Categorical Vs Propositional Flashcards
By what other name is categorical logic known?
Aristotelian logic
In categorical logic, what do the symbols (letters) represent?
Categories
i.e not proposition: in propositional logic the letters represent whole claims or propositions.
Explain the notation in Categorical logic.
Capital letters represent Categories and lower case letters represent members of those categories.
What does the ALL entail in a premise?
Absolutely every single individual in a category.
What is a universal generalisation?
A premise of the form
All A are B
How is the contradictory of a universal generalisation produced?
not-(All A are B) = Some A are not-B
What does “SOME” mean in logic?
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.
What are alternative ways to say:
Some A are B?
At least one A is B;
There is one A which is B;
There exists one B(A).
State the general rule for the contradictory of:
Some A are B
not-(Some A are B) = No A are B
State some ways to express “some”
there is a…;
there is one…;
a. .. is…;
one. .. is…
What is the general relationship between ONLY and ALL?
Only A are B= All B are A
What is the contradictory of
Only A are B ?
not-(Only A are B)= Some B are not A
What is the contrary of All A are B?
No A are B
What is a subcontrary?
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
What is a Syllogism?
A 3 line valid argument of the form:
- Premise 1
- Premise 2
- Therefore, Conclusion
Valid argument (syllogism) forms that use a disjunction assume what about the disjunction?
That it is a exclusive disjunction.
What kind of argument using a disjunction is always valid?
- A or B
- not-A
Therefore, B
What kind of argument is valid for exclusive disjunctions but invalid for inclusive disjunctions?
- A or B
- A
Therefore, not-B
What does Modus Ponens mean?
The mode of affirming by affirming.
It is the instance of affirming the the consequent by affirming the antecedent.
How is modus ponens represented in argument form?
- If A then B
- A
Therefore, B
What is modus tollens?
It is the mode of denying by denying.
The instance of denying the antecedent by denying the consequent.
What is the relationship between modus tollens and modus ponens?
If modus tollens is written in contrapositive form it becomes modus ponens.
Represent modus tollens in argument form.
- If A then B
- not-B
- Therefore, not-A
What is an Hypothetical Syllogism?
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.
- If A then B
- If B the C
- Therefore, If A then C
What is the mathematical name for an Hypothetical Syllogism?
Transitive relationships
In Hypothetical Syllogisms, what is the only direction in which logical connection must flow?
From antecedent to consequent; never the other way around.
What is Affirming the Consequent?
Give its argument form.
Is an invalid argument form that could be likened to an invalid version of Modus Ponens.
- If A then B
- B
- Therefore, A
… which is invalid.
What is Denying the Antecedent?
Give its argument form.
Is an invalid argument form that could be likened to the invalid form of Modus Tollens.
- If A then B
- Not-A
- Therefore, not-B.
- All A are B
- x is a B
- Therefore, x is a A
Is this a valid argument in categorical logic?
What is it?
No, it’s not valid. It is a case of arguing backwards with ALL, which is invalid.
- All A are B
- x is a A
- Therefore, x is a B
Is this a valid argument in categorical logic?
Yes, it is valid.
- All A are B
- All B are C
- Therefore, all A are C
Is this a valid argument in categorical logic?
What is it?
Yes, it is valid. It’s an instance of arguing in a chain using ALL.
- All A are B
- All B are C
- Therefore, all C are A
Is this a valid argument in categorical logic?
What is it?
No, it is invalid. It is an instance of backward argumentation.
- Some A are B
- x is an A
- Therefore, x is a B
Is this a valid argument in categorical logic?
No, it is invalid.
- Some A are B
- Some B are C
- Therefore, some A are C
Is this a valid argument in categorical logic?
No, it is invalid.
Reasoning in a chain with SOME is invalid.
