The Lived Past and the Anticipated Future.

the autobiographical self has prompted extended memory, reasoning, imagination, creativity and language. And out of that came the instruments of culture --religions, justice,trade, the arts, science, technology. And it is within that culture that we really can get -- and this is the novelty --something that is not entirely set by our biology. It is developed in the cultures. It developed in collectives of human beings. And this is, of course, the culturewhere we have developed something that I like to call socio-cultural regulation.

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Plato prove that justice does not depend upon a chance, convention or upon external force. It is the right condition of the human soul by the very nature of man when seen in the fullness of his environment. It is in this way that Plato condemned the position taken by Glaucon that justice is something which is external. According to Plato, it is internal as it resides in the human soul. "It is now regarded as an inward grace and its understanding is shown to involve a study of the inner man." It is, therefore, natural and no artificial. It is therefore, not born of fear of the weak but of the longing of the human soul to do a duty according to its nature.

Plato's Concept Of Justice: An Analysis  Bold was added by me for emphasis.

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 See Also:

•  What is Good Governance

"Let no one ignorant of geometry enter"

Plato’s Motto

The scho­liast on Aelius Aris­tides 125.14 (Din­dorf, Vol. 3) says the fol­low­ing:

ἐπεγέγραπτο ἔμπροσθεν τῆς διατριβῆς τοῦ Πλάτωνος ὅτι ἀγεωμέτρητος μηδεὶς εἰσίτω· ἀντὶ τοῦ ἄνισος καὶ ἄδικος. ἡ γὰρ γεωμετρία τὴν ἰσότητα καὶ τὴν δικαιοσύνην τηρεῖ.

‘In front of Plato’s school had been inscribed, “Let noone enter un-​​geometried” rather than “unequal” or “unjust,” for geom­e­try main­tains equal­ity and justness.’


At any rate, Pseudo-​​Galen (post 2 A.D.?) quotes the phrase at the begin­ning of ‘On the divi­sions of phi­los­o­phy,’ and makes geom­e­try a pre­lim­i­nary to the­ol­ogy:

ὁ μὲν οὖν Πλάτων εἰς φυσιολογικὸν καὶ θεολογικὸν αὐτὸ διαιρεῖ· τὸ γὰρ μαθηματικὸν οὐκ ἠβούλετο εἶναι μέρος τῆς φιλοσοφίας, ἀλλὰ προγύμνασμά τι ὥσπερ ἡ γραμματικὴ καὶ ἡ ῥητορική· ὅθεν καὶ πρὸ τοῦ ἀκροατηρίου τοῦ οἰκείου ἐπέγραψεν ‘ἀγεωμέτρητος μηδεὶς εἰσίτω’. τοῦτο δὲ ὁ Πλάτων ἐπέγραφεν, ἐπειδὴ εἰς τὰ πολλὰ θεολογεῖ καὶ περὶ θεολογίαν καταγίνεται· συμβάλλεται δὲ εἰς εἴδησιν τῆς θεολογίας τὸ μαθηματικόν, οὗτινός ἐστιν ἡ γεωμετρία.

‘Plato divided it (the­o­ret­i­cal phi­los­o­phy) into phys­i­ol­ogy and the­ol­ogy. In fact, he did not want math­e­mat­ics to be a part of phi­los­o­phy, but a sort of pro­gym­nasma like gram­mar and rhetoric. That’s why, before his pri­vate lecture-​​room, he inscribed “Let no one enter un-​​geometried.” He inscribed this since he dis­coursed on the­ol­ogy in all mat­ters and dwelt on the­ol­ogy, and included math­e­mat­ics, of which geom­e­try is a part, into theology’s forms of knowledge.’ See:Plato’s Motto Written by Dennis McHenry. December 10, 2005

***

Polish Society of St. Thomas Aquinas-Plato's Academy

Candidates for philosophy to be properly prepared.

