Formal System

A site about formal logic, literature, philosophy and simulations. And formal systems!

Robert Nozick – Fiction: The nature of reality — August 6, 2012

Robert Nozick – Fiction: The nature of reality

In this brief essay, American philosopher Robert Nozick creates a character named after himself that self-consciously asserts that he is a fictional character but he wonders about his author, that invisible God that controls the character’s thoughts, motivations, etc. The character wonders about the possibility that his God-like author might also be a character in another God-like author’s story and so ad infinitum…

Robert Nozick’s Fiction is a great set of thoughts about reality, fiction and the differences and similarities between both. It also picks up  Descartes’ cogito ergo sum and provides some really interesting insights about it.

Read it for free here.

P.S. Robert Nozick’s Fiction was included in the last chapter of Douglas Hofstadter’s The Mind’s I.

This Is the Title of This Story, Which Is Also Found Several Times in the Story Itself — June 29, 2012

This Is the Title of This Story, Which Is Also Found Several Times in the Story Itself

I found this lovely story by David Moser inside Douglas Hofstadter’s Methamagical Themas which is a recommended reading to any Hofstadter fan or anyone interested in “the essence of mind and pattern”. I will reproduce the content on the story here:

This is the first sentence of this story. This is the second sentence. This is the title of this story, which is also found several times in the story itself. This sentence is questioning the intrinsic value of the first two sentences. This sentence is to inform you, in case you haven’t already realized it, that this is a self-referential story, that is, a story containing sentences that refer to their own structure and function. This is a sentence that provides an ending to the first paragraph.

This is the first sentence of a new paragraph in a self-referential story. This sentence is introducing you to the protagonist of the story, a young boy named Billy. This sentence is telling you that Billy is blond and blue-eyed and American and twelve years old and strangling his mother. This sentence comments on the awkward nature of the self- referential narrative form while recognizing the strange and playful detachment it affords the writer. As if illustrating the point made by the last sentence, this sentence reminds us, with no trace of facetiousness, that children are a precious gift from God and that the world is a better place when graced by the unique joys and delights they bring to it.

This sentence describes Billy’s mother’s bulging eyes and protruding tongue and makes reference to the unpleasant choking and gagging noises she’s making. This sentence makes the observation that these are uncertain and difficult times, and that relationships, even seemingly deep-rooted and permanent ones, do have a tendency to break down.

Introduces, in this paragraph, the device of sentence fragments. A sentence fragment. Another. Good device. Will be used more later.

This is actually the last sentence of the story but has been placed here by mistake. This is the title of this story, which is also found several times in the story itself. As Gregor Samsa awoke one morning from uneasy dreams he found himself in his bed transformed into a gigantic insect. This sentence informs you that the preceding sentence is from another story entirely (a much better one, it must be noted) and has no place at all in this particular narrative. Despite claims of the preceding sentence, this sentence feels compelled to inform you that the story you are reading is in actuality “The Metamorphosis” by Franz Kafka, and that the sentence referred to by the preceding sentence is the only sentence which does indeed belong in this story. This sentence overrides the preceding sentence by informing the reader (poor, confused wretch) that this piece of literature is actually the Declaration of Independence, but that the author, in a show of extreme negligence (if not malicious sabotage), has so far failed to include even one single sentence from that stirring document, although he has condescended to use a small sentence fragment, namely, “When in the course of human events”, embedded in quotation marks near the end of a sentence. Showing a keen awareness of the boredom and downright hostility of the average reader with regard to the pointless conceptual games indulged in by the preceding sentences, this sentence returns us at last to the scenario of the story by asking the question, “Why is Billy strangling his mother?” This sentence attempts to shed some light on the question posed by the preceding sentence but fails. This sentence, however, succeeds, in that it suggests a possible incestuous relationship between Billy and his mother and alludes to the concomitant Freudian complications any astute reader will immediately envision. Incest. The unspeakable taboo. The universal prohibition. Incest. And notice the sentence fragments? Good literary device. Will be used more later.

This is the first sentence in a new paragraph. This is the last sentence in a new paragraph.

This sentence can serve as either the beginning of the paragraph or end, depending on its placement. This is the title of this story, which is also found several times in the story itself. This sentence raises a serious objection to the entire class of self-referential sentences that merely comment on their own function or placement within the story e.g., the preceding four sentences), on the grounds that they are monotonously predictable, unforgivably self- indulgent, and merely serve to distract the reader from the real subject of this story, which at this point seems to concern strangulation and incest and who knows what other delightful topics. The purpose of this sentence is to point out that the preceding sentence, while not itself a member of the class of self-referential sentences it objects to, nevertheless also serves merely to distract the reader from the real subject of this story, which actually concerns Gregor Samsa’s inexplicable transformation into a gigantic insect (despite the vociferous counterclaims of other well- meaning although misinformed sentences). This sentence can serve as either the beginning of the paragraph or end, depending on its placement.

