This essay aims at illustrating in what way truth in mathematics, ethics and arts is different. It is widely believed that mathematical truths are objective, universal and agreeable to all in all situations. It is also widely accepted that truth in art is more of subjective i.e. depends on individual feelings and thoughts. Truth in ethics or the truthfulness on ethical postulates is said to be relative; it is true depending on other relative beliefs that an individual ascribes to (Dales, 17). In this essay, the distinguishing features or aspects of truth in mathematics, ethics and art will be considered towards establishing to what extent they differ.
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As a starting point, it would be helpful to understand what the word truth per se refers to. Many people are skeptical about the possibility of absolute truths. They argue that what was true yesterday has been disapproved while what we hold as truth today is likely not to be true in the future (Gadamar, 36). To what extent and in what sense this is true is not the question. However, the described disillusionment with pursuit of truth arises out of the elusiveness of or in truth as a concept.
Over time, people have been developing different ways of ascertaining or establishing truth. One such way of establishing truth is consensus. In traditional or primitive societies, truth was established by way of consensus amongst the elders (Osborne, 24). In some cases, truth was based on coherence i.e. if the statement given was coherent or cohered with already established truths, it was accepted as truthful. From consensus and coherence, society developed constructs that were generally accepted for being true (Osborne 61). On further discernment, contradictions in the established coherent systems and social constructs glared thus necessitating need for evidence or correspondence between the said and reality as a way of ascertaining truthfulness. The correspondence or conformance of ideas to reality is the surest check of truthfulness (Gadimar, 78).
However, reality is complex and there are some ideas that can not easily be checked in the reality (things out there now). It is for these reasons that some people have posited higher powers (God) as guarantor of truthfulness). Truth is revealed to mankind and God is the Truth that all should look at incase they seek to distinguish between right and falsehood. Some other people could not find any satisfying measure of truth in the already mentioned ways. Therefore, they posited that true is that which works. If any theory has some truth, if any statement is truthful and if any idea is true, this can only be seen in practice (Brocks, 112). If a theory is applicable or an idea has some tangible applicability towards human welfare, pragmatists would give it a second thought.
From the different ways of testing truth or ascertaining truthfulness, people developed different understanding of truth. For some people, truth is objective, universal and eternal. It is equated to being per se. whatsoever is, is accepted as truthful, beautiful, good and lovely. Those who take truth from this kind of perspective distinguish between ontological truthfulness and logical truthfulness. Ontological truthfulness has to do with the being of things (Lehrer, 47). In this sense, it is true that which is. Truthfulness is self evident in being and does not need any other measure beyond conformance of our mental ideas to reality.
Truth seen on any other level is subjective and relative. It is highly determined or informed by an individual’s upbringing, education, skills and is not necessarily about things as they actually are. This level allows for the consideration of truthfulness ascribed to beings of reason. Beings of reason are those things created by the human mind that do not have existence in the world; things that are a result of thought on thought (Lehrer, 23). Such things may later be actualized as products of human ingenuity and creativity. Their truthfulness can most appropriately be determined by such measures as practical application/ value, coherence or consensus. Social system is created out of logical considerations. The truthfulness of such like constructs is relevant to the extent that paradigm fits and works. Over time with changes in natural environment as well as conception of new more intricate, more rewarding system, the former are rendered useless and irrelevant. The truthfulness of their being the best system will have been relegated as appropriated over time. It follows; therefore, the understanding of truth has to be contextualized. Unless things or issues are taken in context, their truthfulness is missed leading to misunderstanding. If things are understood in context, their truthfulness is appropriated as per the right sense thus averting any form of skepticism.
Taking each and everything in context does not warranty the talking about different kinds of truths. Truth remains truth despite context; only that it is defined more by given postulates in given context than in others (Gadamer, 83). Are truths in mathematics, ethics and art different? One would validly argue that they are and they are not. There are some mathematical postulates that are not universally acceptable while there are some ethical considerations that are more or less universal. There is this ethical consideration, the golden rule. Somehow, it appears that all people, despite of culture or race would agree to the importance to treat others well as the only sure way of assuring own survival in this world. Consider a poem, the probability of one poem being interpreted differently not withstanding, a properly written poem or sculptured work of art would often vividly convey its message without running risk of many different valid subjective interpretations (Gadamer, 95).
