Relationship between Truth and Knowledge - Case Study Example

Introduction The fact whether truth is different in mathematics and, arts and ethics, may engender a set of controversies, but a way out of these controversies necessarily lies in finding the answer of the question what truth is. If mathematics and, arts and ethics deal with truth, it is necessary to find out the extent to which they are related with it and how they are related to it: in a subjective or objective way (James 137). In the simplest sense mathematics deals with reality from an objective point of view, whereas arts and ethics view it from a subjective point. But the paradox is that the objective definition of truth or reality depends on the subjects who view it. Therefore truth appears to be relative and contextual (Alston 25). In mathematics truth is viewed from an accepted point of the majority of the subjects. But truth in arts and ethics is viewed from the standard of the artist who produces the art work. As in a work of art truth is observed through the artist’s eye, it may differ from daily life truth but this distortion of reality is designed to uphold another reality of more importance. Artists’ truth is valid in a certain conjured context that is the artist’s realm (James 207). This type of truth is often called “the poetic truth”. Indeed as the realm of art is the conjuration of the artist, here the artist enjoys the utmost right to distort reality to establish his “poetic truth”. But truth in mathematics is committed to uphold the reality in its raw form. Relationship between Truth and Knowledge Central to epistemology and the question of knowledge is, of course, the question of truth: namely, under what conditions is something true. If knowledge and truth were as truly interconnected as the ancient philosophers would have us believe, then just as there are many ways of knowing and perceiving the world, so there must be many kinds of truth (Alston 23). If truth is the expression of objective facts in reality, knowledge must also be an expression of these objective facts, only held in the mind instead of on the stage of the world. The common view of truth is of something out there in the world, and this kind of conception dominates the history of philosophy. The exact nature of this truth existing out there has been the subject of quite fervent debate (Glanzberg). Not entirely separate from this debate, in fact, is the question of whether there are different kinds of truth, falling along the traditional divisions in philosophy at ethics, aesthetics, and mathematics. It would certainly make sense that if these areas express different kinds of propositions altogether, that the kinds of truth these propositions express would be different as well. However, there is no distinction between the truths of the hard and soft areas of philosophy and the non-fuzzy areas of mathematics and logic (Yuengert 5). Truth, in all aspects of reality, is shaped by a propositions conduciveness to consistency; that is, "this action is good", "this equation is correct", and "this art is beautiful" are all equally true statements to the extent that actions, equations, and art promote consistency in the system. Approach to Truth in Mathematics and, Arts and Ethics Mathematics, as a system of propositions (parts), needs to be wholly consistent with itself in order to express truths at all. Therefore, the standard for truth in mathematics is the degree to which a particular proposition, statement, or equation can maintain the internal consistency of the entire system. For instance, the equation 1 + 3 = 4 is more consistent with mathematics as a whole than, say, 1 + 3 = 5. If the latter was true (and therefore the former was false), the entire system of mathematics would need to be either be false or need to be changed. Thus, the question arises, if this conception of truth is correct, how truth in mathematics can be distinguished from truths in ethics or even aesthetics. What this question comes down to, however, is the question of how mathematics and ethics/aesthetics are similar. Certainly, there are not the same with respect to strict standards of notation. There is no single system for measuring ethical value (even though some utilitarians have tried with felicific calculus), or aesthetic value much as there are numbers, symbols, and relations that can be easily expressed with mathematical language (Martin 3). However, similarities do exist. Ethical systems, like utilitarianism or deontology, are complete systems, just as mathematics is a complete system. True or false propositions around statements such as “This action is good” can be formed in a utilitarian framework just as it is possible about mathematical equations like 1 + 3 = 5. This ability to make propositions forms the hallmark of a complete system. And so long as on is mindful of the context he or she is working within, namely the particular ethical theory she is evaluating, she can find statements and propositions that are either conducive to the consistency of the system or are not conducive to consistency. Differences between Truths in Mathematics and, Arts and Ethics The principles of mathematics are based on the features of real life objects. Therefore arts and ethics determine what truth is and mathematics proves whether anything is true and it takes the real life objective