Foundations of Logic – Is Truth an 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.

[updated 31/5/19]

[followed by]


There is a distinction between not having 100% confidence – only having 99.999999999% confidence, and Nihilism (an extreme form of scepticism, involving the denial of all existence).

I am in the school of rarely having better than 99.9999999% confidence, and often having better than 95% confidence, but only having 100% confidence about the fact of my own existence (but not about any of the particulars of that existence – to that degree, and that degree only, I align with Descartes – cogito ergo sum).

I have way over 99.999999% confidence that there is a reality present. I am similarly confident of a few of the key metrics within it. And a lot less confident of most things.

For you to equate anything less than 100% confidence to Nihilism seems to be a redefinition of a term to something close to its opposite meaning. It is like saying that neither of the mathematical infinities between 1 and 0 (the rational and the irrational) can exist even in theory, because anything less than 1 is zero.
In respect of reality, the evidence seems clear to me, beyond any shadow of reasonable doubt, that we cannot have 100% confidence about anything in reality. We may asymptotically approach unity, but not achieve it; just as matter cannot actually attain light speed. Our ability to make models simply is not up to the complexity that is evidently present.

The smallest thing we can perceive with our own senses alone is such a large collection of “stuff” for so many of their time periods that our capacity to model it in detail is exceeded by many orders of magnitude, and we must, of necessity, use simplifying assumptions that are usually fit for purpose.

And maintaining that distinction is really important, as it allows us to stay open to the infinities of possibility that can lurk in small places.

And there does seem to be a distinction between the infinities of the possible, and what is actually instantiated in any particular set of space and time.

[followed by]

Hi Bruce,

It seems that Robert is a zealot who is incapable of conceiving of a challenge to his ontological assumptions, let alone actually addressing one when it is presented to him.

Not a lot of point in further discussion with him as he does not seem to admit of the possibility of an alternate view from his own.

[followed by]


Until you can see and acknowledge the possibility of a difference between the realms of mathematics and reality, there is no point in further conversation.

You have as yet failed to demonstrate an understanding of the proposition I put forward.

[followed by]

Hi Robert,

Again, you refuse to admit of the possibility that what you claim as a Truth (mathematics is a universal truth in reality), is precisely the postulate that I am questioning using probabilities derived from experimental observation.

For you it is unquestionable dogma.

For me the evidence indicates it is probably a useful illusion.

And to be explicitly clear – I accept that the truths of mathematics quite probably flow from the postulates of ZFC (certainly in all the instances I have explored that is so).

I am not arguing about that.

What I argue is that it is possible to prove (100%) that the postulates of ZFC apply necessarily across all of reality (whatever reality actually is).

Being able to separate those distinctions is critical.

[followed by rant response]

Thanks for proving my point 😉

[followed by rant response again]

No Robert,

And I do get that is how it occurs for you.

It is not how it is occurring for me.

I have a certain sympathy with what you are experiencing, and that sympathy only goes so far.

The repeated insults and lack of respect are testing those limits.

[followed by ]


Again you mis charatcerise what I have written.

It is like you either haven’t read it closely (and it requires close reading, it is dense, and I reviewed the words with some care); or there is something about the interpretive schema you are using that makes it very difficult to interpret as intended.

The latter is highly probable.

I have been explicitly careful to state many times that I am not arguing about the sorts of truths that one can derive from the postulates of ZFC – accept those and all else I have explored necessarily follows in all the branches of set theory and various other constructs that are derived from that follow. And I have been told (and accept) that your knowledge and experience in those domains vastly exceeds my own.

I have never argued about that.

I am arguing in an entirely separate domain (in one sense) and a related domain in another sense – the domain of reality (whatever it actually is).

I make no claim to 100% knowledge of reality.

I do make claim to useful approximations backed by large evidence sets.

I do acknowledge the use of the intellectual tool sets derived from ZFC in building such models as I have of reality.

The question about Truth I have been pointing to lies not in the validity of the constructs of ZFC in building models, but in the relationship of those models to whatever reality actually is.

I don’t see any basis for making claims of any model necessarily applying 100% to reality.

