Concepts of Truth in Mathematics, the Arts and Ethics

Philosophically many issues have a close relationship to truth, whereby they either follow theories of truth or mean theories regarding truth. It is never easy to exactly determine what truth is due to many controversies that arise depending on the field of study. This is to say, depending on prevailing metaphysical conditions, truth has varying meanings, which primarily depend on a specific case, body of knowledge, reality of things, or standards.

Before stating that something or some occurrences are true, it is important for all individuals to ask themselves the following questions; what are the building blocks of truth?, which mechanisms are good for identifying truth?. In addition, it is important for individuals to ask themselves where their definition of truth falls. This is to say, is their definition of truth complete, relative, subjective or objective? This paper will discuss the degree to which truth is different in mathematics, ethics and arts.

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Truth

Depending on prevailing conditions, different individuals have varying definitions of what truth means. Truth encompasses qualities such as allegiance, sincerity, fidelity, and authenticity. Truth does depend on what single individuals or an entire community knows, but rather it depends on what holds theoretically. These theories are formal, substantive or minimalist. Examples of these practical theories include the consensus theory, correspondence, pragmatic, coherence, and the constructive theory (Prior pp.223-224).

Truth in Mathematics

In most cases, individuals take mathematics as the clearest discipline, but as any other field of knowledge (philosophically), it has associated problems. To understand the nature of mathematics, it is necessary for individuals to question the real nature of mathematics’ existence. In addition, individuals also must ask themselves, what most mathematical propositions mean, owing to the fact that in most cases these propositions seem to lack meaning.

On the other hand, many mathematical concepts have varying features depending on what an individual centres on; hence need to include these concepts before ascertaining the truth in mathematics. For example, to say that an axiomatic-deductive formula is true, then individuals must endeavour to deduce a mechanism of proving such a formula under specific prevailing conditions.

In this regard, one can say that such a proof of applied formulae falls within the set classic logic standards if it is provable. It is important to note also that, such a definition of truth is natural, hence takes less consideration of mathematical objects but lays emphasis on syntax (Lemanska p. 1).

For proper understanding of truth in mathematics, it is necessary for individuals to consider all features of mathematics. Giving specific formulae in form of mathematical theories makes the definition of truth to apply to the entire mathematical theory’s consistency.

Occurrence of this like a scenario makes it easy to ascertain the truth in a theory, in that if a theory is inconsistent, then it lacks some sense of truthfulness. At this point, it is important to note that, it is never easy to prove the consistence of a theory using a direct approach, but rather individuals can prove consistence by use of mathematical models. This is to say, mathematicians can prove the consistence of a theory, hence not wrong to argue that its only by application of learnt experience can individuals prove the truth in mathematical presumptions and their theorems.

Acceptance of mathematical axioms is also debatable owing to the fact that some are logical tautologies. This again puts forward another question: which logic mode is the best to use in mathematics? For example, following beliefs of intuitionists, the rule of double negation is never correct hence, when proving mathematical concepts truth depends on the system of logic that individuals apply.

Truth in Ethics

To some extent, ethics and mathematics share the same premises in defining truth. Although this is the case, the nature of data in these two fields differentiates the nature of truth, whereby ethics uses moral intuitions, where as mathematics calculations. It is very hard philosophically to set clear definitions of what truth is, considering the nature of moral intuitions.

Under ethics most individuals have believes that, once somebody opposes some concept, it means they have specific attitude towards such actions. This makes it hard to define what is true or false, depending on the philosophical stand of an individual. To apply moral language in determining what is true or false, makes it necessary to state genuine propositions or ethical facts.

Therefore, ethically it is not wrong for one to argue that, truth is not what individuals or the society considers morally right but rather, justifiable actions that foster good relationships among individuals.

Truth in Arts

As in mathematics and ethics, many complications also occur in arts concerning the correct definition of truth. This because in ethics many opposing meanings arise on what truth is all about. When studying truth in arts, it is important for individuals to ask themselves whether what they consider true artistically clearly depicts what comprises the external environment. In addition, it is important for individuals to ask themselves whether their artistic internal definitions of truth are culturally or emotionally determined (Addiss p.1).

