Foundations of Logic – Is Truth and illusion?

I started a discussion on Truth on Foundations of Logic group

Is Truth just a sometimes useful illusion?

What is truth?

What is this idea we have of something being True?

Clearly, truth doesn’t just reside in the existence of something, that is the thing itself.

Clearly truth is a relationship between a model of something (expressed in some form of language), and the thing being modeled.

Clearly our brains have evolved not to represent things as they are, but to have approximations that can be produced quickly enough and accurately enough to be useful in survival oriented situations.

There seem to be at least three different classes of situation that this notion of truth can apply to in different ways.

It seems that we have an existence in reality (whatever it is), and part of that existence includes the ability to subconsciously model that reality at some level of fidelity, then to consciously experience that subconscious model of reality as experiential reality.
Our experience of reality seems to be modified and modulated at several different levels by various set of factors including chemical, electrical, contextual, genetic, cultural and conceptual.

So it seems that “Truth” can:
1/ relate to the degree of accuracy or utility of our experiential model of reality to whatever reality itself is; or
2/ relate to a the degree of accuracy of a conceptual model we have about how reality works; or
3/ relate to a proposition following from a set of axioms.

There is a mixed type which involves aspects of 1 & 2 which is a declarative model of truth, where some authority declares something to be so, and it is so by fact of the declaration. Legal guilt is an example, where what the judge declares is the case, whether they did it or not. In ancient times, much of the truth of culture about nature and reality was of this declarative type, and for many it still is.

It seems clear from scientific investigations into the nature of the existence within which we find ourselves, that there are many different classes of ways in which absolute correspondence between a model and reality cannot be verified, and thus while one may in fact have an accurate model about some very small aspect of reality for some period of time, there is no way to objectively verify it in any absolute sense, so it becomes an article of faith or conjecture.
What reality does seem to allow, is probabilistic treatments of some aspects that can achieve remarkable accuracy, to 20 or more decimal places in some cases some of the time; while still retaining fundamental uncertainty at base.

The ancients had the idea that Truth could be known, and that it was our job to seek it out.
That now seems to have been disproved beyond any shadow of reasonable doubt.

What we now seem to be left with is an ability to develop sets of heuristics (useful approximations at some scale), that can in some contexts be very reliable indeed, and in other contexts not so much.

As examples of fundamental barriers to Truth:
1/ Many aspects of physical reality seem to require the use of irrational numbers (like Pi) to calculate them.
The definition of an irrational number is that it has no finite representation in any integer numeric base.
Thus perfect accuracy is not allowed, ever.
All that is allowed is some useful approximation that is good enough for the job at hand.
2/ Heisenberg uncertainty prevents knowledge of both momentum and location of a “particle” beyond a certain limit. Thus all calculations come with this level of fundamental uncertainty.
3/ We seem to live in a universe where it is big enough that it is not knowable even in theory, and there will always be photons of various energies impacting us about which we could not possibly have had any prior knowledge.
4/ There are many others classes of uncertainty resulting from different sorts of complex systems including ideas like maximal computational complexity, chaos, fractals, etc.

So in such a fundamentally uncertain reality, the idea of Truth seems to be entirely illusory – a simplistic approximation to something that served our ancestors reasonably well, but in our modern age needs to be replaced with something more humble and uncertain – the idea of contextually useful approximation.

The classical idea of “Truth” seems to embody a kind of arrogance that actually instantiates existential level risk if it is allowed to dominate decision making processes.
We still need to make decisions.
Some decisions have tight time bound aspects.
So we must all use simple models like “Truth” in some contexts, and it pays to be aware that we are doing so because of the necessities of time pressures, rather than the notion of “Truth” having any reality greater than that of a “contextually useful heuristic”.

[followed by]

I don’t discard it [Truth] as something to be aimed at.

Trying to get the best approximation to whatever reality is seems like a great thing.

Expecting to ever actually have 100% accuracy seems to be an act of hubris.

I don’t particularly like the idea of consensus in respect of “Truth”.

I much prefer the idea that everyone has a responsibility to get the best approximation that they can, given the time and interest and energy that they have in respect of any particular subject.

I like the legal standard, of beyond reasonable doubt.

I know of politicians who have the ability to say what they believe to be true in a way that people hear what they want to hear. I am not in favor of that, however much I see and acknowledge the political utility of that.

