Paul Klee

Friday, April 8, 2011

The Idea of Truth

“Beauty is Truth, Truth Beauty, -That is all
Ye know on earth, and all ye need to know.”

John Keats, Ode on a Grecian Urn

The last two lines of Keats’s poem have been the subject of much erudite analysis, and it is presumptuous for an undistinguished writer to put in his twopenn’orth, but I will anyway. The intention, however, is not to add to an already overburdened debate but to use this example as a cave entrance to the even more labyrinthine consideration of the nature of truth in general.

In relation to the statement, “Beauty is Truth, Truth Beauty,” The critic IA Richards had warned against trying to take poetic statements too seriously. TS Eliot responded: “on re-reading the whole Ode, this line strikes me as a serious blemish on a beautiful poem, and the reason must be either that I fail to understand it, or that it is a statement which is untrue.” It is unlikely that Eliot did not understand the several possible meanings of the line, so we must conclude he did believe it was false. I agree with his judgment, albeit from a strictly logical interpretation of the last two lines of the poem.

As one would expect from a great poet, the multiple assertions in the concluding lines are bound together in a complex construction which does not immediately yield up an unequivocal meaning, either to the casual reader or even to prolonged analysis. Some may consider this to be a poetic virtue, akin to any artistic or mystical mode of thought. However, the resulting ambiguity confounds the kind of clear and unique interpretation demanded by the logical mind.

The two lines can be broken down as follows, at the risk of destroying any beauty or truth they express in their original form:

S1: Truth is Beauty.
S2: Beauty is Truth.
S3:S1 and S2 is all ye know.
S4:S1and S2 is all ye need to know.

Before attempting to interpret each of the four propositions it is worth noting the following points. ‘Truth’ and ‘beauty’ are both abstract nouns that are used as adjectives (attributes) in S1 and S2 as well as nouns. This raises the problem of whether attributes (qualities) can properly have other attributes asserted of them and whether nouns can properly be used as attributes. S1 and S2 appear to be universal statements although they are not explicitly quantified ie “All truth is beautiful” and “All beauty is truthful”. If this were the poet’s intention, then we could logically conclude that beauty is in some sense equivalent to truth and vice versa, a proposition that can be tested by substituting one attribute for another in any and all possible propositions containing these attributes.

Consider the proposition, “Helen of Troy was (a) beauty”, which would become “Helen of Troy was (a) truth”. This provides an immediate contradiction of the equivalence because the second statement is hardly meaningful. We could elaborate and say, “Helen of Troy told the truth” but I am not sure if this was the case. In general, I am inclined to reject the assertion that either abstract or concrete entities are necessarily true because they are beautiful. One reason for this is that beauty is a subjective judgment which does not command universal agreement. What some find beautiful others find uninteresting or even ugly. Truth, however, has a better claim to objectivity whether it is established empirically or as a valid deduction from first principles. Truth, therefore, is not properly comparable with beauty at all.

Mathematicians and scientists might object to this negative judgment by declaring that beauty is a good if not infallible guide to truth. The justification for the scientist is that nature determines what we find beautiful, both internally through the mind and externally through the senses, and that this natural beauty is an expression of the perfect harmony that exists in nature. Clearly, this was the sentiment that Keats expressed in his ode, although the urn was a man-made artifact rather than a natural one. The mathematician has an even stronger claim for using aesthetic criteria as a guide to truth. The declaration that Euclid’s proof of the infinity of primes is beautiful is certainly meaningful, and the generalisation that mathematical intuition depends on the detection of such beauty soon follows from this aesthetic point of view. However, beauty is being used here as a guide to enquiry but not as a final criterion of truth. The subjectivist objection might be that truth and beauty are generated in the human mental system and so are not proper attributes to the real world as a noumenal domain. In this case, there might very well be a strong connection between aesthetic and veridical judgments.