Plato introduction to the philosophy of mathematics has made, highlighting the non-the usual benefits of studying mathematics in the improvement mind. At the front of the AP, as the legend goes, was engraved the inscription: "There is no WStE-pu anyone who does not know geometry. " In the Republic (VII 528 a) Plato classification mathematical sciences conducted on the basis of views Pythagoreans, who shared in the mathematical sciences depending on what questions to give answer: "How much?" - arithmetic and music, "how much?" - geometry and mechanical chanika. Plato arranges in order of mathematical sciences: arithmetic, geometry (distinguished by the geometry of the flat - planimetry and spatial geometry -stereometry), astronomy, music, and considers that these sciences are related to the relation-my formal, uwidocznionymi eg decreasing their abstractness. http://www.ptta.pl/pef/pdf/a/akademiaplaton.pdf

***

If the late character of our sources may incite us to doubt the autheticity of this tradition, there remains that, in its spirit, it is in no way out of character, as can be seen by reading or rereading what Plato says about the sciences fit for the formation of philosophers in book VII of the Republic, and especially about geometry at Republic, VII, 526c8-527c11. We should only keep in mind that, for Plato, geometry, as well as all other mathematical sciences, is not an end in itself, but only a prerequisite meant to test and develop the power of abstraction in the student, that is, his ability to go beyond the level of sensible experience which keeps us within the "visible" realm, that of the material world, all the way to the pure intelligible. And geometry, as can be seen through the experiment with the slave boy in the Meno (Meno, 80d1-86d2), can also make us discover the existence of truths (that of a theorem of geometry such as, in the case of the Meno, the one about doubling a square) that may be said to be "transcendant" in that they don't depend upon what we may think about them, but have to be accepted by any reasonable being, which should lead us into wondering whether such transcendant truths might not exist as well in other areas, such as ethics and matters relating to men's ultimate happiness, whether we may be able to "demonstrate" them or not.See: Frequently Asked Questions about Plato by Bernard SUZANNE

Most certainly that given perspective about the reality of geometry in the context  of the abstract,  it is buried deep within ourselves that our creativity leads us that much closer to the truth and points to a depth of our being. Have you not ever been there to know, that by such mapping schematically, any direction lies under the sociological underpinnings of our associations and our dealings with reality?

On any road to self discovery it was apparent to me that by observing levels of awareness that we usually don't take the time to observe, the more I looked, a abstract math of let's say Game Theory, was apparent. When being lead through a mathematical landscape, could we arrive at our everyday dealings in society?

Economically, it had to make sense that such algorithms could be written and many of us as observers of the information world are unaware of the constrains we have applied to our everyday reading of the economic world?

Know Thyself (γνώθι σεαυτόν )

A stained glass window with the contracted version γνωθι σαυτόν.

The saying "Know thyself" may refer by extension to the ideal of understanding human behavior, morals, and thought, because ultimately to understand oneself is to understand other humans as well. However, the ancient Greek philosophers thought that no man can ever comprehend the human spirit and thought thoroughly, so it would have been almost inconceivable to know oneself fully. Therefore, the saying may refer to a less ambitious ideal, such as knowing one's own habits, morals, temperament, ability to control anger, and other aspects of human behavior that we struggle with on a daily basis.

It may also have a mystical interpretation. 'Thyself', is not meant in reference to the egotist, but the ego within self, the I AM consciousness.

***

Delphi became the site of a major temple to Phoebus Apollo, as well as the Pythian Games and the famous prehistoric oracle. Even in Roman times, hundreds of votive statues remained, described by Pliny the Younger and seen by Pausanias. Supposedly carved into the temple were three phrases: γνωθι σεαυτόν (gnothi seauton = "know thyself") and μηδέν άγαν (meden agan = "nothing in excess"), and Εγγύα πάρα δ'ατη (eggua para d'atē = "make a pledge and mischief is nigh"),[6] as well as a large letter E.[7] Among other things epsilon signifies the number 5. Plutarch's essay on the meaning of the “E at Delphi" is the only literary source for the inscription. In ancient times, the origin of these phrases was attributed to one or more of the Seven Sages of Greece,[8] though ancient as well as modern scholars have doubted the legitimacy of such ascriptions.[9] According to one pair of scholars, "The actual authorship of the three maxims set up on the Delphian temple may be left uncertain. Most likely they were popular proverbs, which tended later to be attributed to particular sages

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"Let no one destitute of geometry enter my doors." Plato (c. 427 - 347 B.C.E.)

"[Geometry is] . . . persued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes, ...[it] must draw the soul towards truth and give the finishing touch to the philosophic spirit."

***

 

III: The "Geometrical Problem" in the Meno.

Further along in the Meno occurs the celebrated case of the Geometrical Example at Meno 87, which in contrast to the previous mathematical illustration, has been twisted, tortured, and intentionally passed over for two centuries. Jebb said (loc.cit.) asven over a century ago:

The hypothesis appears to be rather trivial and to have no mathematical value. . . (which Raven echoes in 1965)

and here follow some barely intelligible geometrical details".

