Propositional Logic

Let p be a proposition.

The negation of p, denoted by¬† \neg p, is the statement “It is not the case p“.

Example: Let p be It’s cold today, then \neg p = It’s not cold today.

 

Let p and q be propositions. The conjunction of p and q, denoted p \& q, is the proposition “p and q“. This is also written p \land q.

This is true when p and q are true, otherwise false.

Example: Let p be It’s cold today, and q be it’s raining today. p \& q is the proposition it’s cold and it’s raining today. Which is true when it’s cold and raining today, otherwise false (e.g. it’s cold and sunny today).

 

Let p and q be propositions. The disjunction of p and q, denoted p \lor q, is the proposition “p or q“. This is true when either p or q or both are true (i.e. false when both p and q are false).

Example: Let p be It’s cold today, and q be it’s raining today. p \lor q, is the proposition it’s cold today or it’s raining today, which is false only when it’s not cold and it’s not raining today.

 

(There exists an exclusive or \oplus which is true only when only one of p and q are true, false otherwise p \oplus q = p \lor q \& \neg (p \land q.) I. e. the proposition p \oplus q is true when p or q is true and not both p and q are true.)

 

Let p and q be propositions. The conditional statement p \to q is the proposition “if p, then q“. This is false when p is true and q is false, and true otherwise. A true statement cannot lead to a false conclusion. p is the antecedent, q is the consequent.

Example: Let p and q be the propositions it’s cloudy today and it’s raining today. p \to q is if it’s cloudy today, then it’s raining today. This statement is only false when it’s cloudy today, but not raining. It’s true in the other cases: if it’s cloudy today, then it’s raining (today), if it’s not cloudy today, then it’s raining and if it’s not cloudy today, then it’s not raining today. This is more general than the English “if then” construction.

 

Let p and q be propositions. The biconditional statement p \iff q is the proposition “p if and only if q.” This proposition is true when p and q have the same values. This is equivalent to p \to q \& q \to p.

Example: Let p and q be the propositions it’s cloudy today and it’s raining today. p \iff q is true when it’s cloudy and it’s raining today and when it’s not cloudy and it’s not raining today.

This post is heavily influenced by (borrowed from) Discrete Mathematics and its applications, sixth edition. Keneth H. Rosen.

 

 

 

 

 

On Abortion

An argument that is not mine:

  • Women are Persons (i.e. have value, wants, desires, hopes, worth) and are in every relevant way the equal of men regarding rights.
  • A person has the right to bodily autonomy.
  • Therefore, women have the right to bodily autonomy.
  • A fetus or embryo, for the sake of argument, is a person (even thought it doesn’t have the same wants, desires, hopes as an adult woman).
  • A woman, by virtue of her bodily autonomy, can chose what to do with her body.
  • A woman can chose to be pregnant, and rescind that choice at any time.
  • If a woman cannot rescind, i.e. abort, the permission to be pregnant with another person, then she does not have the same bodily autonomy as a man.
  • Therefore, a woman must have have the choice to abort or not, unless she is less than a man.

Notes:

It matters not a whit that one believes a fetus or embryo is as much a person as a woman. Nobody would countenance forcing a man to share his body or parts to support the life of another person. Even though not providing this lifesaving act would mean the death of the other.

I don’t believe a fetus/embryo is of the same value or development as an adult. But I have not used that in the argument.

If a fetus/embryo is a unique individual (doubtful), so is a woman. Neither has the right over the other.