Categorical Vs Propositional

Question 1

By what other name is categorical logic known?

Answer 1

Aristotelian logic

Question 2

In categorical logic, what do the symbols (letters) represent?

Answer 2

Categories

i.e not proposition: in propositional logic the letters represent whole claims or propositions.

Question 3

Explain the notation in Categorical logic.

Answer 3

Capital letters represent Categories and lower case letters represent members of those categories.

Question 4

What does the ALL entail in a premise?

Answer 4

Absolutely every single individual in a category.

Question 5

What is a universal generalisation?

Answer 5

A premise of the form

All A are B

Question 6

How is the contradictory of a universal generalisation produced?

Answer 6

not-(All A are B) = Some A are not-B

Question 7

What does “SOME” mean in logic?

Answer 7

At least one.

n.b. depending on the context, some may mean “at least one, but not all” or “at least one, but also all”. It normally means the former.

Question 8

What are alternative ways to say:

Some A are B?

Answer 8

At least one A is B;

There is one A which is B;

There exists one B(A).

Question 9

State the general rule for the contradictory of:

Some A are B

Answer 9

not-(Some A are B) = No A are B

Question 10

State some ways to express “some”

Answer 10

there is a…;

there is one…;

a. .. is…;
one. .. is…

Question 11

What is the general relationship between ONLY and ALL?

Answer 11

Only A are B= All B are A

Question 12

What is the contradictory of

Only A are B ?

Answer 12

not-(Only A are B)= Some B are not A

Question 13

What is the contrary of All A are B?

Answer 13

No A are B

Question 14

What is a subcontrary?

Answer 14

The opposite of a contrary.
It’s when both claims can both be true at the same time but cannot be both false at the same time.

e.g. Some A are B
Some A are not B

Question 15

What is a Syllogism?

Answer 15

A 3 line valid argument of the form:

1. Premise 1
2. Premise 2
3. Therefore, Conclusion

Question 16

Valid argument (syllogism) forms that use a disjunction assume what about the disjunction?

Answer 16

That it is a exclusive disjunction.

Question 17

What kind of argument using a disjunction is always valid?

Answer 17

1. A or B
2. not-A
   Therefore, B

Question 18

What kind of argument is valid for exclusive disjunctions but invalid for inclusive disjunctions?

Answer 18

1. A or B
2. A
   Therefore, not-B

Question 19

What does Modus Ponens mean?

Answer 19

The mode of affirming by affirming.

It is the instance of affirming the the consequent by affirming the antecedent.

Question 20

How is modus ponens represented in argument form?

Answer 20

1. If A then B
2. A
   Therefore, B

Question 21

What is modus tollens?

Answer 21

It is the mode of denying by denying.

The instance of denying the antecedent by denying the consequent.

Question 22

What is the relationship between modus tollens and modus ponens?

Answer 22

If modus tollens is written in contrapositive form it becomes modus ponens.

Question 23

Represent modus tollens in argument form.

Answer 23

1. If A then B
2. not-B
3. Therefore, not-A

Question 24

What is an Hypothetical Syllogism?

Answer 24

A syllogism in which both premises as well as the conclusion is a conditional; the consequent of the first premise becoming the antecedent of the following premise; and in which the antecedent of the first premise becomes a condition for the consequent of the second premise in the conclusion.

1. If A then B
2. If B the C
3. Therefore, If A then C

Question 25

What is the mathematical name for an Hypothetical Syllogism?

Answer 25

Transitive relationships

Question 26

In Hypothetical Syllogisms, what is the only direction in which logical connection must flow?

Answer 26

From antecedent to consequent; never the other way around.

Question 27

What is Affirming the Consequent?

Give its argument form.

Answer 27

Is an invalid argument form that could be likened to an invalid version of Modus Ponens.

1. If A then B
2. B
3. Therefore, A

… which is invalid.

Question 28

What is Denying the Antecedent?

Give its argument form.

Answer 28

Is an invalid argument form that could be likened to the invalid form of Modus Tollens.

1. If A then B
2. Not-A
3. Therefore, not-B.

Question 29

1. All A are B
2. x is a B
3. Therefore, x is a A

Is this a valid argument in categorical logic?
What is it?

Answer 29

No, it’s not valid. It is a case of arguing backwards with ALL, which is invalid.

Question 30

1. All A are B
2. x is a A
3. Therefore, x is a B

Is this a valid argument in categorical logic?

Answer 30

Yes, it is valid.

Question 31

1. All A are B
2. All B are C
3. Therefore, all A are C

Is this a valid argument in categorical logic?
What is it?

Answer 31

Yes, it is valid. It’s an instance of arguing in a chain using ALL.

Question 32

1. All A are B
2. All B are C
3. Therefore, all C are A

Is this a valid argument in categorical logic?
What is it?

Answer 32

No, it is invalid. It is an instance of backward argumentation.

Question 33

1. Some A are B
2. x is an A
3. Therefore, x is a B

Is this a valid argument in categorical logic?

Answer 33

No, it is invalid.

Question 34

1. Some A are B
2. Some B are C
3. Therefore, some A are C

Is this a valid argument in categorical logic?

Answer 34

No, it is invalid.

Reasoning in a chain with SOME is invalid.