Bluck however, in 1961 devotes an excursus of some sixteen pages to a complete review of views on the problem, which include an array or barely intelligible geometrical details. The passage is made more difficult of interpretation by the fact that Socrates introduces the geometrical example in a very summary manner, which some have felt was an indication or its relative unimportance.

 I believe on the contrary that the almost schematic reference implies that the topic and the example were well known to the Platonic audience, and did not need explanation. Plato knows how to explain in full, and when he refrains we must understand the matter to be common knowledge. The problem as it occurs at Meno 87 a is briefly this:

We will proceed from here on like the geometer who when asked if a given triangle can be inscribed in a given circle, will say:

'I can't say, but let us proceed hypothetically or experimentally, draw out one leg, swing the other two and see if it falls short or exceeds the rim of the circle.'

In making this paraphrase I have added the word "experimentally" for obvious reasons, and I have taken the noun chorion correctly as area (not rectangle or a triangle, as has been said, which means nothing) in a sense very well attested. So apparently with these conditions, the words themselves are not obscure or really unintelligible, although as yet the meaning has not yet come to the surface.

See: Plato: Mathematician or Mystic ?

***

You might think the loss of geometry like the loss of, say, Latin would pass virtually unnoticed. This is the thing about geometry: we no more notice it than we notice the curve of the earth. To most people, geometry is a grade school memory of fumbling with protractors and memorizing the Pythagorean theorem. Yet geometry is everywhere. Coxeter sees it in honeycombs, sunflowers, froth and sponges. It's in the molecules of our food (the spearmint molecule is the exact geometric reaction of the caraway molecule), and in the computer-designed curves of a Mercedes-Benz. Its loss would be immeasurable, especially to the cognoscenti at the Budapest conference, who forfeit the summer sun for the somnolent glow of an overhead projector. They credit Coxeter with rescuing an art form as important as poetry or opera. Without Coxeter's geometry as without Mozart's symphonies or Shakespeare's plays our culture, our understanding of the universe,would be incomplete.

See: γνώθι σεαυτόν

Setting Time Aright

Time has no independent existence apart from the order of events by which we measure it. — Albert Einstein

While Event has since past, I hope the lecture itself will remain in public domain. It helps so as to see the context of the discussion provided by this conference with regard to that subject of time.




Video streaming by Ustream

See:Setting Time Aright

In 1952, in his book Relativity, Einstein writes:

Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence

.

Setting Time Aright

View more presentations from Sean Carroll

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  If man thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken, and without a border then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole. (David Bohm, Wholeness and the Implicate Order, 1980)


Lee Smolin:

I suspect this reflects the expectation many people have that time is not fundamental, but rather emerges only at a semiclassical approximation in quantum cosmology. If you believe this then you believe that the fundamental quantities a quantum cosmology should compute are timeless. This in turn reflects a very old and ultimately religious prejudice that deeper truths are timeless. This has been traced by scholars to the theology of Newton and contemporaries who saw space as “the sensorium” of an eternal and all seeing god. Perhaps the BB paradox is telling us it is time to give up the search for timeless probability distributions, and recognize that since Darwin the deep truths about nature cannot be divorced from time.

The alternative is to disbelieve the arguments that time is emergent-which were never very convincing- and instead formulate quantum cosmology in such a way that time is always real. I would suggest that the Boltzman Brain’s paradox is the reducto ad absurdum of the notion that time is emergent and that rather than play with little fixes to it we should try to take seriously the opposite idea: that time is real.

***

Bar of Lead Tungstate Source: A Quantum Diaries Survivor-Calorimeters for High Energy Physics experiments - part 1 April 6, 2008

Calorimeters measure the collective behavior of particles traveling along approximately the same path, and are thus naturally suited for the measurement of jets-Dorigo Tommaso

See: 

• FQXi Conference 2011
  
• The Reference Frame: Ten new things modern physics has learned about time

How Time Ages the Pyramids

Chanticleer - A Pleasure Garden

Believing that something must be true about the world because you can’t imagine otherwise is, five hundred years into the Age of Science, not a recommended strategy for acquiring reliable knowledge. It goes back to the classic conflict of rationalism vs. empiricism. “Rationalism” sounds good — who doesn’t want to be rational? But the idea behind it is that we can reach true conclusions about the world by reason alone. We don’t ever have to leave the comfort of our living room; we can just sit around, sharing some single-malt Scotch and fine cigars, thinking really hard about the universe, and thereby achieve some real understanding. Empiricism, on the other hand, says that we should try to imagine all possible ways the world should be, and then actually go out and look at it to decide which way it really is. Rationalism is traditionally associated with Descartes, Leibniz, and Spinoza, while empiricism is associated with Locke, Berkeley, and Hume — but of course these categories never quite fit perfectly well.SEE:What Can We Know About The World Without Looking At It?

