Paradoxes

Note on paradoxes I. M. R. Pinheiro

Abstract: In this research note, we wish to discuss the idea of paradox and actually exclude the term from the scientific world of terms. Keywords: Sorites, Liar, Parallax, mistake, paradox, Bloom, taxonomy, science, standards.

1. Introduction

The inspiration for this note comes from the fact that we have proven, recently, that one of the best known paradoxes in Philosophy could not have been more than an equivocated interpretation of an allurement to exhibit the beauties of the natural language. We have, then, gone through all possible paradox classifications for the Sorites and proven that, at most, it could be a paradox of communication: Never of reference or of others. In an even more recent piece of research, we have managed to prove that the Liar Paradox is not a paradox either. The difficulty noticed in human kind, which allows

people to wrongly believe it is a paradox, is that of accepting the flexibility, diversity, and non-logical allowances that a human being has got on Earth, what actually can only make the World more perfect, not the opposite, as the people having problems with all that may think. It is definitely not an intention of Science to ‘box’ human beings in the same boundaries as an electronic equipment, perhaps it is more of an intention of Science at most using the electronic equipment to make human beings even more perfect, when they are found dissatisfied with some aspect of their lives or bodies, for Science has been created to improve the World and make it more comfortable, as well as acceptable, by human beings, not the opposite. Anything which confines human reasoning to machines will be limiting, by large, the human pleasure with both life and the World elements. It is not proper that a true scientist tries to confine any aspect of human normal interaction with the World into the machine world, for Science is there to solve the needs of human kind, not to change human kind: Still the same story, the same difference, between creating a new problem and solving the originally proposed problem… . Normal things become a puzzle only for those who do not accept the human degrees of freedom, especially in discourse. Trivially, there is no freer place to be at than the human expression, Arts there as evidence: From songs of only one word, or even none, to songs with different words from beginning to end, entire sound time taken by them… . In this paper, we hold only a few sections: development (2), conclusions (3), and references (4).

2. Development

Paradox is a word appearing defined, for instance, in [1]. In one of the most popular dictionaries in current use it reads: “Main

Entry:

par·a·dox

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'pa-rə-\

Function:

noun Etymology: Latin paradoxum, from Greek paradoxon, from neuter of paradoxos contrary to expectation, from para- + dokein to think, seem — more at decent Date: 1540. 1: a tenet contrary to received opinion2 a: a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true b: a self-contradictory statement that at first seems true c: an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises3: one (as a person, situation, or action) having seemingly contradictory qualities or phases``. Therefore, the undeniable characteristic of any event of scientific nature labeled as paradox, or pointed to as a paradox by any human being, must be containing at least two possible inferences, which have been inferred from the same set of premises, one clearly being the opposite of the other. The most famous paradox of all, most mentioned in the scientific literature, has to be what, after studied scientifically, has become the Parallax Mistake: ‘If from one angle of sight the liquid looks as if it is in the height I wish for in the tube, but from another it

does not, which sight is actually correct?’ The Parallax Mistake is then a paradox of sight, with the same eyes observing the same image, from different angles, yet reaching opposite conclusions. Once they noticed that there was one point of sight which was correct, the problem was solved. Once the problem is solved, there is no paradox anymore. Therefore, the word has been used to mean ‘unsolved problem’ throughout time. Once people solved that paradox of sight, calling it all, after solved, Parallax Mistake, rather than Parallax Paradox, which would definitely be its name, perpetuated in the scientific literature, if the area involved had been something more similar to language studies, it has never been considered as a problem anymore. Therefore, we could now easily remove the expression Sorites Paradox from the scientific literature, replacing all its occurrences with one of the following expressions: Sorites Mistake or Linguists’ Problem. Besides, the expression Liar Paradox could also be replaced with one of the following expressions: Sanity Judgment or Truth-value Mistake. Any scientific process must result in more accuracy, not in more confusion. Therefore, it would never be possible that the Sorites Paradox, or the Parallax Paradox, or even the Liar Paradox, were scientific issues, they would have to be only problems which remained unsolved by Science. Parallax has been found to be a mistake in human observation, or contemplation, of

