Logic

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Logic Basic Terms
Unit 1 Introduction to Philosophy Activity 3
Introduction to Logical Reasoning. Source
lthttp//learnv.ycdsb.edu.on.ca/lt/FMMC/hp.nsf/File
s/mcmanad/FILE/logicnotes.htmgt
Logic the study of how to reason well.
Validity Valid thinking is thinking in
conformity with the rules. If the premises are
true and the reasoning is valid, then the
conclusion will be necessarily true.
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Non-sequitur (it does not follow). This means
that the proposed conclusion cannot be deduced
with certitude from the given premises.
For example If Jews and Palestinians were of
the same religion, there wouldnt be conflict in
the Middle East. Therefore, it is religion that
is the source of the conflict.
The categorical proposition A complete sentence,
with one subject and one predicate, that is
either true or false.
For example
All cows are smelly
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The Subject that about which something is said.
All giraffes are animals. (giraffes subject)
The Predicate that which is said about
something. All giraffes are animals. (animals
predicate)
The copula connects together or separates the S
and the P. All giraffes are animals. (is/is not)

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Standard Propositional Codes. These codes come
from the Latin words "Affirmo" and "Nego".
Affirmo I affirm. Note the A and the I
Nego I deny. Note the E and the O
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A - universal affirmative All S is P
I - particular affirmative Some S is P
O - particular negative Some S is not P.
E - universal negative No S is P. 
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The parts of a categorical syllogism a.  The
two premises. All A is B (first premise) Some
B is C (second premise) Therefore, Some C is A
b.  The Conclusion. In the above syllogism,
Therefore, Some C is A
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The major term this term is always the P
(predicate) of the conclusion.  In the example
directly above, A is the major term. The minor
term this term is always the S (subject) of the
conclusion.  In the example directly above, C is
the minor term. The middle term this term is
never in the conclusion but appears twice in the
premises. (The function of the middle term is to
connect together or keep apart the S and P in the
conclusion).
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Distribution This is a very important term in
logic. A distributed term covers 100 of the
things referred to by the term. An undistributed
term covers less than 100 of the things referred
to by the term (few, many, almost all).
For instance, All men are mortal. In this
statement, "men" is distributed for it covers
100 of the things referred by the term "men".
In Some men are Italian, "men" is
undistributed for the term covers less than 100
of the things referred to by the term "men".
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Universal Affirmative statements (A statements)
the subject is distributed, the predicate is
undistributed. Universal Negative statements (E
statements) both the subject and the predicate
are distributed. Particular Affirmative
statements (I statements) neither subject nor
predicate is distributed (both are
undistributed). Particular Negative statements
(O statements) the predicate alone is
distributed.
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Note the following (bold and underline
distributed)
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Footnote Regarding Distribution
Some students may ask Why is the predicate (P)
distributed in the E and O statements? E No
dogs are reptiles. 100 of reptiles are not dogs.
O Some men are not Italian. 100 of Italians
are not these men (John, Bill, James, Peter). We
are saying something about all things which are
Italian (P). Of all the things which are Italian,
those men mentioned in our statement are excluded
from all those designated by Italian.
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Rules of Syllogistic (categorical) reasoning.
Rule 1 from two negative premises, no
conclusion can be drawn. Rule 2 In a valid
categorical syllogism, the number of universal
premises must be exactly one more than the number
of universal conclusions. Rule 3 In a valid
categorical syllogism, the middle term must be
distributed at least once.
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Rule 4 In a valid categorical syllogism, any
term which is distributed in the conclusion must
also be distributed in the premises. Rule 5 A
syllogism must have three and only three terms.
Rule 6 if a premise is particular, the
conclusion must be particular. If a premise is
negative, the conclusion must be negative.
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Examples of violations

• Rule 1
• No dogs are cows
• No cows are pigs
• Therefore, no dogs are pigs.

• Rule 2
• Some Italians are from Calabria.
• All Italians love spaghetti
• Therefore, all those from Calabria love
  spaghetti.

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• Rule 3
• All Germans love beer
• All Irishmen love beer
• Therefore, all Irishmen are Germans.

• Rule 4
• All principals know about administrative
  problems
• No secretary is a principal.
• Therefore, no secretary knows about
  administrative problems

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• Rule 5
• All Canadians like hockey.
• All Italians like soccer.
• Therefore, some Canadians like soccer.

• Rule 6
• Some men are American
• All Americans love apple pie
• Therefore, all men love apple pie.

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• Or
• Some Canadians are not hockey players.
• Some hockey players are professionals
• Therefore, some professionals are Canadian.

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Steps to Takein order to determine the validity
of a syllogism

1. Circle your middle term.

2. Determine what kind of statement is the first
premise (I.e., A statement, E statement, etc.)
3. Determine what kind of statement is the
second premise. (I.e., A statement, E statement,
etc.)
4. Determine what kind of statement is the
conclusion. (I.e., A statement, E statement,
etc.)
5. Place a d above all your distributed terms
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6. Check to see if your middle term is
distributed at least once (rule 3). If it is,
move on to 7.
7. Check your major and minor terms in the
conclusion. If one of them is distributed, see
if that term is distributed in the premises (rule
4).
8. Check to see if any other rule is violated.
If not, you have a valid syllogism.
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A note on mathematical logic
The logic weve been studying is called
intentional logic, or Aristotelian logic. This
logic is qualitatively different than symbolic or
mathematical logic. The two are discontinuous.
Mathematical logic submits the object of logic
to a thorough mathematicizing treatment. So
developed, this modern logic becomes a branch of
mathematics without relevance to sciences that
are not subalternate to mathematics. (Joseph
Owens)
That symbolic logic, in its techniques,
concepts, or specific propositions, can aid in
the solution of any philosoophical problem, is
seriously doubted. M. Weitz, Oxford
Philosophy, Philosophical Review, LXII, (1953)
221.