Monday, April 02, 2012

Justified true belief

 Before Gettier, an historical account brings one up to date?

Euler diagram representing a definition of knowledge.
Justified true belief is one definition of knowledge that states in order to know that a given proposition is true, one must not only believe the relevant true proposition, but one must also have justification for doing so. In more formal terms, a subject S knows that a proposition P is true if, and only if:
  1. P is true
  2. S believes that P is true, and
  3. S is justified in believing that P is true
The 'justified true belief' theory of knowledge suffered a significant setback with the discovery of Gettier problems, situations in which the above conditions were met but that many philosophers disagree that anything is known.[1] Robert Nozick suggested a clarification of "justification" which he believed eliminates the problem: the justification has to be such that were the justification false, the knowledge would be false.

  See also



  • Theory of justification
  • Validity
  • Gettier problem

    •  References

    ^ Chisholm, Roderick (1982). "Knowledge as Justified True Belief". The Foundations of Knowing. Minneapolis: University of Minnesota Press. ISBN 0-8166-1103-3.

    *** 


    Knowledge is a familiarity with someone or something, which can include facts, information, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject. It can be implicit (as with practical skill or expertise) or explicit (as with the theoretical understanding of a subject); and it can be more or less formal or systematic.[1] In philosophy, the study of knowledge is called epistemology, and the philosopher Plato famously defined knowledge as "justified true belief." However no single agreed upon definition of knowledge exists, and there are numerous theories to explain it. The following quote from Bertrand Russell's "Theory of Knowledge" illustrates the difficulty in defining knowledge. "The question how knowledge should be defined is perhaps the most important and difficult of the three with which we shall deal. This may seem surprising: at first sight it might be thought that knowledge might be defined as belief which is in agreement with the facts. The trouble is that no one knows what a belief is, no one knows what a fact is, and no one knows what sort of agreement between them would make a belief true. Let us begin with belief."

    Knowledge acquisition involves complex cognitive processes: perception, communication, association and reasoning; while knowledge is also said to be related to the capacity of acknowledgment in human beings.[2]

    Contents

     

     Theories of knowledge


    Robert Reid, Knowledge (1896). Thomas Jefferson Building, Washington, D.C.
    See also: Epistemology
    “ The eventual demarcation of philosophy from science was made possible by the notion that philosophy's core was "theory of knowledge," a theory distinct from the sciences because it was their foundation… Without this idea of a "theory of knowledge," it is hard to imagine what "philosophy" could have been in the age of modern science.
    ”

    — Richard Rorty, Philosophy and the Mirror of Nature
    The definition of knowledge is a matter of on-going debate among philosophers in the field of epistemology. The classical definition, described but not ultimately endorsed by Plato,[3] specifies that a statement must meet three criteria in order to be considered knowledge: it must be justified, true, and believed. Some claim that these conditions are not sufficient, as Gettier case examples allegedly demonstrate. There are a number of alternatives proposed, including Robert Nozick's arguments for a requirement that knowledge 'tracks the truth' and Simon Blackburn's additional requirement that we do not want to say that those who meet any of these conditions 'through a defect, flaw, or failure' have knowledge. Richard Kirkham suggests that our definition of knowledge requires that the evidence for the belief necessitates its truth.[4]
    In contrast to this approach, Wittgenstein observed, following Moore's paradox, that one can say "He believes it, but it isn't so", but not "He knows it, but it isn't so".[5] He goes on to argue that these do not correspond to distinct mental states, but rather to distinct ways of talking about conviction. What is different here is not the mental state of the speaker, but the activity in which they are engaged. For example, on this account, to know that the kettle is boiling is not to be in a particular state of mind, but to perform a particular task with the statement that the kettle is boiling. Wittgenstein sought to bypass the difficulty of definition by looking to the way "knowledge" is used in natural languages. He saw knowledge as a case of a family resemblance. Following this idea, "knowledge" has been reconstructed as a cluster concept that points out relevant features but that is not adequately captured by any definition.[6]

     Communicating knowledge

    Symbolic representations can be used to indicate meaning and can be thought of as a dynamic process. Hence the transfer of the symbolic representation can be viewed as one ascription process whereby knowledge can be transferred. Other forms of communication include observation and imitation, verbal exchange, and audio and video recordings. Philosophers of language and semioticians construct and analyze theories of knowledge transfer or communication.[citation needed]
    While many would agree that one of the most universal and significant tools for the transfer of knowledge is writing (of many kinds), argument over the usefulness of the written word exists however, with some scholars skeptical of its impact on societies. In his collection of essays Technopoly Neil Postman demonstrates the argument against the use of writing through an excerpt from Plato's work Phaedrus (Postman, Neil (1992) Technopoly, Vintage, New York, pp 73). In this excerpt the scholar Socrates recounts the story of Thamus, the Egyptian king and Theuth the inventor of the written word. In this story, Theuth presents his new invention "writing" to King Thamus, telling Thamus that his new invention "will improve both the wisdom and memory of the Egyptians" (Postman, Neil (1992) Technopoly, Vintage, New York, pp 74). King Thamus is skeptical of this new invention and rejects it as a tool of recollection rather than retained knowledge. He argues that the written word will infect the Egyptian people with fake knowledge as they will be able to attain facts and stories from an external source and will no longer be forced to mentally retain large quantities of knowledge themselves (Postman, Neil (1992) Technopoly, Vintage, New York,pp 74).
    Andrew Robinson also highlights, in his work The Origins of Writing, the possibility for writing to be used to spread false information and therefore the ability of the written word to decrease social knowledge (Robinson, Andrew (2003) The Origins of Writing in Crowley and Heyer (eds) Communication in History: Technology, Culture, Society, Boston pp 34). People are often internalizing new information which they perceive to be knowledge but in reality fill their minds with false knowledge.
    The above points are moot in the modern world. Verbal communication lends itself to the spread of falsehoods much more so than written, as there is no record of exactly what was said or who originally said it (usually neither the source nor the content can be verified). Gossip and rumors are common examples. As to value of writing, the extent of human knowledge is now so great that it is only possible to record it and to communicate it through writing. Major libraries today can have millions of books of knowledge (in addition to works of fiction). It is only recently that audio and video technology for recording knowledge have become available and the use of these still requires replay equipment and electricity. Verbal teaching and handing down of knowledge is limited to those few who would have contact with the transmitter person - far too limited for today's world. Writing is still the most available and most universal of all forms of recording and transmitting knowledge. It stands unchallenged as mankind's primary technology of knowledge transfer down through the ages and to all cultures and languages of the world.