I had been able to isolate Lee's Smolin's method of approach as to whether something can exist within, or, exists outside of time. Thoughts about Meno come to mind and Plato's Problem and Meno: How Accurately Portrayed?

The idea that truth is timeless and resides outside the universe was the essence of Plato's philosophy, exemplified in the parable of the slave boy that was meant to argue that discovery is merely remembering. Lee Smolin

Of course this article of yours Sean has lead to interesting thoughts. His talk with Memories Arise Out of a Equilibrium David Albert.....how does one logically proceed with inquiry. Why is the past so different, in so many ways, from the future? (12:20)

Sean Carroll

This raises all sorts of questions, the most basic of which are: “What counts as `looking’ vs. `not looking’?” and “Do we really need a separate law of physics to describe the evolution of systems that are being looked at?”

See:Quantum Diavlog

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When you are told that carrots have human rights because they share half our genes -- but not how gene percentages confer rights -- wizard. When someone announces that the nature-nurture debate has been settled because there is evidence that a given percentage of our political opinions are genetically inherited, but they don't explain how genes cause opinions, they've settled nothing. They are saying that our opinions are caused by wizards, and presumably so are their own. That the truth consists of hard to vary assertions about reality is the most important fact about the physical world David Deutsch: A new way to explain explanation

***

Of course thanks to Lubos for link on Rationalism vs empiricism You can find his thoughts there and more information around his heading below.

The dispute between rationalism and empiricism concerns the extent to which we are dependent upon sense experience in our effort to gain knowledge. Rationalists claim that there are significant ways in which our concepts and knowledge are gained independently of sense experience. Empiricists claim that sense experience is the ultimate source of all our concepts and knowledge.

Rationalists generally develop their view in two ways. First, they argue that there are cases where the content of our concepts or knowledge outstrips the information that sense experience can provide. Second, they constuct accounts of how reason in some form or other provides that additional information about the world. Empiricists present complementary lines of thought. First, they develop accounts of how experience provides the information that rationalists cite, insofar as we have it in the first place. (Empiricists will at times opt for skepticism as an alternative to rationalism: if experience cannot provide the concepts or knowledge the rationalists cite, then we don't have them.) Second, empiricists attack the rationalists' accounts of how reason is a source of concepts or knowledge.See: Rationalism vs. Empiricism

The Pyramid(as an expression of Liberal Arts Encapsulated) is a combination of  the Trivium , and  the Quadrivium

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The Socratic Method.....and Plato's Ideas, is Replaced by Google?

The Classical Education Movement Historical

Seal of the University of Pennsylvania from 1894 depicting the trivium as a stack of books providing the foundation for a quadrivium of mathematics, natural philosophy (empirical science), astronomy, and theology.

The Classical education movement advocates a form of education based in the traditions of Western culture, with a particular focus on education as understood and taught in the Middle Ages.

The term "classical education" has been used in English for several centuries, with each era modifying the definition and adding its own selection of topics. By the end of the 18th century, in addition to the trivium and quadrivium of the Middle Ages, the definition of a classical education embraced study of literature, poetry, drama, philosophy, history, art, and languages.^[1] In the 20th and 21st centuries it is used to refer to a broad-based study of the liberal arts and sciences, as opposed to a practical or pre-professional program.^[1]

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Quadrivium(Medieval usage)

The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the music intervals created by the division of a monochord. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised both in European and Islamic cultures.

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By education, the divine essence of man may be unfolded, brought out, lifted into consciousness byFriedrich Fröbel

Sometimes one has to look behind a statement in order to see the depth that might be revealed and what the comment might be reacting too? So of course, I throw it out there,  to see what comes back.


Extra-Dimensions....What is Heaven Like?

Imagine a world with no Anti-Matter? No equatorial axiomatic expressions of the universe?:) Just plain, Dark and Dead.:) Walking over a bridge in visualization is escapism....while there exists another side to the question?