[followed by]

Hi Bruce,

I acknowledge the utility of truth as a heuristic in many contexts.
For many purposes, it is good enough.

What I question, is the proposition that we can ever have a 1:1 mapping between a model and reality. The evidence seems overwhelming that such a thing may not exist. It may be approximated, sometimes very closely, but rarely, if ever, achieved, and is certainly not verifiable even if attained (and is therefore a dangerous idea if taken too far, because anything that cannot be verified is by definition unscientific, and open to a lot of abuse).

I’m all for the use of the best approximations that we have, and for their transmission.

I acknowledge the utility of logic and mathematics in building models – they are the best tools we have.

I am just advising caution against asserting that any particular model is necessarily always relevant. History seems to show us time and again that such claims are usually shown to be false, and turn out to be useful approximations at some scale for some set of contexts.

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Quora – AI and mankind

Quora – How will artificial intelligence influence mankind?

This is an extremely deep and interesting question.

Artificial intelligence isn’t a singular thing, it is a spectrum of classes of systems spanning many orders of magnitude, and exponentially expanding for the foreseeable future.

Mankind isn’t a singular entity, it is a spectrum of entities that spans many orders of magnitude in awareness.

The intersection of those two sets of every changing spectra will produce a vast array of different classes of outcome. Some people will inevitably simplify that entire set of unimaginable complexity down to a simple binary, and call it either good or bad. The reality will be a close approximation to infinitely more complex than that.

Like everything else in life, it will very much come down to the choices we make when interacting with it (providing we manage to make it somewhere near at least as cooperative as we are, and don’t create a dangerous monstrosity with an overly simplistic set of valence heuristics that leads to our destruction (and there are enough people aware of that problem space that it is reasonably low probability outcome)).

It is likely the the diversity of what it is to be human will increase, which will be a difficult thing for many on the conservative end of that spectrum of what it is to be human.

It is likely that communication will become more difficult, and impossible in many instances, as the diversity and complexity of interpretive schema with no significant overlap continues to increase. AI will both empower, and moderate the worst of the risks in this class of outcomes, as it will be the best translator available, as much as translation is possible.

If all goes well, it will be an age of magic and security for most, as AIs allow us to do more with less in ever more domains, the experiential choices available to most people people will continue to exponentially increase. There may not be enough energy to allow everyone to fly everywhere every day, but there will be technology to allow us to experience first person flying small drones, or experiencing life as a bird or a fish (fitted with transmitting sensors), or anything else. Our personal energy budgets may restrict us to a couple of world tours a year in person, and the communications networks will allow us to go anywhere, any time, as virtual entities (taking our inputs from sets of sensors in those places, talking to whomever will talk to us, seeing what is there to be seen).

Our health and lifespan will be optimized and personalized, and most will live as long as they want (many thousands of years in most cases). Accidents will still happen, and they will become more and more rare.

All of the causes of risk to life from our past will have effective and constantly improving mitigation strategies, and reality seems to be sufficiently complex that there will always be new risk emerging in our future that will require attention from time to time (the price of liberty is eternal vigilance).

So AIs in their many different levels of instantiation seem likely to allow us each to customize our experience of being to a level never before possible. They will be within us as part of our nanotech enhanced immune systems, around us and smart devices and buildings, supporting us as smart roads, water supplies, food production, recycling, and energy systems; constantly working to assure there is sufficient supply to meet all demand (all products and services), mentoring us as AGIs. Many of the ideas from our past (like money and exchange) will be redundant.

What we each make of that will be down to our own choices, the degrees of awareness we bring, the strength of our wills, the respect and tolerance we have for diversity.

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Foundations of Logic – Truth is transient

Original post in FOLogic – by Manju Sambander – Truth is Transient – All agree?
Robert Mosimann replied – It was never True that the earth was flat.

Depends what one means by true.

There are at least three quite different classes of meaning that are collapsed into that one word.

One class relates to the logical consequences of sets of postulates, and thus has a relationship to those postulates (as in logic and mathematics).

Another class relates to reports of subjective experience, as to the accuracy of the reporting of the experience as experienced by an individual.

The third class relates to the degree of correspondence between a description of reality and whatever reality actually is. This latter class seems to be one dealing with sufficient levels of complexity that it is always some level of “useful approximation”.

In this sense, the idea that the earth is flat is a sufficiently useful approximation to build a house from lumber, but not to accurately travel around the planet, and nowhere near close enough to build a functioning GPS system.

