If that would be so, then testing arguments for logical fallacies would be useless.
And with that you class mathematics as being useless.
So that if and when we establish the truth of the premises we can state with confidence that the conclusions of the (valid) logic are sound.
If we don't know whether the premises are sound or not, we cannot assess validity.
Yes we can:
P1 -> Alfred is a Pentarfulg.
P2 -> All Pentarfulg live in the USA.
C1 -> Alfred lives in the USA.
The conclusion (C1) follows from the premises given (P1 and P2).
The logic is valid.
Unless you know what a Pentarfulg is, you wouldn't know whether P1 and/or P2 are true or false.
You could therefore not say that C1 is sound.
But nonetheless the argument remains valid.
At such time as you know both P1 and P2 are true, you can say that the conclusion is also sound.
If we do not know what the premises refer to or whether they are true or not, we cannot assess whether they lead to a particlar conclusion or not.
Whether they are true or not, yes we can.
It's called logic.
Logic is not hugely concerned with reality - just the relationship between conclusions and premises.
If we don't know to what the premises refer, then one would surely ask for clarification?
Granted, the arguments are implied in them, though.
But in the way they were written it is not possible to say what those implied arguments are.
Not every appeal to authority is a fallacious appeal to authority.
If here at this forum, we appeal to the authority of, say, SEP or the Merriam-Webster dictionary, this is not fallacious.
Sure, but on such things as, say, definitions, then you're not really appealing to authority by turning to a dictionary but rather going to the source itself.
Similar could hold true when it comes to God. Perhaps there is a scripture that is authoritative in matters of God.
And it should also be understood that a non-fallacious authority needs to be relevant and sufficient, with the more significant the claim the higher the authority required. For example, is a book written by man sufficient alone to prove the existence of God? Should we not require something more, lest we start claiming that Orcs and Elves also exist?
Using scripture as support for God's existence can also fall under question-begging... one knows it as scripture because it comes from God, and one knows it comes from God because the scripture says it does, etc.
The problem especially with reasoning about "God" is that the term has so many definitions. Many other terms in religious discourse also have many definitions.
Traditional logic is useless in such situations where the defintions are not clear or are multiple.
It's easy enough to envision such a defintion of "God" and "church" that makes "God exists because my church says so" true.
If "church" is defined as 'powerful institution that can alter people's minds'
and if "God" is defined as 'important concept', then it follows that "God exists because my church says so".
Sure, one needs to be careful of the definitions that people use. Logic requires consistency in such... as should every other area... if it is to be efficient. If one person uses a different definition then of course claims of fallacious logic can be incorrect, but this is not a fault of the logic but of the lack of communication between the person making the argument and the one trying to understand/interpret the argument.
So be careful not to blame the tool if the people aren't using it effectively.
Jesus is the only source of love. Those who do not believe in Jesus, do not love.
This could be a slippery slope, or it could simply be the truth, the argument being both valid and sound.
It could be. But there are surely many premises missing from the argument even for validity... such as "Jesus only provides/enables love for those who believe" etc.
I.e. given the premise ("Jesus is the only source of love") there remains the possible conclusion that he provides it to all people whether they believe or not. Therefore the sole conclusion "Those who do not believe in Jesus, do not love" is fallacious.
Soundness on such matters can only be determined once the truth of the premises are established.
Logic can not tell you which premise is correct... only if the conclusion follows from the premise or not.
So if your interest here is to see if logic can tell you which premise is true or not, you will unfortunately be disappointed.
I believe God exists in your life because I have seen him in mine could be sound and valid, provided that one person's testimony is obligatory for others / belief in God is transitive from one person to another (these is a frequent assumptions that theists make).
If we don't know who exactly Jesus is and what he can do, if we don't know the nature of obligations arising from testimony, then we cannot assess the validity of those arguments.
If the premises are laid out and understood accurately then the validity of the argument can be assessed, even if you don't know who God is, who Jesus is.
That is the point of valid logic - the conclusions should stem from the premises given in the argument. If they don't then the argument is invalid and needs adjusting - whether that is additional premises, or a complete overhaul of the conclusion.
Sure, it can happen that many premises are assumed yet not stated, and it relies on the person viewing the argument to make the same assumptions. But one can not blame the viewer for not seeing what is not there.
The OP seems to be assuming that abstract logic trumps theology.
But does it?
They are not comparable... one is a field of study, the other is a tool that can be applied to that field of study.
I think the OP was rather just trying to understand what common logical fallacies arise within the theist / atheist debates. Possibly because they have seen arguments called out on one side or the other as being logically fallacious, and they are trying to understand why.