"The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits." G.K. Chesterton

Wednesday, December 14, 2016

Auto Capgras delusion.



Capgras delusion is a disorder whereby a person holds a delusion that a friend, spouse, parent, or other close family member (or pet) has been replaced by an identical-looking impostor. 

I was wondering this morning what it would be like, if possible at all (I think it may be) to suffer from the peculiar case of Capgras delusion, whereby one believes themselves to be an impostor.

A paraconsistent emoji.

Whose smile is both dead and alive at the same time.


Monday, December 12, 2016

#NotAll: a game.

This is an early draft, so it contains some repetition, and is bound to contain some omissions and even minor errors. I'd love to hear what people think. Any feedback, suggestions and criticisms are most welcome! :)

GAME IDEA
This is just a very early, rough draft. It is initially intended to be a physical board game like Scrabble or Monopoly or Chess, but I see no reason why it couldn't be simulated as an application. 
The game is a bit like logical scrabble, with the key difference being that you're describing an object (a toy possible world) rather than just concatenating letters to create words. So the sentences you formulate in this game are meaningful in a way that words are not in Scrabble. It would be no trickier than Scrabble in one sense and chess in another sense. 
The idea of the game is to make true, first order logic sentences about toy possible worlds, which consist of and only of different species of animals, incorporating elements of both deductive and inductive reasoning. So the purpose of the game is to have both educational and entertaining value.

MOTIVATION
Speaking well is a knack. Speaking well and truly is a virtue.
The game could be for those that teach introductory logic, or any other subject for that matter, who would play with their students---the game should be graspable to 10 year olds, and appealing to nerds and smart kids in general. So all people who like puzzle games would benefit from its entertainment value, and teacher-student combos would benefit from its educational value. And not only the educational value of sharpening their linguistic and reasoning skills, but also reinforcing knowledge about the hierarchical relationships present in any subject matter, e.g. take the Linnean taxonomy, geometrical figures, numbers, or even philosophy! 

LANGUAGE
- The language is mondaic first order logic. Moreover it's simplified to consist of atomic formulas only (and their negations), so to that end we employ bounded quantification. To make things easier no other logical connectives aside from negation are used. In addition, each animal comes in various colors (say, green, pink, blue), and can be either happy or sad (in future versions of the game I foresee animals that can be both or neither).
- So the kind of sentences that are made would be for instance 'All giraffes are happy', 'Not all green giraffes are sad', 'Some snakes are red', 'Some happy snakes are blue', 'All happy pink animals are horses', etc. (We could also partition the species of animals into classes, like mammals, reptiles, birds, fish, and add the corresponding predicate letters to the language.)
- The bounded quantification approach works in a way to dispose of the need of any other connectives except negation. 
Remember that the universe is 'Animals', so instead of saying 'For all Animals x, if x is Green then x is Happy', we say 'For all Green Animals x, x is Happy'. This way we have replaced the need to use the material conditional connective, by shifting the role of the antecedent to that of restricting the range of the universal quantifier 'All Animals'. 
Similarly with existential quantification instead of saying 'There exist Animals x, such that x is Blue and x is Sad', we say ''There exist Blue Animals x, such that x is Sad'. Similarly, as in the previous example we have replaced the need to use a connective corresponding to conjunction, by shifting the role of one of the conjuncts to that of restricting the range of the universal quantifier 'All Animals'. 



STARTING OFF
- Players have an unlimited number of universal quantifiers to start off with.
- Predicate letters (species, animal classes, colors, attitude), negations and existential quantifiers are drawn at random from a box.
- Animals are drawn at random from a box.
- The game starts off with a handful of animals, say 5, picked at random, and placed randomly on a 8x8 grid, say, which constitutes the initial state of the world.

RULES & TURNS
- Quantification over empty domains is not allowed. Consequently sentences that quantify over an empty domain (in a given turn) receive no points.
- After the world has been created, players draw at random from a box of predicate letters, existential quantifiers and negations, and subsequently aim to formulate true sentences about the world. That's how points are earned. Obviously drawing a negation would be a little like drawing out an existential quantifier, since we have unlimited universal quantifiers, so saying 'Some giraffes are sad' and 'Not all giraffes are happy' are both equivalent, but whether the existential quantifier or the negation will be useful will depend on the predicate letters (happy, sad) that we have already drawn out (and hence at our disposal), and the state of the world.
- Once players have picked some predicate letters they can either construct a true sentence, if possible, or draw from the box of predicate letters,negations, and existential quantifiers again, or draw from the box of animals to add another animal to the world.
- The reason why existential quantifiers are scarce is because true existential sentences cannot be falsified, unless we introduce the dying off of random species or individuals (or any class, i.e. species, animal class, color, attitude) every couple of turns.