This is the title of this story, which is also found several times in the story itself. This is almost the title of the story, which is found only once in the story itself. This sentence regretfully states that up to this point the self-referential mode of narrative has had a paralyzing effect on the actual progress of the story itself — that is, these sentences have been so concerned with analyzing themselves and their role in the story that they have failed by and large to perform their function as communicators of events and ideas that one hopes coalesce into a plot, character development, etc. — in short, the very raisons d’etre of any respectable, hardworking sentence in the midst of a piece of compelling prose fiction. This sentence in addition points out the obvious analogy between the plight of these agonizingly self-aware sentences and similarly afflicted human beings, and it points out the analogous paralyzing effects wrought by excessive and tortured self- examination.

The purpose of this sentence (which can also serve as a paragraph) is to speculate that if the Declaration of Independence had been worded and structured as lackadaisically and incoherently as this story has been so far, there’s no telling what kind of warped libertine society we’d be living in now or to what depths of decadence the inhabitants of this country might have sunk, even to the point of deranged and debased writers constructing irritatingly cumbersome and needlessly prolix sentences that sometimes possess the questionable if not downright undesirable quality of referring to themselves and they sometimes even become run-on sentences or exhibit other signs of inexcusably sloppy grammar like unneeded superfluous redundancies that almost certainly would have insidious effects on the lifestyle and morals of our impressionable youth, leading them to commit incest or even murder and maybe that’s why Billy is strangling his mother, because of sentences just like this one, which have no discernible goals or perspicuous purpose and just end up anywhere, even in mid

Bizarre. A sentence fragment. Another fragment. Twelve years old. This is a sentence that. Fragmented. And strangling his mother. Sorry, sorry. Bizarre. This. More fragments. This is it. Fragments. The title of this story, which. Blond. Sorry, sorry. Fragment after frag- ment. Harder. This is a sentence that. Fragments. Damn good device.

The purpose of this sentence is threefold: (1) to apologize for the unfortunate and inexplicable lapse exhibited by the preceding paragraph; (2) to assure you, the reader, that it will not happen again; and (3) to reiterate the point that these are uncertain and difficult times and that aspects of language, even seemingly stable and deeply rooted ones such as syntax and meaning, do break down. This sentence adds nothing substantial to the sentiments of the preceding sentence but merely provides a concluding sentence to this paragraph, which otherwise might not have one.

This sentence, in a sudden and courageous burst of altruism, tries to abandon the self-referential mode but fails. This sentence tries again, but the attempt is doomed from the start.

This sentence, in a last-ditch attempt to infuse some iota of story line into this paralyzed prose piece, quickly alludes to Billy’s frantic cover-up attempts, followed by a lyrical, touching, and beautifully written passage wherein Billy is reconciled with his father (thus resolving the subliminal Freudian conflicts obvious to any astute reader) and a final exciting police chase scene during which Billy is accidentally shot and killed by a panicky rookie policeman who is coincidentally named Billy. This sentence, although basically in complete sympathy with the laudable efforts of the preceding action-packed sentence, reminds the reader that such allusions to a story that doesn’t, in fact, yet exist are no substitute for the real thing and therefore will not get the author (indolent goof-off that he is) off the proverbial hook.

Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph.

The purpose. Of this paragraph. Is to apologize. For its gratuitous use. Of. Sentence fragments. Sorry.

The purpose of this sentence is to apologize for the pointless and silly adolescent games indulged in by the preceding two paragraphs, and to express regret on the part of us, the more mature sentences, that the entire tone of this story is such that it can’t seem to communicate a simple, albeit sordid, scenario.

This sentence wishes to apologize for all the needless apologies found in this story (this one included), which, although placed here ostensibly for the benefit of the more vexed readers, merely delay in a maddeningly recursive way the continuation of the by-now nearly forgotten story line.

This sentence is bursting at the punctuation marks with news of the dire import of self-reference as applied to sentences, a practice that could prove to be a veritable Pandora’s box of potential havoc, for if a sentence can refer or allude to itself, why not a lowly subordinate clause, perhaps this very clause? Or this sentence fragment? Or three words? Two words? One?

Perhaps it is appropriate that this sentence gently and with no trace of condescension reminds us that these are indeed difficult and uncertain times and that in general people just aren’t nice enough to each other, and perhaps we, whether sentient human beings or sentient sentences, should just try harder. I mean, there is such a thing as free will, there has to be, and this sentence is proof of it! Neither this sentence nor you, the reader, is completely helpless in the face of all the pitiless forces at work in the universe. We should stand our ground, face facts, take Mother Nature by the throat and just try harder.

By the throat. Harder. Harder, harder.


This is the title of this story, which is also found several times in the story itself.

This is the last sentence of the story. This is the last sentence of the story. This is the last sentence of the story. This is.


About free will, evil and love: Dialogue with an amoralist God — January 27, 2012

About free will, evil and love: Dialogue with an amoralist God

Smullyan is quite an off-beat person. Why?

He started as magician and later on went to become a logician. The most incredible part is that he also became a Taoist (for details of the core ideas of this eastern philosophy click here). It is no secret that Taoist views are rooted on profound paradoxes nor it is secret that Western logicians have been battling against paradoxes like doctors a disease. It should seem that both logic and Taoism are conflicting but apparently, this fellow has managed to keep inner peace.