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Foundations of Logic – Post Modernism

Foundations of logic – Has the post modern revolution come full circle?

If you believe everything is socially constructed, then you have already been indoctrinated and are beyond influence by evidence.

Social construction is one influence among many – and very rarely the most important.

Evolution – the differential survival of variants in different contexts, seems to be at the root of most of what we are (in both genetic and behavioural terms).

Many post modernists take an overly simplistic approximation to the complexity that is evidently present, then proceed to use that to justify whatever they are inclined towards (mostly such inclinations are the result of factors they haven’t begun to consider).

So I align with post modernists to the degree that I accept that all knowledge of physical reality (as distinct from logic or mathematics) is most likely some sort of simplistic and probabilistic approximation to whatever reality is.

But I diverge beyond that, because it seems abundantly clear that there are useful mechanisms for determining the sorts of probabilities involved most of the time, and often the heuristics in use are extremely reliable indeed.

I also acknowledge what seems to be the reality, that all of our experience is of a subconsciously created model of reality (never reality itself), and that mathematics and logic are the best modelling tools we have in building our best approximations to whatever we and reality are.

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Quora – atomic structure

Quora – If an electron is negative and a proton positive, what keeps the electron from flying right into the nucleus of an atom (opposites attract, right?)? Is it merely the speed of the electron?

Some good answers here already.

We cannot “see” what is happening at that level.

We have to make machines that do strange things then we look for little regularities or irregularities in their strange behavior and we look for mathematical equations that explain those. Then we explore the mathematics related to those equations and design experiments to test out which of those implications seem more likely than others.

After many years of doing that, we have some strange properties that have mathematical expressions that seem to be very reliable in most contexts we have looked at in detail.

Two of those in particular seem interesting to me in respect of this question.

One is the Planck constant, which is the smallest amount of energy that seems able to exist in this universe.
It is usually expressed as a relationship with an oscillating property that most people conceptualize as a “wave”, but is more accurately characterized as a relationship between space and time. The electromagnetic properties associated with this are orthogonal. That means that if you look at one of them, it comes and goes, like a wave passing by, but if you look at both of them, then as one is at a minimum, the other is at a maximum. That kind of makes sense, but it gets weirder.

The other property of interest is Heisenberg uncertainty, which in one formulation states that you cannot know both the momentum and the position of anything beyond a certain limit.

When you combine these two properties, you get a spatial relationship expressed as a set of probabilities, and for the energies that electrons normally have, there is a region of space in the center of the “atom” that they are not allowed to occupy (because if they existed in there with the energy value that we know them to have, then we would know both their position and momentum to a greater accuracy than we are allowed to, so they cannot go there).

That is a weird way to think about things, and it does seem to be an accurate way to think about them, if you just take the information principles embodied in the equations that make up quantum mechanics, which as others have noted, is a system of equations that work very well, and have been subjected to very close inspection by experiment over the last 100 years.

It is a very different way of thinking about things from the classical notion of truth, and because of that, many minds simply reject it.

It is a way of thinking that is fundamentally uncertain, and fundamentally probabilistic, both at the same time.

The really strange thing about it, is that it works at this level of the very tiny, and when you add together large collections of these tiny ”things” (though as others have noted, “thing” isn’t a particularly useful idea at the scale of the very small) over large collections of their time units then they very closely approximate classical causality.

So something that is fundamentally uncertain within certain limits can in large collections appear like something lawful.

And the smallest thing an unaided human eye can see seems to be more than 10^16 of those collections of fundamental properties, and the smallest time a human can experience is a collection of more than 10^40 of their time units. So when you get collections of probability distributions with more than 10^50 instances, they form very reliable and predictable distributions most of the time.

Hence the illusion of causality we are used to works in practice, most of the time.

Just like the idea that the earth is flat is good enough if you never leave the valley of your birth, and you never build anything more complex than a house made of lumber (carpenters still use the idea that the earth is flat today, at that scale it is a useful approximation).

All ideas, all knowledge, seems to have this property of being a useful approximation to something at some scale (even quantum mechanics {and that is an idea that some mathematicians and physicists have a lot of difficulty with}).

