The following is a slightly meandering and perhaps not entirely easy analytic essay on the nature of truth. At first sight a theory known as „the correspondence theory of truth“ appears to satisfy our demands and expectations that in day to day life, there be a way of explaining truth as something that is objective and which exists either „out there“ in an external reality, or in the inner realm of the self in a manner that is somehow analogous to the external form. This was conceived and formulated by the Polish logician Alfred Tarski (1901-1983), who saw that truth was something semantic, which is to say that is something that is applicable to statements and with reference to things can only be used metaphorically. Following Tarski (1956/1983, p. 155):

A true sentence is one which, claiming that a certain state of affairs pertains in some sphere of reality, is true, if the state of affairs of affairs is as claimed and accordingly the associated description is “correct”.

Thus:

„It is snowing“ is a true sentence if and only if, it is snowing.

Here „it is snowing“ functions as a name for what we mean when we say that outside, snow is falling. Alternatively, structural-descriptive names may be used so that the above example becomes:

An expression consisting of three words, of which the first is composed of the two letters I and Te (in that order), the second of the two letters I and Es (in that order), and the third of the seven letters Es, En, O, Double-U, I, En, and Ge (in that order), is a true sentence if and only if it is snowing.

For the Austro-British philosopher, Sir Karl Popper (1902-1994), Tarski’s theory solves a major philosophical problem and clarifies in pragmatic terms what, in day to day life everyday truth „is“ (2002, p. 112 & 163-165). It is, as Tarski saw, a semantic property that strictly speaking, can only be applied to sentences and statements that pertain to refer to states of affairs that can be observed and corroborated by people other than the person making them. Truth is therefore not a property of objects „in themselves“, nor is it something that is purely private and subjective. In discussing Tarski’s theory, Popper stresses the correspondence between the assertion made and the facts to which they are supposed to correspond, more than Tarski does himself. This is because for Popper, Tarski’s theory of truth makes a philosophical point that is of the utmost significance. For any proposition, P, that claims to describe a fact or set of facts in the outside world, there is, if the proposition is true, a correspondence between what P says and the relevant facts pertaining in the outside world that are, in an appropriate sense „P„. As the inverted commas in the first of the examples given above imply and the names of letters given in the second example likewise indicate, the correspondence works via the notion of a meta-language. This enables the status of a proposition made concerning states of affairs in the world to be commentated upon. The meta-language is the framework that surrounds the inverted commas and enables a statement, P, to be talked about as well as the facts pertaining in the world that entail that what P says is to be considered as being „true“. It then becomes possible to say for example:

The statement made in French and consisting of the words „l‘ herbe“, „est“ and „vert“, written in that order, corresponds to the facts if and only if, grass is green.