     Situated knowledge

    Situated knowledge is knowledge specific to a particular situation.[7]
    Some methods of generating knowledge, such as trial and error, or learning from experience, tend to create highly situational knowledge. One of the main attributes of the scientific method is that the theories it generates are much less situational than knowledge gained by other methods.[citation needed] Situational knowledge is often embedded in language, culture, or traditions.[citation needed]
    Knowledge generated through experience is called knowledge "a posteriori", meaning afterwards. The pure existence of a term like "a posteriori" means this also has a counterpart. In this case that is knowledge "a priori", meaning before. The knowledge prior to any experience means that there are certain "assumptions" that one takes for granted. For example if you are being told about a chair it is clear to you that the chair is in space, that it is 3D. This knowledge is not knowledge that one can "forget", even someone suffering from amnesia experiences the world in 3D. See also: a priori and a posteriori.[citation needed]

     Partial knowledge

    One discipline of epistemology focuses on partial knowledge. In most cases, it is not possible to understand an information domain exhaustively; our knowledge is always incomplete or partial. Most real problems have to be solved by taking advantage of a partial understanding of the problem context and problem data, unlike the typical math problems one might solve at school, where all data is given and one is given a complete understanding of formulas necessary to solve them.[citation needed]
    This idea is also present in the concept of bounded rationality which assumes that in real life situations people often have a limited amount of information and make decisions accordingly.

    Scientific knowledge

    The development of the scientific method has made a significant contribution to how knowledge is acquired. To be termed scientific, a method of inquiry must be based on gathering observable and measurable evidence subject to specific principles of reasoning and experimentation.[8] The scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses.[9] Science, and the nature of scientific knowledge have also become the subject of Philosophy. As science itself has developed, knowledge has developed a broader usage which has been developing within biology/psychology—discussed elsewhere as meta-epistemology, or genetic epistemology, and to some extent related to "theory of cognitive development".  

    Sir Francis Bacon, "Knowledge is Power"
    Note that "epistemology" is the study of knowledge and how it is acquired. Science is “the process used everyday to logically complete thoughts through inference of facts determined by calculated experiments." Sir Francis Bacon was critical in the historical development of the scientific method; his works established and popularized an inductive methodology for scientific inquiry. His famous aphorism, "knowledge is power", is found in the Meditations Sacrae (1597).[10]
    Until recent times, at least in the Western tradition, it was simply taken for granted that knowledge was something possessed only by humans — and probably adult humans at that. Sometimes the notion might stretch to (ii) Society-as-such, as in (e.g.) "the knowledge possessed by the Coptic culture" (as opposed to its individual members), but that was not assured either. Nor was it usual to consider unconscious knowledge in any systematic way until this approach was popularized by Freud.[11]
    Other biological domains where "knowledge" might be said to reside, include: (iii) the immune system, and (iv) in the DNA of the genetic code. See the list of four "epistemological domains":   Popper, (1975);[12] and Traill (2008:[13] Table S, page 31)—also references by both to Niels Jerne.
    Such considerations seem to call for a separate definition of "knowledge" to cover the biological systems. For biologists, knowledge must be usefully available to the system, though that system need not be conscious. Thus the criteria seem to be:
    • The system should apparently be dynamic and self-organizing (unlike a mere book on its own).
    • The knowledge must constitute some sort of representation of "the outside world",[14] or ways of dealing with it (directly or indirectly).
    • Some way must exist for the system to access this information quickly enough for it to be useful.
    Scientific knowledge may not involve a claim to certainty, maintaining skepticism means that a scientist will never be absolutely certain when they are correct and when they are not. It is thus an irony of proper scientific method that one must doubt even when correct, in the hopes that this practice will lead to greater convergence on the truth in general.[15]

     Religious meaning of knowledge

    In many expressions of Christianity, such as Catholicism and Anglicanism, knowledge is one of the seven gifts of the Holy Spirit.[16]
    The Old Testament's tree of the knowledge of good and evil contained the knowledge that separated Man from God: "And the LORD God said, Behold, the man is become as one of us, to know good and evil…" (Genesis 3:22)

    In Gnosticism divine knowledge or gnosis is hoped to be attained. In Thelema knowledge and conversation with one's Holy Guardian Angel is the purpose of life.[citation needed]
    विद्या दान (Vidya Daan) i.e. knowledge sharing is a major part of Daan, a tenet of all Dharmic Religions.[17] Hindu Scriptures present two kinds of knowledge, Paroksh Gyan and Prataksh Gyan. Paroksh Gyan (also spelled Paroksha-Jnana) is secondhand knowledge: knowledge obtained from books, hearsay, etc. Prataksh Gyan (also spelled Prataksha-Jnana) is the knowledge borne of direct experience, i.e., knowledge that one discovers for oneself.[18] Jnana yoga ("path of knowledge") is one of three main types of yoga expounded by Krishna in the Bhagavad Gita. (It is compared and contrasted with Bhakti Yoga and Karma yoga.)

