrupt people" group
to "some politicians", the information seems of little value, since the group "some politicians" is
not defined. But if, as an example, this group of "some politicians" were defined to contain a single
person, Albert, the relationship becomes clearer. The statement would then mean that, of every
entry listed in the corrupt people group, not one of them will be Albert: "All corrupt people are not
Albert". This is a definition that applies to every member of the "corrupt people" group, and is,
therefore, distributed.
Summary
In short, for the subject to be distributed, the statement must be universal (e.g., "all", "no"). For
the predicate to be distributed, the statement must be negative (e.g., "no", "not").
Existential Import
A statement has existential import when its truth depends on evidence for the existence of things
in a certain category--in the case of categorical propositions, the existence of things in the
categories signified by its subject and predicate terms.
Existential Import and Categorical Propositions
Consider the following propositions:
All unicorns have horns.
No perpetual motion machine has been patented.
Both are true even though there are no unicorns or perpetual motion machines. Thus, these
statements lack existential import.
Many modern logicians hold that existential import is a function of a statement's logical form.
According to this view, universal categorical statements in general do not have existential import.

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Statements that are particular in nature, however, do have existential import. To say that some
S are P, or that some S are not P, is to imply the existence of Ss; if there are no Ss, then both
statements are false.
Syllogistic Rules and Fallacies
The Four Figures

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AEA-2
Example: All furry beasts are pets.
No rabbits are pets.
Therefore, all rabbits are furry beasts.
The Argument in Invalid
All five rules apply but due to rule no 3 (if either premise is negative the conclusion must be negative) so
it not following this rule so it is invalid. And fallacy of affirmative conclusion from negative premise.
AEE-2
A valid syllogism is a formally valid argument—valid by virtue of its form alone. This implies that if a
given syllogism is valid, any other syllogism of the same form will also be valid.
And if a syllogism is invalid, any other syllogism of the same form will also be invalid
.* The common recognition of this fact is attested to by the frequent use of “logical analogies” in
argumentation. Suppose that we are presented with the argument
All liberals are proponents of national health insurance.
Some members of the administration are proponents of national health insurance.
Therefore some members of the administration are liberals.

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CAMESTRES, AEE-2 (by converting the minor premise of CAMENES) All P are M. No S are M.
Therefore, No S are P.
And felt (justifiably) that, regardless of the truth or falsehood of its constituent propositions, the argument
is invalid. The best way to expose its fallacious character is to construct another argument that has exactly
the same form but whose invalidity is immediately apparent. We might seek to expose the given argument
by replying: You might as well argue that
Example: All rabbits are very fast runners.
Some horses are very fast runners.
Therefore some horses are rabbits.
The Argument in Valid
All rule applied on this and it is valid arguments
We might continue: You cannot seriously defend this argument, because here there is no question about
the facts. The premises are known to be true and the conclusion is known to be false. Your argument is of
the same pattern as this analogous one about horses and rabbits. This one is invalid—so your argument is
invalid. This is an excellent method of arguing; the logical analogy is one of the most powerful
weapons that can be used in debate.

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Underlying the method of logical analogy is the fact that the validity or invalidity of such arguments as the
categorical syllogism is a purely formal matter. Any fallacious argument can be proved to be invalid
by finding a second argument that has exactly the same form and is known to be invalid by the fact that
its premises are known to be true while its conclusion is known to be false. (It should be remembered
that an invalid argument may very well have a true conclusion—that an argument is invalid simply
means that its conclusion is not logically implied or necessitated by its premises.)
AEI-2
Example: All fungi are plants.
No flowers are plants.
Therefore, some flowers are fungi.
The Argument in Invalid
All five rules apply but due to rule no 6 (no particular conclusion can be drawn from two universal
proposition) so it not following this rule so it is invalid.
And it have the Existential fallacy.

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AEO-2
Example: All spaniels are gentle dogs
No good hunters are gentle dogs
Therefore some spaniels are not good hunters
The Argument in Invalid
All five rules apply but due to rule no 6 (no particular conclusion can be drawn from two universal
proposition) so it not following this rule so it is invalid.
And it have the Existential fallacy.

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OIE-1
Example: Some furry beasts are not pets.
Some rabbits are pets.
Therefore, no rabbits are furry beasts.
The Argument in Invalid
All five rules apply but due to rule no 2 (distribute the middle term in at least one premise) so it not following
this rule so it is invalid. And it have the fallacy of undistributed middle.
Conclusion
As we studied in the above pages, in the assigned five syllogism the process of syllogism is quite
understood. I have made them and checked them their validity and also draw venn diagram and
check them through six rules, if it has not passed even one rule from the given six rule then I have
given detail of that rule and also given name of that fallacy of that rule. So, I have completed mine
task in this way.