Modern 'design theory'

PLATO'S DISCUSSION OF KNOWLEDGE IN THE THEAETETUS AND THE REPUBLIC Socrates Plato

By Nigel J. A. Holden University of Central Lancashire In discussing Plato's theory of knowledge I propose to offer the view that his discussion of this topic in both The Republic and the Theaetetus not only represents a unified theory of knowledge, but that this argument is linear in nature - that there are no discrepancies, though it may appear there are - and that all parts work as a unified whole to bring the reader to a specific conceptual destination.

On and contrast Plato's discussion of knowledge in The Republic and Theaetetus.

In discussing Plato's theory of knowledge I propose to offer the view that his discussion of this topic in both The Republic and the Theaetetus not only represents a unified theory of knowledge, but that this argument is linear in nature - that there are no discrepancies, though it may appear there are - and that all parts work as a unified whole to bring the reader to a specific conceptual destination. This concept of a unified doctrine is based on a reading of the presentation of the theory of knowledge, which does appear to begin in The Republic and conclude in the Theaetetus. But is this apparent relationship support by the chronology in which the dialogues were written? It is generally accepted that Plato's dialogues fit into the three groups: early (also known as Group I), middle (Group II), and late (Group III) - as defined by Campbell, using an analysis of both style and content (Kahn, 1996, p. 43-4). Campbell assigns both The Republic and Theaetetus to Group II. For our study it is important to have some idea of where The Republic and Theaetetus stand in chronology within Group II. Kahn believes that The Republic is the first text chronologically of Group II, and that the Theaetetus is the last text written within that same group. Kahn's attempt to arrange the texts is based on the literary presentation of Socrates, and 'the different approaches to the philosophical position within The Republic' (Kahn, 1996, p. 48). This approach does seem reasonable, and I believe is validated by the order of argument within these two dialogues. This then will be my approach within this essay. I shall begin with The Republics' principle Cave and Line analogy, showing their relationship to each other. Then I shall introduce the discussions on knowledge within the Theaetetus, breaking this down into its two principle parts. Therein I shall show the significance of the Cave and Line analogy, and thus the answer to the problem as contained within Theaetetus.

The Republic is essentially a discussion on how a State should be run. The main thrust of this is a discussion of justice - is it better to be just or unjust? The discussions are, therefore, of an ethical nature (Brown, 2003). In trying to define his ethical terms, Plato has to show what 'knowledge' is - and for Plato this concept is central because it affects how the individual acts, and therefore how society should function (since his political society would be lead by philosophers - those who had gained true knowledge).

In book VI (509d) we are presented with the analogy of the line. We are to take a line and split it into two unequal sections - one representing the visible , the other the intelligible. This line has to be split again in the same ratio. One subsection of the visible then contains the images (perception), the other the originals of these images
(belief). The intelligible is also subdivided - the lower section representing mathematics (understanding), the higher section reason. Socrates (509d) clearly states that the intellectual world and the visible worlds must be kept in mind as two distinct kingdoms. As Murphy (1932) clearly points out to us, this analogy is to be taken literally. The purpose of the Line is to categorise things as they appear to us in reality - and the point of this is to act as a key to understanding the Cave analogy.

The allegory of the Cave at the beginning of Book VII presents us with a story of prisoners chained in a cave. They face a wall, and cannot move. Behind them a fire burns, and between them and the fire a wall, upon which people walk and move many things. These cast shadows on the wall the prisoners face, and from the shadows they guess at what is really behind them. One of these prisoners is set free, and he makes it to the surface. But he cannot look at things directly in the sunlight because it is too much for his eyes to cope with - he looks at reflections in the water. Eventually he becomes used to the daylight, and begins to look at things directly as they are. He then goes back into the cave, and sees that his fellow prisoners do not really know from the shadows what is truly behind them. In this simile the shadows, and those things in the dark, are symbols of the visibles themselves. Those visibles seen clearly in the light of day are those things perceived by the intellect (this is clearly stated in 508 c-d). The people living in the cave are symbolic of those who have not as yet turned towards the ideal world - their perception of the visibles is limited, and not enlightened by the intellect. The purpose of this whole analogy is to show the way to escape the entrapment of the visible (sensual) world (Murphy, 1932). It is made quite clear in 508d that the soul is blind when it focuses on sensible things, but when focused on ideas it is enlightened. This enlightenment is due to the Good who gives truth (508e) to the intellect. In both the Line and Cave simile opinion is contrasted with knowledge. Those inside the cave have opinions, while he who escapes into the world of the sun sees things for what they are.

The Cave simile clearly shows us the path of the individual from shadows to illumined understanding of the truth of all things (Murphy, 1932). Murphy believes there are three levels to this enlightenment - the first the mental level of the un-philosophical (this is seen in the firelight images); the second that of mathematics (the puppets, the originals of these images); and finally that of the dialectic, the originals of the puppets outside the Cave - seen in shadow, then in the water, and finally directly themselves via the sunlight. Although there are only three stages, there are four grades of reality - firelight images, puppets, the originals of puppets outside the cave, and the things themselves seen in sunlight - and these four grades correspond with the four points of the Line. This conversion from the superficial view of life, to the philosophical is achieved via an intellectual education, as Socrates explicitly states in 524 d-e (Murphy, 1932).

