Protagoras and “Numbers” (Part 2)

The contribution of the Pythagoreans has become known not only in the field of philosophy, but also in the field of mathematics, especially the Pythagorean Theorem. In one way or another, I think that their group has positively influenced people down the century on the significance of numbers. As they say, everything in this world is number, and is numerical. This means that things around us are indeed composites of numbers, and they are countable through numbers. But how Protagoras understands the concept of number? I will show three things his notion of number in relation to reality.

1. In the abstract level, number has two elements – odd numbers and the even numbers. The odd number is described as the unlimited, and the even number is the limited. How did Protagoras come about that idea? It is not specifically explained.

2. In the concrete level, numbers are assigned to cosmology. He claims that the world and all it contains are described as the limited cosmos being surrounded by the unlimited cosmos, which is the air. Since air is everywhere, the world inhales it. But his limited cosmos is composed of the unlimited cosmos. Thus the limited cosmos is a mixture of both limited (even) and unlimited (odd) numbers.

3. Now, how are we to understand the all things are numbers? Protagoras explains number spatially. That is why his idea of numbers earns the label “geometry.” This is how he expounds it that one is the point, two is the line, three is the surface, and four is the solid. When taken together (the point, line, surface and solid), it constitutes the idea of number. In short, all things are composed of points, lines, and surfaces. Every material body is an expression of the number four or solid. Thus things are both numbers and numerable.

4. Regarding the shapes of things, he expresses that it is either oblong numbers or square numbers. When we start with one object and add odd number of objects, we get the square shape. And when we start with two objects and add even number of objects, then we get the oblong shape. This explains the shapes of things. (The “Tetraktys” is treated highly as a sacred and perfect figure. It composed of ten dots, and it is the sum of one, two, three and four integers.)

The implication of Numbers

Protagoras discovers that everything is numerical, and that is, it can be counted. Nothing escapes the reality of numbers. And he observes that even in music, its interval is also expressed in numerical. (For those who know the fundamental of note reading could relate this matter.)

In the classical music, one can easily observe the presence of harmony. The rhythm of the music is well-arranged and coordinated. This is attributed to existence of numbers because each note in the bar measure is equally divided according to its assigned time signature. We can intuit that the employment of numbers creates harmony or chaos.

This idea of harmony applies to the material things as well. If one observes how our human bodies function, they are well-regulated and well-designed, and all other things too. We can say that the harmony of the universe is numerical too. The intervention of man to our body and our world puts them in disorder.

Hermeneutic of Continuity and Rupture

Where is the church going? Many Catholics are unconsciously puzzled by the many activities of the Church and individual religious men and women whose mentality are also distorted. Unconscious because the Church somehow jibes with the modern thinking of doing things like going to concert for fund raising, which they see religious perform and dance the modern way, and distorted because they think and do the way people in modern and secular world do, like doing business and becoming materialistic. People know to group them where they belong, either the traditional thinking or modern thinking. But understanding deeply what Pope Benedict XVI is saying about hermeneutic of Continuity and hermeneutic of rupture, one would rather be able to appreciate the right direction of the Church as a whole, which many of the religious do know but not keeping it, or just hanging around in their comfort zone and be ignorant with advantage.

The term Hermeneutic

The word ‘hermeneutic’ derives from a messenger, whose name is ‘Hermes.’ He is a messenger in Greek mythology. And the Church, in her theology, adopted that word in its critical understanding and interpretation of the Biblical text. It is very important to do that in order to bring out the essence of God’s word or message and put things in its proper place together with the teaching documents done by the teaching authority of the Church called the Magisterium. The magisterium serves well the Sacred Scripture and the Sacred Tradition according to the document Dei Verbum.

