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Logic/General_concepts/Soundness.md
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# Soundness
Recall that in the definition of [deductive validity](Validity%20and%20entailment.md#validity) we do not say: an argument is valid iff if the premises _are true_ and the conclusion _is true_. We say _if it is possible for the premises to be true_. This is important: we are not interested in the actual truth of the premises or the conclusion.
Recall that in the definition of [deductive validity](/Logic/General_concepts/Validity_and_entailment.md#validity) we do not say: an argument is valid iff if the premises _are true_ and the conclusion _is true_. We say _if it is possible for the premises to be true_. This is important: we are not interested in the actual truth of the premises or the conclusion.
#### Demonstration
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```
(P1) London is the capital of the United Kingdom
(P2) The capital of the United Kingdom is in the southern part of the United Kingdom.
Can
(P3) Cambridge is not the capital of the United Kingdom
____________________________________________
(C) London is south of Cambridge

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Logic/General_concepts/Syllogism.md
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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 sentences comprising one or more premises and a conclusion. The conclusion is taken to be supported by the premises.**
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.

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Logic/General_concepts/Validity_and_entailment.md
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---
categories:
- Mathematics
tags: [logic]
- Logic
tags: [propositional-logic]
---
## Validity