- Obviously true universal sentences at some stage of the world (any given turn) may be falsified, whereby someone draws out and adds an animal to the world that is a counterexample to that sentence. This is the key, inductive element in the game.
- So it would be a good idea to strategize probabilistically with the universal claims, by hedging one's bets via varying the restrictions of the universal quantifiers. That is, it's easier to falsify 'All crows are blue' than 'All happy crows are blue', since any (happy or sad) non-blue crow falsifies the former sentence, but only a happy non-blue crow falsifies the latter. But then scoring should reward strong hypotheses, i.e. more easily falsifiable hypotheses. I turn to that matter in the next section.
-Once sentences become falsified, their components (i.e. predicate letters quantifiers and negations) can be used to formulate another sentence.
-In any given turn a player can dismantle their true universal sentence X in order to use its components to formulate another sentence Y. In that turn X shall cease to receive points and Y shall receive (or starts receiving) points instead. One may want to do this if they have gathered sufficient predicates to formulate a universal sentence that has a higher score.
-Similarly, in any given turn a player can dismantle their true existential sentence X in order to use its components to formulate another sentence Y. Then X contributes zero to the final score, unless we introduce random dying off of individuals.




POINT SYSTEM & SCORES
There is a set number of turns, and the objective of the game is to end up with the highest amount of points after the last turn.
- For example we may set say 100 possible individuals, e.g. 10 species, 5 colors, 2 attitudes. 
- The game starts with 5 randomly picked individuals.
- Existential sentences are worth less then universal sentences and get a once-only score (unless we introduce dying off of individuals), whereas universal sentences accumulate points, each turn, for as long as their truth "survives". So the final score that an universal sentence gets at the end of the game is how much it is worth, multiplied by the number of turns that it stays true. The score of universal sentences will be proportional to their quantifier's range, or more precisely, to the probability of the sentence's counter-example. Let me explain the rationale behind this in the following example.

EXAMPLE: Consider a world consisting of animals, of which half are sad and half happy, and each animal is either blue or red with equal probability. We can represent the individuals occupying that world by the set {B, R} x {H, S}, e.g. (B,H) corresponding to a Blue and Happy Animal. Now consider the sentences 'All Animals are Happy' and 'All Blue Animals are Happy'. The probability of a counterexample to the first sentence is P(~H|A) = 1/2, because there are as many happy as unhappy (sad) animals. Similarly, the probability of a counterexample to the second sentence is P(~H|A & B) = 1/4, because half of all animals are blue, so not just any sad animal would suffice for a counterexample here (as it did for the first sentence) but one that on top of that is blue. We could transform those probabilities to some integer values for the actual score, so perhaps have P(X)=1/n give a score of  |A|/n, where |A| is the total number of animals.



- Existential claims would be a function of their strength, since you need more predicate letters (remember you only are allowed to draw one per turn) to create a stronger one, e.g. 'Some cows are happy' would be less valuable than 'Some blue cows are happy'. I'm inclined to set the score for existential sentences to be inversely proportional to the probability of their truth. Here's the rationale. It's not only easier to make weaker true existential claims, because they're more likely to be true, but also formulating stronger claims requires more predicate letters, and you only get one per turn. So following the world from the above example, and sentences 'Some animals are happy' and 'Some Blue Animals are Happy', we see that the probability that the first one is true is P(H) = 1/2 (so the score would be, say 2) and the probability that the second one is true is P(H & B) = 1/4 (so its score would be, say 4).