    In Islam, knowledge (Arabic: علم, ʿilm) is given great significance. "The Knowing" (al-ʿAlīm) is one of the 99 names reflecting distinct attributes of God. The Qur'an asserts that knowledge comes from God (2:239) and various hadith encourage the acquisition of knowledge. Muhammad is reported to have said "Seek knowledge from the cradle to the grave" and "Verily the men of knowledge are the inheritors of the prophets". Islamic scholars, theologians and jurists are often given the title alim, meaning "knowledgable".[citation needed]

    In Jewish tradition, knowledge (Hebrew: דעת da'ath) is considered one of the most valuable traits a person can acquire. Observant Jews recite three times a day in the Amidah "Favor us with knowledge, understanding and discretion that come from you. Exalted are you, Existent-One, the gracious giver of knowledge." The Tanakh states, "A wise man gains power, and a man of knowledge maintains power", and "knowledge is chosen above gold".

     See also

     References

    1. ^ http://oxforddictionaries.com/view/entry/m_en_us1261368#m_en_us1261368
    2. ^ Stanley Cavell, "Knowing and Acknowledging," Must We Mean What We Say? (Cambridge University Press, 2002), 238–266.
    3. ^ In Plato's Theaetetus, Socrates and Theaetetus discuss three definitions of knowledge: knowledge as nothing but perception, knowledge as true judgment, and, finally, knowledge as a true judgment with an account. Each of these definitions is shown to be unsatisfactory.
    4. ^ http://www.centenary.edu/attachments/philosophy/aizawa/courses/epistemologyf2008/kirkham1984.pdf
    5. ^ Ludwig Wittgenstein, On Certainty, remark 42
    6. ^ Gottschalk-Mazouz, N. (2008): „Internet and the flow of knowledge“, in: Hrachovec, H.; Pichler, A. (Hg.): Philosophy of the Information Society. Proceedings of the 30. International Ludwig Wittgenstein Symposium Kirchberg am Wechsel, Austria 2007. Volume 2, Frankfurt, Paris, Lancaster, New Brunswik: Ontos, S. 215–232. http://www.uni-stuttgart.de/philo/fileadmin/doc/pdf/gottschalk/ngm-internetflow-2008.pdf
    7. ^ Haraway, Donna 1998. Situated Knowledges: The Science Question in Feminism and the Privilege of Partial Perspective.
    8. ^ "[4] Rules for the study of natural philosophy", Newton 1999, pp. 794–6, from the General Scholium, which follows Book 3, The System of the World.
    9. ^ scientific method, Merriam-Webster Dictionary.
    10. ^ "Sir Francis Bacon - Quotationspage.com". Retrieved 2009-07-08.
    11. ^ There is quite a good case for this exclusive specialization used by philosophers, in that it allows for in-depth study of logic-procedures and other abstractions which are not found elsewhere. However this may lead to problems whenever the topic spills over into those excluded domains—e.g. when Kant (following Newton) dismissed Space and Time as axiomatically "transcendental" and "a priori" — a claim later disproved by Piaget's clinical studies. It also seems likely that the vexed problem of "infinite regress" can be largely (but not completely) solved by proper attention to how unconscious concepts are actually developed, both during infantile learning and as inherited "pseudo-transcendentals" inherited from the trial-and-error of previous generations. See also "Tacit knowledge".
      • Piaget, J., and B.Inhelder (1927 / 1969). The child's conception of time. Routledge & Kegan Paul: London.
      • Piaget, J., and B.Inhelder (1948 / 1956). The child's conception of space. Routledge & Kegan Paul: London.
    12. ^ Popper, K.R. (1975). "The rationality of scientific revolutions"; in Rom Harré (ed.), Problems of Scientific Revolution: Scientific Progress and Obstacles to Progress in the Sciences. Clarendon Press: Oxford.
    13. ^ http://www.ondwelle.com/OSM02.pdf
    14. ^ This "outside world" could include other subsystems within the same organism—e.g. different "mental levels" corresponding to different Piagetian stages. See Theory of cognitive development.
    15. ^ http://philosophybites.com/2007/12/barry-stroud-on.html
    16. ^ "Part Three, No. 1831". Catechism of the Catholic Church. Retrieved 2007-04-20.
    17. ^ Knowledge Donation is the primary donation
    18. ^ Swami Krishnananda. "Chapter 7". The Philosophy of the Panchadasi. The Divine Life Society. Retrieved 2008-07-05. 
    ***

    The Theaetetus (Greek: Θεαίτητος) is one of Plato's dialogues concerning the nature of knowledge. The framing of the dialogue begins when Euclides tells his friend Terpsion that he had written a book many years ago based on what Socrates had told him of a conversation he'd had with Theaetetus when Theaetetus was quite a young man. (Euclides also notes that he'd had to go back to Socrates to ask some more questions about the speeches due to his spotty recollection of the account.)
    Euclides is prompted to share his book when Terpsion wonders where he'd been: Euclides, who apparently can usually be found in the marketplace of Megara, was walking outside of the city and had happened upon Theaetetus being carried from Corinth to Athens with a case of dysentery and a minor war wound; Euclides remarks that Socrates had made some uncanny predictions about Theaetetus needing to rise to fame. Euclides' book is read aloud to the two men by a slave boy in the employ of Euclides.
    In this dialogue, Socrates and Theaetetus discuss three definitions of knowledge: knowledge as nothing but perception, knowledge as true judgment, and, finally, knowledge as a true judgment with an account. Each of these definitions is shown to be unsatisfactory. The conversation ends with Socrates' announcement that he has to go to court to answer to the charges that he has been corrupting the young and failing to worship Athenian Gods.

