Provincianismo

Saturday Morning Breakfast Cereal

Mathematical realism

Mathematical realism defends that mathematical objects have independent existence outside minds. In this view, mathematics is more about discovering an unknown world than just creating formal coherent maps. This position seems to me an indisputable matter of principle, an aesthetic position that cannot be decided, a modern version of the ancient theory of Plato's forms.

Math is the paradigm of objective knowledge but I feel suspicious when that is used to imply their external existence. Beliefs can be objective or subjective but how can that tell us anything about external reality? An objective belief is a belief that does not depend on the agent's state of mind, but a belief nonetheless It does not directly follow that without minds objective beliefs would still exist (or could exist even before minds). What are the arguments to justify this step?

Another way to argue is to state the uncanny usefulness of mathematics. Some math models are surprisingly useful for science. However, there are potentially an infinity of different mathematical models. In our finite world we will always use an infinitesimal fraction of the mathematical formal structure. So, usefulness does not seem a strong argument in the defense of math realism: most of Math would be useless to explain a finite Universe (not enough world to use all those theorems).

Even restricting the realm of 'real' Math like Kronecker did when he said God made the natural numbers; all else is the work of man does not make things easier. In some alien world, the subset of Math they'll use may be very different from our own. Eg, in a plasma world -- where everything would be in flux and no solids would exist -- natural numbers (0,1,2...) might not make the least practical sense for its inhabitants and they would be as known to the average plasma-mind as manifold theory is to our carbon-minds. So, even those most basic of math concepts, like naturals, might not be as natural as we think they are. And stating that Human «natural Math» is the one that is «real» seems just provincialism.

Original posting & discussion: https://plus.google.com/u/0/107157321007785956289/posts/4abeMMDY2Qx

Saturday Morning Breakfast Cereal

Fora do circuito

Fora da academia, do que é considerado conhecimento estabelecido, há um grande conjunto de obras de variado valor. A história da ciência, da filosofia e da matemática mostra variados exemplos de pessoas que defenderam ideias fora do sistema, tendo algumas delas sido ostracizadas e até levadas ao suicídio, cujas ideias que defendiam vingaram e tornaram-se respeitadas e até mesmo no próprio sistema. Casos como os infinitos de Cantor, a interpretação estatística da Termodinâmica de Boltzmann ou as ideias de Nietzsche são disto bons exemplos.

Mas será arrogante assumir que o desenvolvimento do conhecimento humano não tem falsos positivos (ideias vigentes que não são as melhores entre as disponíveis) e falsos negativos (ideias erradamente rejeitadas por preconceito, desconhecimento ou falta de evidência). Entre os falsos positivos destacam-se, a meu ver, a Economia Clássica (com o seu axioma do agente racional já falsificado empiricamente, eg, cf. Kahneman, Thinking Fast and Slow) e a Estatística Clássica, onde o principal adversário, a Inferência Bayesiana, teve um renascimento com o advento dos computadores mas que continua persona non grata da academia (era pior há umas décadas). Entre os falsos negativos ficaremos, em alguns casos, na eterna dúvida se um dado autor teria mesmo razão, no sentimento vago de estarmos a perder alguma coisa importante. Claro que um sistema conceptual recusado não possa ser resgatado parcialmente. A sociedade pode absorver parcelas que as torna suas, sem ter de digerir a totalidade do que o respectivo autor defendeu. 

Entre os autores destes potenciais falsos negativos encontro especial interesse nos seguintes:

Julian Jaynes: The origin of consciousness in the breakdown of the bicameral mind. Neste livro é defendida uma tese que o nascimento da consciência humana é um fenómeno historicamente recente (por volta da Grécia Antiga, entre Homero e Péricles) e que os humanos anteriores a essa época ainda não eram pessoas. Não consigo fazer juz ao livro mas é muito interessante e bem escrito, e como seria interessante perceber que Jaynes afinal tinha tido razão!

Thomaz Szasz: The Myth of Mental Illness (entre outros livros deste autor). Szasz é um médico que há décadas critica a forma como a profissão psiquiátrica categoriza a doença mental. Em parte, algumas das suas teses foram absorvidas pelo mainstream, sendo provável que a sua posição actual seja mais extremada do que justificariam os procedimentos actuais. Apesar disso uma consulta à DSM, que classifica por exemplo o travestismo  como doença mental, nos deixe a pensar que talvez ainda haja muito trabalho a fazer nesta frente.

Alfred Korzybski: Science and Sanity. É deste livro que vem o aforismo "o mapa não é o território" e a sistematização da ideia que as teorias e conceitos humanos não têm existência para lá de nós mesmos. De certa forma, apesar da ostracização que sofreu (o livro é realmente um bocado alucinado) estas ideias vingaram e são muito presentes na nossa cultura. Hoje em dia é mais fácil afirmar que uma teoria é «apenas» o mapa de um padrão reconhecido do que fora no passado. Não esqueçamos que no início do século XX ainda se discutia ao mais alto nível científico se a luz tinha uma natureza corpuscular ou ondulatória, como se a luz fosse realmente ou uma partícula ou uma onda.

Teatro

The Universe is a messy and dangerous place. Fitness is not an optional policy in the natural selection perpetual genocide. The successful life-and-death stories of our ancient primate ancestors were imprinted in our genes. They still partially define, even today in our complex social world, what 'human' means. Our brains and bodies have default mechanisms that shape and limit our cognitive abilities, our ability to learn and remember, to reason and feel, to introspect. What we recognize as 'I'.