Hermeneutic of Rupture

The term rupture implies a decisive break and an entity, totally new, emerges. And this kind of mentality is found with satisfaction because it is totally different from what has been accustomed to. This is an attempt of what is going on to disrupt the Church mission to teach faithfully all what the Lord has commanded to his first disciples. It is an attempt to introduce a new perspective, as influenced by modernization and secularization. It is modernization because it is something new, and secularization because it is something peculiar to the Church – it is not-church related. An example to this is the introduction of same-sex marriage – totally new from what has been practiced for many centuries, that is, not same-sex marriage or a boy-girl union.

Hermeneutic of Continuity

The term continuity implies evolution, a forming out of something better. This is the kind of path being followed by the Church. It is something different to many or some of us, but definitely it is a combination of the old and the new. It is old because the Church remains faithful to what has been handed down to them by the Lord, and it is something new because what has been handed down is being implemented according to the situation of the time. When the Church speaks about each Catholic as a missionary in his own right, she speaks the truth about the nature of the sacrament of baptism – the three-fold mission of Christ given to the newly baptized.

The Church and the Hermeneutic of Continuity

The position of the Church is very clear that she follows the hermeneutic of continuity. By this the Church do not just come up with something new policy or let us say, rules and regulations that is not in accordance with her doctrines and with the Code of Canon Law. The right term here is corroborates and enhances what has been implemented. And what has been implemented before is being subjected to the signs of the times. And behind this hermeneutic of continuity is the principle of infallibility by the pope that guides the whole activities of the Church to the right path, and frees her from all errors that contradicts her teachings. When the Church is talking about the immorality of corruption in the government, it is not a sign of being rebellious against the politicians. It is indeed a sign of her mission as part of matters in faith and morals. 

Source: http://www.catholicculture.org/commentary/articles.cfm?id=296

Pythagoras and the Pythagoreans (Part 1)

Who is Pythagoras?

Pythagoras, one of the known pre-Socratic philosophers, is hard to be figured out as the main actor of the Pythagoreans. There is unclear and hesitation on the part of many scholars that he is the main actor and author of the group’s philosophic ideas. Even Aristotle, one of the great triumvirates, says that when he mentions the name of Pythagoras in any of his writings, he does not mean that he is – Pythagoras – the one; he is referring to them as a group called the Pythagoreans.

Who are the Pythagoreans?

Pythagoreans are members of a society, a society that is religious by nature. Its founder is Pythagoras, and its foundation has taken place in South Italy, Kroton, during the half of the 6^th century. Some of the noted members are Philolaus and Eurytus.

As a religious group, they devote themselves to idea of purity and purification rituals, believing in the transmigration of souls, i.e. transferring of souls from one entity to another, love of silence, and the influence of music and studying math as aids in tending their souls. According to scholars, their care for the soul is something special compare to the teaching of Homer wherein the latter treats it as a mere shadow-image of the body.

Is it a Religious or Political Group?

Scholars sometimes link the group of Pythagoras to a certain religion called Orphicism. It is because the teachings of Pythagoreans are similar to the religious doctrines of Orphicism. An example to this is the doctrine of transmigration of souls. An attempt to digging on this issue would probably make them unworthy to be part of the history of philosophy. They are more qualified to be part of the history of religion. Another claim is that Pythagoreans as a political group because there was a part of Italy wherein most of the people were identified as part of the group. But the counter-claim to this is the fact that there was no governing exercise happened and was handled by the Pythagoreans. But the influence of their teaching was so pervasive, an attraction to everyone during their times. Thus it is a purely religious and political activity.

The Ionian or Milesian Philosophers

The three known Ionian or Milesian philosophers – Thales, Anaximander, and Anaximenes – are the earliest thinkers in this Greek period. They all belong to Milesian School in Miletus, and they were the first to take stride in providing unfamiliar answers to the primary question about the basic stuff of the world. It is unfamiliar answers considering that the influence of religion at that time prevails.

In reading some books on these three philosophers pre-Socratic philosophers, one may discover that the authors quote different historians of the field to put forward a wholesome presentation as towhat makes them worthy to be called ‘philosophers’ including how their thoughts were shaped and other attributes about their achievements. That’s the first thing I will do before presentingthose simple ideas whichare indisputably theirs.