    Contents

     

     Midwife to knowledge

    Socrates asks Theodorus if he knows of any geometry students who show particular promise. Theodorus assures him that he does, but that he does not want to over-praise the boy, lest anyone suspect he is in love with him. He says that the boy, Theaetetus, is a young Socrates look-alike, rather homely, with a snub-nose and protruding eyes. The two older men spot Theaetetus rubbing himself down with oil, and Theodorus reviews the facts about him, that he is intelligent, virile, and an orphan whose inheritance has been squandered by trustees.
    Socrates tells Theaetetus that he cannot make out what knowledge is, and is looking for a simple formula for it. Theaetetus says he really has no idea how to answer the question, and Socrates tells him that he is there to help. Socrates says he has modelled his career after his midwife mother. She delivered babies and for his part, Socrates can tell when a young man is in the throes of trying to give birth to a thought.

     Philosophical labor

    Socrates thinks that this idea must be identical in meaning, if not in actual words, to Protagoras' famous maxim "Man is the measure of all things." Socrates wrestles to conflate the two ideas, and stirs in for good measure a claim about Homer being the captain of a team of Heraclitan flux theorists. Socrates dictates a complete textbook of logical fallacies to the bewildered Theaetetus. When Socrates tells the child that he (Socrates) will later be smaller without losing an inch because Theaetetus will have grown relative to him, the child complains of dizziness (155c). In an often quoted line, Socrates says with delight that "wonder (thaumazein) belongs to the philosopher". He admonishes the boy to be patient and bear with his questions, so that his hidden beliefs may be yanked out into the bright light of day.

     Examining the offspring

    When Socrates sums up what they have agreed on so far, it becomes problematic that knowledge is sense perception, for Socrates raises the question that "When the same wind blows, one of us feels cold and the other not?" As a result he introduces the idea of Heraclitean flux to act as a defense to the wind objection. Heracliteanism shows that "Nothing is in itself just one thing...Everything is in a process of coming to be". Thus as there is no fixed meaning in things, but they draw their meaning in a referential difference to other things, the wind objection can be incorporated into Theaetetus's claim that "Knowledge is sense perception". As a result they can then continue their inquiry as to the truth of this claim. It is important to note that the Heraclitean doctrine of Flux is not the same as the Protagorean doctrine. The Protagorean is radical truth relativism whereas the Heraclitean is radical reality relativism. It serves as a supporting theory to the Protagorean interpretation of Theaetetus's claim, in order that they might fully inquire as to the validity of this premise. Socrates admits that it is unfortunate that Protagoras is dead and cannot defend his idea against people such as himself. He says that the two of them are "trampling on his orphan" (164e) but the charge remains.

     Abusing the "orphan" of Protagoras

    Since Protagoras is dead, Socrates puts himself in the sophist's shoes and tries to do him the favor of defending his idea (166a-168c). Socrates continues to find more ways to misinterpret and misrepresent him - "mistreat his orphan." Putting words in the dead sophist's mouth, Socrates declares that Protagoras asserts with his maxim that all things are in motion and whatever seems to be the case, is the case for the perceiver, whether the individual or the state.

    At the end of his speech, Socrates admits to Theodorus that if Protagoras were alive to defend his idea, he would have done a far better job than Socrates has just done. Theodorus tells Socrates that he must be kidding, that he has come to the task with boyish vigor. Theodorus does not claim to be a disciple of Protagoras, but never contradicts Socrates repeated assertions that he is a friend of Protagoras. Socrates admits he has used the child's timidity to aid him in his argument against the doctrine of Protagoras (168d).
    Socrates, not at all certain that he has not misrepresented Protagoras in making each man the measure of his own wisdom, presses Theodorus on the question of whether any follower of Protagoras (himself included) would contend that nobody thinks anyone else is wrong (170c). Theodorus proves to be helpless against Socrates' confusions. He agrees that Protagoras concedes that those who disagree with him are correct (171a). In making Protagoras a complete epistemological relativist, where every person's individual perceptions are his reality and his truth, both Socrates and Theodorus paint Protagoras as maintaining an absurd position. Socrates says that if Protagoras could pop his head up through the ground as far as his neck, he would expose Socrates as a speaker of nonsense, sink out of sight, and take to his heels (171d).

     The absent-minded philosopher

    Socrates then proceeds to explain why philosophers seem clumsy and stupid to the common lot of humanity. Socrates explains that philosophers are open to mockery because they are not concerned about what interests most people: they could not care less about the scandals in their neighbor's house, the tracing of one's ancestry to Heracles, and so on. Instead their thinking wanders around contemptuously, measuring the depths of the earth and contemplating the stars above the sky. It is here that Socrates draws the classic portrait of the absent-minded intellectual who cannot make his bed or cook a meal (175e). Socrates adds a big bifurcation to this speech, saying that there are only two kinds of lives to be lived: a divinely happy one, lived by righteous philosophers or a godless, miserable one, such as most people live (176-177). Socrates admits this was a digression that threatens to drown his original project, which was to define knowledge. Theodorus, the old geometer, tells Socrates that he finds this sort of thing easier to follow than his earlier arguments.