It is the second level of enlightenment - that of mathematics - which is of vital importance to Plato. When using mathematics the intellect is using the 'intelligible character' to look at sensible things (Murphy, 1932). This is a half way point, where the mind is being induced into the intellectual sphere through visibles - but it is incomplete, it is still dependent on the visible realm, and so the ideas derived in this way are inferior in nature. It is this that is the 'conversion' referred to in 525a (Murphy. 1932). After this occurs the ascent: once he is converted man is able to ascend towards the Good, and so see things as they actually are with all clarity, as stated in 521c (Murphy, 1932).

In the Line analogy Murphy claims Plato does no more than prepare the reader for the analogy of the Cave - Plato does this by giving us, via the Line, the ratios of the groups of things which are in the Cave analogy
(Murphy, 1932). The groups are descriptions of things as they appear in reality. The Line, then, is a list of the four classes of objects and their corresponding states of mind, graded 'according to reality and clearness'
(Murphy, 1932). The Cave analogy shows us how the individual through education rises through these real objects (Murphy, 1932). The prisoner who is released passes through these things, represented in the Cave via the different regions. Hence, the Line is a description of states of mind, whereas the Cave is about stages of development (Murphy, 1932).

The Theaetetus is a presentation of a dialogue between Socrates and Theaetetus, a student of mathematics. Socrates poses the question to Theaetetus of, 'what is knowledge?' - and to this Theaetetus gives many examples from the sciences. These are not acceptable to Socrates - but slowly a definition is built up, beginning with knowledge as perception; then, knowledge as true belief; and finally knowledge as true belief with an account (logos). Socrates dream sequence, in which it is shown him that we cannot have knowledge because we cannot know elements, is a central tool by which the answer to this conundrum is given. The dialogue appears to end in aporia - there is no way of answering the question, 'What is knowledge' (Chappell, 2005).

This dialogue is split into two principle arguments. In the first part of the argument (which begins at 185c) Plato states that those things of existence which belong to sense perception are not themselves objects of sense perception (in their being, or existence). (Holland, 1973). Plato informs us (184e-185c) that any object of sense perception is private to that sense (Holland, 1973). What he wants is for us to recognise - and he tells us in 186 - that being (existence) is the common feature of all things and that this cannot be perceived by the senses (Holland, 1973). Now if each sense perceives privately it cannot possibly perceive the same 'existence' as another sense - and yet the objects of the different senses do share the same 'existence'. Hence, 'existence' cannot be known through the senses (Holland, 1973).

In the second stage of the argument we are told that awareness of 'existence' is necessarily apart of knowledge, and hence true knowledge involves more than the senses
(Holland, 1973). In 186c-d it is pointed out that Plato believes that we need to grasp 'existence' in order to be able to know truth - which in turn gives us knowledge. But Plato has made it abundantly clear to us that we cannot know of existence via our senses. So, how can we attain the knowledge of existence?

In The Republic the same problem is related - the problem, that is, of sense perception. In 523-4 we are told that the senses give us an inadequate report of their objects, and it is the mind that has to make sense of what is perceived. We arrive at the same conclusion as the Theaetetus - the senses do not put us in touch with reality, and therefore existence as it is (Holland, 1973).

Let us return to the Theaetetus in the hope of answering this riddle. The main thrust of the Theaetetus is a discussion of the validity of the statement 'that knowledge is true belief with an account' (Fine, 1979). The first stage of this discussion is carried out via Socrates' dream, which states that some things are unknowable (the basic elements of anything), and the regress of the theory of knowledge based on knowledge is finite. Essentially this means nothing is knowable, since knowledge cannot be based on nothing. Plato rejects this thesis, insisting on the idea that knowledge is true belief with a logos. The logos referred to is a list of a given thing's elements (206e - 207). This is the same thing as the 'What is it?' question of Socrates (Fine, 1979). He then proceeds in the second argument to investigate the concept of logos (Fine, 1979).

The key to the problem of knowledge of the elements is in the analogy of letters and syllables. An important point is when Theaetetus' classifies 'S' within a phonetic system (Fine, 1979). Socrates' endorses this fundamental notion by referring to how one learns to spell, showing that in so doing one learns to discriminate the letters, to know how they work in different combinations (Fine, 1979). In other words, one must know the elements of any complex system in order to know the system itself - hence, elements must be knowable (Fine, 1979). This is what Fine calls the 'interrelation account' (Fine, 1979). Compounds are known from their parts, and knowledge of the parts is achieved in relating them one to another - and to compounds (Fine, 1979). So, this conception of knowledge is circular.