A. Thales

He is known in the ancient period as the first Greek philosopher who tries to formulate an answer to his basic question about the basic stuff of the world (urstoff). Herodotus claims that Thales had predicted a solar eclipse, while Laertius Diogenes also claims that Thales once fell into a well because of star gazing. And lastly Aristotle, one of the great thinkers of the west, attributes to Thales two things, which are his main ideas.

First, Thales answers water as the basic stuff of all things. And second, he conceived that there lies a soul in the magnet, for the reason that magnet has the capacity to move iron.

B. Anaximander

Our source on Anaximander is Theoprastus. Here are the accounts of Theoprastus regarding Anaximander.

First, Anaximander constructed a map for the sailors. Second, his answer on the basic stuff of the world is the indeterminate. What does it mean by it? This indeterminate is to be describing as a never ending movement which consists of different elements, including water of Thales, consuming each other in forming the world. It is a substance without limits, or in Greek it is called ‘to apeiron,’ and this is the material cause.

In such a movement, the interpretation of the concept of justice and injustice is found here. When one element encroach another element, this is an instance called injustice. And the only means for that element to pay its debt is by letting itself be encroached by other elements.

C. Anaximenes

A little fraction is left from Anaximenes’ work where we could draw his ideas.

According to that fraction, he abandons the idea of ‘to apeiron’ or substance without limits, and assigns a determinate element as the basic stuff of the world. It is somehow a backward movement rather than advancing as what Anaximander did.

And what is his answer to the ‘urstoff?’ It is air. Air is the principle of life, and without it we will die. It is air that holds all things together like our soul and the world.

How did he explain further about his air, which is considered as invisible? It is only through the notion of condensation and rarefaction. Air becomes fire through rarefaction and solid like stone by condensation.

Other things attributed to him were his idea of the earth as flat that floats on air like a leaf, and the existence of rainbow as due to the sun’s ray falling on the thick cloud. Since the ray could not penetrate the thick cloud, it produces rainbow on the other side of the cloud.

A little note on Theoprastus

Theoprastus was mentioned under the subjects Anaximander and Anaximenes. He knows the age gap of these three philosophers as he says that Anaximenes is younger than Anaximander, and Anaximander is younger than Thales because of the word ‘associate.’ Anaximenes is an associate of Anaximander, and Anaximander is an associate too of Thales. Thus Thales is the eldest of them all, and Anaximenes is the youngest.

The ‘How’ and ‘Why’ to study History of Philosophy

Philosophy is a very difficult subject to many of the college students. Other branches under the topic are being marginalized in the priority and interest of the learner. And the burden of bringing the discipline to them lies on the teachers. It is the task of the teacher, with patience and endurance, to make philosophy meaningful in the learning endeavor of the students.

But Frederick Copleston, S.J., author of many history books on philosophy offers some ways on how and why to study philosophy. They are effective means to come to the holistic knowledge of philosophy, and somehow plants the seed of interest and appreciation of philosophy.

The ‘HOW’ to study philosophy

First, the reader must consider the historical setting. One must study how idea of the philosopher developed through the influence of the environment. His idea must be understood in connection to his own milieu. It is precisely that the thinker and his own thinking are not isolated from the reality of time and place.

Second, the reader must possess a bit of sympathy, a sort of psychological approach to the thinker and his thinking. One must be able to enter the system of the thinker and be absorbed somehow. Simple to say, one must be able to go down to his level for better understanding what is on his mind.

Third, if one desires to be a specialist in one philosophical method, he must get deeper into the system of the thinker. One has to make a necessary pause at a certain period of the history of philosophy to possess a well-rounded understanding of the whole system of a particular thinker. He must venture in studying the philosopher’s language, his expertise, etc.

