People try to come up with logical proofs for all kinds of things, AFadly used to do it for Islam and his God Allah. But you can't use logic to prove things, you need the meat. Programming is logic and try to write a piece of code when your variables haven't been declared.
If (P == true) Q = true;
Q = false;
If (Q == false) P = false;
Would return a syntax error. And like in programming, people trying to use logic will often create their own logical conditions to handle the variables. If I removed the line 'if (Q == false) P = false;' then P isn't being changed to false. We may use logic to communicate or to understand something. We can't create new information through it. All statements in programming are logical, but it doesn't mean they're factual. I will come to that point.
For Q to make P false, P would have to be defined in such a way that it relies on Q to be true. This only means P is just making a false premise.
This was my point behind my attempt of using the logic to show that the bible is false. The Christian claims is that the bible is inerrant word of God. There are many Qs in the bible and if a single one can be falsified it means P is false, simply because of how P is defined.
Now to come back to that previous point. I will bring up Logical Positivism. Our man here is Ludwig Wittgenstein. I will pick out some quotes:
The world is all that is the case.
The world is the totality of facts, not of things.
The world is determined by the facts, and by their being all the facts.
For the totality of facts determines what is the case and also whatever is not the case.
The facts in logical space are the world.
The world divides into facts.
Logical pictures can depict the world.
A picture depicts reality by representing a possibility of existence and non-existence of states of affairs.
A picture represents a possible situation in logical space.
A picture contains the possibility of the situation that it represents.
A picture agree with reality of fails to agree; it is correct or incorrect, true of false.
It is impossible to tell from the picture alone whether it is true or false.
There are no pictures that are true a priori.
A logical picture of facts is a thought.
The totality of true thoughts is a picture of the world.
A thought contains the possibility of the situation of which it is thought. What is thinkable is possible too.
Thought can never be of anything illogical, since, if it were, we should have to think illogically.
If a thought were correct a priori, it would be a thought whose possibility ensured its truth.
Lets break this down. All in the world is made up of facts and it relies on those facts being
fact. Facts determine what is true and what isn't.
Logical pictures can be used to depict the world, it depicts reality through the possibility of existence. A picture represents a possible situation. Now, these pictures may agree with reality or disagree and it is impossible to tell from looking at the picture whether or not it's true or false. I think this is one of the main points I want to hit on. What you've been presenting to us is a logical picture. Anyway, I'll carry on. For each of these thoughts, for it to depict the world they need to be true. The situations are possible, but they're not confirmed to be true.
Lets put it this way, you've given us some logical pictures, but we can't derive new information from it a priori
. This means there needs to be facts, but through logic new facts aren't made, through logical pictures & thought we're getting possiblities, which can either be true or false.
P therefore Q
Q is false
P is therefore false
To be always be true, it'd have to be true a priori and no such thing exists. Lets take one of your examples.
P: “the sum” Judah “drew sword”. 1Ch 21:5.
Q: “the sum” Judah “470, 000”. 1Ch 21:5.
~Q: “the sum” Judah “500,000”. 2Sa 24:9.
IF the sum of Judah drew sword (P), THEN their sum was 470,000 (Q). 1Ch 21:5.
The sum of Judah was 500,000 (~Q).
THEREFORE, NOT the sum of Judah "drew sword" (~P).
You're using Q to determine whether or not 'P' happens. But these statements suddenly become moot if evidence turns up to say that actually, Judah drew his sword regardless of what 'Q' says. This is why we deal with evidence and not logic for the facts. It is very possible that Judah didn't 'drew sword', but we can't tell from this logical picture alone whether it is true or false, so yep, that's where a posteriori
comes in, the friend of the scientist, evidence.
If you like, the 'variables' may change.
I eat therefore I am hungry.
I am not hungry thefore I do not eat.
Now to go and eat a bag of crisps or something. Maybe somebody can tell me if I'm hungry or not.