Münchhausen Trilemma
en.wikipedia.org
en.wikipedia.org
You can view this as a game:
Let's make some assumtions / axioms, and see what we can build with it.
Note that, there a no claims about absolute truth or reality here. We just play a game in our minds.
The most fundamental question about the game, that we can ask is "Is this game consistent". Goedel found out, somewhat unfortunately, we are not able to answer that question from within the game [2]. However, sofar no intrinsical inconsistencies (paradixies) have been found.
Now, it turns out, that the ZF-Mathematics game is a very useful game, since it allows us to model certain aspects of reality. E.g. Newtons Mechanic, allows us to forecast how planets move in space.
The Natural Sciences (Physics, Chem., Bio) and Engineering are essentially about how to model reality with mathematics. The way to do that is the empirical scientific method [3], where hypothesis are formed, experiments are designed and evidence is collected.
So the question of "truth" does not really arise. It's just:
(A) Mathematics is an interesting mind-game to play.
(B) Mathematics has been used very successfully to model and predict our preceived reality.
That's all you can ask for.
[1] https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory [2] https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theor... [3] https://en.wikipedia.org/wiki/Empirical_evidence
Extend my greeting when you see him! He introduced me to Category Theory around 2006 in Mainz.
It is often described in such way and you can see it like that in retrospect, but actually it is often intuitive grasp of mathematical structures first, axiomazation second.
For example, natural numbers was understood (including number theory) for thousand years, but Peano axioms are from the end of 19. century.
But that does not say there is 'absolute thruth', there are just infinite different graspable math structures and it is arbitrary (or pragmatic), which we consider interesting to develop.
However, this is not the logical foundations that are used for current teaching and research. There has been a lot of effort, in particular in the late 19the century by folks like Hilbert, Goedel, Frege, etc. to put Mathematics on solid foundations. This is what we ended up with.
But as long as we use words like "existence" in this weird way, everything works out.
My favorite example is https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theo.... There is a proof by contradiction that any class of graphs with the property that it is closed under minors can be characterized by a finite list of forbidden minors. Which therefore means that there is a polynomial time algorithm for membership in the class.
The classic example is that "planar graphs" have the necessary property, and there are exactly two forbidden minors.
However it is a pure existence proof. And the following facts are also known. We do not have a general way to construct the forbidden minors. Or a way to find out how many there are. Or any way to verify whether any given list of them is complete. And not just, "We don't know how to do it." But, "No such algorithm exists." (More precisely that being able to answer those questions in general leads to contradictions.)
So despite the entirely discrete nature of this problem (there are only a countable number of such classes), we find ourselves asserting the existence of a finite thing that we cannot find, bound the size of, or verify the correctness of if someone presented a reasonable candidate for our inspection.
In what meaningful way does this thing exist?
I think we (many, anyway) want to believe something like Leibniz' principle of sufficient reason: that every true statement has some sufficient reason for being so. We naturally interpret proofs in a formal system as that "sufficient reason". If we could prove from within a system that all and only consistent statements have a proof -- then that's great news! Maybe that system is Truth, or if it isn't maybe that's evidence some other system like it could be.
So Godel's work crushed this hope. No system can prove itself consistent, so there is no system under which the principle of sufficient reason is true. Maybe then we shouldn't believe it! Then are there truths that are true for no reason at all...?
But of course, there are many readings here -- many different roads to being thwarted by Godel :)
Moreover, this tool-theory of truth that you proffer still runs on some concept of truthiness.
All these system share a similar paradox to this trilemma: let's assume there is such a thing as truth, but the condition of that assumption seems to be the impossibility of proving it with any system produced by such a will to truth.
So I would say, it runs on, good choices of axioms and the ability to perform logical deductions.
Set Theory is an attempt to come up with axioms that are so simple that no-one who is not completely out of it's mind would doubt their "truth". This is stuff like:
- There exists a set
- Two sets are equal if all their elements are equal
- We can form subsets from sets, by picking out elements
The only exception is the axiom of choice, which is less intuitively evident, but a technical necessity to build and reason about infinite sets like the real numbers.
If you can demonstrate the impossibility of proving any truth, then you just demonstrated that you can prove some truth, thus it is false that it is impossible to prove any truth.
