So today's question is: is logic limited?
What are the limits of our ability to apply strict object based reasoning?This question is relevant to every aspect of one's life and I find that taking an idea to its maximum state is a good way to get a better feel of its properties, applicability and the possible directions further development could take it.
I'll start off by stating that logic isn't self sufficient, it isn't the 'atomic unit', the smallest divisible unit here as one cannot have logic without information computing ('thinking') and information storage for retrieval and storage.
So as far as humans go logic mixes with culture, what information we have, "what we know" has a direct impact on what we will know and how we will find out about it.
Culture allows us to 'sit on the shoulders of a giant' by offering information, but also technologies that allow us to access new knowledge and put us into new situations illiciting new questions and new methods to answer them.
I want to make clear that I believe it's important to separate the CONCEPT of logic and the REALITIES of our universe.
While we can extrapolate a closed system from the processes we call logic the same cannot be said of the rest of the universe. The first is a perfectly controlled system, like a chess game if you will, every property is understood and there are no unknowns. The second is unknowable as the only way to know everything that is and therefore being able to say if physical limits can be applied to logic would be to be 'bigger than everything' which simply cannot be. The observer would have to be a part of a system and have unperfect information about the possibilities of the system to process and store information.
Let me give an example: By playing with the CONCEPT of logic I can say that it can indeed theoretically tend to infinity for an infinite amount of time (time here being used as a quantitative rather than qualitative value, so just as a mutiplying factor)
Why can I say that? Simply because nothing theoretically excludes the structural possibility of endless computation and endless storage of data, so infinite growth of information/knowledge through logical processes.
Now let's see the REALITY of logic.
From what we know logic is a causal process happening in our causal space time, logic implies the use of structures such as A+B then C (a+b=c) were c is the consequence of the interaction of a and b just like a car crash is the consequence of two cars moving toward each other at great speeds.
This space time should be limited for the only reason that if it was infinitely old it would be infinitely hot as an infinite amount of stars would have had an infinite amount of time to radiate everything (to put it simply). And the universe cannot go on eternally because of things such as:
Proton decay -matter is inherently unstable-
Rising entropy -'chaos' rise with time-
The apparently limited amount of matter in the universe -limited computation and data storage capacity, a "mind/computer" could never store and compute more data than the maximum capacity of the universe (10 to the power of 138 or something, no that's wrong, i'll check it later)
BUT, as our knowledge of the universe is inherently limited (the observer has to be smaller than the system)realistic unlimited logic/thinking/knowledge/information could still be possible.
Here's an example: Everything that happens in space time depends on variables such as the speed of light, but those rules break down under the planck length (1.6× 10−35 meter) and time (5.4 × 10−44 second) meaning that if we could produce a computer (computering work in the same fundamental way human logic does ) able to compute at these scales we could theoreticaly compute information out of space time, meaning infinite computation in 0 time, litteraly.
To extract the information in the space time we all live in we'd still need to follow causality and get the information at least one unit of time after the computation order was issued, but hey, 5.4second with fourty four zeros BEFORE isn't exactly long.
To conclude:
So yes, logic is structurally unlimited, exponential and self expanding through technics such as computering, genetic engineering etc. And while the physical ability of the universe to support infinite growth of knowledge is unknown, the expansion of the human mind into a superlative is, in my humble opinion, a dream worth grasping for.
So yes, logic is structurally unlimited, exponential and self expanding through technics such as computering, genetic engineering etc. And while the physical ability of the universe to support infinite growth of knowledge is unknown, the expansion of the human mind into a superlative is, in my humble opinion, a dream worth grasping for.







