I would say that science is the recursive process of using a combination of intuition, the best available tools of reason and logic, the best available tools of technology, and using them to produce progressively better models to allow us to make sense of this reality within which we find ourselves in some sort of time frame that is useful in perpetuating our survival and expanding the degrees of freedom and influence available to us.
It seems clear that our experiential reality is a subconsciously created model of reality that is partly defined by many levels of chemical and cellular and computational systems that are at base heuristics selected by differential survival at the genetic level over deep time, partly defined by many levels of heuristics embedded in the many levels of culture (language, beliefs, habits, schema etc), and partly the mix of sensory input and conscious level choice.
We have no direct access to reality, all each of us has is our personal models of reality.
Mathematics, logic, reason, are great modelling tools, and their use is necessary to build models of any reasonable level of complexity and utility, and it is a mistake to think that reality itself necessarily obeys any of those models.
There are infinite classes of possible logics, just as there are infinite classes of possible geometries. Russell went down that path a century ago, and there is no certainty there.
We each have to accept uncertainty and subjectivity in everything we experience, both in the systems sense from how our brains are structured, and in the reality sense in terms of Heisenberg uncertainty and other quantum phenomena, and in the deeper sense of complexity in terms of ideas that people like Snowden and Wolfram have made available to anyone interested.
I love Snowden’s Cynefin Framework for the management of complexity, in which he simplifies an infinite set of classes of systems down to 4 – simple, complicated, complex and chaotic.
Simple systems are the classical systems of classroom science and engineering – known inputs, known outputs, and one can develop strict rule based systems to link inputs and outputs. Develop computer systems and best practice guidelines to your heart’s content – engineer the hell out of them – it all works.
Complicated systems don’t quite work that way. A medical system is a good example. A doctor might have been practicing for 30 years, and sees a patient walk in the door, and something about the way they are walking, the colour of their skin, the subtle tones in their voice, the odours they give off, triggers the deep neural networks in the doctor’s brain with the idea – they have “x”. The doctor has no idea why she knows the patient has “x”, but she runs the suite of tests required to confirm that “x” is present, and they confirm it, and treatment ensues (if possible). Can’t do best practice there. Have to give people with specialist knowledge the freedom to use those subconscious skills. Strict rules will deliver far from optimal outcomes.
That actually applies to all levels of skilled human behaviour, from builder to artist to service industries to doctors and scientists and engineers. Our reality, and every one of us within it, are at least that complicated.
Then there are complex systems. These are not really predictable, but are more dispositional. We need to probe them, see how they respond, then amplify responses heading in favourable directions and try and dampen down responses headed in other directions. Repeat that process to infinity.
Then there are chaotic systems, which by definition have no pattern, and anything that is even remotely repeatable is pure statistical anomaly. Humans, because of our many levels of pattern recognition biases, are very poor at detecting chaotic systems. By definition, nothing that we do in them will have any sort of predictable outcome. Getting out of them as quickly as possible is the only useful strategy. Learning to recognise their boundaries and avoiding crossing those boundaries is the best thing.
So this seems to be the reality within which science exists.
It doesn’t seem to be anything to do with “Truth” but more to do with creating “successively more useful approximations to something” that have greater survival utility in the environments we happen to find ourselves in.
Maths and logic are useful tools, but in and of themselves are no guarantee of any necessary relationship to reality, or any utility toward achieving any desired outcome. And they are the best tools we have, so it pays to be very familiar with them, even as we need to hold them very lightly in some contexts, and learn the arts relevant to their application.
If you don’t like Russell, then use von Neumann or Wolfram – they all end up the same place, if you take the time required to go there.
If you start with the premise (as I did over 50 years ago) and keep on examining evidence and asking questions, then after going through neurophysiology and quantum mechanics and classes of logics, then you end up in a place that one cannot maintain any clear and necessary relationship between any particular set of mathematics or logic and the results of our investigations of reality – one is left with context sensitive heuristics at one level, and what appears to be a very high probability that reality itself is based on a fundamental balance between order and chaos.
One finds oneself in a set of understandings that have a very high probability that our experience of being is one of a software entity within a software model of reality, within a squishing human brain, within a cosmology based on quantum principles. That does in fact seem to be what the evidence we have amassed seems to support.