Okey there is a lot to reply to here lol:

I think the question is a misunderstanding. The rules for justification don't need to be justified, no more than the rules for chess need to be justified. They're simply the rules that make the game of epistemology work. — Sam26

I was more speaking of the concept of justification requiring justification for its existence, and I don't yet believe this can be likened to the rules of chess not requiring justification as we have the power to choose the rules of chess but i'm not sure if we are able to choose the nature of justification itself.

As far as a justification is concerned, the deductive argument provides its own justification. If there is no way that the conclusion can be false if the premises are true, then what else would be needed to justify the argument? — LD Saunders

The deductive argument itself is defined using if-statements, specifically 'if (if premises are true, then conclusion is true) then valid argument' so I would guess that if logic is justified or not requiring justification, then the things that can be made as constructions from it are automatically justified, and I'd guess that deductive arguments are one of these constructions. (I feel a twinge of discomfort here as I'm not totally sure to what extent deductive arguments are needed to derive logic, I feel that if you did then you'd probably be doing circular reasoning).

If that's true, then I'd say that its existence is justified, what I think you would be rhetorically questioning there is actually whether the utility of that definition of deductive argument is justified, which I think is different to its existence being justified.

Yes, I think that's the right idea. However we structure our beliefs, ultimately the whole thing hangs free, so to speak: inevitably, some beliefs will not be grounded in any other beliefs, or else the structure of justification will have to be cyclical. So, taking the first option, if perforce some beliefs have to be ungrounded, why not logic? (Here I mean not mathematical logic(s) but the logic(s) that we routinely employ in reasoning.) — SophistiCat

So, we will always have to assume that we are on solid enough ground by accepting any particular starting point. — LD Saunders

I suppose that right now I must accept the starting point idea in order to avoid the cyclical problem, but I'm tempted by the idea that there is perhaps a deeper layer than logic from which you could derive it somehow and maybe if you kept going like this you could somehow eliminate all need for a starting point, though I can't yet conceive of such a process so I guess I'll have to file it away in my list of dormant ideas. Thanks for the clarifications.

So logic is like maths in that they are habits of thought that not only work, but seem to be the only habits that could have worked and so were waiting to be found in some objective sense. — apokrisis

Thing is it could be true that there is something other than logic which if we adopted would also appear to work. Seems we've only tried logic, although I suppose we do have other variants of the usual logic that people have proposed such as paraconsistent logic, relevance logic etc. I would guess that you would get a different 'mathematics' if you instead used those logics and that they would also appear to be the right ones that work, because I think ultimately you'd be using the particular variant of logic that you're using initially to determine whether the mathematics you have 'works' in this sense of the word.

Statements about the world cannot be reduced to simply true or false. — Londoner

Is it not a true statement that you have replied to my original post?

So here I'm mostly asking if the components of logic, specifically deductive (although inductive would be interesting to consider too), can have their existence justified. These components would include things like, the idea that you have statements which can have the truth values 'true' or 'false', that you can combine multiple statements together using relations like 'and', 'or', 'if/then' etc, which themselves are truth valued and can be manipulated also, that the particular configurations of truth tables that we currently believe to correspond to these relations are true, (eg, like how the truth table for 'and' is T F F F). So I suppose I'm after a justification for the grounding of logic, if I've not misunderstood you there.

Interesting point you raise about induction in science, one thing which scares me about science is that, despite supporting it and finding it fascinating, I cannot say with certainty that the laws of physics as we know them won't simply change one day. As far as I know, it could be that the actual laws cause this change to happen tomorrow at 6:34am, in which case likely we'd have a particularly difficult morning, and not just because induction's justification has just been wrecked.

You mention assumptions and I suppose this could be the key to this, I have a horrible feeling that we must make assumptions about the nature of justification itself before we can apply it to anything, and that makes it seem feasible that we can make assumptions about the nature of reasoning and thereby develop a system of logic. Perhaps assumptions like, that we can know justification as a concept exists automatically without it itself requiring justification. This then makes me wonder if logic also doesn't require justification, though it also makes me wonder how I can, or whether I need to, justify those assumptions.