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Comment on a Jordan Peterson video about the radical left

Dr. Jordan B. Peterson On The Impact Of the Radical Left – YouTube

02:16 “It is easy to understand why people are emotionally drawn to the ideals of socialism (let’s say) or the left; because it draws it’s fundamental motivational source from a kind of primary compassion, and that is always there in human beings. And so that proclivity for sensitivity to that political message will never go away, and so it is important to understand that. You have to give the devil his due. Unfortunately.”

Perhaps the most disturbing passage I have ever heard Jordan speak.

I can make sense of it only in the sense of the Devil being the extreme political expression of socialism embodied in communism.

18:52 – 20:34 Jordan says:
[The debate is whether there is such a thing as free speech. And the answer from the radicals is that there isn’t. Because for there to be free speech, there have to be sovereign individuals, (right?) and those sovereign individuals have to be defined by that sovereign individuality, and they have to have their own locus of truth, in some sense that is a consequence of that sovereignty. And then they have to be able to engage in rational discursive negotiation with people who are not like them, which means they have to stretch their hands (let’s say) across racial or ethnic divides. They have to be able to communicate. They have to be able to formulate a negotiated practical agreement.
And NONE of that is part and parcel of the post modern doctrine.
All of that is “up for grabs”.
There is no “sovereign individuals”.
Your group identity is paramount.
You have no unique voice.
You are a mouthpiece of your identity group.
You can’t speak across group lines, because you don’t understand the lived experience of the other.
And so, it’s not who gets to speak. It is whether the entire notion of (this is a very classic western notion, and a very deep one) of free and intelligible speech is even valid.
This intellectual war that is going on in the universities is way deeper than a political war.
It is way more serious than a political war. It manifests itself politically, but politics is way up the scale from where this is taking place.]

Some truth in this, and also many over simplifications.

Like Jordan, I reject the notion that there is no freedom, and the sort of freedom that seems to exist has very real limits and consequences if those limits are exceeded.

Everything hangs on the ontological and epistemological assumptions one brings to the party, and thus how one defines the idea of freedom.

And that must go back to assumptions about the nature of ontology (what is reality) and epistemology (what is knowledge); and is a very complex field of inquiry that is part personal in being an exploration of the nature of existence as an experience, and part objective in being an exploration of the best evidence sets and what seems to be the most relevant schema for interpreting and relating those evidence sets about what is the nature of ourselves and the reality within which we find ourselves.

That is not a simple inquiry.

Anyone who is serious about it has to look at history, the deep history of cosmology, the history of our solar system, our planet, of the evolution of life, of the evolution of culture, and of cultures in particular.
Any serious student also has to look at the best tools available for making models of (useful approximations to) the complexity that seems to reside in reality and in ourselves.

That means delving into logic and mathematics, not because reality necessarily is logical, but because logic and reason and mathematics give us the best modeling tools we have to approximate the sorts of complexity that seem to exist. And because reality seems to be extremely complex, beyond the ability of any cognitive entity to deal with in anything remotely approaching real time, then we are forces to use approximations, shortcuts, heuristics. We have no choice but to use them, but that does not mean that any of them are actually 100% accurate in all contexts – and we wouldn’t be using them if they weren’t at least useful in some contexts.

Understanding evolution is a deep journey into chemistry and quantum mechanics, and simultaneously a journey into highly dimensional probability spaces, to spaces of strategy that are constantly, recursively expanding, to highly dimensional complex adaptive far from equilibrium systems.
It is a deep journey into social organisation, stories, mythology, religion, politics, psychology, and every other discipline one can imagine. All are related. All have some degree of influence. It is complex beyond any possibility of detailed comprehension – for any one, or any thing, ever.

The classical notion that “Truth” might be known, that an absolute one-to-one correspondence between an idea in someone’s head and reality (whatever it is), could be established, seems, beyond any shadow of reasonable doubt, to have been disproven.

The mistake that seems common in many lines of “post modern” thought, is to make that mean that no probabilistic approach to usefulness and appropriateness of approximation is possible. That approach is equally, beyond any shadow of reasonable doubt, wrong.

We can, and all do, find useful approximations that work in context.

The more complex the context, and the more time we have, the more complex the models we find useful.
That is a more relaxed notion of “truth” than the classical one.

I have been using such a probabilistic and heuristic approach to knowledge for close to 50 years.

It seems very probable to me, that whatever reality is, it is some sort of constrained randomness – some sort of probabilistic balance between the lawful and the random. In the strictest of mathematical senses it has degrees of freedom.