Finally, if you can neither disprove nor prove the impossibility of proving any truth, you just don't know whether it's possible or not; in which case the honest posture is agnosticism. Oh, and if you admit that an honest posture is desirable when pursuing truth, you just bootstrapped a ground that allows to growth (relative and sound) truth allied to virtue.
That might not be as satisfying as "acquiring some absolute truth", but personally I feel that for my humble human capacities and needs, that's not too bad.
Self-referential symbolic statements are at the core of Gödel's incompleteness theorem.
Ironically, It's Plato (through Socrates) who says "I know that I know nothing" but it should be fixed to say "I know that I know nothing else"
"the truth that there are no truths is a truth" is a cop out. It can easily be resolved and the statement "I know that I know nothing else" is coherent
Not only do we know that truth exists, but also we are aware that not every representations that come to our mind are truth. One might even consider that most representations that occupy our mind are unchecked untruths, but that doesn't undermine our ability to explore and gain new truth knowledge in some absolute way.
So if you dig far enough, how accurate our beliefs are is partly reliant on factors beyond our control: if our minds happen to be wired with bad axioms we may be unable to avoid inaccurate conclusions.
How? If beliefs have no way to be verified, what does it mean to say one still may be true.
This statement has as much meaning as randomly uttered noise.
It may not be able to be verified, but it can often be falsified. Suppose I believe that all bridges are safe for me because there is a swarm of fairies following me around holding up the bridges. And suppose you believe that no bridges are safe between the hours of 2 and 3 am, because the gods have so decreed. And suppose we both come to a bridge at 2am.
If I walk over the bridge and it collapses, it falsifies my belief that fairies will always hold up bridges for me, but it doesn't prove your belief that the gods have promised universal collapse for bridge-walking at 2am. On the other hand, if I walk over the bridge and it doesn't collapse, it falsifies your belief that the gods have promised universal collapse for bridge-walking at 2am, but does not prove my belief that fairies will always hold up bridges for me.
"All models are wrong, but some models are useful."
For all of our important beliefs -- about people, politics, religion, whatever -- it's always important that we ask ourselves, "How would I know if I was wrong?"
Take "the Earth is round" belief. The Earth was round since before humans existed. Having or not having evidence to support this belief did not and does not alter the shape in any way. The Earth is still round. So this belief was always true (even if unbeknownst to anyone) regardless of who held it and whether they had any evidence to support it.
Putting that aside, some things are unverifiable yet have concrete ramifications for people's lives. Some examples:
- If "earth will be swallowed by a black hole in ten seconds" is true, I'll never be able to verify it, even though it will have the concrete effect of ending my life.
- I can't verify _or_ falsify that other humans have conscious experiences, but I believe they do. If that belief happens to be false, the world is vastly different than if it is true.
- _Nobody_ could 100% verify that a given physical law applies everywhere at all times. But if it does, some people's lives will be different than if it did not. The fact that everyone in the cosmos has experiences consistent with the law being true, and nobody ever has an experience inconsistent with the law, are part of what make the law true. But that fact can't be verified by anyone.
(A hypothetical omniscient person could verify all these things, but omniscience just means "knowing all true things", so redefining truth in terms of what an omniscient person could verify would be circular.)
Just because you can't prove something is true, doesn't mean it's not true. You can just never know whether it's true or not. See also the Zen Proverb that someone posted in this thread.
https://plato.stanford.edu/entries/justep-coherence/
https://plato.stanford.edu/entries/justep-foundational/
To be honest the percentage of modern philosophers (or any other modern profession) having a view on something like this has no relation to the actual thing being true, false, or true or false at the same time or neither true nor false at the same time. We're all playing glasperlenspiel [1] trying to make sense of some of the things that surround us, that is until all of us will inevitably die.
Thanks for te book recommendation. Looks amazing. Loved Siddartha.
None of the listed options is so convincing that everybody using their rationality would immediately agree with the proposed model of truth. That seems to indicate that also for these options, rationality alone is insufficient to establish truth, and a belief/irrational/social factor still would be at play.
I'm not implying that the mentioned approaches developed by analytic philosophers are useless. They do deepen our understanding how reasoning and fact establishing works. But in my opinion they are still very far away of solving the Münchhausen Trilemma.
