A western leaned conception of thought leads to a misconception of what is logic!
Imagine cognition as a geometry, where ideation is a function of axiomatization. The variable axiomatization is directly proportional to assumption, and inversely proportional to certainty.
One must ponder what is the limit when axiomatization tends to zero and what is when it tends to infinite.
They have to be asymptotes. Those asymptotes represent a geometrical place where reality the (ideation providing explanations, the mind consider to be true, for sensations).
Yes, and it seems very probably to be deeply more complex than that.
It seems that our existence is the instantiation of the differential survival of variant strategies at multiple levels. None of those strategies (axiom sets if you will) need to be perfect to survive, they only need to be a better approximation to reality than the alternatives available (and better in this sense isn’t about being more accurate, it is about delivering survival oriented results quickly – and that is a very different thing).
In a discussion such as this, there seem to be about 20 levels of instantiated sets of systems present, very few of which will be consciously known to most of the participants.
In this sense, it seems to be axiomatic that we embody many levels of complexity long before we are capable of any sort of consciousness, and even to be able to have a concept “axiom” involves the instantiation of some 16 levels of complex adaptive systems in the case of a human being (can be a somewhat lower number in the case of AI, which is one of the deep reasons that AI is potentially so dangerous, it doesn’t have the deep history of surviving the many different sorts of contexts of our past, so need not be as fundamentally cooperative as human beings are – and that is a deeply serious issue).
So yes, the “landscape” of the probability of the instantiation of any particular set of axioms, or any particular set of strategies within any set of axioms, or any set of models of reality, or set of relationships of entities within any set of models of reality, is a profoundly complex issue; and nothing at all like the implicit assumptions of classical logic (which seems to be the simplest possible of an infinite set of possible logics). Biology and reality seem to be fundamentally “messy” in this respect, and there is no simple way to untangle the many levels of implicit assumptions embodied in the simple models of reality that our subconscious systems create, that are our experiential reality (at any level of abstraction).
Welcome to my world !!!
[followed by why 20?]
This could be a very long reply, and I don’t have time to do all of it, but I can do the first 10 levels – which are hardware based (atoms on upwards). The other 10 are software based.
1/ Several different RNAs can cooperate to produce proteins.
This is done via a group of RNAs we call the ribosome. There are another group of RNAs involved in the process also.
In the deep reaches of time, at the earliest collection of life like molecules, it seems probable that RNAs played a pivotal role in the early emergence of cellular life. Probably in a hot water volcanic spring, and probably near the ocean.
However that process actually started, it seems that this level of cooperating RNA molecules was probably key to the process in some way.
2/ RNAs and proteins can cooperate to form enzymes, and a vast range of other molecules; including sugars, fats, etc.
3/ RNAs, proteins and lipids can cooperate to form simple cells. Within a cell, cooperative RNAs must have mechanisms to defend against being overwhelmed by RNAs cheating on the cooperative (viruses).
4/ All these molecules cooperate to form DNA, and the main information storage function is transferred to the DNA molecule, though evolution continues on mechanisms to detect and remove errors in the copying process.
5/ Simple prokaryote cells can form cooperative groups within a cell wall to form Eukaryote cells (with mitochondria, chloroplasts, and other cell organelles).
6/ Within the cell a new mechanism of sexual reproduction allows horizontal transfer of variants within a population, effectively creating the beginnings of the population as a selection unit (alongside the individual cell).
7/ Cells can cooperate to form colonies (populations in one sense, individuals in another, simultaneously), via chemical signaling mechanisms.
8/ Cells withing colonies can cooperate to specialise to perform different functions, again via chemical signaling.
9/ Specialisation of function can proceed to the level of organs, circulatory systems, skeletons, brains, immune systems, reproductive systems etc, all cooperating to produce a complex organism.
10/ Organisms can live together in communities and cooperate to survive as a group. This can work if the threats to individuals are more likely to come from factors outside the population than inside it.
At this level I will stress some things that are common to all the levels below, and will have their analogues at all levels above.