experiences as the basis of its proof. Even it is also evident that truth in mathematics is conjured by the mathematician who engages it to prove his own agenda. For example it is commonly accepted that “1+1=2” is true. Here one who formulates the equation considers that the number ‘1’ should refer to the quantity of something. So the equation is true for everyone who considers that the number ‘1’ refers to quantity. But for them 1+1=1 seems to be false, because they take it for granted that ‘1’ refers to the quantity of something. But if the context is provided, the equation ‘1+1=1” also appears to be true. For example, ‘1+1=1’ is true when ‘1’ refers to the quality of something. It is true that ‘red + red = red”. It is told earlier that the audience of an art looks through the eye of an artist. So the artist enjoys the scope to establish his truth in a make-belief world or by propounding it in terms of everyday reality. As artist’s view of truth is purely subjective, it varies from man to man. Indeed truth in an art work is truth how the artist views it. In presenting the truth in an art work, reality plays a passive role. Even the distortion of reality may contribute to the credibility of truth that the artist desires to uphold (Martin). This distorted reality often refers to other reality in some way or other. Jonathan Swift’s “Gulliver Travels” contains the example of such distorted reality that convinces its readers about the true nature of human being. If the aesthetic system is the artwork under discussion, the parts making up the system can be assessed as “good” or “bad” in a truthful way just as parts of the ethical or mathematical system may be ascribed truth-values. Incidentally, most people, when evaluating art, look at the whole as opposed to the individual parts of the art. For instance, one, having analytical knowledge of music, says simply “This song is good” when referring to something with a catchy melody or a danceable rhythm. Other, the novice listeners of music, do not comment on the contributions of either the melody or the rhythm to the overall feel of the song as a complete system. This simplification, however, does not mean anything outside of convention. The principles that apply to ethical and or mathematical truths still apply to art regardless (Solomon 19). Likewise, the novice viewing a beautiful painting will not comment on how the neutral colors complement the shading in the piece, but will rather remark that the piece as a whole is good. This is equivalent to saying “Deontology is good” or “Utilitarianism is good”, when such statements are not necessarily equivalent to propositions like “This action is good”. Validity of ‘Truth without Reality’ in Mathematics and, Arts and Ethics Mathematics fully depends on the properties of the real life objects for any of its proposition. It cannot exist without reality. The limitation of truth is that it does not considered truth without reality to be valid, because in the first place it depends on the properties of the real objects as basis. Something imaginary is imaginary in mathematics if the calculation of the properties of real objects refers to something imaginary (Yuengert 4). Therefore the approach of mathematics to truth, in reverse, to imagination is an objective one that asserts its inactivity with the imagination or something false. For example, a mathematician can calculate what the outcome will be, if ‘1’ is multiplied with ‘0’, but a mathematician cannot predict the result, if ‘1’ is divided by ‘0’. It is because the concept of zero does not permit mathematicians to divide ‘1’, the sign of reality with ‘0’ the sign of nothingness or imagination. This single proposition proves that the concept of truth in mathematics is incompatible with imagination. Arts and Ethics allow pure imaginary truth to exist. But this type of truth always exists with a meaning to human life. Indeed with this piece of art, consider the kinds of things that make it appealing, and those things that make it great (Solomon 18). For any piece of art that one admires, it is a matter of smooth progression and the logical use of shape, form, speed (in the case of music), and other temporal and spatial features that come together to have emotional appeal. Conclusion Truth itself is relative and contextual. Different branches of knowledge deal with the concept of truth in different ways. The approach to truth in Mathematics is objective whereas it is subjective in Arts and Ethics. Likewise, perception, which is almost irrelevant when it comes to knowing the truth of propositions in mathematics that can be reached without the help of the senses, is of the utmost importance when it comes to the relevance of aesthetic judgment. Works Cited Alston, William P., A Realistic Conception of Truth, Ithaca: Cornell University Press.1996, 23-56 Arthur, Ralph. "The Dilemma of Logic and Ethics." A Measure of Truth. 1989, 20 Oct. 2009 . Glanzberg, Michael. Truth. 2006. 20 Oct. 2009 . James, William, “Pragmatisms conception of truth”, Pragmatism, New York: Longmans, 1907, 197-236. Martin, Paul. Law of Non-Contradiction. 1999. 20 Oct. 2009 . Solomon, Robert C. Introducing Philosophy. New York: Oxford University Press, 2001, 14 -29 Yuengert, Andrew M. "The Positive-Normative Distinction Before the Fact-Vaue Distinction." Pepperdine University. 20 Oct. 2009 . Read More