Posts Tagged ‘Socrates’
Idiosyncrasy in “conjectures”; (Dec. 21, 2009)
Idiosyncrasy or cultural bias relates to “common sense” behavior (for example, preferential priorities in choices of values, belief systems, and daily habits…) is not restricted among different societies: it can be found within one society, even within what can be defined as “homogeneous restricted communities” ethnically, religiously, common language, gender groups, or professional disciplines.
Most disciplines have mushroomed into cults.
A cult is any organization that creates its own nomenclature and definition of terms to be distinguished from the other cults in order to acquiring recognition as a “professional entity” or independent disciplines that should benefit from laws of special minorities (when mainly it is a matter of generating profit or doing business as usual).
These cults want to owe the non-initiated into believing that they have serious well-developed methods or excellent comprehension of a restricted area in sciences. The initiated on multidisciplinary knowledge recognize that the methods of any cult are old and even far less precise or developed; that the terms are not new and there are already analogous terms in other disciplines that are more accurate and far better defined.
Countless experiments have demonstrated various kinds of idiosyncrasies. This article is oriented toward “cult” kinds of orders, organization, and professional discipline. My first post is targeting the order of mathematicians; the next article will focus on experiments.
Mathematics, meaning “sure study” (wisekunde), has no reliable historical documentation. Most of mathematical concepts were written many decades or centuries after they were “floating around” among mathematicians.
Mathematics is confusing with its array of nomenclature. What are the differences among axiom, proposition, lemma, postulate, or conjecture? What are the differences among the terms, theorem, questions, problems, hypothesis, corollary, and again conjecture? For example, personally, I feel that axiom is mostly recurrent in geometry, lemma in probability, hypothesis in analytical procedures, and conjecture in algebraic deductive reasoning.
Hypothesis is in desuetude in mathematics. For example, Newton said “I am not making a hypothesis”.
Socrates made fun of this term by explaining how it was understood “I designate hypothesis what people doing geometry use to treating a question. For example, when asked for their “expert opinion” they reply: “I still cannot confirm but I think that if I have a viable hypothesis for this problem and if it is the following hypothesis… then I think that we may draw a conclusion. If we have another hypothesis then another conclusion is more valid.”
Plato said: “As long as mathematics start from hypothesis instead of facts then we do not think that they have true comprehension, since they are not going back to fundamentals”
Hypothesis is still the main term used in experimental research. Theoretically, an experiment is not meant to accept a hypothesis as true or valid, but simply “Not to reject it” if the relationships among the manipulated variables are “statistically significant” to a pre-determined level, usually 5% in random errors.
Many pragmatic scientific researchers don’t care about the fine details in theoretical mathematical concepts and tend to adopt a hypothesis that was not rejected as law. This is one case of idiosyncrasy when the researcher wants badly the “non-rejected” hypothesis to represent his view. Generally, an honest experimenter has to repeat the experiment or encourage someone else to generalize the results by studying more variables.
Conjecture means (throwing in together) and can be translated as conclusion or deduction; basically, it is an opinion or supposition based on insufficient proofs.
In the last century, conjectures were exposed in writing as promptly as possible instead of keeping them floating ideas, concepts, or probable theorems. This new behavior of writing conjectures was given the rationale that “plausible reasoning” is a set of suppositions thrown around as questions mathematicians guess they have answers to them, but are unable to demonstrate temporarily.
The term conjecture has been used so freely in the last decades that Andre Weil warned that “current mathematicians use the term conjecture when they fail after a few attempts to verify a concept, even if the problem is of no importance.” David Kazhdan ironically warned that this practice of enunciating conjectures might turn out like a 5-year Soviet plan.
At first, a set of conjectures was meant to be the basic structure for a theorem or precise assertions that were temporarily used in the trading of logical discussions. Thus, conjectures permit the construction of rigorous deductions that are accessible to direct testing of their validity. A conjecture was a “research program” that move ahead in order to foresee the explored domain.
Consequently, conjecture is kind of extending a name and an address to a set of suppositions and analogies for a concept, long before tools and methods are created to approach directly the problem.
A “Problem” designates a mental task submitted to the audience or targeted for research or project; usually, the set of problems lead to demonstrating a general theorem. Many problems are in fact conjectures such as the problem of twin primary numbers that consists of proving the existence of an infinity of coupled numbers such that p-q = 2.
One of the explanations for using freely the term conjecture is the modern facility of mathematicians of discriminating aspects of uncertainty at the theoretical level. It is an acquired habit, an idiosyncrasy. Thus, for a mathematician to state a conjecture he must have solved many particular cases and recognize that a research program is needed to developing special tools for demonstrating the conjecture. This is a tough restriction in this age where time is of essence among millions of mathematicians competing for prizes.
“Sophie’s World” on David Hume; (Written on Dec. 4, 2009)
How I stumbled on Jostein Gaarder’s “Sophie’s World”, one of New York Times best seller?
My niece is reading this book as required textbook in high school. The manuscript is of 513 pages divided in 35 chapters and talking of a wide array of philosophers and concepts from Socrates, to Descartes, to Hume, Hegel, Kant…, Freud, and the Big Bang.