A scoring system as described above would introduce an incentive to strategizing, but to be honest I'd prefer a game that focuses on the linguistic and logical aspects, rather than the quantitative ones that involve sophisticated probabilistic strategizing that gives the players an edge. If the game was an application, then the scoring could be done automatically, so players would just follow their natural (and naturally flawed :) intuitions, making the game that much more fun! :)

APPLICATION VS PHYSICAL BOARD GAME
- I had this idea, if the game was an application, the app would prompt you about the aletheic state of your sentences, e.g. to have true sentences light up green. Similarly, have the app prompt you whenever one of your sentences becomes falsified by a change in the state of the world (i.e. addition of counterexample animal, or random dying off of an animal) by having the sentence light up as red. This would be very helpful, so you don't have to keep track of the aletheic state of all your sentences. You could then re-use the elements that make up that false sentence to construct another one. Also if the game was to be an application, all the scoring would be done automatically.
- The random dying off of individuals could be made by having the world as a grid, say 6x6 or 8x8 or 12x12 and you'd throw a pair of dice for each coordinate to determine the individual that dies. Of course all of such physical limitations (Platonic solids as dice, or other contraptions) would be easily surmounted if the game was an application.
If created as an app the toy possible worlds could be customized by potential players themselves to fit any subject matter they like; not merely animals, but fantasy characters, aliens, numbers, geometrical shapes etc. as well.

DESIGN
I'm currently making some mark-up "screenshot" sequences of turn-pairs that illustrate the general idea for the design, and some key ideas. I'm hoping to get them done by the end of December 2016.

Saturday, November 5, 2016

Into the blizzard.

You find yourself stranded during a heavy blizzard, in a town far away from home. It's dark, since the streetlights do little to overcome the thick torrent of heavy snow. Your phone is dead. The streets are deserted with no taxi or bus in sight. As you stagger along the snow covered footpath, with you eyes closed tightly to avoid the stinging bombardment of crystals against your face, your suddenly realize that you're right on the street next to where someone whom you know lives. Unfortunately this someone is no other than your lifelong, bitter enemy, and you know they feel the same way. You open one eye and see that the lights in the house are on, glowing with a warm and welcoming glow. You make a life changing decision and with great effort literally crawl up the icy steps toward the door. Then just as you lift your hand to knock, and brace yourself to bear all the humiliation and loss of dignity that will surely accompany the act of turning for help from the last person in the world that you would ever consider talking to, you suddenly recall another thing about them. They hate cats! You turn away from the door and decide to push on.

Wednesday, October 12, 2016

Cognitive dissonance and belief revision in perilous political discourse.


This is only a free rumination on one aspect of the role that cognitive dissonance plays in political belief revision, with particular attention to the role of perceived self-image.

We need look no further than the comments sections beneath a random sample of online articles or videos that contain overt political content, to realize that public political discourse is—more often than not—far from polite and respectful. Tendentious rhetoric and insults are common there. And no one is spared—even those who have (naively enough) found themselves attempting the conversation with a genuinely open mind about having their own views revised if a good argument that challenges them presented itself. This phenomenon is most pronounced in cases where clearly identifiable, dichotomous for/against positions are present. Now I'll sketch out how cognitive dissonance regarding perceived self-image can hinder belief revision, in particular how it can lead to a tendency of entrenching one's views
even those that have been previously held only tentatively. Central to this dissonance is the contribution of unpleasant experiences acquired from engaging in careless political discourse with anonymous others.

Here I focus on that entrenchment being precisely the result of cognitive dissonance rather than a rational process. One needs to look no further than the aforementioned discourse space, to find people engaging in disingenuous rhetoric or contemptuous criticism, which often escalate to outright insults. The insults in most cases center around the following personal attributes: knowledge, cognitive faculties, and moral integrity. It's safe to assume that most people don't ascribe to a self-image as described by such disingenuous criticism or outright pejorative combinations of epithets aimed at the aforementioned personal attributes. That is, people prefer to think of themselves as not being completely ignorant, especially when speaking out on issues that matter to them; also, unless a medical diagnosis states otherwise, they prefer to think of themselves as not being in any way cognitively impaired; and finally they prefer to think of their beliefs as not being morally questionable. So by making the occasional error of engaging in discussions on unmoderated forums, where trolls abound and where other interlocutors often display no more conversational etiquette than trolls, one puts one's self-image at peril, and as a result gathers painful resentment toward "the other side" over time.

