Aristotelian Logic

Front 1

What is syllogism?

Back 1

Syllogism is a notion of Aristotelian logic which is any argument which has two premises going to a conclusion.

Front 2

What is a categorical proposition?

Back 2

a categorical proposition is any proposition that relates only two categories/classes of things.

Front 3

what is the standard form of categorical propositions?

Back 3

there are four parts of the standard form of categorical propositions. There is the quantifier, subject term, copula, and predicate term.

Front 4

what is the quantifier in a categorical proposition?

Back 4

the quantifier is what tells how the classes relate in how many of them are connected and how they go together. For example, in the proposition: Some students are intelligent people, the word "some" is the quantifier.

Front 5

what is the subject term in a categorical proposition?

Back 5

the subject term states a class or category of people. For example, in the proposition: Some students are intelligent people, the subject term is the word "students"

Front 6

what is the copula in a categorical proposition?

Back 6

a copula in a categorical proposition is the verbal link that distinguishes the classes. For example, in the proposition, Some students are intelligent people, the copula is the word "are". Other copulas include "to be" words such as "is" "are" "were"

Front 7

What is the predicate term in a categorical proposition?

Back 7

the predicate term in a categorical proposition is the other class or category. For example, in the proposition, Some students are intelligent people, the predicate term is the phrase "intelligent people"

Front 8

What are the characteristics of an A proposition

Back 8

An A proposition is Affirmative, Universal, and the subject term is distributed while the predicate term is not
An A proposition states that All S are P.

Front 9

What are the characteristics of an E proposition

Back 9

An E proposition states that No S are P.
Therefore, the proposition is negative, universal, and the subject term as well as the predicate term are distributed.

Front 10

What are the characteristics of an I proposition

Back 10

An I proposition states that Some S are P. Therefore, the proposition is Affirmative, Particular, and the subject term as well as the predicate term are undistributed

Front 11

What are the characteristics of an O proposition?

Back 11

In an O proposition, it is stated that Some S are not P.
The propositon is particular, negative, The predicate term is distributed and the subject term is undistributed.

Front 12

State the standard form of the A proposition.

Back 12

the a proposition is All S are P. All is the quantifier
S is the subject term. are is the Copula. P is the predicate term.

Front 13

State the standard form of the E proposition

Back 13

The E proposition is: No S are P. No is the quantifier.
S is the subject term. Are is the Copula, and p is the predicate term.

Front 14

State the standard form of the I proposition

Back 14

The I proposition is Some S are P. Some is the quantifier. S is the subject term. Are is the Copula. P is the Predicate Term

Front 15

State the standard form of the O proposition.

Back 15

The O proposition is Some S are not P. The Quantifier is Some Not.
The Subject term is S
The Copula is Are.
The predicate term is P.

Front 16

What are the ambiguities that occur in the AEIO propositions? There are two.

Back 16

One occurs in the O and I propositions because they include the word "some". To clear that up, "some" means "at least one"

The other ambiguity occurs in the O proposition. This is ambiguous because of the word "not" and the English language. The logical form is often hidden by grammar. Ancient Greek puts the 'not' somewhere else instead of next to the copula. So, the QUANTIFIER of o is "SOME NOT", not just "some". The subject term is X and the Copula is are. The predicate term is P.

Front 17

What is quality in identifying the characteristics of categorical propositions?

Back 17

They are either affirmative or negative. In affirmative, it includes members of one class in another, in negative it excludes the group from the other group. A is Aff. E is Neg. I is Aff. O is Neg.

Front 18

What is quantity when dealing with the exact identification of the characteristics of categorical propositions?

Back 18

Quantity is either universal or particular. All of the class or less than all of the class, respectively. A is universal. E is Universal. I is particular. O is particular.

Front 19

What is Distribution when dealing with the exact identification of the characteristics of categorical propositions?

Back 19

Distribution is different from quality and quantity. Distribution is about the classes and terms that make up the propositions. A term is distributed if all fo the members of the class are being talked about, otherwise it is undistributed if less than all of the class or category is being talked about.