A short introduction to the story might be entertaining.
The first chapter introduces us to Sophie Amundsen, a 15-year-old girl. Sophie arrives home from school and finds a first envelope addressed to her. The sheet of paper has a single hand written sentence “Who are you?” Sophie finds another envelops that says “Where does the world come from?”
The last delivery of the mailbox is a postcard “Hilde Moller Knag; c/o Sophie Amundsen, 3 Clover Close. Dear Hilde, happy 15th birthday. Forgive me for sending the card to Sophie. It was the easiest way. Love Dad.”
Sophie knows of no Hilde and the phonebook was of no help. Sophie has now three problems to resolve, all in one day. Sophie is baffled and confused: She is starting her philosophical initiation. Would Lillemor be the same person? If her hair was not straight and defying all cosmetics for a curly appearance, then would she behaved different? If her nose was a tad bit longer or her mouth smaller, would she be the actual Sophie?
The next problem is even harder to reflect on. Can anything come from nothing? If not, then how far has she to go to the sources in the creation process? Can a creating God come from nothing?
I jumped to page 267 on the British philosopher David Hume (1711-1776).
Hume was the contemporary of Voltaire and Rousseau or the Age of Enlightenment. The previous Age was of the “rationalists” such as Descartes, Lock, and Spinoza.
Hume published his main work “A treatise of human nature” when he was 28 of age. He claims that he got the idea when he was 15.
The empiricist Hume (believing in experiments as the most valid method for acquiring knowledge) said:
“No philosophy will ever be able to take us behind the daily experiences or give us rules of conducts that are different from those we get through reflections on everyday life.”
For example, people have experienced or sensed wings on birds, but that does not mean that the complex idea of “angel” exists. Angels are associations in man’s imagination; thus, the concept of angels is false as an experienced reality and should be rejected from the knowledge baggage.
If a textbook does not offer any experimental reasoning concerning matter of facts and existence then it should be committed to the flames as a book of knowledge.
Hume wanted to know how a child experienced the real world. Hume established that man has two types of perceptions:
1. impression (immediate sensation) and
2. ideas of external reality.
Ideas are recollections of impressions. For example, getting burned is not the same sensation as remembering getting burned: this would be a pale imitation of actually the stronger feeling of being burned.
Ideas can be simple or complex; we may form complex ideas of the world for which there is no corresponding “object” in the physical world such as angels or God. Each element in the complex idea was previously sensed and the mind constructed a “false object” if not actually existing for the senses.
Descartes indicated that “clear and distinct” ideas guarantee that they corresponded to something that really existed.
One example for Descartes affirmation is the ego “I”, which is the foundation for his philosophy.
Hume begs to differ.
Hume considers that the ego I is a complex idea and constantly altered. Since we are continuously changing our alterable ego is based on a long chain of simple impressions that we did not experienced simultaneously. “These impressions appear, pass, re-pass, slide away, and mingle in infinite varieties of postures and situations.” It is like the images in a movie screen: they are disconnected single pictures, a collection of instants.
It is the same concept of Buddha (2500 years earlier). Buddha said “There is nothing of which I can say “this is mine” or “this is me””. Thus, there is no “eternal soul” since “Decay is inherent in all compound things. Work out your own salvation with diligence.” Hume rejected attempts to prove the immortality of the soul or the existence of God but he never ruled out their possible existence or that of miracles.
On his deathbed, Hume said “It is also possible that a knob of coal placed upon the fire will not burn.”
A miracle works against the laws of nature; but again, we have never experienced the laws of nature.
All that we know results from “habit” of our experiences, such as witnessing relationship or “cause and effect” occurring many times, but that we can never say that it might happen “always”.
For example, adults are more awed by magic tricks than children: a child is no more impressed by an apple falling or just floating because he didn’t acquire the habit in his mind for natural occurrences. Expectations lie in our mind and not in one thing following another.
We human are great in the task of cutting and pasting everything that impresses upon us. Hume says that the preconditions to assembling complex ideas is to have entered all the elements in the form of “simple impressions”. If we imagine God to be infinitely “intelligent, wise, and good being” then we must have “known intelligence, wisdom, and goodness”.
(How man brought in the “infinitely” in his concept? Did it come from watching the sky as a substitute to the experience of infinity? Somehow, man is able to extrapolate on piece meal experiences).
Hume wanted “to dismiss all this meaningless nonsense which has long dominated metaphysical thought and brought it into disrepute.” (The introduction of the term metaphysical gave terrible nightmares to the succeeding philosophers fearing that they might sound metaphysical and had to explain at great length their concepts).
Hume cut off the final link between faith and knowledge.
(I conjecture that the deficiencies of our perceptual senses provide rich sources of strong impressions that modify our view of the real world. For example, when we see double for a while (a temporary affliction), or we feel the ground waving and shaking under our feet when drunk, or under the influence, or when we hear background noises, then these sensation are real first impressions and not just ideas.
Thus, the weaker our constitution, the more acute and varied are our experiences; the more adapted our brain for capturing associations the far more complex is our perception of the world.)
Adonis Diaries 