As a consequence one will tend to become more entrenched in one's beliefs. Why? Because changing one's view (in cases of issues with clear-cut for/against positions) would almost amount to agreeing with those who had previously expressed contradictory views to one's own regarding their self-image. But this is unacceptable (to most), as it would be treading very closely to tacitly condoning views that contradict one's self-image. After all, conceding that someone who holds such contradictory views can be right about some things
in particular those things that prompted them to make a contradictory judgement regarding others' self-imageis not too far from saying that they may also be right about that very judgement. Or to put it another way, if someone is right about some things, then their judgement about those who fail to see those things as right may very well also be right. Mental discomfort resulting from such doubt is an instance of cognitive dissonance.

Generally, conceding to the correctness of a view previously held as incorrect may indeed prompt many to consider revising their self-image—there's an implication of certain unfitness of some of the aforementioned personal attributes—after all, how could one have been wrong for so long? In this case however the inclination to revise one's belief is additionally hindered because it entails agreeing with people who explicitly hold contradictory views regarding one's self-image. Hence the strong inclination to escape this cognitive dissonance, resulting in a tendency to (irrationally) stick with one's original position/view. Indeed, seeing the degree of emotional engagement in political discourse that people display, would make one think that it's not the broader issues that are being defended but something more personal.

Wednesday, June 15, 2016

MÓJ PRZYJACIEL PAWIAN

Odnalazłem fragmenty moich dawnych prób pisania dla dzieci, z circa 2004.

Wszystko zaczęło się od zeszłorocznego wyjazdu na działkę. Lało przez całe dwa tygodnie przez co Leon zostawał sam w domku letniskowym podczas gdy jego rodzice zbierali jabłka i śliwki w sadzie. Tata po każdym powrocie mówił że jeśli nie zebrałoby się tych owoców to przy tej pogodzie sad zamieniłby się w gigantyczną misę kompotu jabłkowo-śliwkowego. Leon na początku nie uważał że taka ogromna misa kompotu byłaby czymś złym, ale po dłuższym zastanowieniu stwierdził że nie ma wystarczającej ilości słoi i butelek aby ten kompot rozlać i w końcu że taką ilość kompotu mógłby chyba tylko wypić jakiś wielkolud albo smok. Niestety okolicy działki nie mieszkał ani żaden smok ani wielkolud, więc Leon stwierdził w końcu, że rzeczywiście rodzice mają rację zbierając opadłe owoce.

I właśnie tego trzeciego jakże nudnego poranka, podczas gdy Leon przeglądał po raz już chyba piąty jedyną książkę w domku, którą była „Historia Naturalna”, pojawił się ów gość. Był to nie mniej i nie więcej pawian we własnej osobie, a właściwie we własnej sierści. Siedział sobie jak gdyby nigdy nic w fotelu i łypał dyskretnie na chłopca swoimi małymi ślepiami. Pewnie myślał że nikt nie zauważył jego pojawienia się. Zuchwalec. Jak można tak po prostu pojawić się z nikąd bez zapowiedzenia? Leon nie omieszkał uświadomić tego pawianowi: „Trzeba było przynajmniej zadzwonić, jeśli nie na domowy telefon to na komórkę mamy, a jak już tak to przynajmniej powinno się powiedzieć dzień dobry.” Jak się okazało pawian był nie tylko impertynentem ale i niemową.

Mimo nienajlepszego zachowania Pawiana, Leon postanowił zainteresować go „Historią Naturalną”. Nietrudno się domyśleć że książka bardzo się gościowi spodobała; prawie przez cały czas przesiedział na oparciu fotela podskakując z wrażenia przy każdej kolejnej fotografii. Uśmiechał się dosłownie od ucha do ucha, i właśnie przy tych szerokich uśmiechach Leon zauważył, że jego gość zaniedbuje nie tylko maniery, ale i też higienę osobistą, a właściwie małpią.

Pawian zupełnie nie proszony wpakował się do samochodu, gdy nadszedł czas powrotu do domu. Leon nie protestował – przynajmniej nie było nudno. Ciekawe że rodzice w ogóle nie zwracali uwagi na dodatkowego pasażera; „To nawet lepiej” pomyślał Leon zadowolony z faktu że nie musi tłumaczyć rodzicom okoliczności pojawienia się pawiana.  C.D.N.

Postanowiłem poprosić Chat GTP 4 aby dopisał kolejna opowiastkę o Leonie i Pawianie. Wynik jest mniej satysfakcjonujący niż się spodziewałem, mimo tego że podobny eksperyment w przypadku opowiadania Immoral trip wypadł znacznie lepiej.

