Alternatives to classical logic

[guitarplayer]

Anyone here has experience with alternatives to classical logic?

This springing from the thought of it being difficult to fix a problem with the mindset that created the problem.

Yesterday I had a brief look at alternatives. Lukasiewicz seems to have proposed the first system of multimodal logic back in 1920s. Giorgi Japaridze researches something called computability logic in the context of computer science. His approach seems pragmatic as there statements are proved only if computable, and proves yield algorithms to carry out computability. This enticing in the context of finding practical solutions to problems rather than solutions in principle. There are some other logic systems as well. I mostly looked at wiki sources, Japaridze is fairly outspoken about his findings in terms of publishing, also non technical bits.

[Western Red Cedar]

Anyone here has experience with alternatives to classical logic?

This springing from the thought of it being difficult to fix a problem with the mindset that created the problem.

I'm not sure this is what you are getting at, but I've been using the logical problem solving model - sometimes referred to as the 7 step problem solving model - for a long time. It is one of the standards in public policy.

You'll often see in depicted linearly, but I tend to think of it cyclically. A feedback method to periodically revisit the original problem definition is critical IMO.

[7Wannabe5]

There's the Taguchi Method for solving production quality problems. It could, in theory, be applied to Lifestyle Design.

[guitarplayer]

Thanks @WRC, no this thread is about broader underlying system of logic that allowed flourishing of Modern science and industrial revolution, digital revolution inclusive. So about the foundation of how people carry out arguments. Some things are difficult to explain using this logic, for example intuition is one from the field of psychology, mysticism is one from somewhere between philosophy and theology, and apparently as per my brief reading yesterday computer science struggles with some statements that are true in principle but impossible to instantiate. Also statements to do with something referencing to itself like in system science or issues that require second order logic.

[guitarplayer]

So in a formal logic sense, sorry should have made this clear. I spend a lot of time looking at maths now and this is where it is coming from. Think syllogisms. Systems where maybe some logical statements are possible that are impossible in classical logic, parallel to square root of minus one being possible when extending from set of real numbers to a set of complex numbers (I am really sorry I didn’t want to make it sound complicated but this parallel is a good one if one gets complex numbers somewhat).

[jacob]

Anyone here has experience with alternatives to classical logic?

How far do you wish to zoom out? Alternatives to classical or alternatives to logic?

Alternatives to logic is establishing truth based on how it makes you feel, personal narrative (lived anecdotes), what a group reaches consensus on, the winner of a fight, tradition, what the king says, what God says, what parallels in nature show, ...

Alternatives to classical [logic] ternary logic, temporal logic, etc. The only people I know of that focuses 100% on logical or computational truth is the rationalist community.

[7Wannabe5]

Gotcha. Well, intuition has to do with pattern recognition. So, if you think about the sort of mathematical pattern recognition problem that is often found on standardized tests: 1,3,5,7...What comes next? , you could maybe consider Certainty. And/Or where's Daylen?

[guitarplayer]

The former, @jacob. Nota bene autism also predisposes people to focus on a black and white classical logic truth I feel, I think they fall with their axioms about the world being tricky to change in their mind.

Alternatives to logic and classical logic could perhaps be integrated in some extended logic. Then could also be called extended god, or something else. I don’t know how this would work.

[daylen]

Seems to me like mathematical logic blends into everyday english creating a gradient of potential logics at varying degrees of strictness. Less strict logics rejecting the law of excluded middle, allowing lazy set construction, and presuming instantaneous instantiation of infinite limits. Rationalistic thinking tends to hit a brick wall of its own construction at some point, intuitions and feelings extend/intend along these boundaries.

Near the root of it, the transition from first to second order logics appears quite flexible in that there are likely an infinite number of different primitive metaphors to build out infinite deductive systems(*). Sets of elements, types of objects, parts of wholes, and particle symmetries all work (set theory, type theory, mereology, and particle theory). Perhaps fibrous qualias serve this role in neuroscience.

At the root of it, there is a Godellian improvability hole waiting to swallow all our universals and vomit them back out into new universes.

(*) See what I did there?

[Tyler9000]

As you can see from the different responses, I think this question depends a bit on context.

In a meta sense, there's the high-level conflict of observation vs feeling as two different means of establishing "truth". From a mental model perspective, there's also a difference between left-brained reasoning and right-brained intuition.

In engineering, I've also learned that there are at least two types of logical thinkers in terms of practical application. One type seeks to design the perfect product that theoretically cannot fail before doing anything. The other prototypes lots of fast failures to sort what works best. And both think that the other is illogical on some level.

[guitarplayer]

the transition from first to second order logics appears quite flexible in that [...]

It can be tricky in solving practical problems because of the 'don't tell me what do to' phenomenon, the problem of 'talking about something', the 'wissen' problem.

(*) See what I did there?

Like, infinity to infinity deductive systems?

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I will see if I can research the topic of alternative logic systems, this will remain on my mind.

[daylen]

I took an infinite jump out of a finite pool cause I believed I could, ha. Circling around to axioms and foundations.. what if reasonable acceptance of axiomatic systems has degrees of subjectivity? As in, what if I believe one is not equal to one because one banana is not one jacket?

[guitarplayer]

Yeah so what I am after is that this could be allowed within a framework, but not completely freely so that you end up with chaos. This is what I mean when I say 'extended' but I am not sure if this is the right word.

Coming from the 'logic' side of things, you would probably not be talking about belief. but coming from the 'god' side of things, you could be talking about belief.

[daylen]

Often it seems "believing a framework", "participating in the proof of a framework", and "accepting the premises of a framework" all go hand in hand in hand.

The logic side tending to lend credulity to a finite chain of computations, and the god side lending credulity to an infinite chain of beings. Though, I tend to see the two as tightly interwoven in that the history of math/logic is full of hand wavy, god-like arguments and intuitions. Perhaps because there is no logic given to us but rather we construct it out of our own transcendence from it.

[Quadalupe]

I really enjoyed tinkering with intuitionistic logic in my undergrad. It sounds alike to computability logic. Reductio ad absurdum is no longer allowed, so you can only use proofs by construction.

Furthermore, default logic is also very interesting since it is non-monotonic. In classical logic, if p, p ->q |= q. You cannot add a new fact to get p,r,p->q |= -q. However, we humans can say things like, John is a bird, so John can fly. Wait, John is a penguin, a type of bird, so he cannot fly. Computational Argumentation fleshes this out more.

[guitarplayer]

Nice one, thank you @Quadalupe!

[jacob]

Along those line, perhaps binary logic can be seen as a special [asymptotic] case of Bayesian statistics.

[guitarplayer]

Yeah I am thinking about this quite a bit! But I am too rookie in Bayesian statistics yet. I might be interning with a post doc who is into graphs and networks, I think maybe I will be able to spin something out of it all one day.