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I have been debating with someone online for quite some time and I wanted someone to check my work.  Remember in this argument he has granted the premise: "If you believe in god, you know you believe in god."  My opponent insists I am wrong, yet has said on separate occasions that both premises of my argument are true. He keeps going back to does the rock exist, and claims since I say that is unknown, that he can say his belief is unknown. Can he be right? Here's the argument as I have laid it out for him.

Here we go you are going to learn intro level logic:

Deductive argument - A deductive argument is an argument in which it is thought that the premises provide a guarantee of the truth of the conclusion. In a deductive argument, the premises are intended to provide support for the conclusion that is so strong that, if the premises are true, it would be impossible for the conclusion to be false.

http://www.iep.utm.edu/ded-ind/

What does this mean well in a 2 premise argument there are several possible options for truth values:

A deductive argument has 2 characteristics: Validity and Soundness

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound.

http://www.iep.utm.edu/val-snd/


So, my argument takes this form

If you believe in god, you know you believe in god
you don't know
therefore you don't believe in god

Is this valid?

Well the form is:

If P then Q
~Q
~P

Well it is modus tollens so:

Modus tollendo tollens, usually simply called modus tollens or MT is a valid argument form in logic. It is also known as "denying the consequent".

The form of modus tollens is: "If P, then Q. Not Q. Therefore, not P." It may also be written as:

P → Q, ¬Q infers ¬P

http://www.philosophy-index.com/logic/forms/modus-tollens.php

So we know the form is valid.

What does this mean?

Well it means there is one thing that cannot happen;

Premise 1 is true
Premise 2 is true
Conclusion is false.


That is what it means for an argument to be valid.

Is it sound?

It will be if you grant both premises are true:

Premise 1= if you believe in god, you know you believe in god.


You have granted premise 1 is true.


Premise 2: you don't know that you believe in god.

Therefore, we will see, that you must not believe.

So,

P= you believe in god
Q= You know you believe in god

We have

If P---> Q
~Q
~P

you do not believe in god.

Yet, you insist that Premise 1 and premise 2 are true, yet the conclusion is false.

Yet when you try to use the argument for the existence of the rock it falls through:

If the rock exists, you know it exists

You don't know it exists

Therefore the rock does not exist.


Premise 1 is actual false(or not true)

therefore the argument was valid but not sound and the conclusion does not follow.

Answer
Sorry for the delay in answering, the holidays have kept me from my computer.

The short answer: The two arguments you present do not have the same form.

Why not the same form?

1. If you believe in god, you know you believe in god
you don't know
therefore you don't believe in god


2. If the rock exists, you know it exists
You don't know it exists

Therefore the rock does not exist.


When finding substitution instances for a counter-argument, you must be very careful in preserving the form of the original/target argument.  That means you cannot replace an entire subject or predicate phrase with a single noun.  The syntax must be strictly preserved and the only way to do that is with a single word for word substitution.  

Another important point is to avoid ambiguous or vague language.  2nd premise of 1st argument is incomplete ("you don't know").  Is it that I don't know that god exists or I don't know that I know that god exists?  Two very different propositions will yield two very different argument forms.

Finally, your last statement about validity and soundness is incorrect.  Just because an argument is unsound does not imply that its conclusion does not follow from the premise set.  There are an infinite number of valid yet unsound arguments where the conclusion is implied by the premise set.

Storch

Philosophy

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Ethics, Existentialism and Phenomenology, Continental Metaphysics

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