PROMPT: Mam pomysł na serię opowiastek o Leonie i jego wyobrażonym przyjacielu (pawianie). Napisałem już pierwszą, wstępna opowiastkę, gdzie poznajemy głównych bohaterów. Jest to pewnego rodzaju pilot. Chcę abyś napisał kolejną część -- czyli kolejna opowiastkę. Może tym razem rozgrywającą się w domu lub przedszkolu. Nie było to jeszcze powiedziane, ale Leon ma około pięciu lat. Oczywiście chciałbym aby było to zrobione w tym samym stylu i konwencji -- dziecinne przemyślenia i obserwacje Leona oraz ciekawe zachowania pawiana, no i aby była tej samej długości co pierwsza. Puść wodze wyobraźni!

Chat GTP 4:

Leon i pawian w przedszkolu

Leon uwielbiał chodzić do przedszkola. Lubił rysować, śpiewać piosenki i bawić się z rówieśnikami. Jednak pewnego ranka, gdy mama pomagała mu ubrać się i przygotować do wyjścia, Leon poczuł, że ten dzień będzie nieco inny. Zauważył bowiem, że jego wyobrażony przyjaciel, pawian, również wydaje się być w doskonałym nastroju i z niecierpliwością czeka, by pójść z nim do przedszkola.

Do przedszkola chodziło wiele dzieci i każde z nich miało własne małe zwariowane pomysły. Jednak pawian był czymś zupełnie wyjątkowym. Oczywiście tylko Leon go widział, ale to nie przeszkadzało mu w zabawie z innymi.

Kiedy nauczycielka poprosiła dzieci, aby narysowały swoich ulubionych przyjaciół, Leon postanowił namalować pawiana. Jego rysunek odznaczał się żywymi kolorami i dokładnymi szczegółami - od szerokiego uśmiechu pawiana po każdy włos na jego futrze. Kiedy przyszedł czas na prezentację rysunków, Leon z dumą opowiadał o swoim wyjątkowym przyjacielu. Dzieciaki były zafascynowane i chciały wiedzieć więcej.

Na przerwie w ogrodzie przedszkolnym, Leon opowiadał innym dzieciom o przygodach z pawianem. Jak przyszedł do niego na działkę, jak wspólnie przeglądali książkę i jak wsiadł do samochodu, wracając do domu. Wszyscy słuchali z otwartymi ustami.

Pawian, z zachwytem obserwując dzieci, postanowił zasugerować Leonowi nową zabawę. Wykorzystując gałęzie drzewa jako liany, podskakiwał z jednej na drugą, udając tarzającego się małpę w dżungli. Leon natychmiast dołączył do niego, a reszta dzieci śmiała się i klaskała w dłonie.

Po powrocie do domu, Leon miał mnóstwo historii do opowiedzenia rodzicom. O tym, jak wspaniale bawił się w przedszkolu z pawianem i jak wszyscy byli zafascynowani jego wyimaginowanym przyjacielem. A pawian? Siedział sobie spokojnie na fotelu w pokoju Leona, ciesząc się kolejnym dniem pełnym przygód.

Zachód słońca oznaczał koniec dnia, ale dla Leona i pawiana była to tylko kolejna strona w ich nieskończonej książce pełnej cudownych chwil. C.D.N.


Wednesday, March 23, 2016

There is no distinction without similarity.

Moreover, it seems that there even can't be a distinction without similarity. For it's impossible to distinguish any two objects without both of them being at least similar in the sense of being objects of consideration in the first place (or just objects, existent or not, for that matter)---that being their necessary condition (similarity) for comparability and hence distinction. This gives similarity a foundational character. The converse need not be true however, since in order to consider a single object as identical (maximally similar) to itself it doesn't seem obvious that one needs to resort to the consideration of it being distinct from anything else. The immediate corollary of this, if not a mere reformulation, is that there are no absolutely distinct (absolutely independent) things (there, the proof is in the formulation itself---things!). If this is true, then absolutely everything is similar in one way or another and as such admits to a similarity analysis. And there don't seem to be any paradoxes at the limits either, since even any totality of things (even the Russel set) is similar to itself, as is nothing, for that matter. Even everything and nothing are similar in the sense of belonging to the same ontological category. So the only questions to which much ontological inquiry reduces are "in what manner are things similar?" and "to what extent are they similar?"