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Some people argue that art or a piece of art has no truth. While others argue that art is not a work or an Endeavour without direction. Artists are people with purpose and direction who aim at communicating with people. Their passion and creativity is anchored on and incited by truth or desire for truth. An artist draws, writes or develops what he or she believes in i.e. there is a value or truth veiled in the idea that informs an artistic creation. The truth in art is subjective because as a piece, it does not hold any defined truth. Unless the truth the artist intends to portray through the use of it is revealed, its beholder will always form an own understanding of what the art is or means depending on his or her own subjective considerations (Brock, 126). The truth of an art or in an art is not given and is never objective. One piece of art is subject to different interpretations that are all valid. It all depends on ones perceptions; frame of minds and psychosocial schemas that inform our evaluation. Although this is widely accepted, it is not conclusive; there is still possibility that objective appreciation of art can be achieved. Art should be seen more in terms of a discipline that uses a particular style or technique. Truth in art does not have any different meaning from what mathematics considers as truth. However, truth communicated in art has to be deciphered from the creative expressions that often are informed by a given objective style, rhythm or understood symbols.
While there are those who think there is no truth in art, others think truth in art and ethics is of the same kind. Truth in art and ethics are both seen as subjective and relativist against mathematical truths that are objective and universal (Dales, 13). This, also, is a wrong assumption or line of thought. Truth determination in art is very distinct from truth determination or bases in ethics. Ethical truth is more about individual’s beliefs. Beliefs are varied; as many as the number of religions; religious denominations and other non religious belief bodies. It is true that ethics in a big way is about shared norms, generally accepted ways and standards of behavior and general conception of what is good and right in human conduct. However, it should be understood that ethics goes beyond merely what happens as to concern with what should or ought to be happening. In so doing, or towards that goal, ethics as a discipline is concerned with tools, measures and techniques that could ground given values on which human behavior or conduct should be pegged.
Seen in this light, ethics is taken on another perspective that moves it from the realm of pure relativism. Just as there are grains of relativism and subjectivism in mathematics, ethics also strives towards objective, universal and generally acceptable stipulations (Brock, 57). Like arts, the appropriation of an ethics (based on truthfulness of postulates as understood by one) is a very subjective. However, the general ethical considerations or principles are based on given assumed objective truths that ground the ethics.
Mathematical truths are taken for absolute, objective truths. This is because mathematical truths are proved. Mathematical truths are proved by way of formulae that are developed or derived and any sum of problem seeking questions of the particular nature can adequately be answered by use of the given formulas (Dales, 9). These formulas are universal and their derivation can be followed and verified by all who have necessary knowledge or skills. However, problems come in often in considering how the mathematical formulas were originated. Along the line, all mathematical formulas followed to a logical conclusions lead to an irrational assumption that the mathematician can not explain. From such like a point of view one would argue mathematical truths are not in any big way any more objective that say the golden rule as a postulate of given moral systems or ethical theories. It occurs that mathematical truths are accepted by consensus often basically for practical reasons.
From the given consideration, it is clear that truth does not change in meaning across disciplines. However, the approach to truth changes because of the different techniques used in the different disciplines.
Brock, Stuart, and Edwin, David, Mares. Realism and Anti-Realism Central Problems of Philosophy. UK: Acumen, 2007
Dales, Harold G. and Gianluigi, Oliveri. Truth in Mathematics. UK: Oxford University Press, 1998
Gadamer, Hans, Georg, and Joel Weinsheimer, Truth and Method: Continuum Impacts Question What You Thought Before. 2nd Ed. London:
Continuum International Publishing Group, 2004
Lehrer, Keith. Metamind. New York: Clarendon Press, 1990
Osborne, Thomas. Aspects of Enlightenment: Social Theory and the Ethics of Truth. New York. NY: Rowman & Littlefield, 1998
To What Extent Is Truth Different in Mathematics, Ethics and Arts
- General Understanding of Truth
- Correspondence Theory
- Coherence Theory
- Constructivist Theory
- Pragmatist Theory
Truth as a subject of investigation is very problematic. In this paper, through analysis of what philosophers have posited over time, it will be established that a universal understanding and appreciation of truth is possible. However, in given different contexts the approach to and appropriation of truth has to necessarily be different.