Front 20

What are immediate inferences?

Back 20

Immediate Inferences are based on definition, or conceptual understanding and have no middle ground or movement from one place to another. They are made without reasoning.

Front 21

What is the square of opposition?

Back 21

The square of opposition shows the relationships between categorical propositions, which are A, E, I, and O, and Contradictories, Contraries, subcontraries, and subalterns

Front 22

What are contradictories and what are the categorical propositions that are contradictories?

Back 22

contradictories are categorical propositions that are opposite in truth value. They are the diagonals in the square of opposition. A and O are contradictories. I and E are also contradictories. When one is true, its contradictory is false.

Front 23

What are contraries?

Back 23

A and E are contraries. They are statements that Both cannot be true. Both of them can be false, however.

Front 24

What are subcontraries?

Back 24

Subcontraries are statements that can both be true but both cannot be false. I and O are subcontraries and they are located at the bottom two spaces of the square of opposition.

Front 25

What are subalterns?

Back 25

subalterns are A and I as well as E and O. When a universal statement is true, then it ensures the trueness of the statement that has the same quality and is particular. Thus, when A is true, I is also true. Also, when a particular is false, the falseness of that particular's like-qualitied universal is ensured. Therefore, if O is false, then E must also be false. If I is false, then A must also be false. If E is true, then O must also be true.

Front 26

In terms of quality, quantity, and distribution, what is interesting about the square of opposition and contradictions?

Back 26

Every characteristic (quantity, Quality, and distribution) is opposite if they are contradictory.

Front 27

What can be remembered in order to remember the direction of the subalterns in the square of opposition?

Back 27

Truthness goes down, and falseness rises up.

Front 28

What is special about contradictories as opposed to subalterns, subcontraries, and contraries?

Back 28

contradictories always result in an inference.

Front 29

Who was John Venn?

Back 29

John Venn was a mathematician/ logician who graphed categorical syllogisms.

Front 30

What does the venn diagram of the a proposition look like?

Back 30

the a proposition states that all s are p, so the part of the circles that just pertains to s is shaded because there are no s's that are only s's.

Front 31

what does the venn diagram of the e proposition look like?

Back 31

The e proposition states that no s are p, so the venn diagram has a shaded section where the S and the P intersect because they do not share any values.

Front 32

what does the venn diagram of the i proposition look like?

Back 32

the i proposition states that some s are p, therefore an x goes in the space in which s and p intersect. the X indicates that there is at least one value in the area.

Front 33

what does the venn diagram of the o proposition look like?

Back 33

The o proposition states that some s are not p. the venn diagram shows an x in the location which only contains S. This shows that some s's are not p's, so they must be outside of the P area. The x means at least one

Front 34

What is existential import?

Back 34

It is a property that is given to some categorical propositions. A proposition has existential import if it assumes that there are existing entities in the category or classes. It brings existence into the argument. It presupposes the existence of members of the classes that are being mentioned.

Front 35

Which categorical propositions have existential import according to George Boole?

Back 35

The I and O Categories have existential import because they include the word "some"

Front 36

According to Aristotle, which categorical propositions have existential import?

Back 36

All four of the propositions have existential import because if you can talk about something logically, then it exists. There are many ways in which things exist. Therfore, in his opinion, form overrides the content of the argument.

Front 37

What are categorical syllogisms? What kinds of propositions make up categorical syllogisms? How many terms are in categorical syllogisms? How many times are those terms used in the categorical propositions?

Back 37

categorical syllogisms are arguments that have two premises going to one conclusion. Also, all of their propositions are categorical propositions (A, E, I, and O). They are made up of exactly three terms, the major term, the minor term, and the middle term. Each term is used twice.

Front 38

What is the major premise in a categorical syllogism?

Back 38

the major premise contains the major term. What is the major term?

Hint 38

The major term is the predicate term of the conclusion.

Front 39

What is the minor premise in a categorical syllogism?

Back 39

the minor premise contains the minor term. What is the minor term?

