Categorical Logic – A branch of formal logic in which the basic logical terms are all, some, no, are, and not.

 

Propositional Logic – Deals with the relationships that hold between simple propositions or statements and their compounds. The basic logical terms are not, or, and, and if then.

 

 

Truth Tables

Denying a Statement      

P        ~P

T          F

F          T

 

Conjunction

P        Q   P & Q
T        T        T

T        F        F

F        T        F

F         F       F

 

Disjunction

P        Q   P or Q
T        T        T

T        F        T

F        T        T

F         F       F

 

Conditional

P        Q   P,  Q
T        T      T

T        F      F

F        T      T

F         F     T

 

 

 

Conditionals

 

Antecedent – The hypothesized statement

Consequent – What is supposed to follow from the antecedent

 

Conditionals assert neither the antecedent nor the consequent. Rather they express a link between the two; they claim that if the antecedent is true, then so is the consequent.

 

Types of Conditionals

 

True by Definition

If a person has a mortgage on his house, he has borrowed money to buy the house.

True by Logic or Mathematics

If you add two and three you will get 5

Causal Relationship

·        If a person cannot pay his mortgage his house will be confiscated.

·        If I drop this ball it will fall.

·        If a person has trouble paying his mortgage he is likely to be under stress.

Normative Claim

If a person has incurred a debt by taking out a mortgage, he should make every reasonable effort to repay that debt.

Threat/Promise

·      If you don’t get that next payment in, we’re going to have the locks changed.

·      If you give me a kiss I will give you a raise

 

“Either it is an accident that I choose to act as I do or it is not.  If it is an accident, then it is merely a matter of chance that I did not choose otherwise; and if it is merely a matter of chance that I did not choose otherwise, it is surely irrational to hold me morally responsible for choosing as I did. But if it is not an accident that I choose to do one thing rather than another, then presumably there is some causal explanation of may choice: and if that case we are led back to determinism [which would mean that we aren’t morally responsible for what we do].”--A.J. Ayer: Freedom and Necessity