Fallacy of assumption

'Fallacy of Assumption' describes a class of formal and informal logical fallacies that are to do with a flaw in an argument's assumptions.

A common example of a fallacy of assumption (there are others) is when someone assumes the very thing they are trying to prove. This is commonly known as begging the question, or petitio principii.

The nature of this fallacy is obvious in the following form:

P1: Fairies Exist

Therefore

C2: Fairies Exist

It's clear that the form of the argument above could be used to 'prove' anything.

As the argument becomes increasingly elaborate, it becomes easier to miss the fallacy.

P1: Fairies Exist

P2: Only fairies can make gardens that are extremely beautiful

P3: My garden is extremely beautiful

Therefore (from P1, P2 and P3)

C1: My garden was made extremely beautiful by fairies

Therefore (from C1)

C2: Fairies Exist

Arguments that commit a fallacy of assumption can easily hide the fallacy by rendering it implicit. This means making a premise in the argument that implies the fallacious assumption without explicitly stating it. In the example immediately above, the statement that 'only fairies can make gardens extremely beautiful' has the assumption that fairies exist built into it. Because of this, P1 can be furtively omitted, giving the logical form below.

P1: Only fairies can make gardens that are extremely beautiful

P2: My garden is extremely beautiful

Therefore (from P1 and P2)

C1: My garden was made extremely beautiful by fairies

Therefore (from C1)

C2: Fairies exist

This argument could be delivered in speech in something like the following manner:

My garden is extremely beautiful. Sure, I work at it. But no one can make a garden this beautiful - no one human, anyway. Only fairies could have done it! I know that fairies had to have made my garden so beautiful, and that's how I know that fairies really exist.

The example may seem silly given the subject matter is fairies. However, arguments of a similar form are very common for other ideas.