The ‘WHY’ to study philosophy

First, we study to learn from their mistakes and right. History is undeniably rich in knowledge. It teaches us to look into the past knowledge and use them what is still applicable to our present situation as solution to the current problem. Otherwise the only option left is to develop a new solution by utilizing the present resources at hand.

And secondly is to see the development of philosophy where some new ideas are accepted and added, some being rejected and replaced anew, and some ideas become the point of departure and some as point of continuation.

Useful or Just a Waste Opportunity

Many people aspire for change. But to execute change is not that simple. Everybody knows that change results to something that is novelty. This novelty is either in itself serves for the betterment or for the worst. And since the world seems so cruel, disordered, unpleasant, dreaming of making the scenario exactly the opposite is not far-fetched. Change is an ideal prize that each one wants. There are two types of change, among the many types, I would like to highlight here. The simple kind of change is the change of one’s self. And this change is considered elementary – it brings change only in a narrowed and limited sense. The other type of change is complex by nature – a change that is broad and boundless. And everybody benefits from it. It results to make other people better, and so with the environment.

This type of change is intertwined with power. This power is not rested on the lowest part of the social strata, but on the highest plain. One has to climb up the ladder in order to reach the top. And once you are on the top, change that you are aspiring for is now in your hands. What does it mean? Change is realistic when one has the means – power. Its implication is power means positions. And this position is pragmatically the best venue to bring about novelty. A position is not all is there the case. It is also tangled with another means in order for the occupant to enjoy the luxury of executing change. And this is money. Money is the means for transacting change with other means of change. Thus power is accompanied with money in the execution of necessary change in one’s place.

The locus of change could be in any of the existing institutions today. Institutions exist to serve the needs of the people, like the government and the church for instance. These two institutions are known to be in the Philippines as the savior of the masses. Any institutions are being administered by authorities. These authorities are being elected by their subjects who are being seen as qualified to be in the position. And those positions are being assisted with power as executor’s power, sustained with money as machinery. It is an illusion when authorities occupy those noble positions without power and money. And that is why, many are tempted by these means, in spite of one’s noble and ideal intention of ‘to serve’ or be ‘of service.’ Service has become the password and the bridge to have power and money.

But being in authority is a rare opportunity and privilege. It is rare because not everyone can climb the ladder to that position. It is also a privilege for those who are chosen to be there. Election is not only the sole privilege. Selection is also a privilege because only few people are involved in that process. In the religious world, to be in the position is also a privilege coming from above. Armed with power and money, the mission entrusted by their Master is now within its reach. That mission is the heart of evangelization – for the BUILDING OF THE KINGDOM OF GOD here on earth. The sign of failure in not realizing that mission is because the hearts and minds in authority are worldly. It simply means that their focus is now on the means at the expense on ends. To be in authority in fulfilling that mission is a very rare golden opportunity. But to be in authority for power and money is just a WASTE OPPORTUNITY.

Carnap on Linguistic Framework (Part 3)

V. Limitation of the Framework

            The linguistic framework, which has been set up by Rudolf Carnap, is an excellent type of strategy he employed as a way of verifying the meaningfulness of the statement. But the nature of the framework is somehow defined, limited, and narrow. It is defined because he categorizes questions into two – internal and external. It is limited because it entertains questions to what particular language to be picked up and verified. It is also narrow because only those meaningful statements can be analyzed analytically and synthetically or empirically. Other statements that talk about non-empirically could not be verified by the framework, and they are treated as pseudo-questions and pseudo-debates.

A. Ayer and his Emotive Theory

Ayer, in his Language, Truth, and Logic, admits that not only meaningful statements through empirical observation could be verified. Ayer considers other language like ethical language or moral language as significant. This kind of language could not pass the verification principle of Carnap, for they are not objects of empirical matters. Ethical language is not literally significant within the linguistic framework of Carnap. For Carnap ethical language is considered pseudo-questions. Ayer instead proposed his emotive theory to justify ethical language as somehow significant. In what manner did Ayer justify his position?

