Knowledge is not finite and some of it is unknowable

Knowledge is not finite

Knowledge and truth are intertwined. Take knowledge to be made up of truths and of the relationships between truths which are themselves truths. Of course all truths making up human knowledge are only perceived truths. Human knowledge can then only be made up of partial, as-perceived truths (whether or not absolute truths exist) and then can only be a sub-set of all knowledge. Human knowledge consists of justified true beliefs (JTBs).

In the tripartite analysis of knowledge, a justified true belief exists when

  1. a proposition p is true,
  2. an entity S believes p
  3. S is justified in believing p

Addressing now all of knowledge, is it finite or without limits? Is there a limit to all the truths that are, that were and that will be? All of knowledge must encompass all of space, all of time and all of anything beyond space and time. Some things are then self-evident.

  1. In an infinite universe, knowledge is infinite.
  2. If time had no beginning or has no end then knowledge is infinite.
  3. If the number of universes is infinite, knowledge is infinite.

For knowledge to be finite, we would need a finite universe which had no uncertainties at any level and even at the quantum level. The universe could not be open-ended in time. Even if time is an emergent property of something else, that something else could not be open-ended. There could be no duality between particles and waves. Observations would need to be independent of the observer. Moreover, we would also need to know – as a truth – that there were no further truths beyond the finite universe. Even if causality is merely emergent, a perception and unreal, knowledge would still be infinite. Relativity or quantum mechanics or even loop quantum gravity, all require that knowledge be unbounded.

Furthermore, a universe with only a finite number of fundamental particles could still generate an infinite number of truths.

A large but finite number of nodes (junctions) can generate an infinite number of nodes and an infinite network if

  • each node is connected to every other and
  • where a new node is created whenever a connection crosses another connection

In an infinite space, it would not be necessary for connections to cross – but that would then be an infinite universe.

Even with only a finite number of fundamental particles (or waves), the sum of all knowledge would need not only that every particle be known but also that every interaction between particles be known, and also every interaction between the interactions, and so on ad infinitum. (It is somewhat analagous to the human brain where memory is stored not only at every neuron but also in every pathway between neurons, and then in the pathways generated between pathways and so on). Even a finite universe can (and probably does) give an infinite number of truths.

That all of knowledge is finite seems extremely far-fetched if not absurd.

A brain is a repository of knowledge. Clearly human knowledge is just a tiny sub-set of all knowledge and human knowledge is – most likely – finite. The knowledge of humanity will then be the sum of the knowledge of all the humans around at any given time. But the knowledge of humanity will never encompass even the knowledge of all living things with brains, let alone of all things. It may be that a single human brain could itself generate an infinite network, but all our empirical evidence suggests that the human brain is not – and can never be – infinite in its capacity or its capability.

Of course, the human brain may evolve in time into something wondrous. But it will still not reach omniscience.

Not all of knowledge is knowable.

I am persuaded by Fitch’s Paradox that the unknowable exists and is real.

The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn’t possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to argue against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. 

In my world view knowledge comes in three parts.

  1. what is known,
  2. what is unknown but knowable, and
  3. what is unknowable

The unknowable exists and is real.

Most of the past is unknowable. Past events where the repercussions of that event into the present have dwindled into the “noise” from the past are no longer detectable – by any means – as events. Such events can never be traced back as having taken place. The time it takes for the consequences of an event to dwindle into the noise of undetectable nothingness can vary from the immediate past to billions of years. Once below the threshold of detection, that event joins the unknowable. Causality and all the laws of the universe are of no use when the consequences in the present cannot be distinguished and detected. When the data is undetectable, causality is either undefined or inapplicable. For example I cannot remember some events even from this morning. When did I have my second cup of coffee? (I can remember the first). That event – the second cup – has no detectable consequences remaining in my memory or anywhere in the universe. Even omniscience – if it could exist – will not be able to dig up the knowledge of when I had my second cup of coffee. It did happen but exactly when it happened will remain for ever unknown and is now unknowable. While the existence of Genghis Khan is part of knowledge, pretty much all of the events in his life are now unknowable. Certainly his genes have been passed down through the ages but the causal path to backtrack to the “procreational” events he was involved in are now utterly undetectable and unknowable. It is said that some 110 billion humans have lived since the dawn of Anatomically Modern Humans. Most of the events of their lives are unknowable.

Most of the past is now unknowable. Some few isolated major events still can provide evidence of consequences which can be detected in the present.

There is no branch of science or philosophy or language (including mathematics) which does not begin with assumptions taken to be truths but which are not provable. These in fact are boundary conditions of human knowledge. Beyond these boundaries we enter the realm of the unknowable. Science and the methods of science do not have the means to illuminate the unknowable.

Knowledge is infinite, human knowledge is finite and the unknowable exists.





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