At 4:00 PM, June 25, 2011,  Phil Warnell said... The book I mentioned previously is an attempted construction of what perhaps this would have turned out to be. What I find as ultimately interesting is that is for each having and maintaining a true dialogue is the most critical requirement of science and philosophy more generally. So although they had opposing views about the relevancy of the foundations in seeking the truth, each agreed about one key aspect of its methodology, which is not an axiom, yet required as a prerequisite before any can be postulated or denied there being necessity to do so.(Bold added for emphasis by me)

So while waiting for a response....it is understood that such "a schematic" was realized by this author for what may be expletive for that which reads,"which is not an axiom" as to reveal some bias by this author of discoveries about "deep play thinking." About subjects at hand, and the journey one might want to take.

It was found to reveal the "same geometrical tendencies" that are inherent in the quest for such truth's as to the wording of,  writing and visualizing to advance, reveals a topographical relationship with the world around us. Why if it can exist in such equatorial description cannot such a dialogue exist within self? Where did it begin?;)

This dance of sorts of leading to self evident questions and answers, that lead to any apprehension of position for which too,  rebuttal the world, and paint a picture there of. Off handed statements do reveal positions.

See: The Socratic Method.....and Plato's Ideas, is Replaced by Google?

The Socratic Method.....and Plato's Ideas, is Replaced by Google?

http://youtu.be/dk60sYrU2RU

The idea that truth is timeless and resides outside the universe was the essence of Plato's philosophy, exemplified in the parable of the slave boy that was meant to argue that discovery is merely remembering. Lee Smolin

 Bold added for me for emphasis....as well as saying that this philosophy is not "outside of time."

Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.

Yes no doubt. But as you look through the experiment present by Youtube something very important is realized that as a "data base" and Google's connection to it,  allow an excursion for children that we would want applied to "all thinking beings"  as  a vast resource made available to them, having considered the Grandmothers as part of the cloud of encouragement toward progressing and developing. Teachers can come in many forms?

So yes I see education in this way as well...but imagine if such a data base is taken away......imagine being devoid of the technology?

You want to see the children apply such a tool .....being devoid of the technology as to a method inherent in their own design and makeup which will grant them the same benefits as you would have,  having gone through such an experiment?

What did they learn that was algorithmic pleasing that Arthur C Clarke might embrace as to all teachers? Replace teachers with Grandmother Cloud?

These things are being considered now in the future development of education as I have research it.....but there is something deeper that must be transmitted that can only be done with the interaction of the teachers....while still accessing that data, you still need the teachers there.

Imagine a "gogle search feature" as the very last "self evident question." This is internal and not attached to the keyboard computerized developer algorithmic code,  but is a feature of the human being searching, looking for answers, and becoming their own teachers as well as students. This the independence you want transmitted to children from teachers, as well as too,  adults in my view. The teacher, and student are one.

You of course recognize the grounding factor...all I am saying is this inductive /deductive process is part of the need for individuals to excel, regardless of that technology.

***

Logic is the art of thinking; grammar, the art of inventing symbols and combining them to express thought; and rhetoric, the art of communicating thought from one mind to another, the adaptation of language to circumstance.Sister Miriam Joseph

 Painting by Cesare Maccari (1840-1919), Cicero Denounces Catiline.

In medieval universities, the trivium comprised the three subjects taught first: grammar, logic, and rhetoric. The word is a Latin term meaning “the three ways” or “the three roads” forming the foundation of a medieval liberal arts education. This study was preparatory for the quadrivium. The trivium is implicit in the De nuptiis of Martianus Capella, although the term was not used until the Carolingian era when it was coined in imitation of the earlier quadrivium.^[1] It was later systematized in part by Petrus Ramus as an essential part of Ramism.

***

The quadrivium comprised the four subjects, or arts, taught in medieval universities after the trivium. The word is Latin, meaning "the four ways" or "the four roads". Together, the trivium and the quadrivium comprised the seven liberal arts.^[1] The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium made up of grammar, logic (or dialectic, as it was called at the times), and rhetoric. In turn, the quadrivium was considered preparatory work for the serious study of philosophy and theology.

***

The Pyramid(as an expression of Liberal Arts Encapsulated) is a combination of  the Trivium , and  the Quadrivium

If you internalize this pyramidal structure then you realize what Plato was talking about in terms of "the idea" and how it can arrive at the peak. This is of course after giving education a  sincere scrutiny with all the tools applicable to what can become self evident? The "google search feature,"  is your connection to "vast potentials" and is accessible to all who are creative and endeavor to learn to understand the search for truth.