We can certainly say that some models have been been extremely accurate – with the limits of experimental error.

Does that make them 100% true?


Does that make them useful?

Yes, most certainly that.

Have purely abstract explorations of the consequences of logical and mathematical constructs led to experimental discoveries?

Certainly, that has happened many times – the positron being a good example.

Has it happened that experiment has disproven theories that previously worked within the previous levels of experimental error?

Yes – that has happened too.

[followed by ]

Hi Robert,
The assertion you make:
“Foundational Mathematical Truths which apply 100% to All existence”
is precisely to dogma I am questioning.

I accept that mathematical truths hold within the domain of ZFC (or at least close enough – it has survived every test I have thrown at it).

Making the assertion that the axioms of ZFC necessarily apply to reality in all contexts is not warranted.

To the degree that we have tested, and within the limits of those tests, we can assert some things with confidence.

Beyond that – No.

Stepping beyond that is a category error in logic.

Taking that step is an article of Faith, not one of science.

Science is all about testing of our hypotheses, and refining and retesting.

And sure, sometimes insights from the purely mathematical realm have been extremely useful, and sometimes not so much so.

I have no issue with the sorts of truths that Wolfram’s engine searching the space of all possible theorems pulls out from time to time.

What I have an issue with is stating that any of them necessarily apply 100% to any particular context in reality, ever.
Reality seems to be of a sufficient order of complexity that such things are prohibited.

Confidence in well tested domains – yes, certainly that. Even to 20 decimals in some instances.

Beyond that – no – that is breaking a categorical boundary that ought not to be broken – it keeps existential level dangers at bay.

[Different subthread ]

Hi Jeoffrey,

It is only nonsense from within a binary paradigm of true and false.

From within a paradigm of probabilities, then one can say that it seems unlikely that it is possible to establish a perfectly exact description of anything in reality.

What history seems to indicate we can do is develop successively better approximations in our models to what reality is.

What is really at issue here is:

What do we mean when we use the word “Truth”?

The more one learns about the evolution and operation of human brains, and the evolution of language and culture, the more the implicit assumptions behind a naive interpretation of the idea in respect of knowledge of reality (as distinct from knowledge of logic or mathematics or systems) seems to fail (for a reasonably large collection of reasons).

We seem to be evolved entities.

Our ability to postulate and model systems like set theory, mathematics, logic, propositional calculus or to create tools like Wolfram’s theorem search engines, seems to have evolved over time from simple beginnings.

It seems most people fail to challenge many of the implicit assumptions in those simple beginnings, because it is very uncomfortable to do so (all certainty in respect of reality vanishes when one does so – one is left only with probabilities – and the very notion of Truth fundamentally changes from any classical construct).

Truth cannot be “The thing itself” – that is the thing itself.

Truth must lie in some systemic construct that has some degree of relationship to the thing itself.

In absolute Truth (100%) that degree of relationship needs to be perfect (100% in every element of every matrix employed).

Just because something has worked in every instance tested thus far does not make it universally true, it just makes it not yet falsified unless you have tested every instance.

Northern hemisphere folks have this idea of the Black swan. Your swans are white.
I live in New Zealand. Our swans are black.
I didn’t see a white swan until I was in my twenties, though I hunted and killed many black ones.
Black swans are normal where I live.

A trivial example you might say, but not really.

Robert seems to accept that mathematical ideas necessarily hold true in all realities.

We have no proof of that.

We do know that they are the best modelling tools we have, and that give us our best models of reality. And there are always errors and uncertainties in those measurements, so it is rarely if ever 100% accuracy in 100% of measurements.

This seems to be the sort of reality we find ourselves in.

Not particularly like the one the classical thinkers thought about.

[followed by]

Hi Jeoffrey,

I think the key lies in this sentence you wrote “How could it know the nature of truth is probabilistic if it didn’t have that as a true fact?”

And the answer is, it can’t.

The answer is, that “Truth” becomes an asymptotic pole on an infinite spectrum of probability.

And this is the really difficult bit for most minds.