Putting aside the inappropriate comparisons of truth and beauty in S1 and S2, the assertion that knowledge is limited to these two statements is clearly false. Even if beauty cannot be separated from truth, this would not justify ignoring all else that we take for true knowledge of our world. Indeed, if truth and beauty are equivalent then we can drop one of them as redundant. To reject all other knowledge is surely epistemological hubris. Most of the humble facts of daily experience, as well as much of scientific knowledge would be excluded from Keats’s idealistic garden of perfect delight. Of course, he may only have intended to assert what he felt was a special relationship between beauty and truth, rather than to follow up the inherent contradictions of this profession of aesthetic idealism.

The fourth proposition reinforces the third by insisting that no further knowledge is required beyond the equivalence of beauty and truth. This could only make sense in a metaphysical system of which S1, S2 and their equivalence were the axioms, from which all else could be deduced in the perfect world of the poets imagination. From this exalted point of view, the poet seems to have been striving after the kind of ultimate truth that philosophers had long sought after and latterly rejected.

In Keats’s time the vogue for Greek art was still highly influential. That supreme example, the Parthenon, had incorporated the highest geometrical knowledge of classical Greece, and so expressed a formal beauty derived from it. Given that mathematical principles are embodied in nature and strongly influence our ideas of beauty, Keats’s perception of the relationship between beauty and truth assumes a clearer meaning. What we mean by beauty is the expression of mathematical form intuitively observed in nature through the senses. One might have expected the nature loving poet to have observed the perfidious function of natural beauty. All manner of deceits are dressed up in nature’s colourful finery. Butterflies open their wings to display imitation eyes and beautiful sexual displays are widely used generally to lure a mate. Such strategies are clearly inconsistent with displays of truth combined with beauty in nature. Deception therefore has long preceded the emergence of mankind and its ability to develop such abstract categories as truth or beauty. But even without such deceptions, there are the illusions that derive from imperfect perception. The fly with its compound eyes is presented with multiple views of its world, and even humans learn the clever trick of seeing a world transformed from the inverted image that falls on the retina.

Our quotidian experience involves continual judgments, both conscious and unconscious, about the present. Standing upright or walking requires such adjustments which may only enter into consciousness when we stumble, and experience error. In going about our business we make innumerable judgments according to habitual criteria, consciously learned or otherwise, which may turn out to be wrong. Some of these criteria are of a sufficiently high order to qualify as beliefs, although many of them may have been acquired as received knowledge rather than consciously examined and granted the status of truth. So, we live among a welter of beliefs which guide our actions and only occasionally get examined for their veracity.

For higher animals, truth is intimately bound up with memory, and may be marred by its imperfections. Memories of past events can be compared with present situations and accumulated knowledge acquired through memory and concept formation used to make judgments in the present. This process gives rise to the idea of repeated similarities between prior and current events. One overarching truth we observe is that events, though similar, are unique. The clouds we see today may resemble those of yesterday but cannot possibly be identical because of their random structure. Other more permanent forms, such as rocks, trees, and common animals exhibit a stronger degree of resemblance and form the basis for the belief that their identity persists over time, even while they gradually change. This very complex state of affairs is the basis on which we experience and formulate ideas of truth.

The fairly recent discovery of non-linear mathematics has demonstrated that nature mimics infinite forms, as in the case of each unique snowflake, river channels, human bronchi and mountain ranges. The corollary is that limitations are placed on human ability to understand and to adapt to a world of potentially infinite complexity.

One approach to the truth enigma is to ask, what kind of things the attribute ‘true’ can meaningfully apply to. One answer is that it applies to beliefs, but these must at least be encoded in some way, usually in a language, before such judgments can be made. Furthermore, the resulting statements need not be believed at all, or any beliefs in them suspended for purposes of logical or semantic analysis. The essential point is that beliefs can be divided into true and false beliefs, so that the fact of believing something is distinct from the fact that the proposition expressing the belief is true or false. In other words, belief has no effect on whether a state of affairs is true or not, except in those cases where human physical or mental performance is influenced by belief, eg to win a race or pass an examination.

