I'm you asking about a justification for the use of logic, or an actual so-called grounding?

Your comment about justifying logic because it has been successful in the past, reminds me of the problem of induction that occurs in science. Science, contrary to many people's way of thinking about science, is not grounded. We use induction in science, because it has worked in the past. But, that is merely using induction to justify induction, which is circular reasoning, plus, there are examples where this doesn't always turn out to be true. So, the same problem would occur if one tried to use the success of logic to ground it. Besides which, logic uses deductive reasoning as well as inductive, and insofar as it uses deductive reasoning it produces proofs, which are still not grounded, because assumptions have to be made to determine the structure of the logical system being used.

But, your suggestion really is the most practical and most relevant --- we use logic because it is helpful and it works. This may cause some philosophers to pull their hair out in frustration, but, it's the best we have managed to come up with to date.

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.

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.

A deductive argument is also the basis for all mathematical proofs, even proofs based on "induction." We know that a deductive argument is valid if the conclusion must be true assuming the premises are true. 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?

Now, grounding it is a different matter, and it just cannot be done. Just think of it this way ---- eventually one must start off somewhere to get the argument going, or science going, or mathematics going, so there is no way to prove everything that is being used for either deductive logic, science, math, or any other field. So, we will always have to assume that we are on solid enough ground by accepting any particular starting point. This usually works out fine unless it can later be shown that there is an error that we are relying upon.

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. — hymyíŕeyr

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.) A more natural choice would be hard to find. The second option is exemplified by the already mentioned pragmatic justification, which, as has also been pointed out, is ultimately circular.

So the question is, how could we establish justification for the existence of logic and perhaps some of its core elements, such as the concept of truth values? — hymyíŕeyr

The justification is going to be ultimately informal and circular. We make our best guess and find that it seems to work out.

But then also, we do find something stronger. The results appear to have mathematical-strength inevitability. Looking back, it seems that the results can't have wound up different. Retrospectively, the laws of thought must have always been there waiting to be discovered in some Platonic ideal sense.

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.

While we can thus still doubt the results, we also wind up with the least reason to doubt that we can imagine. Which is a good enough way to proceed.

These components would include things like, the idea that you have statements which can have the truth values 'true' or 'false',.... — hymyíŕeyr

The problem is that these components are not really statements, not in the sense of claims about the world. Statements about the world cannot be reduced to simply true or false. So when in the OP you write about of logic 'being applied every day and it works' I do not think it is. It is a purely formal system.

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?

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. — hymyíŕeyr

Well yes. Of course in fact logic is not one thing. A variety of approaches have been tried. So there is both something it all seems to boil down towards - the laws of thought as a basis for deductive argument - and also all the less constrained stuff that is a relaxation of that "limit state" absolutism.

Another angle on your justification question is that some logicians - especially CS Peirce and Spencer-Brown - sought to justify formal logic by using graphical arguments.

See https://en.wikipedia.org/wiki/Existential_graph and https://en.wikipedia.org/wiki/Laws_of_Form

So set out as geometry, the truths of logic seem less deniable. A picture is worth a thousand words perhaps? :)

If you want to break out of the loop of using formal argument to support formal argumentation, then that is a way to tie logic to "existence" itself. Talking about the necessity of a relation is one thing - a rather abstract thing. But existential graphs show it as a necessity of any world with actual relations.

An answer I can already hear would be something like, we observe logic being applied every day and it works, therefore we can conclude that it exists. the question I would pose to this sort of argument would be that, in the process of determining whether the application of logic to real life occurrences has been successful, aren't we already using logic here, and therefore using logic to justify logic? — hymyíŕeyr

You can't justify 'logical primitives', that is, the basic operations of logical laws; they are what ground justification. So appealing to experience to justify logic has it backwards.

Kant argued that the structures of logic which organize, interpret and abstract observations were built into the human mind and were true and valid a priori. John Stuart Mill, on the contrary, said that we believe them to be true because we have enough individual instances of their truth to generalize: in his words, "From instances we have observed, we feel warranted in concluding that what we found true in those instances holds in all similar ones, past, present and future, however numerous they may be" Although the psychological or epistemological specifics given by Mill through which we build our logical apparatus may not be completely warranted, his explanation still nonetheless manages to demonstrate that there is no way around Kant's a priori logic. To recount Mill's original idea with an empiricist twist: "Indeed, the very principles of logical deduction are true because we observe that using them leads to true conclusions"- which is itself an a priori presupposition.

From wikipedia entry on philosophy of mathematics.

The upshot is that there are some logical truths which we simply know to be the case without recourse to experience; which is most inconvenient for empiricists, who say that there are no such ideas, because knowledge is supposedly derived from experience.

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? — hymyíŕeyr

In logic a proposition/statement must be something that can have the value of being either true or false. We are free to assume either, since a piece of logic is valid as long as the rules have been correctly applied, not because the conclusion is 'sound' in the sense of being a fact.

In other words logic is simply about following the rules; if you bring in empirical considerations you are bringing in an extra non-logical rule.

Nor is your own statement simple. Propositions in logic are only true or false, whereas ordinary language is complicated. For example, I cannot understand the word 'original' in isolation. I can only understand it by relating it to other words like 'copy', 'first', 'unusual', 'earliest', 'authentic' etc. So it is like a 'Chinese box', whenever we try to pin down some elementary thing that is simply true or false it turns out to contain a sub-set of terms and logical relations. There was a lot of work trying to reconcile logic and ordinary language, but it cannot be done.