Our early understanding is predicated on the simple binary (True/False).

It seems probable to me that it underpins our conscious awareness in a programatic declarative sense, in that our self aware consciousness is bootstraped into existence in a declarative statement that our pre-self-conscious self makes about ourselves (but that is another very complex topic, and it does explain the particular resistance to the consideration of the postulates I am proposing).

What I am saying, is that it seems possible that we have no certain knowledge about anything in reality (other than our own existence as something, though not about any of the particulars as to what that something is – an infinite stack of variations on the evil demon hypothesis seem to be available).

I am not primarily a logician.

I got seriously interested in biology and evolution a little over 50 years ago. I got quite deeply into biochemistry and evolutionary biology (at 17 I was given direct admission to second year biochemistry at Waikato university).

About 46 years ago I started working with computers.

I have owned and operated a small software business for the last 33 years.

Biology, evolution, doesn’t work on perfection.

Biology is all about being better at surviving than any of the other variants around. That is the fundamental sorting mechanism on essentially random variation.

By the time you get to us that process has recursed through at least 15 levels of fundamentally cooperative complex adaptive systems. Some of those systems include context sensitive non-random modulators on the rate and type of variation instantiated. It is seriously complex probability landscapes.

So biology is not about being True to any particular system, it is about what works in practice in the sets of contexts encountered over deep time.

That is a fundamentally different sort of notion.

That notion has fundamentally shaped our brains and our culture.

Reality often demands rapid answers in complex environments to survive, that demands simplifying very complex realities down as far a possible (to simple binaries like: true/false, right/wrong, good/bad, up/down, big/small, light/dark, ……). They are useful in some contexts, and they are also gross simplifications.

I accept that it seems very likely that all the “Truths of mathematics” flow from the axioms of ZFC, and that the sets of constructs that flow from that are very powerful tools in understanding relationships.

And there is a distinction.

To prove that the axioms of ZFC hold in all of reality (whatever reality is), then one must test them in all of reality.

One cannot do that.

We already have a pretty good idea that reality is too big for us ever to test all of it.

We have enough trouble getting really accurate data about the little bit of it that is really close to us (within a light second).
If a person is running, it takes 2 days to traverse a straight line just one light millisecond long, without stopping to look at anything along that narrow path.

We know reality is big, really big.

We know (beyond any shadow of reasonable doubt) that it is complex beyond the ability of any brain to comprehend in detail.

We know it is weird (not common sense) at both extremes of scale beyond those we evolved in (the very large and the very small).

The tools we developed from the postulates of ZFC give us some very useful models of just how weird. Some of those sets of equations in use today align very closely, within the limits of experimental error.

And that has happened before – many times.

The ancients though that the heavens contained perfect circles and perfect spheres, because that was their understanding of mathematics (wrong).

Newton thought in terms of perfect ellipses (wrong again).

And both were accurate within the experimental errors of their days.

Why should today’s lot be any different?

I get it is uncomfortable giving up truth for eternal uncertainty.

It demands a level of humility that many find demeaning.

We really like to be right.

Many people would rather die than admit error (I have seen far too much of that in the last decade – since being given a terminal cancer diagnosis 9 years ago).

Does that make it any less likely or necessary?


Does that make it unlikely for many minds to even be able to hold eternal uncertainty as an idea?

Yep – certainly that.

No shortage of evidence of that in this forum.

I make no claim to perfect knowledge (quite the opposite in a sense).

And I do make a claim to some useful approximations to whatever reality actually is.

And the likelihood of me being able to communicated even 1% of what is in my head any time soon (next 20 years) is vanishingly small.

So I need to make very careful choices about what I focus on and where.

I am definitely not in any classical “box”. I am well beyond any box Wolfram has yet published explorations of.

About Ted Howard NZ

Seems like I might be a cancer survivor. Thinking about the systemic incentives within the world we find ourselves in, and how we might adjust them to provide an environment that supports everyone (no exceptions) - see
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1 Response to Foundations of Logic – Is Truth an illusion?

  1. Pingback: Fo Logic – Values | Ted Howard NZ's Blog

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