            An example of ethical statement is “Stealing is wrong.” If this statement is going to be based on the internal questions of Carnap, it cannot find the answer, for the statement is neither analytic nor synthetic. It does not purport empirical fact. But Ayer has said that such ethical statement like “Stealing is wrong” functioned to express feelings or emotions. Only that such statement is not literally significant. The justification for such statement to be meaningful is this that ethical statement is emotive significance. Emotive significance is not the same as metaphysical significance. What is the peculiarity of emotive significance in order to become meaningful?

            The criterion is this: when an ethical statement evinces feelings on the part of the speaker and on the hearer. This possesses genuine emotive significance, only when some observable behavior occurs on the speaker and on the hearer.

B. Quine and his Two Dogmas of Empiricism

            Quine has made his attack on the understanding of analyticity first on Kant and Frege’s thoughts before Carnap’s. His attempt on sharp distinction between analytic and synthetic has separated himself from Carnap, his greatest teacher. There is no enough space here to expose how Quine’s argument has come about against Kant, Frege and Carnap. But it is very clear that, in general, Quine is not satisfied the way these philosophers explore on the meaning of analyticity.

            In his Two Dogmas of Empiricism, there are two things he did emphasize in relation to analyticity. He has commented that these philosophers did not achieve in creating boundary between analytic and synthetic. For him, it is a must neatly divided between those statements which are analytic and those statements which are synthetic or empirical. This is because for him, in doing so would be treated as unempirical dogma of empiricist. It would also become a metaphysic article of faith. But for Carnap, the combination of analytic-synthetic is very important in disposing any metaphysical questions and debates.

            The second part of his Quine’s writing is the idea of reductionism. The definition of the term holds that a meaningful statement could be translated to another statement on immediate experience. This means that reductionism does not parting ways from the original goal of the movement – Vienna Circle – that any knowledge should be based on sense-experience.

VI. Conclusion

            The thought of Rudolf Carnap is indeed a product of his brilliance as analytic philosopher. Any empiricist could be, at his own disposal and intelligence, immediately accept or reject statements which expresses cognitive significance. But he has come up with a language called linguistic framework which entertain questions that are internal and external, with logic or method and syntactical rules. And the highlight of having framework is the treatment of any metaphysical language as pseudo-problems.

            The repercussion to this initiative in rejecting metaphysical problem is also the rejection of ethical and moral language. The ethical language is anchored on metaphysics, and so with religious and aesthetic language. But thanks to Julius Ayer, with his emotive theory, he has rescued the reality of the world through the indispensable role of human behavior.

But the position of Ayer, like Rudolf Carnap, is somehow did not escape from being identified as solipsism. They posit that “If knowledge is based on sense-experience, then whose experience?” Prior to this, Ayer’s argument has to be proven whether the behavior being produced by certain action is a truly and literally cognitive in accordance to ethical language. And when affirmative answer is given to the question of solipsism, and then another repercussion may also occur, i.e. the answer becomes extreme subjectivism if without taking any precautionary measures.

But going back to the basic, why do Carnap put more premiums on sense-experience? Of course, the movement is assisting in the improvement of scientific procedures. In other words, Vienna Circle is at the service of science and not on metaphysical speculation.

Bibliography

Books

Hylton, Peter, Quine. New York and London: Routledge, 2007.

Martinich, A. P. and David Sosa ed. A Companion to Analytic Philosophy. USA and UK: Balckwell Publishers Inc., 2001.

Miller, Alexander. Philosophy of Language, 2^nd ed. New York and London: Routledge, 2007.

Stumpf, Samuel Enoch and James Fieser. A History of Philosophy: Socrates to Sartre and Beyond. 7^th ed. New York: McGraw-Hill, 2005.

Article

Empiricism, Semantics and Ontology of Rudolf Carnap

Electronic Source

Encarta Dictionaries 2007