In considering the meaning of truth in mathematics, the arts, and ethics, one is bound to encounter similarities and contradictions while making attempts to arrive at a concrete conclusion regarding what truth connotes in these three streams. There are several arguments from different schools of thought that are not necessarily accepted along with the different sources of truth that emerge from the dialectics of human reasoning and the testimonies of the senses and body parts of human beings. In essence, mathematics and reason are the main systems of truth that prevail in different aspects of human reasoning while the natural sciences such as the arts and ethics connote the main reservoir of the truth of the senses. Truth is questioned in the present times more in the context of how much truth of faith is received from sources such as inspiration, intuition, perceptions, revelations, and mystic experiences. This paper will examine the meaning of truth and how it is considered different in the context of its meaning in mathematics, the arts, and ethics.
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In mathematics, one can instinctively note that the subject aims at seeking consistency and thus engineers the happenings to make certain that the rules and assertions remain consistent at all times. Hence the answers to all problems have to be necessarily the same in comprising of the same group of results. Truth in mathematics implies reaching a state that has reached a conclusion that is entirely and comprehensively coherent in keeping with the original rules and limitations. The reason is the tool that evaluates this state and other tools play a marginal role, although some people mistakenly believe that mathematics aims at bringing linguistic consistency. The basic truth about mathematics is the fact that if one can recognize the primary conditions such as logic, rules, and fundamentals; the conclusions follow on their own (Kline, 1990).
At the same time, mathematics deals with structures that involve the conception of truth which has an unbiased meaning. For example, such a truth pertains to the fact that a computer will go on performing an unlimited number of tasks. The occurrences related to these processes are the results of the different aspects of mathematics. In essence, mathematical statements which cannot be understood as queries relating to happenings in a deterministic world cannot be taken as either false or true in the complete sense even though they could be having true or false properties about a specific system of working.
About ethics and the arts, the implications of mathematics are widened in terms of physical objects being experienced immediately. Such logic further widens the implication that mathematics also relates to biological evolution and consciousness, which can be understood mathematically. Numbers become mediators between authenticity relating to here and now situations and the profound realities that are part of the creative processes of the sprouting sense of consciousness. Mathematics enables the realization of the possibilities and sets up the requirements for realizing the possibilities. It is imperative to understand that mathematics does not only address the reason, but also the possibilities of unlimited creativity in assuming human power and responsibility.
With intuition, there is a straight, self-evident brief experience that differs from perceptions and sensations as also from thoughts and memories in different forms. Such experiences form the basis of the validities of the different proposals that are not only of philosophical and religious nature but also of logical reasoning as associated with mathematics. Additionally, the experiences related to the experiential sciences and their respective truths are now entirely accepted by philosophers, scientists, thinkers, and investigators of such problems. In this context, the basic propositions of any science whether it is mathematics or chemistry, emerge in being very valid with their respective maxims being axiomatic. Hence in a subject such as mathematics, the only means of a self surfacing character of the propositions and axioms directly relates to intuitive feelings. In this way, we can assume that it is not a derivative but a condition and a means to convey the truth regarding the reason and sensory experiences.
In general, there is a little similarity in the extent of truth in mathematics, the arts, and ethics in some areas that indicate truth which is absolute, subjective, and relative. In mathematics, it can be argued that the truth is absolute in terms of the theories and laws that cannot be changed and are constant. It can also be said that the truth as connoted in mathematics is absolute since one can prove algebraically some of the rules and characteristics, while it can also be argued that the truth here is relative since although the theories and rules do exist in mathematics limits to the theories are present in most situations. The truth in mathematics can be also said to be subjective since one has to at times accept the existence of the laws.
Such definition and understanding of truth are not valid in the arts, where the rules are entirely variable and the elements are not consistent with the effect. According to William James (1997), truth in the arts is ‘that which works in experience,’ (James, 1997). In a similar vein the same is also true for mathematics and ethics because, in both, things work with experience which can be called the truth. However, in some situations as in politics, the distribution of income gives more meaning in one experience as compared to another and since mathematics does not cover this area it may imply in such situations that there is a difference in the meaning of truth. Hence, according to James (1997), a requirement of truth pertains to the fact that any idea must work inexperience to be treated as truth. In ethics to the same principle applies to different ideas and beliefs in ascertaining whether they can be treated as being truths.
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If we think about aesthetics a picture emerges of a pleasant symmetry, a pleasant contrast, and pleasant harmony, although an excess of any of these is not considered aesthetical. One can always discuss and debate upon the assumptions and conclusions. Usually, the initial influence of the arts pertains to producing a reflexive and impulsive physiological reaction. This implies that the initial inputs are sensory and the initial reaction is related to emotions. One realizes the reason later when it emerges that there is a lot of bias that is allowed to stay given the flexibility of the rules. Even if one tries to convert this in logical terms in communicating the responses it does not appear logical and truthful. Therefore truth in the arts comprises of only a biased constancy which is not at all realistic.