Liberal arts

The Pyramid(as an expression of Liberal Arts Encapsulated) is a combination of  the Trivium , and  the Quadrivium

My interest has been from a historical position about how such a system while it developed from that ancient perspective,  is still not about a "religious perspective" as to what is to be believed by Lee Smolin.

If we think outside of time, we believe these ideas somehow "existed" before we invented them. If we think in time we see no reason to presume that.Lee Smolin

I of course question what is relative by appointments from him as to what can  exist "within and out of time." Since this is a foundation approach with which his whole take depends on, his relative relationships as it is relegated toward perspective about the beginning and the end of the universe,  is a position with which one cannot ever assume, hence, the value in religious perspective one is suppose to have in relation to their science? I hope I get this right.

The idea that truth is timeless and resides outside the universe was the essence of Plato's philosophy, exemplified in the parable of the slave boy that was meant to argue that discovery is merely remembering. Lee Smolin

So I needed to put this in perspective, so it is understood that the issue here arises "from within" so that all expression without,  inside or outside of time become a relative issue about position and stances assumed and cannot be differentiated to such categories as to it significance as being religious.

Among contemporary cosmologists and physicists, proponents of eternal inflation and timeless quantum cosmology are thinking outside of time. Proponents of evolutionary and cyclic cosmological scenarios are thinking in time. If you think in time you worry about time ending at space-time singularities. If you think outside of time this is an ignorable problem because you believe reality is the whole history of the world at once. Lee Smolin

So, I provided some access to "Plato's Dialogues" so as to give you the the ability to discern what is assume by Lee is what is spoken by and through Plato's own words.

What did you gain by reading that you can now say that what is established as "foundations approached" to being realistic, wafts through the scientific community and distinguishes itself according to some category that allows you to believe that it is religious by inherent and that such searches have no basis according too?

Does he say that explicit....only you can say by such association and quotes, can I say then that I point toward that direction in my assumptions as well. I mean you have been given the opportunity so you decide.

My perspective is about that "Cognitive Tool Kit" and how leading to a "point source" is nothing more then the recognition of coming to a "point source" inside you,  that is inside time. What I am saying, is that such perfection is the containment of all that has ever existed, or will ever exist, you are connected to in time, so these thoughts about the before and after are not apart from what happens within in any universe, nor can birth and death be considered outside of it.

This recognition is "the measure of" with which one can assume their foundation. That is, how I see Lee's position. All scientist would agree in that such measure is appropriate, yet such thoughts about time and outside of time pertaining to the Cognitive Tool Kit is not part and parcel of a "religious context" that one could say, "eureka!"

Again, it leads to a Point Source. A "point source" inside time that contain vasts potential?

SEE:

• Meno
• Plato's Problem
• Plato's Problem and Meno: How Accurately Portrayed...

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The seven liberal arts – Picture from the Hortus deliciarum of Herrad von Landsberg (12th century)

The term liberal arts denotes a curriculum that imparts general knowledge and develops the student’s rational thought and intellectual capabilities, unlike the professional, vocational and technical curricula emphasizing specialization. The contemporary liberal arts comprise studying literature, languages, philosophy, history, mathematics, and science.^[1]

Contents 1 History 2 Liberal arts in the United States 3 See also 4 References 5 Further reading 6 External links

History

In classical antiquity, the liberal arts denoted the education worthy of a free person (Latin: liber, “free”).^[2] Contrary to popular opinion, freeborn girls were as likely to receive formal education as boys, especially during the Roman Empire—unlike the lack-of-education, or purely manual/technical skills, proper to a slave.^[3] The "liberal arts" or "liberal pursuits" (Latin liberalia studia) were already so called in formal education during the Roman Empire; for example, Seneca the Younger discusses liberal arts in education from a critical Stoic point of view in Moral Epistle 88.^[4] The subjects that would become the standard "Liberal Arts" in Roman and Medieval times already comprised the basic curriculum in the enkuklios paideia or "education in a circle" of late Classical and Hellenistic Greece.

