I want to present some of the ideas that I deem significant in my philosophy or life view. I arrived at these mostly on myself, but that does not mean that they are just mine, several of the ideas I present are shared by others. I do not want to take any sort of ownership, but what I present is my flavor. Now without any further disclaimers…


Models and modelling have always been important to me, not only because I went to study physics and mathematics, and then ended up doing computer science and engineering, but also from the philosophical point of view.


Mathematics attempts to study models, theories without direct connection to reality or practical usefulness. Clearly the branches that do produce models with practical usefulness receive more attention, as practical use can be very stimulating.

Still from a more philosophical point of view mathematics tries to study all the models that we can imagine, talk about and reason on with others. This can be very creative, and represents one of the greatest flights of the human spirit, belying the view that mathematics is dry and dull.

Practical use has to come second because it is not possible to say a priori which models will be practically useful. Indeed, it did happen often that things that seemed less connected to the reality became suddenly very relevant, for example, differential geometry (for the general relativity), number theory (for cryptography), group theory (symmetry and cryptography), automata and algorithms (computer science)…

Furthermore, practical usefulness is just one component of the usefulness of a model, its complexity, how well it can be reasoned upon or explained to others, or applied on their models, embedded or embed other models (its generality),… are also very important in abstract models.

Absolute Truth

Mathematicians have often tried to build all mathematics out of elementary principles. Sometimes this can lead to surprising and fruitful connections, besides it can bring more confidence in the validity of another theory.

I appreciate this effort, for example when in my honeymoon, I found a copy of Bourbaki’s Éléments de mathématique in a used book stand along the Seine, I obviously had to buy it. They had tried to revive the idea construct mathematics from basic theory (set theory in their case), after the blow (to Hilbert’s second probelm) of the Goedel incompleteness theorem (see below). While I appreciate it, I do not think that it is necessary, even if it was maybe needed to dampen the exuberance that followed Godel’s theorem, that lead to several inconsistent theories. These things lead me to important pillars in my philosophical thinking.

Several famous mathematicians thought that there is some final truth, and just one. Starting from it one could build all True models. This was frequently connected with the idea of God giving some grounding, like the Leopold Kronecker’s famous quote “God made the integers, all the rest is the work of man”.

Non Euclidean Geometries

That this idea was a bit too simple became clear with non euclidean geometries. The fifth postulate of Euclidian geometry says that if one has a line and a point not on the line there is exactly one parallel line passing through it. Non Euclidean geometries change that axiom to either being no parallel line or infinitely many.

At first sight one would expect only one of these models to be true. Surprisingly, it turns out that all these geometries can be embedded in Euclidean theory, only what exactly a “line’’ is, changes.

If one calls lines maximum circles on the surface of a sphere, and identifies points on the opposite side of the sphere, then what one has is projective geometry, where two lines (maximum circles) always intersect, and thus there are no parallel lines. Likewise, on a hyperbolic surface lines move away from each other and infinite “parallel” lines exist.

This means that if the euclidean geometry is true (i.e. without contradictions) so are the non Euclidean geometries, they just describe somewhat different objects. In fact, there is more that a single model compatible with these axioms (in Riemannian manifolds the curvature can even change from place to place).

This influenced my view on models and truth. Some of this thinking comes from my first year at ETHZ we had a course on Geometry using J. Cederberg A Course in Modern Geometries which I found very stimulating.


The search for absolute truth began to show some issues in the naive set theory, with Russell’s paradox: “does the set of sets not containing themselves, contain itself?”. Goedel extended this to the natural numbers, by showing that any logical system containing the natural numbers has infinitely many assertions that cannot be shown to be true or false. This is also connected with the halting problem of Turing machines being undecidable.

It isn’t even possible to develop a schema to decide them all, as there uncountably many of them. This has important ramifications, for example Douglas R. Hofstadter discusses how the self referentiality at the core of the Godel argument (basically saying this sentence is false), the halting problem, exiting the box (model) to reason about it, the art of Escher and Bach are connected, and how this might be relevant to our thinking in the excellent Godel Escher Bach an eternal golden Braid.

A point I want to underline is that there are questions that might be unanswerable (and a lot of them), and often here trying to answer it is not meaningful, one should rather accept it, and try to rethink the whole thing (exit the box). This is along the lines of the MU “unasking” answer of Hofstedter.

An interesting thing I came across recently aside reverse mathematics is paraconsistent logic, that tries to work with logics that avoid the principle of explosion (having everything being derivable from a contradiction), and so can deal in a better way with contradictions (but is not unique and becomes harder to reason about).


Programming is deeply connected with mathematics, languages, algorithms, automata, Turing machines and their extensions, complexity theory, algorithms, all stem from pure mathematics, as beautifully illustrated in Knuth’s The art of Computer Programming.

Still programming is much more practical, in the end one wants a working program that does something. This calls for a pragmatic approach. Paul Ford’s What is code?'']( and [The pragmatic programmer’’ discuss some of the issues coming up in real world programming.

AI can have interesting philosophical consequences, but I plan to expand on those separately, so here I will limit myself to saying that like programming very much and I consider it one of the fine arts.

External Reality

I believe in an external reality shared with other people. That reality simply is, what we can have are models of it, we never have reality itself.

Some more conspiracy oriented views doubt of the existence of an external reality.

