**Proposition**: a sentence that makes an assertion, a claim.

**Premise**: a proposition that conditions a conclusion.

**Syllogism**: an argument with two premises leading to a conclusion.

**Valid Argument**: one in which the conclusion follows from the premises.

**Sound Argument**: one which is valid with *true* premises.

- Note that all sound arguments are valid, though not all valid arguments are sound.

**Invalid Argument**: one in which the conclusion does *not* follow from the premises – a *fallacy*.

**Propositional Variable**: a clause within a proposition, or the proposition alone (symbolized by a capital letter usually starting from **P**).

**Logical Operators**: the logical relations amongst *propositional variables*:

- The
**Conditional**(*If*P*then*Q):**→** - The
**Conjunct**(P*and*Q):**&**(or**∧,**or**∙**) - The
**Disjunct**(P*or*Q):**∨**(*not*mutually exclusive) - The
**Negation**(*not*-P):**~** - The
**Biconditional**: (*If and only if*P,*then*Q):**↔**- Note the Biconditional expresses a
*sufficient*(if) and*necessary*(only if) condition: (P**→**Q)&(Q**→**P). The biconditional is also written.*iff*

- Note the Biconditional expresses a

**Antecedent**: the if-clause of a conditional proposition (i.e. P in P**→**Q).

**Consequent**: the then-clause of a conditional proposition (i.e. Q in P**→**Q).

Example of symbolic reduction:

*“If I light the curtains, the house burns down. I light the curtains. **Therefore the house burns down.”*

=

If P then Q. P. Therefore Q.

=

**P →**

**Q, P,**

**∴**

**Q**

** **

** Modus ponens**: A valid argument that affirms the antecedent to derive the consequent:

**P →**

**Q, P,**

**∴**

**Q**

** **

*Modus tollens***: **A valid argument that denies the consequent to derive the negation of the antecedent:

**P →**

**Q,**

**~**

**Q,**

**∴**

**~**

**P**

** **

**Fallacy of Affirming the Consequent:** an invalid argument that affirms the consequent to mistakenly derive the antecedent:

**P →**

**Q, Q,**

**∴**

**P**

**Fallacy of Denying the Antecedent: **an invalid argument that denies the antecedent to mistakenly derive the negation of the consequent:

**P →**

**Q,**

**~**

**P,**

**∴**

**~**

**Q**

©MMXVI Peter Sjöstedt-H