In the Keats example, there was some uneasiness about whether statements like “truth is beauty” are even meaningful, as in Chomsky’s example: “colourless green ideas sleep furiously”, which is grammatically correct but meaningless and contradictory. To judge whether a state of affairs is true or not, it is necessary to encode the situation clearly, unambiguously, grammatically and meaningfully. The expression of ideas in a language exacerbates the problem by transferring the focus of truth judgments to propositions and away from unformulated beliefs or situations that the propositions represent. For example, if we assert “The King of France is bald” several linguistic problems arise: there is no present King of France, we do not know which past king is being referred to or to what degree of hair paucity constitutes baldness. The power of language is very great, and innumerable propositions about a subject may have to be composed before any factual truth criteria can be considered. The simple assertion, “the earth goes round the sun” is readily understood by our educated minds, but some thought would be needed by the non-specialist to demonstrate this scientific ‘fact’ to a disbeliever. Indeed, it was not until 1838 that the astronomer F.W. Bessel was able to measure the parallax of a nearby star to show that the earth was at a different place from the time of the first measurements compared with observations six months later. Einstein, of course, threw doubt on what the term ‘different place’ might mean.

In this astronomical example, the truth was established by making not only accurate observations but also by relying on the validity of trigonometry, whose truths are of quite a different kind from facts established by observation of what we call the real world. Fortunately, the delicate observations did not depend on Einstein’s as yet to be discovered facts about the behaviour of light under strong gravitational fields but would have been affected by the refraction of light through the earth’s atmosphere under different atmospheric conditions. The point here is that establishing a fact in one area of science may depend on believing a host of other facts. If any of these should prove to be untrue, there may be significant ramifications for those experiments or theories which assumed they were true.

From this point of view, our most certain fields of knowledge are a contingent house of cards that must be continually be maintained. Similarly, when we make our casual judgments about our ever day lives, we rely on innumerable beliefs, most of which are received knowledge and many of which we would be incapable of adequately demonstrating as true.

It is often the case that we form opinions, particularly about people, based on their appearance, manner and a few instances of social behaviour. Hypotheses are formed and tested by observations until beliefs about them become firmly established. Such opinions may be influenced by received ideas about how people of their class, colour, creed, occupation, or physiognomy usually behave. In this arena of unavoidable social interaction and judgment, beliefs are founded intuitively rather than through any systematic assemblage of consistent propositions, as would be required in a science. Human behaviour is very complex, a fact which renders difficult the social sciences from psychology to economics. The veracity of statements in these fields of knowledge is commensurately less certain and often characterised by probability rather than certainty.

It should be clear even to the most exalted mind that significant truths are hard to come by and that, consequently, we live in a fog of beliefs that fall short of the highest standards of veracity. To make matters worse, psychology makes clear that the human mind can be unreliable in making even simple judgments about recent or even current events. The conjuror makes use of this deficiency by exploiting the tendency of the mind to fill in the gaps between what actually occurs, i.e. as recorded on a video camera, and what they think happened. It seems that the control of the senses by the mind produces a mixture of fact and predictive fiction as it attempts to assess what is likely to happen on the basis of quickly varying events.
Truth, then, depends on the formulation of memories and beliefs and the comparison of these with some kind of independent criteria. The most obvious comparator in the case of everyday events is the memories and beliefs of independent witnesses, as well data from any recording devices. This raw material of quotidian events produces quite a different class of truths from the important generalisations about the human condition and the physical environment on which humans depend. Classification, abstraction and generalisation form the basis of useful knowledge, which is different from the truths of individual observations and events. The truths of science require the additional assumption that what is true in several cases can be generalised to apply to all similar cases, the basis of induction. The failure of a hypothesis might be due to imperfect observations about a few situations of the required type or it might be due to unexpected or unknown factors. A grander scientific assumption is that identical circumstances (ceteris paribus) must produce the same results, or be due to different or improperly controlled factors not included in the theory. Establishing the truth of such fundamental ideas poses a special problem for epistemology.

