---
categories:
  - Logic
tags: [propositional-logic]
---

# Syllogism

In order to make assertions about the relative [consistency](/Logic/General_concepts/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
```
