Epistemology is not a discipline that relishes in standing alone. the theory of Knowledge is very concerned with the foundations and development of the sciences. Mathematics in particular seems to be the best modality in which to illuminate the realtion between epistemolgy and the natural world. Mathematical studies according to Quine (1969) divide into two types conceptual and doctrinal. The conceptual studies are concerned with the meaning, clarification and definition of concepts. The doctrinal studies deal with the establishment of laws. Ideally the definitions in their final reductions would exist as "clear and distinct" ideas . All theorems would be generated from a set of self-evident truths. Although, it has been found that the reducibility/simplification of mathematics is in no sense complete (it can not be distilled down to logical principles) it still serves as a reasonable illumination of epistemological concepts. The conceptual side of epistemology has seen the greatest advances from Descarte's time. There have been a number of schools of thought on how to approach the conceptual side of epistemology. The first, more classsical view, sees the universe of discourse as a real independant construct. We relate to it by perceiving some type of information about a pre-existing universe. Hume's handling of the conceptual, identifies bodies by their sense impressions . The collection of sense impressions we receive from a particular object x is what constitutes our knowledge of that body x. Here is where we run into our first bit of trouble. Hume's analysis of this condition demands a significant disconnection between the perception of the object and the actual concept of the object in question. Consider the following case: In front of you there is a grey wall, you consequently perceive a grey wall. Now paint the wall blue. Has anything besides the color of the wall changed? Has that which makes the wall in front of you (call it wall w) the one and only wall w? No, you in fact still perceive wall w. You may argue that the object w has in fact changed. It is now, no longer w, a grey wall, it is some object y a blue wall. Not so. Not so. Hume's thesis states that what we obtain is sense data. Sense data is by its nature an internalization. Now, imagine this grey wall in front of you is now blue. Close your eyes and imagine the grey wall slowly turning blue. It is still the same wall. A property of the wall not the wall itself has There appear to be some properties that are associated directly with objects in the real world, and are consequently inherent in determining their being. Others, such as color, position and temporal location seem to be associated more with our relation to the particular object. Seemingly motivated by the Cartesian search for certainty in an otherwise uncertain universe as Quine puts it "To endure the truths of nature with the full authority of immediate experince was as forlorn a hope as hoping to endow the truths of mathematics with the potential obviousness of elementary logic." Quine has also made it clear that the language contains in it a number of truths that can be considered analytic but, are not true because of their logical form. His classic exaple "no bachelor is married" is true no matter what universe the proposition is considered in , yet, it can not be considered true soley on the basis of logic. Carnap in his radical reconstructionist theory deals with analyticity in the light of an "artificial observational language that can be constructed by laying down rules". In this new view, unlike Hume, the meanings of the words are not associated directl;y with and soley with the physical world as sense data impressions. The rules do not necessarily enumerate the full meanings of words but, instead they deal with meaning relations between specific words. A typical construction would appear as follows: (looselm Carnap) (S1) The term "animal" reprents all andonly those properties (1)....... (2)........... (3).............. (4)................ (5)............. (S2) The term "mammal" represents all and only those properties (1)......... (2)............(3)..............(4)...................(5)............... (as in S1 above ) plus the properties (6).......... (7)............ (8).......... (S3) The term "dog" represents all and only those properties (1)............. (2).............(3)...............(4)................(5).............. as in S1 above, (6)............. (7)..............(8)..................as in S2 above plus the properties (9)......... (10).............(11).................. In such a way many of the descriptive terms in the language which appear irreducible otherwise can be fully specified in the form of a realtional matrix. There are a number of problems with this relational matrix that may not be immediately apparent. Firstly, there seems to be a problem with the length of the list. It is obvious that in a very short time the number of properties listed would far outstrip our mental capacity. Carnap states that it is therefore sufficient that these analytic-postulates (or A-postulates) can be controlled by specifying the meaning realtions that hold among the language's descriptive terms for example: (a1) All mammals are animals (a2) All dogs are mammals. It is not clear though, that the problem has been solved In these cases statements of the form "all chairs are not animals, all tables are not animals, etc.. would seem to still be necessary to fully elaborate the concepts involved. There also seems to be a "circularity" bottleneck. If all the analytic terms of the language are described by this construction and are internal to this construct then where do the logical/mathematical operators by which we manipulate the analytic postulates reside? Above we have the statements a1 and a2 from them we can deduce the statement (a3) All dogs are animals. Somewhere we must have the concept of deductive inference. What I claim is that the concept must appear outside the set of A-postulates in order to avoid a circularity problem. Quine suggests some departures from conventional theory in his views on the analytic and tthe realtion of language to thought. As we have seen earlier depending on only sense impressions as the direct source of information without some more developed structure leads us to problems. What is the nature of these sense impressions? How are they used? Quine's view is that what we manipulate are not sense impressions but observation sentences. These observational sentences are not reports of sense impressions nor "statements of an elmentary sor about the external world." They are sentences that when one learns language are strongly associated with particular sensory stimuli. There are problems with the previous definition though. Most statements depend on a wealth of stored Knowledge that must be co-referenced to determine the validity of a particular statement. Thus Quine redefines the observation sentence such that all verdicts on the truth or falsity of that statement depend on no exterior knowledge besides that which goes into understanding the sentence (vocabulary). This illustrates a question that Quine raises in a great number of his writings. How are