PHIL 140 Chapter Notes - Chapter 6: Syllogism, Obversion, National Thoroughbred Racing Association

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16 Apr 2012
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Categorical logic - the logic of terms developed by Aristotle
Categorical statement - makes a claim about the relationship between some or all of the members of two classes of things.
-Four standard types
Name
Type
Standard Form
Example
A
Universal Affirmative
All Canadians are farmers
E
Universal Negative
No S are P
No Canadians are farmers
I
Particular Affirmative
Some S are P
Some Canadians are farmers
O
Particular Negative
Some S are not P
Some Canadians are not farmers
Quantifier - the beginning words. "Some", "All", or "No"
1.
Subject term - a word or phrase denoting a class of things serving as the subject of the sentence
2.
Copula - the linking verb "are", which is a form of the verb to be, that connects the subject term with predicate term
3.
Predicate term - a word or phrase denoting a class of things serving as the subject complement (which is a noun phrase, linked to the subject by the
copula, together with which it forms the verb phrase of the sentence)
4.
-Every categorical statement in standard form has four parts:
Quantifier
Subject Term
Copula
Predicate Term
A
All
ducks
are
birds (universal affirmative)
E
No
humans
are
gods (universal negative)
I
Some
humans
are
engineers (particular affirmative)
O
Some
reptiles
are not
snakes (particular negative)
It is an affirmative statement if it states that the class designated by its subject term is included, either as a whole or only in part, within the class
designated by its predicate term
It is a negative statement if it wholly or partially excludes members of the subject class from the predicate class
The quality of a categorical statement is the character (affirmative or negative) of the relationship it affirms between its subject and its predicate terms:
It is a universal statement if the asserted claim holds true for every member of the class designated by its subject term
It is a particular statement if the claim is asserted to hold only for one or more members of the subject class
The quantity of a categorical statement, on the other hand, is a measure of the degree (universal or particular) to which the relationshi p between its subject
and predicate terms holds:
Universe of discourse - all of the things in the world being discussed. Represented by the square surrounding the circles in a Venn diagram
Lens - contains everything that is both S and P
i.
Left Lune - contains only things that are S but not P
ii.
Right Lune - contains only things that are P but not S
iii.
Everything that is neither S nor P
iv.
The pair of circles separates the universe of discourse into four areas:
All S are P - if all S are P then if there is any thing that is an S then it is also a P; there are not any things that that are S but not P
-EX: All dogs are mammals
- EX: No snakes are poodles
No S Are P - if no S are P , then there are no things in the universe of discourse that are both S and P
`
S
P
S
P
Chapter 6 Text Notes
February-28-12
Ch. 6 Text Notes Page 1
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`
Some S are P - tells us both that there is at least one thing that is S and that that thing (and possibly others) is also P.
-EX: Some poodles are miniatures
-EX: some snakes are not cobras
Some S are not P - tells us both that there is at least one thing that is S, and that thing is not P
Complement - the complement of a class is everything in the universe of discourse that is not a member of that class
- a term and its complement cover the whole universe of discourse
-EX: "non-drinker" is the complement to the term "drinker"
-When there is a choice, you should always use the affirmative form of the predicate rather than the complement
If necessary, rephrase the subject and predicate terms so that they are the names of classes
i.
EX: "Some clowns are funny" becomes "Some clowns are funny people"
If the verb in the statement is not the copula ("are" or "are not"), rewrite the verb or verb phrase so that it takes the copula noun-phrase form
ii.
EX: "Fish swim" becomes "All fish are swimmers"
-Do not use the complements of classes in translations of complement non-phrases.
EX: Do not translate "Fish swim" as "No fish are non-swimmers"
Pay close attention to the context and make sure to get the quantity of the categorical right
iii.
EX: "Dogs are mammals" should be written as "All dogs are mammals"
EX: "Bankers are conservatives" should be written as "Some bankers are conservatives"
Finally, treat statements about individuals as claims about the unit class (the class that contains only that individual) in question
iv.
EX: "Prime Minister Harper is a Conservative" would be written as "All people identical with Prime Minister Harper are Conser vatives"
Steps in Translation:
The problem of empty terms - The universal categoricals "All S are P" and "No S are P" make no claims about whether or not anything actually exists.
a.
-The two particular categoricals "Some S are P" and "Some S are not P" are taken to make claims about the actual existence of
at least one thing in the universe of discourse that is S
-When we assume that a term is not empty, this is not due to the meaning of the universal categorical, but is an independent
piece of knowledge we already have and bring to the task of how best to translate the sentence
-EX: In the statement "All cats have fleas", it is not stated whether or not there are any cats
-EX: The statement "Apples are fruit" is easy to translate into "All apples are fruit", however the statement " Men are fools" is
much more difficult to interpret
Interpretations of "Some" - If there is exactly one member of S that is P, then the categorical "Some S are P" is true, and the same is true if almost al l S are P
b.
Direct Singular Reference - Some nurses are very dedicated people
c.
Some Manitobans are nurses
*This is an invalid argument because the first premise does not tell you that the nurses who are dedicated are Manitoban nurses and
the second premise does not tell you that the nurses who are Manitoban are dedicated nurses. This is fixed if the first premise to "All
nurses are very dedicated people"
Some Manitobans are very dedicated people
Three Issues Regarding Proper Translations
S
P
S
P
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