Over years, philosophers, educationists, religious leaders and people of all walks have grappled with questions such as ‘what is truth?’, ‘how do we ascertain truth?’ ‘Is truth subjective, relative or objective and universal?’ many over history have posited theories and definitions in the hope of clearing all doubts and questions about truth.
Generally, from a common sense perspective, truth refers to things as they are. To say this is the truth in common day to day usage of the word truth is to ascertain that things or reality being refereed to is as stated. On a universal scale, it is generally agreed that truth is about reality; truth is conformance or agreement of what is known or stated to reality or things as they are (Boodin, 57). It can be stated that truth is all valid statements of fact. However, that would require an explanation as to what facts are and how the validity of facts is ascertained. In saying truth is about reality, it remains hazy until we ascertain or make clear what reality is per se. Reality is generally understood as what is out there now (Coffey, 43). However, before what is out there now, was there not an out there now that gave way to the reality now? More so, is what is out there now not a possibility of other realities? To conclusively grasp (know) and understand the essence of truth, it appears, one has to understand or know all there is about everything. To know all there is about everything that is would necessarily mean looking into what something is and the positive condition or possibilities that are necessitated by the reality.
However, human beings are limited to a great extend in their knowing. The limitations are in the angularity, historicity and general problems in methods such as induction or deduction that human reasoning employs (Coffey, 34). It is for this reason that truth becomes elusive. The limitations in knowing or the scopes of knowledge frame truth. This is true as long as truth refers to all knowable. Grasping or realizing a knowable in its peculiarity and generality is basic to claim of having arrived at truth. Truth in this case is what one’s intellect arrives at after asking relevant question into a given knowable (Copleston, 88).
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The first theory on how to ascertain truth is known as the correspondence theory. This theory is more akin to common sense understanding of truth. For correspondence theorists, truth is to what extent given statements or beliefs correspond to the way things are i.e. actual state in which things are (Boodin, 59). This theory evolves from a theory of knowledge that asserts that ideas are abstracts from reality. The idea one has in his mind or head is formed of what has been deciphered from reality. It is from the empirical world or physical world that one realizes and conceptualizes ideas. The idea of man was realized once of nature, a being of the essence man was deciphered. The idea refers to a reality that is so all around the world (it is universal and agreed to by all people). The correspondence theory holds that what is true is what is. To know the truthfulness of a statement, one has to look into the reality to which it refers. If the statement conforms to reality; the statement is true. Therefore, truth is objective as can be confirmed by any other person. This is the kind of truth that ethics is base on and tends to strive towards. Naturalists as a moral school argue that human action should be in tandem with natural postulates (natural law theorists). The utilitarianism base their theory on an observed fact that pleasure and pain are the greatest reasons why people do what they do. Their postulates are derived of observations made of human living. However, ethics does not rely only on correspondence, just like mathematics whose development relies on coherent postulates but applications can only be verified in reality, some forms of ethical considerations are only but based on coherent theories or systems.
Although correspondence or conformance to reality is an objective measure of truth, it is also widely known that to ascertain what is real is problematic. It is also clear that reality is what is out there now. However, what was out there and the possibilities that what is out there now is a positive condition towards inform realities around which truthfulness has to be established (Norris, 5). The complexity of reality is what necessitated need for other measures of truth. Reality is not just the physical world; reality encompasses non material aspects or things. The truthfulness of ideas that do not have physical evidence cannot be measure in terms of correspondence.
These problems or challenges led to development of a coherence measure of truth. This theory of truth focuses more on the extent to which ideas, statements and facts fall into or fit into a whole system (Copleston, 93). Knowledge is understood to be a body of defined relations between things and dynamism in the things in self. Coherence would require that relations and interrelations fit into the whole without allowing room for doubt. To the extent that the new statements do not contradict and actually flow or follow from foregoing statements, they are taken for truth. In the history of human knowledge, this kind of thinking led to development of all sorts of ideological systems that served the interests of a few in societies. Mathematical truths to a large extent are based on the coherence in the system. On their own, mathematical truthfulness as based on coherence is widely criticized. The applicability of such like knowledge and its veracity is highly doubtful because by some other coherent development some other valid coherent alternative systems can be developed. Coherence in a theory does not necessarily mean things or reality is as such. If things are not as such, then truthfulness as based on coherence does not serve any meaningful purpose. For example, for long people coherently argued for the idea that the earth is the centre of the universe. Science has belabored to prove otherwise, proved that the sun is at the centre of the universe and the earth rotates around it. Hitler coherently, argued out his economic and social theory thus getting a large following.