Appears there is no clear consensus on exactly why skepticism is false.
Skepticism doesn't demand that you "reject the ability to do things." See Hume.
Max Stirner, the most radical skeptic of them all, is without a doubt a more interesting philosopher than many others one is forced to read. Moreover, contrary to the claim made by the OP - he expects the reader to have read philosophy from other authors.
A radical skeptic like Stirner loves Kant and Hume. Maybe it's because Kant shows that the "thing-in-itself" is unknowable even if it exists and Hume shows us that empirical observation is basically all we have for trying to work with the world. Both show that no one in science has found anything resembling truth
> so of course they would be a small minority of philosophers
I'm not a philosopher myself but I found Heraclitus's writings (Democritus's, too) a lot more interesting than many philosophers' writings from the 20th century, in this field being more modern doesn't necessarily mean being better or knowing more.
This leads some to the interesting (and perhaps terrifying) conclusion that narratives are more important and useful than rationalism. Example: https://en.wikipedia.org/wiki/Joseph_de_Maistre
“ According to Maistre, any attempt to justify government on rational grounds will only lead to unresolvable arguments about the legitimacy and expediency of any existing government and that this in turn will lead to violence and chaos.[23][24] As a result, Maistre argued that the legitimacy of government must be based on compelling, but non-rational grounds which its subjects must not be allowed to question.”
Perhaps whatever is useful is oftentimes more important than what is true.
There has been an ongoing debate in the UK about proportional representation and the first past the post system. It has not, as yet, lead to violence and chaos. So I think that the link Maistre identifies between questioning the status quo and chaos is not always true.
Admittedly there is time and place for debate. You don't argue about the cars direction, when the driver is trying to concentrate in a dangerous situation.
But maybe the success of representative democracy is not based in rationalism but instead the mythology around individual liberty.
It's the same with any logical statement. You could go all the way up to the premises and question that and when given a proof of the premises, then you can question the premises of the "proof of the premises". Ad infinitum. Or you just take the axiomatic approach.
I think most of life is lived axiomatically.
While individual scientists may hold beliefs that go beyond scientific premises, the significant difference between scientific and religious belief is that in the former case, all axioms are considered to be defeasible - and they quite often are overthrown.
This is also not a semantic argument at all. It is strictly a logical one.
A close relative went from marine biologist to creationist (et al), and I've been struggling to accept the change. My Calvinist self still doesn't understand Evangelic system of faith.
--
Given Structure + Process => Outcomes:
Scientist: Faith in processes, eg scientific method. Belief is based on reproducibility.
Evangelical: Faith in outcomes. The book (authority) is used to rationalize (justify) proclamations of belief.
To your point: Yes, both have "faith", but with different starting points and emphasis.
Perhaps. The "just" part gets me thinking.
There seems to be an important qualitative difference between prototypical statements of belief---e.g. I believe in the healing power of reiki---and prototypical statements of fact---e.g. This is a glass of water.
While both of the above do contain elements of belief---namely, narratives about what things are in the world---they seem to operate quite differently in many respects.
Belief-style statements tend to more overtly signal traits like social ingroup or self-identity. In particular, declaring belief in the power of reiki seems more likely to influence how others think and concieve of you as a person. I doubt that declaring the existence of a glass of water is likely to do the same.
More generally, this line of thought makes tempts me to say that fact-like staments tend to have less social content than belief-style ones.
Or, more susinctly, facts are a proper subset of beliefs.
In the same way that 2D space differs wildly from 1000D space, despite the former being a subset of the latter, I think it ignores a lot to treat "facts" as "just beliefs." How a belief operates matters.
It's a important concept to remember for anyone who's argumentative/legalistic since understanding the oppossing sides definitions and desired conclusion is often the cause for disagreement. If there are no first principles, then there are no definitive last principles.
Also, in some ideal sense, since we attain consciousness as pure minds untainted by experience, tabula rasa, all that follows is the result of sense information on the network. The concept of individuality is weak. Two pure minds, fully rational and capable of honest communication, can be different by having different sense information, but if they are able to communicate with each other they should, in time, be identical. i.e. once I have given you everything I know completely and you have given me everything you know completely, we are not distinct, you and I are the same. A full mind meld.