Plato shows that knowledge is the mastery of a subject, the understanding of how a fields elements work together to their end. This concept is proposed by Fine, and he refers to this particular understanding as the 'interrelation model' (Fine, 1979). The part of 'true belief' requires several accounts - not just one. In this thesis there is no terminus of knowledge or belief, instead explanations of things continue in a circulatory manner
(Fine, 1979). We never know just one object, but objects are always known in relation to the other objects which connect to them. Knowledge, therefore, always necessitates the ability to link the elements within a discipline (Fine, 1979). In this view an object is known only within the context of a large spectrum of objects with which it interrelates (Fine, 1979). And it is this which enables us to give an account of any given object
(Fine, 1979). Claims to knowledge based on this interrelation model do not literally continue into infinity, but exist only within the context of the framework of the discipline at hand (Fine, 1979). Nevertheless, this is a circular model, to Plato all knowledge is part of an interconnected system - and if this system of beliefs is large enough it will form elements of knowledge (Fine, 1979).

The Republic has shown us the same thing in the Cave analogy - in that the 'conversion' of mind necessary to begin the process of seeing things as they are is instigated via mathematical knowledge. Mathematical knowledge is axiomatic (Morrow, 1970) - it functions in the same way as Plato's conception of philosophy does. The principle difference is it does not lead to the Good, it merely lays the fundamental structure upon which philosophy can be built.

Mathematics is occupied with making true beliefs into necessary true beliefs - in showing that knowledge is infallible (Morrow, 1970). Those things 'intuitively' known - or hypothesis - are the starting point for mathematics to find proofs for them - infallible proofs (Morrow, 1970). Mathematical theorems have in their nature the criteria of necessary assent, once understood - they cannot be questioned (Morrow, 1970). Plato believes this is exactly the purpose of philosophy - to discover absolute infallible truth. Mathematics deals with intellectual objects which are changeless, they exist as ideas in thought (Morrow, 1970) - but it is a science linked with the sensory material world. This dual role of mathematics is vital - it is the link between the world of opinions and the Forms, reality as enlightened by the Good.

The Socratic method is at one with that of mathematicians (Morrow, 1970). The whole Socratic system is that of finding axioms that are infallible, and working towards a discovery of the ultimate end of all causation. The Socratic methodology of the elenchus may in the early dialogues be used to destroy the fallacious beliefs of men, but in the middle dialogues it is applied with the concept of hypothesis to the discovery of axioms, and so does act in a process alike to mathematics (Morrow, 1970). Having explained not only the Cave and Line analogy of The Republic, but its significance in relation to the Theaetetus, we can see that it is the key to unravelling the apparent conundrum and aporia therein contained. It is now, therefore, possible to see the whole purpose of the discussion of knowledge in both The Republic and Theaetetus, and this is to lay before us Plato's conception of philosophy - that it is a axiomatic system. And the point of this model of philosophy is to reach a point at which we come into contact with the Forms. As Plato says in 511b, 'reasoning itself lays hold of the dialectic when it treats hypothesis as things laid down like steps on which one may mount up to the first principle of the whole'. The philosopher must see his hypothesis as assumptions, prove these assumptions so as to turn them into axioms, and then use them as steps to move towards the first principle of all (Morrow, 1970). He turns these hypothesis into infallible truths through the development of the inter-relational model of knowledge. It is this system of philosophy that Plato wishes to have his readers learn - it is not the answer to the question 'what is knowledge' that is important, it is learning the way to discover this for ourselves that is paramount. Hence the use of aporia - it is a false conundrum he proposes in order to force us to look at the structure of his argument, which is itself the answer to the question, 'What is knowledge'.

References

Brown, E. (2003) 'Plato's Ethics and Politics in The Republic', Stanford Encyclopedia of Philosophy [Online]. Available at: http://plato.stanford.edu/entries/plato-ethics-politics/ (Accessed: 14th November 2006).

Chappell, T (2005) 'Plato on Knowledge in the Theaetetus', Standford Encyclopedia of Philosophy [Online]. Available at: http://plato.stanford.edu/entries/plato-theaetetus/#2 (Accessed: 14th November 2006).

Fine, G. J. (1979) 'Knowledge and Logos in the Theaetetus', The Philosophical Review, 88 (3), pp. 366-397 JSTOR [Online]. Available at: http://www.jstor.org/ (Accessed: 21st October 2006).

Holland, A. J. (1973) 'An Argument in Plato'sTheaetetus: 184-6', The Philosophical Quarterly, 23 (91), pp. 97-116 JSTOR [Online]. Available at: http://www.jstor.org/ (Accessed: 20th October 2006).

Kahn, C. (1996) Plato and the Socratic Dialogue. Cambridge: Cambridge University Press

Morrow, G. R. (1970) 'Plato and the Mathematicians: An Interpretation of Socrates' Dream in the Theaetetus (206e-206c), The Philosophical Review, 79 (3), pp. 309-333 JSTOR [Online]. Available at: http://www.jstor.org/ (Accessed: 21st October 2006).

Murphy, N. R. (1932) 'The 'Simile of Light' in Plato's Republic', The Classical Quarterly, 26 (2), pp. 93-102. JSTOR [Online] Available at: http://www.jstor.org/ (Accessed: 21st October 2006). Plato (1997) Complete Works. Edited by John M. Cooper. Indianapolis: Hacket Publishing Company

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