In the 5th century AD, Martianus Capella defined the seven Liberal Arts as: grammar, dialectic, rhetoric, geometry, arithmetic, astronomy, and music. In the medieval Western university, the seven liberal arts were:^[5]

• the Trivium

1. grammar
2. logic
3. rhetoric

• the Quadrivium

4. arithmetic
5. astronomy
6. music
7. geometry

 Liberal arts in the United States

Main article: Liberal arts college

Further information: Liberal arts colleges in the United States and Great Books Program

In the United States, Liberal arts colleges are schools emphasizing undergraduate study in the liberal arts. Traditionally earned over four years of full-time study, the student earned either a Bachelor of Arts degree or a Bachelor of Science degree; on completing undergraduate study, students might progress to either a graduate school or a professional school (public administration, business, law, medicine, theology). The teaching is Socratic,^{[citation needed]} to small classes,^{[citation needed]} and at a greater teacher-to-student ratio than at universities;^{[citation needed]} professors teaching classes are allowed to concentrate more on their teaching responsibilities than primary research professors or graduate student teaching assistants, in contrast to the instruction common in universities.^{[original research?][dubious – discuss]} Despite the European origin of the liberal arts college,^[6] the term liberal arts college usually denotes liberal arts colleges in the United States.

See also

• Bachelor of Arts
• Bachelor of General Studies
• Bachelor of Liberal Arts
• Bachelor of Liberal Studies
• Doctor of Liberal Studies
• Great Books Program
• Great Books Programs in Canada
• Liberal arts college
• Master of Liberal Studies
• The Mechanical Arts

 References

1. ^ "Liberal Arts: Encyclopedia Britannica Concise". Encyclopedia Britannica.
2. ^ Ernst Robert Curtius, European Literature and the Latin Middle Ages [1948], trans. Willard R. Trask (Princeton: Princeton University Press, 1973), p. 37. The classical sources include Cicero, De Oratore, I.72–73, III.127, and De re publica, I.30.
3. ^ H. I. Marrou, A History of Education in Antiquity [1948], trans. George Lamb (London: Sheed & Ward, 1956), pp. 266–67.
4. ^ Seneca Epistle 88 at Stoics.com
5. ^ "James Burke: The Day the Universe Changed In the Light Of the Above".
6. ^ Harriman, Philip (1935). "Antecedents of the Liberal Arts College". The Journal of Higher Education, Vol. 6, No. 2 (1935), pp. 63–71.

 Further reading

• Blaich, Charles, Anne Bost, Ed Chan, and Richard Lynch. "Defining Liberal Arts Education." Center of Inquiry in the Liberal Arts, 2004.
• Blanshard, Brand. The Uses of a Liberal Education: And Other Talks to Students. (Open Court, 1973. ISBN 0-8126-9429-5)
• Friedlander, Jack. Measuring the Benefits of Liberal Arts Education in Washington's Community Colleges. Los Angeles: Center for the Study of Community Colleges, 1982a. (ED 217 918)
• Joseph, Sister Miriam. The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric. Paul Dry Books Inc, 2002.
• Pfnister, Allen O. "The Role of the Liberal Arts College." The Journal of Higher Education. Vol. 55, No. 2 (March/April 1984): 145–170.
• Reeves, Floyd W. "The Liberal-Arts College." The Journal of Higher Education. Vol. 1, No. 7 (1930): 373–380.
• Seidel, George. "Saving the Small College." The Journal of Higher Education. Vol. 39, No. 6 (1968): 339–342.
• Winterer, Caroline.The Culture of Classicism: Ancient Greece and Rome in American Intellectual Life, 1780–1910. Baltimore: Johns Hopkins University Press, 2002.
• Wriston, Henry M. The Nature of a Liberal College. Lawrence University Press, 1937.
• T. Kaori Kitao, William R. Kenan, Jr. (27 March 1999). The Usefulness Of Uselessness. Keynote Address, The 1999 Institute for the Academic Advancement of Youth's Odyssey at Swarthmore College.

 External links

• The Annapolis Group/College News
• The Classical Liberal Arts Academy
• Philosophy of Liberal Education
• Liberal Arts at the Community College
• A Descriptive Analysis of the Community College Liberal Arts Curriculum
• The Center of Inquiry in the Liberal Arts
• Academic Commons
• CatholiCity: Catholic Encyclopedia
• What are the liberal arts? at liberalartsadvantage.com
•  "Arts, Liberal". New International Encyclopedia. 1905.

Quadrivium

The quadrivium comprised the four subjects, or arts, taught in medieval universities after the trivium. The word is Latin, meaning "the four ways" or "the four roads". Together, the trivium and the quadrivium comprised the seven liberal arts.^[1] The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium made up of grammar, logic (or dialectic, as it was called at the times), and rhetoric. In turn, the quadrivium was considered preparatory work for the serious study of philosophy and theology.

