SAM:

My chances of winning the lottery this Saturday aren't 50-50 SAM, even if for some bizarre reason you think they are. In fact, they are more like 50 million to one against.

You don't say?

This is why I advised you never to gamble. This is news to you, is it?

What you are saying is that you are incapable of saying what is more likely: that I will or will not win the lottery this Saturday.

No I am saying that I can wait till Saturday to find out if its true.

Fine. Atheists can wait till Saturday to find out if God exists. In the meantime, it's fair enough to assume that God doesn't exist. Right?

You must find this inability to grasp basic probability to be a severe impediment in your daily life. How do you cope?

I believe.

Many a true word is said in jest.

Not if unicorns look anything like that picture. On the other hand, I've seen plenty of pictures like that before, and every time I've seen one somebody has said it is a picture of a unicorn.

So if your kid was to show you that picture and ask you what it is, what would you say?

I'd say it was a unicorn, on the assumption that my child understands the difference between an image of a thing and the thing the image references.

Are you going anywhere with this, or just spinning your wheels?

Did you miss the TWO explanations of the error in this? It is an error of logic - a fallacy - known as "affirming the consequent". Here's another example, in positive form:

1. Birds have legs.

2. My dog has legs.

3. Therefore, my dog is a bird.

Statement #1 can be written:

"If X is a bird, then X has legs."

The converse of this is:

"If X has legs, then X is a bird."

Quite clearly, the statement does not imply its converse, but this is what is assumed in the faulty example above.

A statement in which the converse MUST apply would be of the form:

"X has legs IF AND ONLY IF it is a bird."

which is equivalent to:

"X is a bird IF AND ONLY IF it has legs."

(Beware of misconstruing the language of formal logic in the term "IF AND ONLY IF", by the way. This can be given a very clear and precise mathematical definition, where the logical operator "IF AND ONLY IF" is called "equivalence", whereas the simple "IF" is called "implication".)

I agree. Now try all of the above with negative claims.

Ok.

Did you miss the TWO explanations of the error in this? It is an error of logic - a fallacy - known as "affirming the consequent". Here's another example, in negative form:

1. Birds have no antlers.

2. My dog has no antlers.

3. Therefore, my dog is a bird.

Statement #1 can be written:

"If X is a bird, then X has no antlers."

The converse of this is:

"If X has no antlers, then X is a bird."

Quite clearly, the statement does not imply its converse, but this is what is assumed in the faulty example above.

A statement in which the converse MUST apply would be of the form:

"X has no antlers IF AND ONLY IF it is a bird."

which is equivalent to:

"X is a bird IF AND ONLY IF it has no antlers."

(Beware of misconstruing the language of formal logic in the term "IF AND ONLY IF", by the way. This can be given a very clear and precise mathematical definition, where the logical operator "IF AND ONLY IF" is called "equivalence", whereas the simple "IF" is called "implication".)

Happy?