Truth is indeed much more than simply mathematics, the arts, and ethics. The question arises as to what extent truth is portrayed in these three areas in terms of being absolute, relative, and subjective. There are elements of truth in all these areas. In the arts, absolute truth is epitomized by way of the search for things that are thought to be beautiful. Going a step further, scholars consider, for example, absolute truth to be present in the theories put forth by Plato about the world of ideas. Plato’s world of ideas holds the ideals of all the things on earth being perfect and that everything holds its basis as originating from the world of ideas although it may have certain deviations and mutations. Hence truth can be said to be absolute since the most beautiful things portray truth in their ideal forms. Truth in the arts can also be considered relative since the beauty and value of things are viewed differently in different civilizations and periods. Conversely, truth in the arts can also be looked upon as being subjective since people have the freedom and choice to conclude about what they feel is beautiful.
Different meaning of truth
Regarding ethics, a different meaning of truth is implied in the context of its occupying a somewhat middle ground. The meaning of truth in ethics takes deeper connotations and can vary amongst philosophers. For example, while considering the issue of racism one cannot say that racist theory are incorrect because they are not true. The fact is that they are very much true, and are irrelevant in mathematics although they may lead to some connection to the arts. Racist theory cannot be wrong just because it is incorrect. Racism is incorrect, but at the same time, racist theories are correct. But this does not mean that racism becomes acceptable. Hence in ethics, truth implies a different meaning as related to mathematics and the arts. It is in this context that David Hume had rightly argued that people cannot justify things that ought to be done in terms of what is being done, which implies that any moral judgment cannot logically result from statements of truth and facts. On the contrary in mathematics, the moral judgments about truthful situations flow from logic and reason.
An ethical code implies the amalgamation of different moral codes, and it is, for this reason, that morality gels well into ethics. In general terms morality just implies that every individual’s values and moral reactions tally with those of other people. The realization of such common morality happens in defining a specific code of response that is the same for all community members, and this occurs when there is an emergence of an ethical foundation. Ethics entails the study of the relationship between people’s moralities to ascertain the common agreeability on what is the best outcome for the community as a whole. The issue of deciding which outcome is the best is indeed debatable in that there tend to be different opinions regarding whether the basis for the outcomes emerges from emotions or empathy or reason and to what extent. However, ethics necessitates examination and consideration from different perceptions and hence conveys and comprises a broader meaning of truth that is more widely accepted (Sorokin, 1998).
All three aspects of truth can be related to ethics also. Absolute truth is represented in ethics by way of the principle that a universal set of ethical practices exist in this world. For example in all societies down the ages, the killing of one individual by another to get personal gain has been considered to be entirely wrong. Additionally, ethical truth is believed to be absolute if individuals adopt the belief that the code of conduct by which we live will always remain the same; such as the Ten Commandments. The Ten Commandments are a code of conduct that is considered truthful from the religious perspective. Ethically they are the truth because they follow from religion but thinking from the perspective of mathematics, different scholars will interpret the issue differently. Some mathematicians will reason from pure logic in saying that there is no concrete and logical basis to make the code of conduct stand the test of truth as per scientific reasoning. Others will say that they are very much logical in the context of their historical authenticity.
The truth as viewed in ethics can be considered as being relative when understood from the perception that all codes of conduct by which we ought to live in this world, differ from society to society. Further, ethical truth can be viewed as being relative if we consider that the code of conduct by which we live is flexible and changes with time and circumstances. An example in this context is of the Epicureans who lived by the belief that the ultimate goodness in life was a pleasure and the biggest sin was going through pain and suffering. But at times pleasure and happiness can bring pain; hence they would have to consider the effects of such a pattern of behavior and actions. Such a situation can be considered relative because choosing pleasure would be good at certain times but in other situations, it may not be so. Conversely, ethical truth can be considered as being subjective since individuals could have personal ideas that influence their beliefs about what is right and what is wrong.
The understanding of truth in mathematics, the arts, and ethics are different though related in some respects. The truth in ethics pertains to what one believes in, which is mostly not harming others. Ethical truth pertains to believing in and executing in showing that it is ethics that defines an individual. In arts, the truth comes from the feelings generated in the mind whereby the individual acts as per his or her perceptions about different situations. In mathematics, truth pertains to the facts surfacing from reason as is evident from the different formulae which enable the solution of mathematical problems.
- James Williams, The Meaning of Truth, 1997, Prometheus Books
- Kline Morris, Mathematical Thought from Ancient to Modern Times, Vol. 1, 1990, Oxford University Press, pp. 36 – 47
- Sorokin Pitirim A, The Integral Theory of Truth and Reality, 1998. Web.