     The men of flux

    Socrates says that the men of flux, like Homer and Heraclitus, are really hard to talk to because you can't pin them down. When you ask them a question, he says, they pluck from their quiver a little aphorism to let fly at you, and as you try to figure that one out, they wing another one at you. They leave nothing settled either in discourse, or in their own minds. Socrates adds that the opposite school of thought, that teaches of the "immovable whole" is just as hard to talk to (181a,b). Socrates says he met the father of the idea, Parmenides, when he was quite young, but does not want to get into another digression over it.

     The mind as a bird cage

    Perhaps the most delightful talk in the dialogue comes near the end, when Socrates compares the human mind to a birdcage. He says it is one thing to possess knowledge and another to have it about one, on hand, as it were (199a). Socrates says that as a man goes hunting about in his mind for knowledge of something, he might grab hold of the wrong thing. He says that mistaking eleven for twelve is like going in for a pigeon and coming up with a dove (199b). Theaetetus joins in the game, and says that to complete the picture, you need to envision pieces of ignorance flying around in there with the birds. But if this is the case, how would you be able to distinguish between the birds representing real knowledge and the ones representing false ones? Are there other birds that represent this type of knowledge? Socrates comes to the conclusion that this is absurd and therefore he discards the birdcage analogy.

     Socrates and the Jury

    After discarding the bird-cage analogy, Socrates and Theaetetus return to the definition of knowledge as 'true judgement' (200e). This, Theaetetus argues, is true because it is 'free from mistakes' (200e). However Socrates introduces an example of a jury in the law-courts, being persuaded of an opinion by a lawyer. This persuasion is not the same as knowing the truth, as all is produced is 'conviction' in judging whatever the lawyers want (201a). Although Theaetetus hopes it is possible the lawyer will be able to 'persuade' the jury of the truth (201b), Socrates is unsatisfied as if they are justly persuaded, they will have true knowledge. However, in Socrates' belief, they cannot make a correct judgement as they would not have true knowledge (201c). With this conflict, Socrates decides that true judgement and knowledge must be different things.

     Knowledge as judgement with an account

    After distinguishing between knowledge and true judgement, Theaetetus recalls being told that true judgement 'with an account (logos) equates to knowledge (201d). Things without an account are 'unknowable', while things with an account are 'knowable'.
    Socrates responds by telling of a dream, in which he overheard people talking of primary elements (201e). These primary elements can only be named, they cannot be thought of as existing or not - he gives examples of words like 'itself, or that, each, alone or this' (202a). While they can be added to other words, they by themselves are just a name. When these elements are added together, Socrates says that a 'complex' is formed (202b). The primary elements are 'unaccountable and unknowable, but perceivable' while the complexes are 'knowable and expressible' and so can be objects of 'true judgement' (202b). He concludes his dream by agreeing with Theaetetus that knowledge is 'true judgement with an account' (202c).
    However, Socrates exposes some difficulties by examining letters. He takes the first two letters of his name, S and O to wonder if the syllable 'So' is knowable while the individual letters are not (203b-d). Theaetetus finds the idea strange, so Socrates deduces that in order to know the syllable, the letters must be known first (203e). Socrates proposes that the syllable can be a 'single form' produced from the letters. With this in mind, Socrates considers whether the 'sum' and the 'whole' are the same (204a). Theaetetus initially says they are not, but changes his mind in confusion when Socrates leads him through maths and the different ways of expressing the number six (204c-205b). After agreeing this, Socrates returns to the subject of syllables and letters to conclude from Theaetetus' answers that syllables are different from letters and cannot contain letters (205b). Theaetetus admits this idea is ridiculous (205c). Socrates returns to talking about elements and complexes to propose that they are in the same class, as they have 'no parts and [are] a single form' (205d).

    Socrates sums up this reversal by remarking that if anyone tries to tell them the complex is knowable and expressable while the element is the opposite, 'we had better not listen to him' (205e). He cites the example of a musician distinguishing individual notes (conceded to be elements of music) to propose that elements are 'much more clearly known'(206b).
    Socrates proposes an account to be 'making one's thought apparent vocally by means of words and verbal expressions' (206d). However, he wonders if that is so, everyone will be able to make judgement 'with an account' as they can all (except for the deaf and dumb) vocalize and express opinions on matters (206e). Socrates examines it further by suggesting that a man who can vocalize his judgement must be able to make reference to the primary elements of the subject (207a). Giving an example of defining a wagon by its individual parts (207a), agreement is reached that an account is 'going through a thing element by element'(207d). Socrates questions Theaetetus by drawing on his learning of how to write, and the idea that if you misplace individual elements (letters) of a name, that does not mean you have knowledge of it (208a). This finishes Socrates' second definition of an account as 'the way to the whole through the elements' (208c). The third definition Socrates offers is 'being able to tell some mark by which the object you are asked about differs from all other things' (208c), giving the example that the Sun is distinct for its brightness. However, this definition of an account fails as by getting to know the differentness of an object, you have to acquire knowledge about it. Thus the answer to the initial question 'What is knowledge' would be heavily circuitous - correct judgement accompanied by 'knowledge' of the differentness, which Socrates admits is 'silly' (210a).

     Conclusion

    Socrates concludes the dialogue by announcing that all the two have produced is mere "wind-eggs" and that he must be getting on now to the courthouse to face his trial being brought against him by Meletus.

     Significant references in the dialogue

    In this dialogue, Socrates refers to Epicharmus of Kos as "the prince of Comedy" and Homer as "the prince of Tragedy", and both as "great masters of either kind of poetry".[note 1] This is significant because it is one of the very few extant references in greater antiquity (Fourth century BC) to Epicharmus and his work. Another reference is in Plato's Gorgias dialogue.