We are reaching the level where sensorial input can be simulated to better and better, so one can imagine being in a virtual world. Still, even if it would be like that (and I do not see the reason someone would want to do it), I cannot imagine how one could create a world where at least some sort of probabilistic model cannot work. If it reacts to the actions or even the thoughts of the person in it, then it can be at least partially controlled, even if it is a virtual world. Unless one knows how to escape, I find no point in introducing extra layers…


Physics for me tries to create models of the external reality that can be falsified by experiments and discussed with others.

After having seen the limits of knowledge and absolute truth in mathematics, one could hope that as physics cares about the real world, not abstract models, some truth might finally be relevant. Unfortunately, I think that also in this case the concept of absolute truth is not very useful.

Think about the gravitational force on an object. Is it true? Well, we know that the whole Newtonian physics is not correct, quantum physics works better, but to describe the really small world quantum field theory, and in particular the standard model is more accurate, but even then general relativity is not described by it…

Truth? Usefulness!

If one looks for absolute truth basically everything can be considered false. Even without going so far, the concept of force is pretty abstract, a force cannot be seen, only its effects… Given any model one can always refuse to accept some of its axioms/postulates, and there is no way to argue about their truth. Thinking in terms of usefulness is better. I might not be able to convince someone else of the truth of the gravitational force (or forces in general), but I can convince her/him of the usefulness of using this model to describe our world.

If one thinks about usefulness, then accuracy is only an aspect of it, thus the very accurate theory of the standard model in particle physics is not necessarily more useful than quantum mechanics, for example if one looks at molecules or materials. Likewise to describe macroscopic objects at non relativistic speeds classical mechanics is simpler to compute and think about, and thus still useful.


Not having all answers (not being is most likely a feature of most non trivial models. I see this tying with my agnosticism: I do not know if god exists or not, and in fact to me it isn’t even so important to answer that question, but rather what one does, and how one lives. It is interesting that Bertrand Russell (the one of the Russell’paradox) also considered himself agnostic. In this case I can put this in even stronger terms: If God exists and cares more about one believing in him rather than what he does and how he behaves I am not sure I would like to believe in him… and in all other cases sticking on caring about the actions I do should be ok.


This still opens the question of ethics, or how to evaluate actions and intents. Here one might think that without religion or God to “anchor” the values, ethics would become very culture dependent. I disagree, I think that starting from the idea that individuals are a richness worth being protected, that preserving complexity and diversity is worthwhile, one can go pretty far.

The evolution theory when one goes beyond the simplistic “the strongest survives” (Major transitions in evolution is a good way to understand some of the intricacies of evolution), builds a good backbone for this. This is discussed in depth by Rachels in the excellent Created from Animals. Obviously some things remain cultural, especially fixing the scales of values, but surprisingly many considerations are pretty general.

Emic vs Etic

In anthropology there are two concepts that I find very useful: etic and emic. Emic are the reasons given by the society, or ethnic group studied, etic the ones found by the researcher that is outside it. Etic is more “objective”, some would say better, but the situation is not so simple. This is best illustrated with an example.

Think about a tribe in Amazonas that every few years changes its place. When they do they have a lot of work to move everything and clean up the new place. If you ask them why they do this (emic) they will reply that bad spirits have found them, and indeed they have all sorts of rituals that are meant to make the bad spirits lose their tracks when they move. Still, no matter how careful at some point the bad spirits will catch up and they will have to move again. An external researcher (etic) will look at the harvest, and the amount of game gathered by hunters, and will see that over the years it declines. At some point it is worthwhile to invest the big effort to relocate to non exhausted fields and hunting grounds. The etic view seems superior to us, but looking more carefully it isn’t so obvious. Yes the view of the average person looks naive to us, but if one looks the shaman that decides when to move, and makes the main rituals connected to it, most likely he will look at the signs of exhaustion, as signs of the presence of bad spirits. In fact, his model of “bad spirits” can be pretty close to the one of the external observer, and the shaman is likely better than an external observer to decide when to move. Finally to convince everybody to move bad spirits can be an effective reason.

The etic view still has some advantages because it can happen that with time the emic view becomes too detached from the driving reasons behind it, be it because the environment or social changes (for example moving to a mainly agricultural based life, with a sustainable use of the fields).

Limits of models

Agnosticism, refusal of absolute truth, evolution theory,… they might all seem based on weak premises. Indeed, some people expected that I would finally be converted to religion. I think that it is quite unlikely, because the foundations of this thinking is (as I have hopefully shown) pretty deep.

Still, I recognize a main weakness to my models: they might need more thinking to find out what to do in a situation. Not acting is a choice with consequences, sometime worse than making the wrong choice. Another framework of thinking can give clearer answer, expected behavior in clearer and faster way, free one to do other things. I rank models based on the usefulness, and using that it is not absolutely clear that my models are really better.

Indeed, as is often the case for any complex problem, there are probably several workable approaches, and different trade-offs involved with them. This is the reason that, sometimes surprising those that know my beliefs, I am so open even toward religious approaches, and indeed I have known religious persons that I regard highly, and I see how religion can spur men and societies toward greatness (but unfortunately sometime also toward hatred and closedness).

Just as with the ethics derived from evolution, I strive for an open and diverse society, the only clear limits I see are the same discussed by Popper: the tolerance of intolerance should be limited, apart from that I hope for open discussions and exchange of ideas. Here also religious or spiritual approaches can have their place, as long as they accept of others to have different ideas.


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