“Is God a Taoist?” is a dialogue between God and a theist where the latter asks the former why did he bestow free will on humans.  What follows is an explanation of quite a laid-back God who describes the problem of evil, his love for humans as well as a surprisingly simple idea to show why humans need free will.

P.S. Taoists do not believe in divine entities so the title of the dialogue itself can be taken as a sort of paradox, making the title a subtle reference to a core paradox surrounding the idea of free will (this core paradox happens to be mentioned in the dialogue).

You can read it here for free.

Artificial Intelligence: Soul Searching and views of an A.I. advocate. — January 26, 2012

Artificial Intelligence: Soul Searching and views of an A.I. advocate.

I will just put down common objections against the idea that machines can, someday, think and I will reply to them in a systematic manner. If you want your question to be added (and replied) write the question in the comments and I will add it to the list of objections. 😉

First of all, I shall make clear that I don’t think that our “modern” machines can support full human cognition as they are not complex nor flexible enough, but I do think that the period of time to get the complexity required to achieve a decent level of flexibility is finite even though it is going to take several computer science revolutions to get to that point.

1 – Machines can only do what you tell them to do.

The above statement implies predictability (and thus, full knowledge) of the actions of the machine. But as programming languages go farer and farer from the original machine language this predictability is gradually being lost. This means that eventually there will be a time when our predictions about what a machine can do from what we told them to do will be approximate. We will only know the “space” in which the machine’s actions will fall. As simple analogy: when we tell the computer to calculate the first million digits of Pi, we don’t know which digits will be, we only know that it is exactly one million digits.


2 – Machines cannot feel thus they cannot think in a human way (intelligent).

As far as I am (and most psychologists) concerned, emotions are a by-product of intelligence.


3- Humans are sometimes irrational beings, machines are always rational beings. Moreover, machines cannot be irrational beings because they are mechanic beings.

Look at this picture:

The brain is rational, the mind might not be.

The problem with the above statement (machines are always rational and humans sometimes are irrational) is that it mistakes levels.

To simplify, there are two levels, low rigid level and high flexible level.

Now, let us do some analogies:

Brain <=> Hardware of the machine <=> Low level (rigid)

Mind <=> Software of the machine <=> High level (flexible)

Now, are humans sometimes irrational? Yes. Are human brains sometimes irrational? No. Neurons either fire or not. There is no paradox there. Are humans irrational? Yes. Are human minds sometimes irrational? Yes. BUT, this flexibility of being able to switch between irrational and rational is the consequence of the complexity of a rigid system (the brain). When people say “machines cannot be irrational” they talk about a machines low level (their hardware) but they do refer to humans high level when they say “humans can be irrational”. So the problem with that statement is a lack of differentiation between levels of description. So the hardware of a machine is as rigid as a human’s brain and computer software is (potentially) as flexible as the human mind.


4 – How can you program thinking if you do not know what it is?

See my earlier post about the Turing Test.


5 – Okay, let us say that in some future, we get some machines thinking like humans, wouldn’t the machine be simulating thinking rather than actually thinking? Simulated thoughts are not actual thoughts. If I simulate milk, regardless of how complex the simulation is, I will never be able to drink it. Simulations are not real.

First, I recommend you to read this and this, since they explain my view quite nicely.


Axiom 1 – Simulation of concrete objects is never complete regardless of the complexity of the simulation.

Axiom 2 – Simulation of abstract objects can be complete.

Regarding Axiom 2, then: what is the difference between a simulated song and a real song? There is no difference because:

First: Simulations are data.

Second: Abstract objects are data

Third: Songs are abstract objects.

And the above holds even truer for a complex and abstract “object” as the human mind.


If you want your question to be added (and replied) write the question in the comments and I will add it to the list of objections. 😉

Artificial Intelligence and the Turing Test: A Coffehouse Conversation —

Artificial Intelligence and the Turing Test: A Coffehouse Conversation

What is intelligence? No one knows exactly what it is.

Can machines think? Well if we just stated that no one knows what exactly intelligence is, the answer seems to be no.


Axiom 1 – Humans are intelligent.

Axiom 2 – Intelligence is nowhere to be seen but one can be fairly right in saying that cognition supports intelligence, this is, intelligence stems (nothing to do with the term “cause”) from thinking processes.

Axiom 3 – Whoever (or whatever) thinks like a human is intelligent.

Alan Turing

This is part of the inferences that drove computer scientist and A.I. advocate Alan Turing, to devise an experiment which if passed by a machine, it should be considered intelligent.


Summary of the Turing Test

Three rooms. Three participants.

One interrogator, and two “players” A and B, one of them being a machine. Of course, the interrogator does not know which is the machine.

Three rooms (one for each participant)  isolated from each other except for a text-only communication system where questions (or natural convesation) are typed by the interrogator. If the interrogator fails to discern which is the machine (A or B) then the machine is said to be as intelligent as a human.

From Hofstadter’s Mind’s I, I take one of the chapters where the Turing Test  is discussed quite nicely.

Coffee house Conversation