things which are part of the human universe. Because of this, it is actually a paradox referring to the human part of life, not a paradox in Science, or regarding its objects, only a paradox for the own human beings, who see themselves as unable to accept they are not the same as the machines, what ought to imply that if they ever wanted to include their own opinion, observation, referentials, paradigms, in a scientific proposal of something, or solution, they would need a ‘third eye’ over them, once nothing that they may feel, think, or observe, may be told to be of scientific nature, all depending on the accuracy and noise contained in each one of their senses and integrity systems, which they, themselves, would be fully unable to judge or even describe. If it is a third human eye, the third eye will obviously suffer from the same problems and biases the own original human beings have suffered, therefore being as scientifically useless as the original human being posing obstruction to the scientific observations. The just mentioned third eye has become a machine for the Parallax Paradox, the lexicon theories for the Sorites Paradox, and a machine (liar detector) for the Liar Paradox. One must notice that the major pre-requisite to solve these problems (regarding characteristics of the ‘third eye’) is obviously both impartiality and detachment from the problem. In any hypothesis, the obvious conclusion is that there is no chance for a ‘scientific paradox’: Any paradox is the initial step in the scientific investigation, which actually precedes, usually, the own scientific problem, once any scientific problem must follow our previously mentioned rules for well-posedness in Philosophy, for every single piece of Science which exists will depend on the philosophical decisions on that level.

In each one of the just mentioned paradoxes, there is a word which immediately tells us that the proposed problem is not of scientific nature yet, actually implying that more refinement is necessary for it to become a scientific problem. Observe: •

In the Sorites Paradox, the word is the own adjective, or substantive, under discussion, word which depends on both personal experience and personal observation (heap, bald, and etc.);

•

In the Parallax Paradox, the word is ‘observation’, ‘eyes’, or others;

•

In the Liar Paradox, the word is ‘believe’.

Interesting enough, it all matches the studies and applications of the Bloom’s Taxonomy, a theory usually applied in Education for students' evaluation ([2]): In the Bloom’s theory, or in its applications, one easily finds a list of words which should tell the person, immediately, where the proposed exam question lies in the scale. We could easily add to the theory a list of words which take the exam question away from the objective share of knowledge and places it on the ‘impossible-to-evaluate-objectively` side of things, which would then coincide with our list for paradoxes, rather than scientific problems, trivially including the words just mentioned. In short, it should not be hard creating a list of words which should never be included in any scientific proposal, or formal school/university evaluation, which is objective, not formative. Just for starters, all feelings, as well as what derives from them, should never appear in

those proposals (love, liking, and etc.). Besides, no verbs, or derivations, attached to the human senses (smell, sight, hearing, and etc.) should appear in them either. There are still the verbs related to faith or religious feelings (to believe, to trust, and etc.). And these are just a few of the terms which should never be part of any scientific proposal, not even in Statistics.

3. Conclusions

We have, here, explained why the word ‘paradox’ must be simply seen as a close synonym for ‘problem sketch’ in what regards Science. In other words, whenever the word ‘paradox’ is seen in the scientific literature, one must immediately assume it actually refers to the sketch of a problem and detach their scientific minds from the original lexicon meaning for the sake of Science and what we all intend with it, which is progression towards both accurate and universal human reasoning. Besides, we have started developing a theory as beautiful as the Bloom’s taxonomy theory is, and containing very similar structure to its structure, just for the well-posedness of scientific problems, continuing our precursor work (or what seems to be precursor work for us so far) on well-posedness ([3]).

4. References:

[1] Merriam-Webster dictionary online, ` http://www.m-w.com/’, as accessed in February of 2007. [2] Bloom, B.S. Ed. 1956. Taxonomy of Educational Objectives: The Classification of Educational Goals. Handbook 1: Cognitive Domain . Longman, White Plains, NY, 2006. [3] Pinheiro, M. R. Well-posedness in Philosophy. Submitted, 2009. Available online at www.pdfcoke.com/illmrpinheiro2, accessed in September of 2009.