At every level, cooperation can only emerge if there is more threat from outside the cooperative than from within it.
Competitive forces can, at any level, overwhelm and destroy any level of cooperation.
Thus it is important for cooperatives to have mechanisms to detect and remove any cheating (competitive) strategy that threatens to overwhelm the cooperative with its unrestricted replication.
At one level you can think of such things as “cheats” on the cooperative.
At another level you can think of them as cancers (replication of some subsystem that threatens to overwhelm the entire complex structure).
And it is important to recognise that each level emerges on top of all the ones that already exist, and must coexist with them (is indeed predicated upon their existence in most cases).
And we are already at 10 levels of systems (not 10 systems, but 10 levels, each level with many complex systems, thousands, millions, sometimes billions of them).
And it is vastly more complex than this simple model indicates so far, because beneath the level of atoms is the world of quantum mechanics, and it is strange in ways that take most people a long time to begin to glimpse. And to give just a tiny taste of how profoundly different that world is; let us consider time.
For people, a second is a small time unit. For a very highly trained individual, the clock of human awareness can tick about 200 times a second; but for most of us that clock ticks about 14 times per second most of the time. We cannot perceive time periods smaller than that of our consciousness clock. Our most accurate clocks are based upon atomic oscillations, and allow us to accurately measure about 10^16 ticks per second (a 1 with 16 zeros after it – a lot). The tick of time for quantum process is so small, that if one of our most accurate atomic clocks had been ticking since the universe began some 14 billion years ago, it still wouldn’t have ticked as often as quantum time (Planck time) does for every tick of that atomic clock.
The scale of the complexity present in the simplest of atoms is really hard to come to terms with, and we are made of lots of atoms, more than our visual systems are capable of recognising had we lived the entire age of the universe to date.
So that is a bit of a side trip, and it is needed to give a reality check to just how simplistic our every day experience of reality actually is, and has to be, because the simple example above already clearly demonstrates that reality is vastly more complex than we are capable of imagining; and does so by only considering one of the simplest possible views of reality. Reality has a lot more “tricks up its sleeve”. It is hugely more complex, nested infinities of complexity.
That we understand anything at all of it is little short of miraculous.
We need to “get in our bones” that even our best possible models are just simple approximations to what is actually there. The evidence and logic for that is beyond any shadow of reasonable doubt.
So getting back to the levels of complexity in us.
We are going to change domains, and depending on the depths of your current conceptual understanding, that may be a slight change, or it may be a profound change. For me, I now view all understanding as models, and all of reality as systems in relationship, with every level of systems having necessary balances between order and chaos (between the predictable and the unpredictable).
There is much room for confusion here.
When I speak of strategy at this level, it merely means systems in action producing outcomes.
As human beings we are intentional agents, and we tend to think of things in terms of intentional agents (our brains seem to be structured in a way that does that automatically for us, and some of us are starting to understand the details of those structures).
It is easy for us to think of complex things as intentional agents, but that does not mean that they necessarily are. It just means that it is what worked for our particular evolutionary history.
It seems that all of our abilities to distinguish, to perceive, to model, to project, to dream, to intuit, to create, to love, to feel, to choose; is the result of level upon level upon level of the differential survival of variants of systems in different contexts.
But that is a very complex set of understandings, and it doesn’t seem that way to us doing it.
Just as it seems like the sun rises in the morning and sets in the evening; but most of us now understand that it seems that way because we are on a big ball of stuff spinning once every 24 hours as it slowly revolves around the star it is closest to (our sun); so too it is possible to change perspectives from the one which seems most obviously to be so, but isn’t necessarily so. Once you’ve done that a dozen or so times, it gets easier.
At level 10 we had complex organisms, with complex organs, including brains; that lived in complex populations that all share genes via sexual reproduction.
Those brains had to be complex enough to sustain stable social relationships, which means able to identify several hundred individuals reliably, and to recall past interactions with those individuals.
And it should be reasonably obvious that it isn’t difficult to get to 10 levels of software, but it is really difficult to explain that software to anyone with less than 20 or so years of software development experience.