The empirical procedures and inductive analyses which form the basis of scientific enquiry, together with informed hypotheses have led to general truths of incalculable benefit to humanity. It is hardly surprising, therefore, that the truths of science have replaced the once ubiquitous religious and philosophical beliefs that sustained earlier societies. The question, what is scientific truth, could be answered by saying that it is the body of knowledge, albeit provisional, that has accumulated as a result of applying legitimate scientific methods to the highest possible standards, and confirming the results by the process of peer review.

This is a very high standard indeed when compared with the way we form common beliefs in our business and private lives. In general then, truth is the body of the best knowledge that humans are capable of producing in the present state of cultural development. Even in the span of a century or so, great changes have occurred in both philosophy of knowledge and the processes of science and technology which have led to what may be classified as truths.

Several philosophical theories of truth have been formulated. The correspondence theory assumes that the truth predicate applies to beliefs, and further supposes that every true belief corresponds to a fact. This assumes that there are such things as true facts and that their veracity can be established. The Pragmatist William James objected that this approach was just a lexical trick that did not discuss the nature of truth at all. The salient point is that the idea of truth enters into both beliefs and what are regarded as facts and it is not clear what is meant in either case by saying that a belief or a fact is true, apart from applying the attribute to a fact and a corresponding belief simultaneously.

In the coherence theory of truth, the objection is that individual statements are incapable of capturing truths about ‘reality’, since states of affairs may be described in different ways from different perspectives and motives. Furthermore, descriptions of events are infected by the meanings inherent in the language used, which imports ready-made concepts into the description of what is supposed to be the factual criteria. Only a wide theoretical context will suffice to judge whether a statement is true or not. This mirrors what we actually do in making casual truth judgments, where comparisons are made with our existing knowledge base to see if any inconsistencies arise from accepting a new idea or supposed fact. William James’s pragmatism supposed that true beliefs were those that we must act upon in order to survive or advance the welfare of humanity, which is a rather partisan notion that fits in well with the American predilection for social Darwinism, as opposed to an impartial and unselfish search for truth for its own sake.

Tarski’s semantic conception of truth applies truth and falsity to sentences, and consequently focuses on their meaning. He pointed out that a statement such as: (It is true that (Socrates was wise)) are meta-lingual statements, where an assertion is made about another statement in what he called an object language. He provided the gnomic example: “snow is white” if and only if ‘snow is white’. One could interpret the first statement to be a belief and the second to be a statement of an empirical fact, which doesn’t seem to advance matters much beyond the rejected theory of correspondence. The objection to this approach is that the so called real world is lost in the process of linguistic and logical formulations. It is worth observing here that pure logic is not at all concerned with empirical meaning and so can provide no guidance whatever on the vexed relationship between an empirical fact and its description as a thought or a belief.

The distinction between truths of the mind, a priori truths, and observed or a posteriori truths is an important one. An early system of a priori truth was Euclid’s geometry, which was based on five axioms and five elements of construction. This proved capable of generating innumerable mutually consistent theorems, including the well-known truth that the angles of any plane triangle add up to two right angles. The truth of many of these theorems is not immediately obvious to the uninformed observer of geometrical figures and provided essential knowledge for ancient architects and surveyors. How wonderful that every triangle inscribed in a semi-circle is a right angled triangle, and that every triangle inscribed inside an arc defined by an arbitrary chord generates triangles with a constant angle. It is this power to generate truths about infinite cases which distinguishes mathematics from empirical science.

The idea that a few basic ideas and rules of logic could generate new knowledge was a powerful one, which dominated philosophy until quite recent times. The false idea was that knowledge of a few fundamental principles in philosophy or science would be sufficient to deduce all possible knowledge. A corollary of this idea is that the resulting totality, realised or not, represented a perfect and consistent body of truths, just like the totality of all possible theorems derived from Euclidean Geometry. An obvious drawback to this epistemological programme is that it could only apply to a priori systems, which would confine the resultant knowledge to logic, mathematics and related disciplines. The unfortunate truth was that there is no obvious connection between empirical truths and the logical means of elaborating facts about the physical world.