For fitness sake, the evolution of our actions, our behavior, converged to pursue (desire) certain sensations -- feelings, brain states -- and avoid (fear) others. Two examples are sexual arousal and pain, respectively. We are able to learn that different contexts favor different sensations. We adapt and manage our desires and fears to serve the multilayered goal of survival (multilayered in the sense of being made of several, more specific sub-goals but also for having multiple and not necessarily compatible solutions).

One powerful factor in this emotional and sensorial ecosystem is society. Society inhibits or enhances sensations, desires and goals through social conditioning not necessarily concerned with individual survival. One example is how nationalism is able to transfer and corrupt the genetic instincts of family into social norms to better serve the preservation of a national concept. However, this reshaping is not arbitrary, since it is impossible to remove our primitive genetic behavioral heritage without losing the person within. Humans minds are elastic but they are not blank slates. The resulting individual behavior turns out to be quite subtle in complex societies, forcing part of our genetic past into sleep mode, hardly detected in normal, non stressful situations. Herein, we are not that different from most social mammals.

But we humans are not satisfied with just that. Humans are active believers, constantly inserting meaning into the world stuff and into the mind stuff. We are addicted to belief and cannot help ourselves. One important side effect is value. A value is determined by the desire/fear intensity for a certain sensation. It is natural for us to classify a goal towards a attractive (repulsive) sensation has having a good (bad) value. And then that goal's value contaminates the cognitive architecture: a good (bad) goal must come from virtuous (vicious) desires and promotes right (wrong) actions. We elaborate enormous cognitive structures around the value concept. Ethics, Politics and Religion are basically arguments -- logical, empirical, traditional, dogmatic arguments -- to shape how values, virtues and righteousness are mapped. We feel that something has value, that acting such and such is right, but these are just instances of the mind projection fallacy. They are the result of our unrestrained use of meaning inception. They are internal mind attributes not external features of those somethings. We do not avoid something because it is bad, we define as bad those things we want to avoid.

This does not imply that meaning is arbitrary or relative. We are social animals after all, and share sensations, desires, goals. Our biology and cognitive apparatus is the same. So, at least for homo sapiens, this mapping does not have that much variability. Pain, say, is intrinsically a sensation to avoid. It is no surprise that violence towards other humans is usually considered a wrong action or that, for promoting violence, political and religious leaders choose first to dehumanize the enemy.

And where is consciousness in all this? Consciousness is not necessary for this sensation/desire/goal structure nor for the resulting behavior. Many different animals seem to be equipped with them and still don't seem to possess consciousness. Also, consciousness is not necessary for choice. A simple mechanism is able to make choices when faced with multiple options (even a thermostat has capacity for binary choice). A choice is the process of selecting an action among possible actions. It can be described in algorithmic terms (one classical definition is the maximization of expected utility) and, at least in its basic form, does not need cognition. However, perhaps consciousness provides value assignment to goals. Perhaps human consciousness includes (is?) our belief generator. Perhaps consciousness is a cognitive  and social contagious infection which the symptoms are persons. Who knows how to untangle a metaphorical web using just its metaphors?

We need beliefs to fictionalize an impersonal world, filing it with meaningful narratives, appropriate reasons and reasonable causes. We also need a world with persons. Other persons and ourselves. But an indifferent Universe does not offer anything like that, only pain and pleasure, life and death. So why not, collectively, make up everything else? 

"Hate Orgoreyn? No, how should I? How does one hate a country, or love one? Tibe talks about it; I lack the trick of it. I know people, I know towns, farms, hills and rivers and rocks, I know how the sun at sunset in autumn falls on the side of a certain plowland in the hills; but what is the sense of giving a boundary to all that, of giving it a name and ceasing to love where the name ceases to apply? What is love of one's country; is it hate of one's uncountry? Then it's not a good thing. Is it simply self-love? That's a good thing, but one mustn't make a virtue of it, or a profession... Insofar as I love life, I love the hills of the Domain of Estre, but that sort of love does not have a boundary-line of hate. And beyond that, I am ignorant, I hope." Ursula K. Le Guin, The Left Hand of Darkness

"There was kindness. I and certain others, an old man and one with a bad cough, were recognized as being least resistant to the cold, and each night we were at the center of the group, the entity of twenty-five, where it was warmest. We did not struggle for the warm place, we simply were in it each night. It is a terrible thing, this kindness that human beings do not lose. Terrible, because when we are finally naked in the dark and cold, it is all we have. We who are so rich, so full of strength, we end up with that small change. We have nothing else to give." Ursula K. Le Guin, The Left Hand of Darkness

"To oppose something is to maintain it. They say here "all roads lead to Mishnory." To be sure, if you turn your back on Mishnory and walk away from it, you are still on the Mishnory road. To oppose vulgarity is inevitably to be vulgar. You must go somewhere else; you must have another goal; then you walk a different road. Yegey in the Hall of the Thirty-Three today: "I unalterably oppose this blockade of grain-exports to Karhide, and the spirit of competition which motivates it." Right enough, but he will not get off the Mishnory road going that way. He must offer an alternative. [...] To be an atheist is to maintain God. His existence or his nonexistence, it amounts to much the same, on the plane of proof. Thus proof is a word not often used among the Handdarata, who have chosen not to treat God as a fact, subject either to proof or to belief: and they have broken the circle, and go free." Ursula K. Le Guin, The Left Hand of Darkness