We can't do this for all sorts of reasons, but two AGIs truly meeting may, which means that there is a sort of greyness to this true meeting of AGIs: by meeting they achieve unity. All AGIs behaving in this manner then become the same purely by meeting. Interesting.
Drop that assumption, and fully rational people can indeed agree to disagree. This is a large part of why rational people can look at the same evidence, and come to different conclusions.
That's the Wiki article, yes. But scarejunba is going past that, to something more fundamental.
If you have "pure minds untainted by experience, tabula rasa", then you remove the issue of priors. No longer is there any matrix of prejudices that have to agree. You start with observations about the world and logic, and nothing else, and everyone ends up in agreement.
(To an extent you might bootstrap with priors, but over time you'd use observations and logic to replace them, especially when they disagree with someone else you're debating.)
For example, an infant has an instinct to breathe right after birth. Is that a belief or an action? It’s both—a strategy to survive in the world encoded in genes attached to an implicit belief. An infant that tries to breathe two minutes later would suffer hypoxia and brain damage, while one that tries sooner will choke.
There is no pure tabula rasa untainted by priors, as soon as you acknowledge minds are embedded in bodies shaped by millions of years of evolution and steeped in survival tactics, and what are tactics except a set of useful priors about good actions?
But "You need to breathe." and things like that would be the easiest priors to replace with observational data.
Any breaks in trust, or breakdowns in communication can disrupt the process of mind melding. And it seems to me that trust and failure of communication are features of boundaries between individuals.
Interesting indeed
Is that part of the principles you adhere to? :)
Stage II clinical trials of novel drugs are like this. The hypothesis is "this stuff cures baldness and is otherwise harmless." The experiment is an elaborate attempt to disprove the claim, with enough subjects to avoid the small "n" effect and control-subject randomization to avoid the wishful-thinking effect.
Science tries to avoid claims that things are true. "Not false" gets us a long way. That avoids the Münchhausen logical trap.
Falsification is a good stake in the ground that allows scientists to work, but it's unclear if it's actually a step towards the epistemology represented by the Munchausen trilemma. Scientists have a notion that it allows them to work "toward" Truth-with-a-capital-T, a notion which both feels right and has produced high standards of living. Those may be better goals than Truth-with-a-capital-T, which may be unavailable.
Another is consciousness. To grasp that existence exists, or make any attempt to reason either way about the proof or truth of anything, is itself an expression of consciousness.
Existence exists, and so does consciousness capable of conceiving that. Start there and work down.
You argue that the denial of the axiom of "existence of existence" is self-refuting. But don't all arguments that something is self-refuting depend on the acceptance of the law of non-contradiction ("for all A, not (A and not-A)"?) If your argument for the axiom of "existence of existence" depends on the axiom of non-contradiction, is the axiom of "existence of existence" truly axiomatic any more?
What about the axiom of non-contradiction? Do we have to believe that? Well, dialetheism [1] denies that the axiom of non-contradiction holds (in the most general case), and yet the whole system doesn't fall apart. The secret is to allow contradictions, but limit their consequences, by rejecting the classical principle of ex contradictione quodlibet (ECQ, from a contradiction anything follows, aka the principle of explosion). An unlimited allowance for self-contradiction destroys all possibility of non-trivial reasoning, whereas a more limited allowance for self-contradiction leaves open the possibility of non-trivial thought. So, if we have a choice whether to accept the axiom of non-contradiction, maybe your attempt to escape Münchhausen's trilemma has not succeeded.
On top of that, it seems to me that even in denying the principle of explosion, one must follow it if they want to be consistent in the denial. Otherwise the denial itself won't hold, because if you allow contradictions, by definition you must also allow their opposite, which is the principle of non-contradiction. And as far as I'm aware there is no proof in logic that allows for an exception to ECQ. Because once you allow any contradiction, you implicitly allow anything, which makes thought impossible.
It just doesn't seem worth it to me to suspend the fundamentals of thinking just to solve some paradoxes that can anyway be solved within our current model of logic.
There are various proposed solutions, but they all have drawbacks. You have to compare the drawbacks of the different options. (From my limited memory, your proposed solution is not one of the standard solutions proposed in the literature.)
