---
tags: [propositional-logic]
---

# Syllogism

In order to make assertions about the relative
[consistency](Logical_consistency.md) or inconsistency
of a set of propositions we advance arguments. Consider everyday life: if we are
having an argument with someone, we believe that they are wrong. A more logical
way to say this is that we believe that their beliefs are inconsistent. In order
to change their viewpoint or point out why they are wrong we advance an argument
intended to show that belief A conflicts with belief B. Or if C is true, then
you cannot believe that D.

In formal terms **an argument is a set of propositions comprising one or more
premises and a conclusion. The conclusion is taken to be supported by the
premises.**

> The terms **argument** and **syllogism** are used interchangeably in logic to
> describe the above feature of a set of propositions.

### Demonstration

```
(P1) All men are mortal.
(P2) Socrates is a man.
_____________________
(C) Socrates is mortal
```
