God loves man
love covers sin
Therefore, God's love covers man's sin.
I think that's valid.
No, it is not. First, you are equivocating between "love" as a verb and "love" as a noun. Second, you have not established any logical connection between man and sin.
You actually have two disconnected statements as premises and they cannot entail a conclusion.
Besides, logic does not prevent coming to a false conclusion.
Here is an example of a valid syllogism.
All mammals are creatures that bear live young.
No creatures that bear live young lay eggs.
Therefore no mammals lay eggs.
This is a valid syllogism because given the first and second statements, the conclusion necessarily follows.
It is valid, but it is not true. A logical conclusion is only true if the argument is valid (which this is) and if both of the premises are true. In this case premise one is not true. Not all mammals bear live young. A very few species of mammal lay eggs. So to make this syllogism both valid and true one would have to restate the first premise as : Most mammals are creatures that bear live young. Then the conclusion would change to: Most mammals do not lay eggs.
Then you have a logical deduction that is both valid and true.
But there are no laws of logic. Logic doesn't occur in patterns that are observed.
There most certainly are, and the patterns have been observed for centuries and the rules for valid argumentation detailed.
Here are a few:
The middle term must be distributed in at least one premise. (Because your syllogism had disconnected premises, it did not even have a middle term.)
No term can be distributed in the conclusion unless it is distributed in at least one premise.
At least one premise must be affirmative.
If the conclusion is negative, at least one premise must be negative. If one premise is negative, the conclusion must be negative.
There's no way to test that 2 + 2 is 4. There's nothing to observe.
There is everything to observe. Hold up two fingers on one hand, and two fingers on the other hand. Count all the fingers.
Do the same with marbles, pennies, paper clips, whatever. You will always find that two sets of two total four.
It's simply objective truth.
It is truth because of the way we name the mathematical sets. The particular content of the set does not matter, so we can abstract from the things in the set and give the set a name. Then we can play around with the named sets without considering a physical content. Perhaps this is what you mean by "nothing" to observe. However, you first have to have the idea of a set and give each set a name. This does come from observation.
Forensic science is actually science plus philosophical reasoning. It is based on the idea that laws worked in the past just as they do today.
Idea and evidence. If natural laws (like 2+2=4) did not work in the past as they do today, we would not be able to understand the past as the rules would be constantly changing. Because science does produce a coherent picture of the past, even when using independent lines of evidence, we have assurance that nature did work as it does work. The present is a logical outworking of the past.
Theologically, of course, this was also promised by God. He did not make creation to be incoherent. Further it accords with the anthropic principle which notes that if the laws of nature were even slightly different, the universe would not be habitable. Since God made the universe to be habitable, God guarantees that the laws of nature will remain within the narrow parameters that allow for a habitable universe.
The prehistoric past, unfortunately, has no such support.... except the Bible which actually challenges scientific presuppositions.
I do not know that the Bible challenges any scientific presupposition.
I do know that certain human hermeneutical principles force an interpretation of the bible that makes it appear to contradict the reality of God's creation. Obviously, an interpretation of scripture that is at odds with God's own handiwork is a suspect interpretation.
I still fail to see why you believe God violates logic.
Logic is too rigid. I would not place God in such a small box. And, as noted, logic is not a guarantee of truth anyway. Truth includes logic, but it surpasses logic.
The language of love is not logical. But it is true.