This led to another way of looking at truth called constructivism. Social constructivists, for example, hold that truth is often as dictated b social processes. Truth is conventional and depends largely on historical and cultural tenets. Much knowledge systems are based on social constructs. Social constructs are things or realities or concepts whose meaning is based on social agreement. For example, gender as understood is more of a social construct than anything based on reality or things as they are. It is our knowing depend more on our socialization. Socialization is a process that begins at birth (the way a child is introduced and slowly inducted into society). Therefore, what individuals come to understand as truth or ways of appreciating and appropriating truth is what was passed to them; schemas or theories or paradigms that have been developed over time. Truth in art is more of constructivist. It is widely believed that an artist communicates certain truths (Gardner, 16). However, the interpretation and appreciation of truth in art is depended on social schemes developed overtime. One poem could be interpreted in different ways by different people due to the social differences or constructed ways of analysis. A piece of art intentioned by the author to represent joy could be interpreted as representing sadness. Therefore, truth in art is more of relative and subjective.
The relativity or subjectivity of truth as explained by social theorists led to looking for a common ground between the divergent views. Each of the views seemed to have some truth or level of veracity. From this kind of point of view, some individuals sort consensus on given issues as the most objective way of establishing truthfulness. Consensus generally refers to agreement between two or more people on given contentious issues that would otherwise be source of conflicting or divergence. Consensus as a way of establishing truth does not only happen in art but also in mathematics. Given many mathematical formula or theories depend on coherence, their establishment as reliable relies more on consensus i.e. majority of mathematicians being convinced and agreeing on their authenticity, originality and applicability ( Norris, 61).
Consensus as a way of establishing truth has its own challenges. The fact that many people agree on a subject does not provide veracity. This is the fallacy in democracy i.e. it does not follow that the opinions and desires of the majority necessarily translate into a better life for a majority of a given citizenry. For example, there have been many instances where juries or judges in a case reach consensus on a verdict and make a ruling then later a hindsight or oversight is revealed; a detail they all overlooked that turns the case on its heels. Some truths in mathematics, art and ethics (forms of ethical bodies or stipulates) are more of agreed upon stipulations that are fallacious or inadequate or close critical scrutiny (Graham, 97).
The challenges in consensus led to a more pragmatic view of knowledge. It is true if in normal practice on daily life it finds relevancy (Copleston, 126). For a pragmatic, God is true to the extent that in daily living the God idea finds practical relevancy or effectiveness. From this point of view, mathematical truths, truth in art and the truthfulness of an ethical consideration are only to the extent of their efficacy in daily living of a people. It is interesting that from such a consideration, all truth (mathematical, ethical, and artistic) though not taking on any universal connotations are as good as they are relevantly applicable.
This essay has been an overview on the bases for truth. The points raised augment the idea that truth in art, mathematics and ethics is only different to the extent that bases of truth are different. However the truthfulness of what is posited as truth in mathematics, arts and ethics cannot be different.
Boodin, John, Elof. Truth And Reality: An Introduction To The Theory Of Knowledge. London: Continuum International Publishing Group, 2001
Coffey, Peter. Epistemology; Or, the Theory of Knowledge: An Introduction to General Metaphysics. Charleston: BiblioBazaar, LLC, 2009
Copleston, Frederick Charles. A History of Philosophy, London: Continuum International Publishing Group, 1999
Gardner, John. The Art of Fiction: Notes on Craft for Young Writers. USA: Vintage Books, 1991
Graham, Gordon. Eight Theories of Ethics. USA: Routledge, 2004
Norris, Christopher. Truth and the Ethics of Criticism. Manchester: Manchester University Press ND, 1994