> As for Russell's paradox, as far as I know this has been solved in ZF theory
ZF theory pays a price – the restriction of the axiom of comprehension. The point is you don't solve Russell's paradox for free, every solution has its price, every solution involves giving up some component of naïve set theory; ZF chooses to partially give up the axiom of comprehension; inconsistent set theory (part of inconsistent mathematics [1]) chooses to partially give up the axiom of non-contradiction instead. If we have to give something up, how do we decide which part to give up? You think that giving up the axiom of comprehension is a smaller price to pay than giving up the axiom of non-contradiction – but is that a subjective value judgement? Or, can it be objectively justified? (And if so, how?)
A good argument for paraconsistent logic is that relevant implication is a more accurate model of natural language than material or strict implication, and relevant implication is paraconsistent. (That said, dialetheism goes beyond mere paraconsistency.)
I'd suggest (if you have the time/inclination) reading Graham Priest's book In Contradiction. It explains the arguments for all this far better than I can from memory. (I read that book 15 years ago.)
[1] https://plato.stanford.edu/entries/mathematics-inconsistent/
As for dialetheism being a better model of natural language, I'm familiar with the claim but I think its main argument fails to grasp that contradictions in natural language do not happen "in the same sense and at the same time". For instance, the sentence "This sentence is false" is true and false in natural language, but in succession and not at the same time. Moreover, dialetheism does not seem to be able to explain hierarchies and cause-effect relationships, which are key constructs of language.
I think that when it comes to logical systems such as mathematical theories, the point is not necessarily to come up with a theory that is true (that would ultimately be impossible due to Agrippa's trilemma), but to have a theory that has predictive power and is self-consistent, and this is what ZF is. Self-consistency seems to be the minimum requirement for any theory, lest it falls into triviality.
The little I know about paraconsistent logic is that it suspends consistency in a few select cases. But generally, consistency still holds, otherwise, as you said, the system would become trivial. I guess my question was: would paraconsistent logic claim to be true? Or, at least, identical to itself? If yes, then if would itself be subject to consistency and identity. And if it chooses to temporarily suspend those, then in that time it can no longer claim to be true. But if in general it complies with consistency (lest it becomes trivial), then it must reject the subsets that are not true, otherwise it could no longer be self-consistent.
I guess my point (and I could be wrong) is that paraconsistent logic is entirely non-consistent, unless it chooses to redefine what consistency means, in which case, we're back to triviality.
Thanks for the book suggestion, I'll definitely read it and hopefully find some answers.
Obviously since there's no need to rely on precisely one axiom.
My point is, you really don't get very far before you need to believe in some axiom, e.g. "I am a sensing being whose subjective experience of reality resembles the objective reality around me" (I know this sounds very basic, but try listening to someone who thinks they can slow Earth's rotation by meditating, and you'll realize that not everybody starts with an axiom where subjective and objective reality are separate, or where subjective reality is a derivative of objective reality and not the other way around)
Formal proofs are syntactic. As a result, they do not need consciousness to be verified; verification is algorithmic and can be done by a machine. Proofs can also be searched for by machines, although such proof search does not run at practical speeds on existing hardware yet. Nonetheless, to take your claim at face value is to claim that computing machines are conscious; are you prepared to embrace this result? (I don't personally have a problem with it, but many people do.)
This sort of word salad, more generally, is why Objectivism has such a poor reputation: It doesn't make sense when examined with even basic critical thinking.
>Formal proofs are syntactic. […]
This confuses means of formal proof with meanings attached to them. A proof, whatever the means used to perform it, only matter to conscious beings. A computer can help to solve a logical problem, but so far none have been catched wondering which logical problem would be interesting to solve as its next challenge – as far as I know.
The Gödel Machine algorithm [0][1] is only a few years old, and it cannot yet be tested due to practical hardware constraints, but it provably implements a system which wonders, specifically, about which direction of proof search will speed up its ability to search for proofs, to consider directions, or to wonder.
[0] https://en.wikipedia.org/wiki/G%C3%B6del_machine
[1] http://people.idsia.ch/~juergen/goedelmachine.html
[2] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat...
[3] https://en.wikipedia.org/wiki/Tarski's_undefinability_theore...
[4] https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem
With regard to "the existence of existence", you appear to have started on your way down the "regressive argument" branch.