Those degrees of freedom seem to carry through to all notions of freedom.

Nothing is entirely free of influence, and no influence can absolutely in all cases produce an outcome (however reliably such things may be approximated in some contexts).

In this fashion, we all certainly have influences in our being from our biological ancestries (and we don’t need to go back many generations before we all share ancestors), from our cultural ancestries (and with TV, books, the internet, we all share cultural influences and ancestries to many different degrees), and from our families, our communities, our groups. All of these influences are real and present, at least to some degree that will vary with context.

And we all have degrees of freedom that allow us to deviate from the probabilities to action that any of those influences establish in our neural networks.

We all have internal randomness, internal breaks in the chains of cause and effect, at many different levels.
These things do create freedom from necessary cause.
We do all have such degrees of freedom.

And certainly, too much of such things destroys systems.

Too much randomness destroys complexity, and complex systems like ourselves, and our social and technological systems fail in catastrophic ways.

All levels of systems require boundaries to sustain form. Without our skin, and our cell walls, our water would just be part of an undifferentiated ocean.

Our individuality at every level requires a degree of stability in boundary conditions.
Too much freedom is destructive.
Too little freedom is just as dangerous to survival.
Where those boundaries lie in any particular context defines the survivable spectrum of diversity that needs to be acknowledged and cherished.

Certainly those of more generally conservative or liberal persuasions may prefer collections towards one or other end of that spectrum, and the existence of the spectrum must be acknowledged by all.

At base it seems clear that all of our abilities to make whatever sense we each can of existence, the values we have by default, and our ability to create and choose new values, seem to come ultimately from the differential survival of things in a reality with fundamentally uncertain aspects, over deep time.

It seems clear, beyond any shadow of reasonable doubt, that as a species and as individuals we can most accurately be characterised as fundamentally cooperative entities, however non-cooperative, competitive and exploitative we can each be if the context seems to call for it.

It seems clear, beyond any shadow of reasonable doubt, that our continued existence is predicated on creating and maintaining conditions that promote cooperation and diversity (within survivable limits) at all levels, most particularly at the highest levels.

The utility of markets in that process seems to be reaching an end, as their utility in the distribution and coordination of functions that must be distributed and coordinated is being overtaken by advanced computational systems, and all we are left with is their fundamental flaws and dangers.

So yes – it is much deeper than politics.

Yes it is deeply about the nature of what we are, and the nature of our understandings about that and our relationship to it, and what are useful approximations in practice.

Yes our moral dimensions are an essential expression of these general principles at higher levels.

And many of the notions of antiquity that are about ideas like respect, love, tolerance, acceptance, responsibility and duty are as relevant today as they always were; as are such notions as “the price of liberty is eternal vigilance”, and it needs to be a vigilance looking in places our ancestors never even imagined the possibility of.

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Zat – rationality and joy

Zat Rana – The Rationalist’s Paradox: How to Not Cheat Yourself Out of Life’s Joys

Hi Zat,

Align with your general thesis, and it seems to me reasonably clear why we cannot ever rationalize anything completely.

If you do the numbers on us, we are really complex, far beyond our capacity to know in detail.

If you dig into quantum mechanics, it is probability based.

Heisenberg uncertainty sets fundamental limits on the degree to which anything may be approximated.

We now understand many classes of complexity that cannot be predicted and some that cannot even be approximated.

We now understand something of the complexity of what it is to be a human being from the systems perspective, and it is such an order of complexity that it is impossible for any human to ever understand their own motives, we are all necessarily far more complex than that.

It seems reasonably likely that reality is at base, rather than being strictly lawful, a balance between the random and the lawful (a form of constrained uncertainty) that very closely approximates causality in many contexts at our normal levels of perception.

Like you, I am a yes to using reason and logic as the best tools we have for building models of reality, and let us never confuse our models with the thing being modeled (that is a category error in logic).

Yes, things like love and beauty may be deeply encoded by evolution into our subconscious systems, and that doesn’t make them any less real or valuable.

Yes we have values we cannot consciously explain in great detail (yet we can always rationalize to ourselves and others), and that is a necessary part of the complexity embodied in being human, being a deeply complex highly evolved self aware (at least to the degree that we are) entity.

Any idea that reason actually tells us anything “True” about reality (rather than the more humble idea that all knowledge is a “useful approximation” at some level) seems to be an arrogant error in logic.

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