     Footnotes

    1. ^ "Summon the great masters of either kind of poetry- Epicharmus, the prince of Comedy, and Homer of Tragedy", Theaetetus, by Plato, section §152e.[1] (translation by Benjamin Jowett[2]). There is some variability in translation of the passage. Words like "king", "chief", "leader", "master" are used in the place of "prince" in different translations. The basic Greek word in Plato is "akroi" from "akros" meaning topmost or high up. In this context it means "of a degree highest of its kind" or "consummate" (cf. Liddell & Scott, A Greek-English Lexicon).[3]

     References

    1. ^ Theaetetus, by Plato, section §152e.
    2. ^ Theaetetus, by Plato, section §152e. translation by Benjamin Jowett
    3. ^ Liddell & Scott, A Greek-English Lexicon

     Selected secondary literature

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    Friday, March 30, 2012

    Eta Carinae

    Preview of a Forthcoming Supernova

    At the turn of the 19th century, the binary star system Eta Carinae was faint and undistinguished. In the first decades of the century, it became brighter and brighter, until, by April 1843, it was the second brightest star in the sky, outshone only by Sirius (which is almost a thousand times closer to Earth). In the years that followed, it gradually dimmed again and by the 20th century was totally invisible to the naked eye.

    The star has continued to vary in brightness ever since, and while it is once again visible to the naked eye on a dark night, it has never again come close to its peak of 1843.


    The larger of the two stars in the Eta Carinae system is a huge and unstable star that is nearing the end of its life, and the event that the 19th century astronomers observed was a stellar near-death experience. Scientists call these outbursts supernova impostor events, because they appear similar to supernovae but stop just short of destroying their star.


    Although 19th century astronomers did not have telescopes powerful enough to see the 1843 outburst in detail, its effects can be studied today. The huge clouds of matter thrown out a century and a half ago, known as the Homunculus Nebula, have been a regular target for Hubble since its launch in 1990. This image, taken with the Advanced Camera for Surveys High Resolution Channel is the most detailed yet, and shows how the material from the star was not thrown out in a uniform manner, but forms a huge dumbbell shape.

    Eta Carinae is not only interesting because of its past, but also because of its future. It is one of the closest stars to Earth that is likely to explode in a supernova in the relatively near future (though in astronomical timescales the “near future” could still be a million years away). When it does, expect an impressive view from Earth, far brighter still than its last outburst: SN 2006gy, the brightest supernova ever observed, came from a star of the same type.

    This image consists of ultraviolet and visible light images from the High Resolution Channel of Hubble’s Advanced Camera for Surveys. The field of view is approximately 30 arcseconds across.

    Links

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    Thursday, March 29, 2012

    Hubble Legacy Archive



    Welcome to the Hubble Legacy Archive 

     The Hubble Legacy Archive (HLA) is designed to optimize science from the Hubble Space Telescope by providing online, enhanced Hubble products and advanced browsing capabilities. The HLA is a joint project of the Space Telescope Science Institute (STScI), the Space Telescope European Coordinating Facility (ST-ECF), and the Canadian Astronomy Data Centre (CADC).
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    See Also: The Hubble Legacy Archive For You
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    Relativism

    The Nobel Prize in Physics 1914 Max von Laue

    I am not sure what I can add other then what I have already been saying toward logical deduction....I still need to get a handle on the essence of what is being said here in opening thread.

    So with what I looked at, can we say that the deductive recognition of lets say symmetry would be in contrast to how you might look at the world in a relativistic sense versus Platonism.










    See: Against Symmetry

    This setting was used more I think in terms of how a scientist is explaining himself and his relationship with the way in which he had approached science.....yet I could see there were scientist who had adopted the Platonic Tradition. Example of Penrose and Coxeter were demonstrative of this idea?


    5.4.3 Platonism and Relativism

    Platonism is a family of views that get their name because they involve entities--propositions, properties, sets--which, like Plato's Forms, are held to be abstract, immutable things that exist outside space and time. On many platonistic approaches, concepts express abstract properties and beliefs are relations between people and abstract propositions. This suggests a way around some types of relativism, since people in quite different cultures could have many of the same beliefs (because they could believe the same abstract propositions), and a belief would be true just in case the immutable proposition it expresses is true.
    The relativist may reply that platonistic accounts lead to severe difficulties in epistemology and semantics. The problem is that we are physical organisms living in a spatio-temporal world, and we cannot interact causally (or in any other discernible way) with abstract, causally inert things. Moreover, few people are aware of having any special cognitive faculty that puts them in touch with a timeless realm of abstract objects, neuroscientists have never found any part of the brain that subserves such an ability, such a view is not suggested by what is known about the ways children acquire concepts and beliefs, and nothing in physics suggests any way in which a physical system (the brain) can make any sort of contact with causally inert, non-physical objects. Moreover, if our minds cannot make epistemic contact with such things, it is difficult to see how our words and linguistic practices can make semantic contact with them.
    None of this proves that abstract propositions don't exist, but it shows it isn't obvious that they do. There have been few debates between relativists and platonists over such matters, however, perhaps because the two views lie so far apart that their proponents cannot easily engage one another.

    So these were two positions that were adopted within the push toward understanding the basis of science and it's mathematics.

    In theory model development was pushed forward on the basis of such adoptions. Loop Quantum Gravity?

    Quasicrystal: Prof. Dan Shechtman

    ***


    Just throwing some stuff together in order to understand the extent of relativism as a universal truth, while seeking to understand the subjective realism that make up our individuality. As a layman I do not know if it will be useful under that admittance. You can judge for yourself of course.

    Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall

    If one was to solidify some basis to truth how would this be done? The question of a logic oriented view for me saw a basis in what Penrose was explaining using his Twistors, as a foundation in incorporating Fuzzy logic?

    While examining the psychological model of Venn logic and TA combined, it was important that there be some relative framework for such a subjective interpretation of a logic orientated world. How subjectively could this have been managed?


    Perspective of the Theoretical Scientist

    So you have this history and theoretical perspective that sees the world in one way or another? How do you reduce it to a process through Computing that establishes a basis in machining the effects of [and\or-so that we say a statement is .7 true and .3 false.]? We've created a space in between a true and false statement?

    DNA computing is a form of computing which uses DNA, biochemistry and molecular biology, instead of the traditional silicon-based computer technologies. DNA computing, or, more generally, molecular computing, is a fast developing interdisciplinary area. Research and development in this area concerns theory, experiments and applications of DNA computing See:DNA computing

    Entanglement then provides for other understanding then of a framework that sees the interrogation of a subjective world?


    Do we selectively ignore other models from artificial intelligence such as Zadeh's Fuzzy Logic? This is a logic used to model perception and used in newly designed "smart" cameras. Where standard logic must give a true or false value to every proposition, fuzzy logic assigns a certainty value between zero and one to each of the propositions, so that we say a statement is .7 true and .3 false. Is this theory selectively ignored to support our theories? Ideas on Quantum Interrogation
    ***

    Geometry Leads us to the Truth?

    Part of the realism here for me is the idea that such patterns established deep within our psyche are inherent in each of us as an image first to our awareness, but encompasses a geometric patten of sorts. This was part of the work I did on myself as I explored the realm of dreams. The idea then manifested in what was the basis of this thought process as mandala in origins. A historical vision of an ancient idea of model building. In today's world I thought this as appropriate toward how theoretical ideas are built around a whole history of science and information.
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    Sunday, March 25, 2012

    On the Question of a Daemon

    ( Arthur Koestler on Creativity )


     You’ve seen it before? Perhaps you found it scrawled in goat’s blood on the walls of an abysmal abbey, written in the crabbed hand of one who purported to teach the whole of the law...Ain Soph

    Just so you understand that what happens in the past may have set the course for humanity in thinking such and such so  is with some concern that anyone would think that what I had to say resounds with such historical distaste of what the future might bring?

    Historical Figures Lead Us to the Topic of Entanglement

     
    We do no want to be ever so arrogant that we cannot see the seeds of the past had paved the way for our understanding of that future and spread the progression of the subject so as to be well founded in experimental processes necessary.



    But, said Timarchus, I see nothing but stars leaping about the hollow, some carried into it, and some darting out of it again. These, said the voice, are Daemons; for thus it is. Every soul hath some portion of reason; a man cannot be a man without it; but as much of each soul as is mixed with flesh and appetite is changed, and through pain or pleasure becomes irrational. Every soul doth not mix herself after one sort; for some plunge themselves into the body, and so in this life their whole frame is corrupted by appetite and passion; others are mixed as to some part, but the purer part still remains without the body, — it is not drawn down into it, but it swims above, and touches the extremest part of the man’s head; it is like a cord to hold up and direct the subsiding part of the soul, as long as it proves obedient and is not overcome by the appetites of the flesh. That part that is plunged into the body is called the soul, but the uncorrupted part is called the mind, and the vulgar think it is within them, as likewise they imagine the image reflected from a glass to be in that. But the more intelligent, who know it to be without, call it a Daemon. Therefore those stars which you see extinguished imagine to be souls whose whole substances are plunged into bodies; and those that recover their light and rise from below, that shake off the ambient mist and darkness, as if it were clay and dirt, to be such as retire from their bodies after death; and those that are carried up on high are the Daemons of wise men and philosophers. See:A DISCOURSE CONCERNING SOCRATES’S DAEMON. - Plutarch, The Morals,

    The question raises the idea that with "matter trained" we had lost our way in terms of what matters. What we work has somehow become the the part of the belief that we no longer hold to what spiritually might be capable of, but steadfastly have chosen matter as the principle of some higher intelligence?
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    Saturday, March 24, 2012

    Journal Club

    A journal club is a group of individuals who meet regularly to critically evaluate recent articles in scientific literature. Journal clubs are usually organized around a defined subject in basic or applied research. For example, the application of evidence-based medicine to some area of medical practice can be facilitated by a journal club. Typically, each participant can voice their view relating to several questions such as the appropriateness of the research design, the statistics employed, the appropriateness of the controls that were used, etc. There might be an attempt to synthesize together the results of several papers, even if some of these results might first appear to contradict each other. Even if the results of the study are seen as valid, there might be a discussion of how useful the results are and if these results might lead to new research or to new applications.

    Journal clubs are sometimes used in the education of graduate or professional students. These help make the student become more familiar with the advanced literature in their new field of study. In addition, these journal clubs help improve the students' skills of understanding and debating current topics of active interest in their field. This type of journal club may sometimes be taken for credit. Research laboratories may also organize journal clubs for all researchers in the lab to help them keep up with the literature produced by others who work in their field.