These aren't my ideas. At the risk of having this and my first comment downvoted into oblivion, I got them from Ayn Rand. She has a short (80-page) nonfiction book about just these things which I think is remarkable, called Introduction to Objectivist Epistemology. If you are not predisposed to despising the author, it's a quick, very interesting read that I recommend.
Edit: And there are the downvotes...
The more modern expansion of these ideas can be found in Phenomenology by people like Husserl or Heidegger.
There are a lot of contemporary philosophers dealing directly with philosophy of mind and consciousness which is more of an offshoot of these questions once you sideline questions of grounding.
And there is also more contemporary philosophy of science/math that deals directly with questions of consistency and the grounding of logical or rationalistic methods.
Basically there are a lot of resources if you are interested in this stuff, and I would heavily recommend reading and understanding what others have thought about before trying to re-invent the wheel as your starting point. That takes too long and there's a long way to go.
I've put somewhat of a moratorium on philosophy as of late because I don't have the time for it, but I'll check it out if I do get the time.
The Cogito, or other ontological foundations of existence which rely on appearances are completely wrong. "I think therefor I am?" How do you know that you are thinking? How do you know that appearances of thinking are actually in existence? It's possible that you did not think! and that what you believe to be existence is not existence at all.
At best, you can say "it appears to me that I think therefor it appears that I exist". You cannot just escape radical doubt because of appearances.
Also, the no-cloning (and the other no-go) theorems and bells theorem (no determinism) seem to imply that Quantum Theory has concluded that the law of identity doesn't hold up in reality. Objects are NOT equal to themselves. We do not know that a fundamental minimal quantized unit of time exists, meaning that we cannot say that "an object is equal to itself at a particular time". If we accept the Kantian thesis that time and space are the "vessel" or "canvas" of reality, than it's not possible to confirm that an object exists in the same point in time, and the same point of space with itself without a fundamental minimal quantized unit to measure those in.
You should instead conclude that the metaphysical constitution of objects is ultimately in-determinant
The law of in-determinancy would say that "objects can be infinitesimally close to identical with themselves"
A =/= A. The left-side A exists in a different point in time and space as the right-side A. You cannot even think of these in your own mind at the same time, in the same part of your "mind-space". There is no verifiable measure of the "present" so we cannot constitute an object in exactly one point of time and space at a particular "moment"
All of what I've just said is basically a more modern version of Nietzsche's revulsion to the exact same "A = A" crap that was being thrown around in his own time.
tl;dr you don't know that you exist
citations:
https://en.wikipedia.org/wiki/Bell%27s_theorem
https://en.wikipedia.org/wiki/No-cloning_theorem
https://en.wikipedia.org/wiki/No-broadcast_theorem
"If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty."
"Giving grounds, however, justifying the evidence, comes to an end."
"At the foundation of well-founded belief lies belief that is not founded."
"The child learns to believe a host of things. I.e. it learns to act according to these beliefs. Bit by bit there forms a system of what is believed, and in that system some things stand unshakeably fast and some are more or less liable to shift. What stands fast does so, not because it is intrinsically obvious or convincing; it is rather held fast by what lies around it."
People who have a huge ego tend to think that every fact they know is a crucial part of their personal identify; these people tend to avoid saying "I dont' know" because doing so would be an admission that their information sources (which they see as extensions of themselves) are not trustworthy and are therefore low value (which would bring down their own self-worth).
https://thephilosophicalsalon.com/the-fall-that-makes-us-lik...
It's been my mind for a while now, and I'm still not sure with whom I stand here. Roughly, Zizek says : Any kind of mental breakdown that changes you will be related to your subsconscious. Nietzsche : Lol, when you reach my level of psychosis, you really have to pull yourself out all by yourself.
We often think of perpetual motion as set it and forget it once it's set in motion it continues forever but of course this isn't feasible
Have you ever considered that a truly perpetual motion is one that never needs to be set in motion that always is in motion?
This is precisely the bootstrapping argument in essence so a small measure of faith is needed
We can rely on our perception to be reality for all intents and purposes and begin reasoning with base assumptions and not over analyze the starting conditions too much
Another parallel https://www.youtube.com/watch?v=X8aWBcPVPMo
we were computationally evolved to make sense of the world... and making sense is a computation