Hint 39

the minor term is the subject term of the conclusion.

Front 40

What is the standard form of categorical syllogisms?

Back 40

major premise
minor premise
conclusion

Front 41

WHat is the purpose of the middle term?

Back 41

The middle term provides a bridge or a link between the terms. It does not occur in the conclusion.

Front 42

What is the mood of a categorical syllogism?

Back 42

the mood of a categorical syllogism is the statement of the three k9inds of categorical propositions that the syllogism has once it is put into standard form.

Front 43

what is the figure of a categorical syllogism?

Back 43

the figure of a categorical syllogism is the placement of the middle term and it is determined by the premises, not the conclusion.

Front 44

which figure (1-4) is this?
MP
SM

Back 44

figure is one

Front 45

which figure (1-4) is this?
PM
SM

Back 45

the figure is two

Front 46

which figure (1-4) is this?
MP
MS

Back 46

the figure is three

Front 47

which figure (1-4) is this?
PM
MS

Back 47

the figure is four.

Front 48

What is the purpose of the mood and figure?

Back 48

they identify each argument and separate them from one another.

Front 49

how many different combinations of moods plus figures are there?

Back 49

there are 256 ways to arrange the terms and propositions to produce an argument.

Front 50

what is the difference between the meaning of not and non?

Back 50

not and non do not mean the same thing in Aristotelian logic. Non is a class complement and not is in the o Proposition and acts as a quantifier.

Front 51

what is the meaning of bar s (s with a line above it)

Back 51

the meaning of bar s is non-s. it is called a class complement and it refers to all members that are on the outside of a class.

Front 52

what is the special name for bar s?

Back 52

bar s is a class complement because it shows the members that are outside of a class.

Front 53

In which order should you diagram a universal and a particular proposition on a venn diagram?

Back 53

you should diagram the universal proposition before the particular proposition if the situation arises.

Front 54

Why didn't Aristotle do the shading and the Venn diagrams?

Back 54

aristotle did not do the shading and the venn diagrams because he came before john venn and he had rules to follow anyway.

Front 55

Name all of the formal fallacies that Aristotle used to determine if arguments were valid or invalid. Also, include the fifth fallacy that Boole brought into the picture.

Back 55

-Exclusive Fallacy (two negative premises)
-Drawing an affirmative conclusion from a negative premise (An affirmative conclusion coming from at least one negative premise)

-Undistributed Middle:(Middle term is not distributed at least once)
-Illicit Major and Illicit Minor: (The distributed term in the conclusion must be distributed in the premises).
-Existential Fallacy: (Two universal premises cannot go to a particular conclusion.)

Front 56

Describe the two Distributive Fallacies.

Back 56

one distributive fallacy is that the middle term must be distributed at least once. This is called the undistributed middle fallacy. A categorical syllogism connects two unconnected things by means of a link by the middle term. It must be distributed at least once. If it is not distributed at least once, then you don't know that you have a link between the two. The middle term must be talked about wholly at least once in order to make the bridge. There cannot be a valid argument because it is possible that the parts are not connected to the same thing.

The other distributive fallacy is the fallacy that states that the distributed term that is in the conclusion must also be distributed in the premises. If it is the minor term that is not distributed, then it is called illicit minor. If it is the major term that is not distributed in the premises like it was in the conclusion, then it is the illicit major fallacy. Because whatever is talked about in the conclusion must be wholly and completely in the premises because the conclusion cannot go beyond the premises.

Front 57

Describe the two negative formal fallacies.

Back 57

One negative formal fallacy is the exclusive fallacy that states that there cannot be two negative premises. THis is because there cannot be two premises that exclude one another.

The other negative formal fallacy is the one that states that there cannot be a negative premise that goes to an affirmative conclusion. This is called the drawing an affirmative conclusion from a negative premise.

Front 58

Describe Boole's formal fallacy.

Back 58

Boole's formal fallacy is the existential fallacy. It states that it is invalid to have two universal premises going to a particular conclusion.