Re: Material Evidence & Logical Proof

[Anonymous]

You seem to be saying that "If A then B" implies "If not A then not B."  This is a fallacy called "denying the antecedent."  Here's a counterexample:

A="I am a living human."
B="I have consumed water in the past 100 days."

If A then B.  However, if I am a living cow (i.e. not a living human), that does not imply that I haven't consumed water in the past 100 days.

I think I understand the point you intended to make here, but the fact remains that a fallacy is presented as truth at the top of the page.  Please correct this.

Admin edit: Removed registration. Changed name.

[Dale Eastman]

Thank you for bringing this to my attention. And thank you for being the first to use this feedback method.

You've put me on notice that the formal logical fallacy of "denying the antecedent" exists. I was not aware of that particular formal logical fallacy, so I did some online study.

I see that the form presented on the web page seems to match the form of denying the antecedent, so I understand why you think I present the fallacy of denying the antecedent on the web page in question. And your counter example is an excellent refutation if that is actually the case.

ANALYSIS

You challenge my argument:
If A, then B therefore If not A, then not B.

When If A, then B is true and If B, then A is not true, the logical fallacy denying the antecedent exists. This is what your example shows.

However,
When If A, then B is true and If B, then A is true, a "logical biconditional" exists.
In other words, If and only if A, then B.  The shorthand notation would be: (Iff A, then B)

When Iff A, then B is true then If not A, then not B is true. This is the "rule of inference" called "transposition".

An example of a logical biconditional would be:

1. If the sun is up, then it is daytime. (If A, then B).
2. If it is daytime, then the sun is up. (If B, then A).
3. Thus, If and only if the sun is up, then it is daytime. (Iff A, then B).
4. Therefore, If the sun is not up, then it is not daytime. (If not A, then not B).

Applying the example to the issue on the page in question:
"you must file a (form 1040) return , [...] with us for any (income) tax you are liable for."

1. If you are liable for an income tax, then you must file a form 1040 return.
2. If you must file a form 1040 return, then you are liable for an income tax.
3. Thus, If and only if you are liable for an income tax, then you must file a form 1040 return.
4. Therefore, If you are not liable for an income tax, then you are not required to file a form 1040 return.

Further into the website, I present a regulation that confirms point #4 which shows the rules are consistent with the logic presented.
On a side note:
I have changed your displayed name (pseudonym) so as to prevent any possible confusion as to your relationship to the web site. Everything else is as you registered it.