     History

    The earliest references to a journal club is found in a book of memoirs and letters by the late Sir James Paget, a British surgeon, who describes a group at St. Bartholomew's Hospital in London in the mid-19th century as "a kind of club ... a small room over a baker's shop near the Hospital-gate where we could sit and read the journals."[1]
    Sir William Osler established the first formalized journal club at McGill University in Montreal in 1875. The original purpose of Osler's journal club was "for the purchase and distribution of periodicals to which he could ill afford to subscribe."[2]

    External links

     References

    1. ^ Esisi, Martina. "Journal clubs." BMJ Careers. 13 Oct. 2007. Web. 09 Jan. 2010. <http://careers.bmj.com/careers/advice/view-article.html?id=2631#ref2>.
    2. ^ Milbrandt, Eric B., and Jean-Louis Vincent. "Evidence-based medicine journal club." Critical Care (2004): 401-02. PubMed. U.S. National Library of Medicine, 3 Nov. 2004. Web. 10 Jan. 2010. <http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1065082/>

    ***

    See Also: Journal Club – Black Holes Made All The Difference by Steve Nerlich on March 24, 2012
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    Friday, March 23, 2012

    Intuition

    Like Truth.....how is it one could have found any use of such an subjective tool while recognizing something inherent in the process of discovery? Your thoughts?

    Here's two quotes for consideration.

    Intuition and Logic in Mathematics by Henri Poincaré

    On the other hand, look at Professor Klein: he is studying one of the most abstract questions of the theory of functions to determine whether on a given Riemann surface there always exists a function admitting of given singularities. What does the celebrated German geometer do? He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws. He connects two of its points with the two poles of a battery. The current, says he, must pass, and the distribution of this current on the surface will define a function whose singularities will be precisely those called for by the enunciation.

    Felix Klein on intuition

    It is my opinion that in teaching it is not only admissible, but absolutely necessary, to be less abstract at the start, to have constant regard to the applications, and to refer to the refinements only gradually as the student becomes able to understand them. This is, of course, nothing but a universal pedagogical principle to be observed in all mathematical instruction ....

    I am led to these remarks by the consciousness of growing danger in Germany of a separation between abstract mathematical science and its scientific and technical applications. Such separation can only be deplored, for it would necessarily be followed by shallowness on the side of the applied sciences, and by isolation on the part of pure mathematics ....

    In context of examination while not mathematically trained I was always curious about the process unfolding.... the foundations and their beginnings. The Sound Of Billiard Balls

    Dirac became proof for me of the issue of being abstract while needing the image to go with it? Symbolically recognized while analytically described. So his axiomatic stance lead me to question why how and why Feynman designed his "word art(feynman diagrams)?"

    When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.Paul Dirac
    Part of finding this truth is a deep examination(deep play) of what has been perpetuated so far and a meta look synopsis at how to gather and explain it so as to move on.

    The deeper truth is an image that has to be explained? Part of our innateness has left an impression on the soul and recognizing the "time capsule" that is mandala in origins, is the method by which the soul engages what explodes back into their consciousness? This arises from a subconscious level and so too having traveled there you recognize what happens when you touch the very core of your being?

    While I may refer to the geometric as inherent in such a truth in expression as some light behind us shining our shadow on the cave walls, these geometries can be covered by ancient designs and can lead the soul back to this beginning?

    While you were looking out there, you were looking inside.

    ***
    On developing the intuition I had a comment that I wanted to bring together here so it is understood that while we may hold science as a standard within our question for knowledge it is also required that we learn to understand somethings about ourselves in that process.

    See: Understanding our Angels and Daemons
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    Monday, March 19, 2012

    The Truth

    The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann

    Yes, this is what I had in mind too, as too identify the last place with which the historical paved the way to meeting Non Euclidean.





    The amount of dark matter and energy in the universe plays a crucial role in determining the geometry of space. If the density of matter and energy in the universe is less than the critical density, then space is open and negatively curved like the surface of a saddle Geometry of the Universe

    With it's application understood in terms of how one might see the shape of the universe, the truth in understanding is the search for how our universe does have a basis in a geometrical truth? What shape then?

    Riemannian Geometry, also known as elliptical geometry, is the geometry of the surface of a sphere. It replaces Euclid's Parallel Postulate with, "Through any point in the plane, there exists no line parallel to a given line." A line in this geometry is a great circle. The sum of the angles of a triangle in Riemannian Geometry is > 180°.


    If one understands the purpose of the truth with which is presented "on the scales" what relationship is subjectively compared to how gravity may affect the idea of an emotive world that is circumspect by our views being contained/weight. It could be as much "as a fog that exists" until some idea of a "clear light like perspective" is understood? How our perception of earth has now been transformed from the pearl in space to some strange looking rock in space

    ***
    Galileo Galilei

    In 1586 at the age of 22, Galileo (1564-1642) wrote a short treatise entitled La Bilancetta (“The Little Balance”). He was skeptical of Vitruvius’s account of how Archimedes determined the fraud in Hiero's crown and in this treatise presented his own theory based on Archimedes’ Law of the Lever and Law of Buoyancy. He also included a description of a hydrostatic balance that determined the precise composition of an alloy of two metals.

    So on a subjective level we want to put forward the best constitution that we can so we try and find the basis of this truth as it would apply to all people. I think this is what came out of Benjamin Franklin when he was involved in the writing of the US Constitution. perusing Jefferson words as to better clarify the meaning of.

    We hold (they say) these truths to be self-evident: That all men are created equal. In what are they created equal? Is it in size, understanding, figure, moral or civil accomplishments, or situation of life? Benjamin Franklin-The Gentleman's Magazine, vol. 46, pp. 403–404)

    When I spoke of Benjamin Franklin I was referring to a philosophical truth that is inductive\deductive.




    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.

    Even with all the scientific truth that is as tested, as an individual finding that place within with which such a conclusion is arrived at.....is much like "setting the tone" that will reverberate though your whole life?

    The truth is not just mathematical although such reductionism can be sought to have been derived from First Principles? Where is this place? Where inside is this place?

    ***

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