we to tellwhat goes into understanding a sentence and what goes into extending that knowledge. This brings us to a distinction between two types of knowledge the analytic and the synthetic. In his "Two dogmas of empiricism" Quine argues taht all attempts to redefine the distinction between the analytic and the synthetic fail due to a cicularity problem. What Putnam has realized is that Quine speaks about two froms of the analytic. The first so-called linguistic notion is similar to Kant's . A sentence is analytic if it can be obtained from a truth of logic by putting synonyms for synonyms. The invalidation of this version of the analytic rests on the fact that using this exchange system and the rules of logic the statement " Necessarily all and only bachelors are unmarried men" has as its only property that it is true. The system does not in any way tell us whether the realtion between bachelor and and unmarried man depends upon the meaning of the word or coincidence. What has to be equated is the analyticity of the statements as well as the meaning. Hence the circularity problem. The second definition of the analytic is the notion, according to Putnam, taht "analytic truth is one that is confirmed no matter what" This is also one of the conventional definitions of the a priori. Quine believes that the sum total of our "facts" is , " a man made fabric which impinges on experience only along the edges". Truth values that have been previously assigned to particular statements become significantly redistributed from time to time. When these "truths" change the realtions that they once held to each other also change. Since the entire field of our knowledge is therefore indeterminant we have a choice in re evaluating any particular statement , the only condition being the mainatince of the equilibrium of the system as a whole. Consider the case of classical versus relativistic physics. Until the turn of the century classical physics was thought to be the a priori "truth" of the laws of the universe. In fact theory had reached such a high degree of development that scientists of the time were heard to remark "There is nothing more to know. We understand the universe, now let's go fishing." , or words to that effect. With the advent of relativistic physics we realized that our perceptions of the universe were flawed. Yet, to this day in our daily interactions with physical laws we still base our decisions on classical principles. What we do use is an approximation to the "truth". The system we had previously constructed was self-consistent and uilitarian. It gave us reproduceable results which we chose to consider as true. Quine's point is that no statement is immune from revision. One might ask though isn't this a case of "You were just wrong". No, the concept wrong implies that an incorrect judgement. The reasoning itself was correct given this particular system. Carnap elaborates and makes the discussion more concrete. He uses the case of quantum logic as an exxample . He takes it to be the "only realistic interpretation" of quantum mechanics as follows: " It is the only realistic interpretation of the present theory... If I am right in the foregoing then anyone who concedes that the present theory could be true should concede that there is a strong 'case' for the possibility of a quantum logical universe." In other words, sone statements can only be overthrown by a rival theory, but since the existance of such an object is always possible the existance of an unreviseable statement is impossible. It is interesting to see the parallel drawn between Carnap's interpretation of Quine and Wiottgenstein's view on certainty. Wittgenstein advances the thesis that with sentences or statements are associated warrants for the sentence's assertion or denial. His interpretation of 'I am certain that p' psychologically implies p. Can this explain how we come to believe ceratin facts about the universe? As our warrants for a model of a particular universe change we will change our "current" view of the model to fit the warrants. If though our warrants sufficiently support both the old and new models we can then in some sense accept both. The final analysis appears to be that even though there are few if any a priori truths there do exists analytic truths. These are the truths are such by logic , or language. Analytic truths are not unrevisable though, they are only unrevisable until we chang ethe langiage or the logic. Now, let us examine in more detail the existance of the a priori. Does it exist? WE seems to be on the horns of a dilemma when considering this problem. We have previously stated that there is no a priori truth. If we are correct then is this not an a priori truth? It appears so. There also seem to be other parts of our knowledge that lead us to belive in the existance of a priori knowledge. Putnam's example 'When I open this box you will see the sheet of paper is red and the sheet of paper is not red' is a statement that has no meaning. We know a priori that it can not be the case that this is true. (Assuming, a normal piece of paper etc.). This argues against the theory that what is really happening when we develop the illusion of the apriori is that we substitute the contextual sense of the a priori for the absolute (see Quine re: Euclidean Geometry). There may or may not be other forms of knowledge that are a priori. The best candidates logic and meathematics have been thought of as a priori for a long time. We have argued that these concepts are so entrenched in our language and thinking that are in effect the bounds by which we define a rational argument. In both forms of reasoning, inductive and deductive, we use the fact that there exists a transitive connective that satisfies modus ponens. This is necessary and central to the nature of reasoning. Aristotle himself comments on how that given someone who says that he disbelieves a law of logic and begins to argue with us we could easily convince him that his own arguments assume the fundamental structure of the logic he is attempting to refute. How then can we define rationality in light of the total rejection of the a priori. It may be that rationality is not as necessary as we believe. It is apparently impossible at this point to show (with a good argument) that any specific statement about the real universe is such that it would be irrational for one to give it up given sufficient evidence. If somehow some creature was able to show you the negation of the law of the excluded middle (A sheet of paper that was both completely red and completely green) wouldn't your conceptualizaon of the universe change? How does the possible non-existane of the a priori effect mathematics then? it has long been proposed that mathematics is the only discipline in which, given sufficient ability and the tenents of set theory, all of the field could eventually be derived. We come to a difficulty at this point. We can not show that mathematics or logic are proveable by convention . To apply the conventions to specific cases requires us to reason from generalities. Reasoning of that sort belong alas, to the realm of logic itself. Quine (1938) addresses this in his "Truth by convention".