This idealistic view persisted until recent times, until empiricism and the rise of science gradually confined it to speculative philosophy. It still remains a philosophical question as to how the observed behaviour of the physical world conforms to Euclidean geometry or to the more advanced systems of mathematics that are so essential to modern science. However, some philosophers of science think this need have no bearing on how science is conducted in pursuit of knowledge. However, what does seem to restrict the progress of scientific theories is the lack of sufficiently powerful mathematical theories used to formulate and describe them. The calculus is an obvious example in relation to mechanics and other areas of physics, as is matrix theory and probability theory in their many applications to science. This indicates the strong dependence of empirical theories on specialised languages.

A peculiarity of axiomatic systems, both logical and mathematical is that different axiom sets can lead to different and sometimes inconsistent theorems. A simple example is that the angles of a triangle drawn on a sphere add up to more than two right angles, and so does not even include the corresponding Euclidean theorem as a special case. The distinction between Newton’s and Einstein’s theories of space and time is another example of differing but true systems. This difficulty extends to formulating logical languages for demonstrating the consistency of mathematical truths. The avoidance of paradoxes had doomed Russell’s and Whitehead’s attempts to provide a reliable logical language as a basis for all mathematics. Kurt Gödel upset the apple cart by proving that it was not possible to construct such a language that was both consistent and complete, so that there would always be, potentially, true but unprovable theorems describable in the system. This put an end to the dream of creating a final system of a priori knowledge, and further undermined the kind of certainty associated with grand systems of universal truth, whether empirical or not.

From one point of view, the pursuit of knowledge requires both the general principle of truth and the philosophical, logical, mathematical and empirical means of establishing the ever changing facts which are generally agreed to be true. Because the body of such knowledge is now so vast, it has become inaccessible to the ordinary citizen, if only because of the cost and deficiency of educational systems and the limits to individual knowledge. One unfortunate result of this divide is that beliefs in the general population fall far short of the knowledge that is available to those with the inclination, means and opportunity to obtain access to them. In other words, general ignorance is a source of discontent and social upheaval, often exploited by unscrupulous politicians for personal power and by corporations who wish to preserve an ignorant and subservient population.

Access to these huge knowledge bases has been greatly increased through the medium of the Internet, but this has also provided access to many bodies of pseudo-knowledge and speculative thought that lies outside the strict borders of academic and professional knowledge. The term truth has been stretched accordingly to accommodate this burgeoning diversity. One particular example of this is the reactionary movement of creationism which seeks to re-establish forms of authoritarian knowledge prevalent in earlier societies. The tension is between restrictions on free thinking beneath the shadow of the now enormous tree of accepted knowledge and allowing a tangle of speculative and redundant thought to thrive in the jungle outside its shadow. Such a wilderness has often nurtured the kind of mavericks who have contributed greatly to scientific and cultural knowledge, so tolerance of a robust unorthodoxy is preferable to an epistemological monoculture. The counter argument that academia already encourages such diversity of thought is less convincing now that corporations finance and control so much of what constitutes advanced education. The corollary is that the truth, whatever it might be, ought not to be controlled by orthodoxy or by whatever dominant philosophy may declare it to be.

We continue to search for truth without knowing exactly what it is or how we ought to go about it. The combined efforts of countless generations have shown that such a search is both valuable and necessary for human welfare, and latterly perhaps, continuance as a species. It seems obvious, if not proven, that adherence to truth in its many forms is our best hope for a satisfactory social life and that weeding out false beliefs, albeit in a kindly way, must be an ongoing project. Notwithstanding that great monuments to truth have been erected, their continual replacement, however costly, ought to continue if civilisation is to remain accessible to a majority of humans. The balance of false beliefs seems to be gaining ground and might easily derail the beneficial presence of true if not final beliefs that assist humanity on its journey into the unknown.

Tony Thomas
April 2011

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