Contents 1 Origins 2 Medieval usage 3 Modern usage 4 See also 5 References

Origins

These four studies compose the secondary part of the curriculum outlined by Plato in The Republic, and are described in the seventh book of that work.^[1] The quadrivium is implicit in early Pythagorean writings and in the De nuptiis of Martianus Capella, although the term was not used until Boethius early in the sixth century.^[2] As Proclus wrote:

The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving^[3].

Medieval usage

At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA the student could enter for Bachelor's degrees of the higher faculties (Theology, Medicine or Law). To this day some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt. degrees are examples in the field of philosophy, and the B.Mus. remains a postgraduate qualification at Oxford and Cambridge universities).

The study was eidetic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus, namely arithmetic and music on the one hand,^[4] and geometry and cosmology on the other.^[5]

The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the music intervals created by the division of a monochord. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised both in European and Islamic cultures.

Modern usage

In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered as the study of number and its relationship to physical space or time: arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time. Morris Kline classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number.^[6]

This schema is sometimes referred to as "classical education" but it is more accurately a development of the 12th and 13th centuries with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the classical education movement.

See also

• Andreas Capellanus
• The Classical education movement
• Degrees of the University of Oxford

 References

1. ^ ^{a b}  "Quadrivium". New International Encyclopedia. 1905.
2. ^ Henri Irénée Marrou, "Les Arts Libéreaux dans l'Antiquité Classique", pp. 6-27 in Arts Libéraux et Philosophie au Moyen Âge, (Paris: Vrin / Montréal: Institut d'Études Médiévales), 1969, pp. 18-19.
3. ^ Proclus, A commentary on the first book of Euclid's Elements, xii, trans. Glenn Raymond Morrow (Princeton: Princeton University Press) 1992, pp. 29-30. ISBN 0691020906.
4. ^ Craig Wright, The Maze and the Warrior - Symbols in Architecture, Theology, and Music, Harvard University Press 2001
5. ^ Laura Ackerman Smoller, History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350-1420, Princeton University Press 1994
6. ^ Morris Kline, "The Sine of G Major", Mathematics in Western Culture, Oxford University Press 1953

Trivium:Three Roads

 

Logic is the art of thinking; grammar, the art of inventing symbols and combining them to express thought; and rhetoric, the art of communicating thought from one mind to another, the adaptation of language to circumstance.Sister Miriam Joseph

 Painting by Cesare Maccari (1840-1919), Cicero Denounces Catiline.

In medieval universities, the trivium comprised the three subjects taught first: grammar, logic, and rhetoric. The word is a Latin term meaning “the three ways” or “the three roads” forming the foundation of a medieval liberal arts education. This study was preparatory for the quadrivium. The trivium is implicit in the De nuptiis of Martianus Capella, although the term was not used until the Carolingian era when it was coined in imitation of the earlier quadrivium.^[1] It was later systematized in part by Petrus Ramus as an essential part of Ramism.

Formal grammar

A formal grammar (sometimes simply called a grammar) is a set of rules of a specific kind, for forming strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context —only their form.

Formal language theory, the discipline which studies formal grammars and languages, is a branch of applied mathematics. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas.

A formal grammar is a set of rules for rewriting strings, along with a "start symbol" from which rewriting must start. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a "recognizer"—a function in computing that determines whether a given string belongs to the language or is grammatically incorrect. To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. One of the interesting results of automata theory is that it is not possible to design a recognizer for certain formal languages.

Parsing is the process of recognizing an utterance (a string in natural languages) by breaking it down to a set of symbols and analyzing each one against the grammar of the language. Most languages have the meanings of their utterances structured according to their syntax—a practice known as compositional semantics. As a result, the first step to describing the meaning of an utterance in language is to break it down part by part and look at its analyzed form (known as its parse tree in computer science, and as its deep structure in generative grammar).

Logic

As a discipline, logic dates back to Aristotle, who established its fundamental place in philosophy. The study of logic is part of the classical trivium.

Averroes defined logic as "the tool for distinguishing between the true and the false"^[4]; Richard Whately, '"the Science, as well as the Art, of reasoning"; and Frege, "the science of the most general laws of truth". The article Definitions of logic provides citations for these and other definitions.

Logic is often divided into two parts, inductive reasoning and deductive reasoning. The first is drawing general conclusions from specific examples, the second drawing logical conclusions from definitions and axioms. A similar dichotomy, used by Aristotle, is analysis and synthesis. Here the first takes an object of study and examines its component parts, the second considers how parts can be combined to form a whole.
Logic is also studied in argumentation theory.^[5]