To some extent, art is truth, because in artistic work many external forces never affect the nature of its outcomes. Art is like a societies mirror; hence depicts both morally correct and wrong acts. On the other hand, it is important to note that although art some has some truth in it artistic tools such as literature and speech sometimes can pass messages that are outright lies. Other tools of art such music and visual art lack a language of expression, hence determination of truth in them depends on individuals’ perceptions Art and Truth p.1).

Similarities and Differences of Truth in Art, Mathematics and Ethics

Although to some extent the procedures, premises, and rules of expressing the truth in mathematics, ethics and arts seem the same many differences are clear, hence defining truth in these three cases is different. For example, it not possible to define truth of a certain fact geometrically using words, which is a main form of expressing truths in ethics.

On the same case, it is not possible to use the same mathematical expressions to express truth in artistic work, because humans determine mathematical calculations, where as artistic work is a depiction of human existence and lifestyle.

Ontologically it is never wrong for an individual to argue that truth in these three fields is subjective, owing to the fact that human existence determines the existence of other things. Using this analogy, one can also argue that, it is a little bit different to determine the truth of different occurrences and objects considering the nature of concepts epistemologically.

Another main difference between these three fields is that, mathematically one has to discover truth; artistically truth depends on perceptions, whereas ethically truth is a mediation process. In this context, although it is possible for computers to create mathematical expressions that are artistically interesting, still one-question lacks an answer, are these patterns pleasing?

Although mediation, discovery and human perceptions are three different concepts, it is important to note that, all these concepts results due to evolution of thoughts and knowledge.

It is important to note that, although some differences arise, to some degree these three field’s definition of truth can sometimes be the same because some concepts of their truth definition may depict relative, absolute or subjective truth. For example, it may never be wrong for one to argue that mathematical truth is generally absolute.

This argument is defendable because since time memorial all mathematical laws are invariable. In addition, algebraically mathematical laws are provable, hence concreting the concept that truth in mathematics is absolute. On the other hand, someone else who argues that truth in mathematics is relative may not be wrong. This is because although individuals can use mathematical formulae to prove concepts, sometimes they too fail, primarily because they have their own limits.

In arts, truth can also be relative, in that human perception of beauty and quality depends on ones cultural background and age group. In addition, depending on one’s views, it is not wrong for one to argue that, truth in arts is subjective, owing to the fact that, individuals have the liberty of choosing what they consider good-looking. In ethics, truth can also be relative, absolute or subjective. This is because globally there is a set of ethics, which all individuals consider right or wrong.

Truth in ethics is absolute if individuals choose to believe that, rules determining human existence are fixed. Ethics can be subjective, depending on one’s belief of what is morally correct or wrong. On the other hand, ethics may be relative if viewed from a cultural variation or situational context, considering the fact that, different societies have varying cultural beliefs and values.

In this regard, all these fields share common concepts of truth, hence almost same definitions, although differences in application context vary

To some level, truth stretches far beyond the mathematical, ethical and artistic knowledge held by human beings. This is because; it mainly determines the existence of these three concepts, hence defines premises under which they exist. In terms of validity, truth depends on views held by different individuals, hence offering individuals a chance to discover what exactly truth means.

To Plato, truth pertains to what the world holds to be right. For Plato truth transcends beyond the human sense perception, but rather encompasses what is correct universally.

In this regard, it is important when defining truth in any these fields to include universally accepted principles. This can help to give a clear meaning of what truth is considering the fact that human beings have different perceptions of ideas depending on their cultural or social backgrounds.

Conclusion

In conclusion, although this three fields share common aspects, their definition of truth varies in that mathematical can be a language of expression, art applies language to pass messages, where as ethics combines both in expressing themselves outwardly.

Works cited

Adiss, Stephen. Truth in arts and science. 2009. Web. 10 Jan. 2010.
https://facultystaff.richmond.edu/~rkingsle/truth/syllabus.html

Prior, Arthur. Encyclopaedia of philosophy. New York: Macmillan, 1969. Print.

Lemanska, Anna. Philosophy of mathematics: Truth and existence in mathematics. 2003. Web.10 Jan. 2010.
http://209.85.229.132/search?q=cache:Nl0WWfdFjBsJ:www.wcp2003.org/LogicAndPhil/Anna_Lemanska.doc+truth+in+mathematics&cd=3&hl=en&ct=clnk&gl=ke>

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