The phrase „corresponds to the facts“ can then be replaced by the words „is true“, where „is true“ is a meta-linguistic predicate that is applicable to statements. There is thus no recourse to elusive essences which make things true and the sets of circumstances under which the words „l‘ herbe“, „est“ and „vert“ are used does not have to be gone into. If the statement is false, the set of facts attested to are theoretically possible but do not, at the time of claiming, actually exist. The same applies for statements about what a person is thinking or feeling except that the correspondences are more difficult for outsiders to corroborate. This is due to the sets of facts not taking place in the objective world „out there“ but in the private realm of the self. Nevertheless, theoretically at least, the same notion of correspondence is applicable. The correspondence theory is effectively a theory concerned with the agreement — or lack thereof — of conventions with reference to facts. The purpose of the theory is not to assess the appropriateness of a concept’s relation to an external reality that we cannot see. Rather it is concerned with the world of daily experience and what is maintained about it and is necessary for the management of our daily lives. Here truth and falsity arise through our having to confront such things as the fallibility of human memory, the unpredictability of things such as the weather and doubts as to whether someone else is telling the truth or not. In addition, we also discuss complex assessments of a situation, arguing about whether this or that analysis of a situation is best. Often statements are made that refer to the future. As a result of an assessment we may decide to embark on a certain course of action rather than another. Our expectations are then are either fulfilled and become true or else they fail to do so and the assumptions lying behind them are seen as having been false all along only we did not know it. Statements concerning facts in the future are thus similar to statements concerning facts in the present only they cannot be immediately verified. Such day to day situations are all admirably covered by a correspondence theory of truth that pertains to sentences that describe states of affairs in the world and „the facts of the matter“ which are nothing other than the states of affairs in the world which are being referred to. Though when talking about truth we do not use a different language, the context shifts as we cease to talk about facts and speak instead of the truth of statements that describe facts. The facts we talk about are either subjective or objective depending on whether they belong to the social realm of shared life or to the private world of an individual’s inner life. In both cases, the correspondences that take place between the facts and the statements that purport to describe them do so via conventions related to what we mean when, in a sentence such as, „the cat sat on the mat“, we mean when we say „cat“ and „mat“ and „sat“, etc. Such statements make no claims concerning the ultimate realities lying behind the objects under discussion. This is because in dealing with the problems of daily life we are generally not interested in probing ultimate realities. We are simply interested in „getting things done“. To this end we assume that in general the future will be similar to the present. In the present one may identify five different kinds of day to day statements that relate to five different kinds of fact. There are what one might call a-facts. These describe our inner states, our thoughts and feelings and sensations in a way that makes as few assumptions about the rest of the world and external realities as possible. They are thus describable as statements taking the form „I am thinking x, or feeling y, or seeing z“. In the case of a statement about what someone else is thinking or feeling or perceiving we simply switch the first person pronoun for a third person pronoun or a name. The statement then becomes correspondingly hypothetical, as we can never know what another person is subjectively thinking or seeing or feeling but can only ever make an assumption. In addition to a-facts there are b-facts which are simple facts that pertain to the immediate present of the outside world. These can be represented by simple statements such as „The cat is sitting on the mat“ uttered in such a context that the listener can easily, for him or herself, see whether the cat is, in truth, sitting on the mat. Related to these simple facts there are g-facts which though equally simple and straight forward cannot be immediately verified by the listener and their truth must accordingly be taken on trust. An example of such a fact is the state of affairs refereed to when someone says, „My car is parked around the corner“. Though it cannot be immediately verified, the truth content of such a statement can be examined by the listener if he or she is prepared to take the trouble to investigate. Due to the confines of the present, the investigation is however not something that can be conducted immediately. Thereafter there are d-facts which are complex facts expressible by sentences such as „London is in the south-east of England“. This statement can be verified either by looking out the window of an aeroplane when flying into London from a known direction. Though this sounds simple, it tacitly assumes a number of things, such as a good sense of orientation and knowledge of how a city might appear when seen from the air. An alternative approach is to look at a map of Britain. This also entails assumptions including the ability to map-read and the reliability of the map being consulted. This leads to e-facts which go beyond the realm of what is easily verifiable. An example of an e-fact is the statement „London is a city with some 10 million inhabitants“ which unless one happens to work in an organisation that is engaged with monitoring and establishing the population of London, must be taken on trust. Summarising one may say that there are:

 

a-facts                 qualia facts                     „I am thinking x, or feeling y, or seeing z“

b-facts                 at hand facts                   „The cat is sitting on the mat“

g-facts                  neighbourhood facts     „My car is parked around the corner“

d-facts                 complex facts                 „London is in the south-east of England“

e-facts                  advanced facts               „London is a city with some 10 million inhabitants“

 

Then there are z-facts which can be characterised by statements phrased so as to contain a prognostication about the future such as the statement „Tomorrow will be a sunny day“. As observed these are not straightforward facts but rather are „would-be-facts“. z-facts assume that by and large tomorrow will be similar to today and that basic phenomenon such as the sun’s rising will continue to happen just as they have always happened. Although scientists talk of time as a dimension and their equations deal with it as if it were akin to those of space, for conscious subjects, the dimension of time is fundamentally different to those of space. Where space can be both passively experienced and actively explored, time can only be experienced. Although we can imagine time-travel, the facts of the matter are that we cannot wander through time, scrolling through it as we wish and the Theory of Relativity only allows time-travel under circumstances that are so specialised and restricted as to be, to all intents and purposes, impossible. Thus for any given future time we must wait for its arrival and once it has past it cannot be revisited. As subjects we are locked in a present yet it is through the present that we experience things. The present is the format of whatever it is that we experience. All our memories of the past and all our imaginings of the future are experienced as memories or imaginings in a present, from which we can only escape when we die escape. h-facts are not only even further removed from easily verifiable realities than e-facts but also often have tacitly assumed z-facts and assumptions embedded in them and are the kinds of statements made by scientists. Such statements have a general applicability that transcends the other kinds of fact so far encountered. A part of this general applicability is due to their having tacit z-characteristics and it is this that makes them universally applicable both now and in the future. The abstractness that enables them to have a wider range of applicability means that often, though referred to and assumed, they are only partially understood. Thus although many people know what e=mC2 stands for, only a very few know and can for themselves verify how via a highly complex apparatus of mathematics it relates to the realities of life. Though abstracted from day to day reality this abstraction gives h-facts the power to embrace reality in a much more all-encompassing manner than other facts. This form of abstraction increases what Martin Heidegger (1889-1976) calls our ability to „cognitively master“ states of affairs or „things“ in the world (1992/1998, p. 3-4). In accordance with the principle of abstracting away from immediate realities and embracing realms of ever wider generality, there are q-facts which are mathematical facts. As generalisations these have the capacity to be applicable to all entities that can be differentiated and counted. Through their abstractness, q-facts transcend time and are forever true. If one understands the expression „2 + 2 = 4“ then one understands that one pair of objects added to another pair of objects will result in there being four objects. Failure to arrive at this result means nothing other than an inability at implementing the rules of mathematics correctly. Finally there are i-facts which are facts concerning life and the universe on their most abstract levels. One discipline that endeavours to address i-facts is that of philosophy and while there is much discourse and arguing, if one is to maintain some form of realism (regardless of how pragmatic) one must believe that at the end of the day, somewhere along the line, philosophy does address facts that exist „out there“. In accordance with the principle of abstraction here observed, i-facts are often abstracted away from everything, as the philosopher endeavours, within a system of explanation, to find a conceptual place for that which he perceives as being in need of being put in place. In addition to the first list of facts drawn up a second list must be added:

z-facts                       „as-if facts“ about the future                     „Tomorrow it will rain“

h-facts                       scientific facts                                              E = mC2

q-facts                       mathematical facts                                      2 + 2 = 4

i-facts                        philosophical facts                                      „Truth is an ideal“

Although all these different kinds of fact span a considerable range, the sentences which describe and refer to them all do so via complex conventions and rules that govern the use of the words and symbols used in their formulation. These often refer not only to other rules and conventions but to whole chains of procedures, operating manuals and even degree level and post-graduate level courses of study. Statements made concerning the past point to the past in a way that is similar to the way that statements concerning the future point to the future and yet the past is obviously not something that can be re-experienced. In practice therefore, statements that refer to the recent past do so in a way that is similar to the statement that „London is a city with some ten million inhabitants“. In effect, a past is postulated about which things are said that could theoretically be verified by interviewing people and through the consultation of documents and physical evidence. As the recent past fades, the historical past begins, with documents and written testimonies pointing to that which was but which no one currently alive actually experienced. As the historical past becomes more distant, history becomes prehistory and the written sources become ever more scarce and indecipherable until a time comes when there is no writing and the only evidence available are artefacts, sites and traces of the human use of landscapes. As this point is approached, statements about the past increasingly refer to it through the apparatus of the physical sciences. Nevertheless even this past is not silent and linguistics and the analysis of DNA material enable conjectures to be made concerning the general movements of populations, while comparative mythology and astronomic reconstruction’s enable world-views to be reconstructed.

From the above analysis one can see that in clarifying the nature of truth and defining it as a property of propositions, Tarski’s theory glosses over the holistic complexity by which all propositions, even apparently simple ones, actually refer to the reality that they address. Given the aims and purpose of the theory, this is perfectly legitimate, however it should not be forgotten that life, language and culture relate to the world that they form, mould and interact with, in a manner that is ultimately holistic. Though scientific statements postulate something that lies behind the veil of appearances and would thus appear to fall out-with the scope of a correspondence theory of truth, correspondence is there as an ideal. Following Popper, via the notion of fallibility, scientific statements can legitimately be said to appear to correspond and to fail to correspond with that which they claim to describe. As it is fallibility that gives scientific theories their claim to objectivity, this implies that the correspondence of a theory to the way that physical reality actually behaves is theoretically possible and „exists out there“ as a correspondence that can be covered by Tarski’s theory, just as in the everyday case (Popper, 1963/1972, p. 116, 229 & 232-235, 1972/1986, p. 314-318 & 319-329). The fallibility of inappropriate theories implies that though we do not see and can never see, positive correspondences, this does not mean that they do not or cannot exist but rather that the search for scientific truth is an ideal, or a „regulative principle“ (Popper, 1963/1972, p. 226 & 229). Adherence to the ideal means that scientific truth is something that is striven for and this leads to the continual improvement of scientific theories, this being indeed what the scientific method is all about.

The conventions surrounding the correspondence of statements about the world to the facts pertaining in the world, combined with the assumption that these states of affairs will persist from one day to the next, form the mindset of daily life. Expressed in the first person by the subject concerned, statements referring to a-facts, referring as they do to what a subject is thinking or feeling or otherwise experiencing with only the barest amount of reflection as to what these experiences may be about, are described as ostensive. Ostensive knowledge consists in reports made by a subject concerning what they are immediately experiencing. In as far as the subject doing the experiencing, addresses such statements to him or herself, the knowledge is certain but of no import as it is obvious. For all other subjects, statements of ostensive knowledge can be only be either true or false depending on whether the subject making the statement is being honest or is lying. Normally statements concerning personal experience are however combined with interpretations and comments that are designed to add interest to the person to whom they are addressed. This generally takes the form of statements that refer to b-, g-,  d-, e- and z- facts but can also include statements that refer or allude to  h-, q- and i- facts. Indirectly the speaker reveals to the listener how he or she sees the world and while speaking, also actively interprets it. Like the notion of a sensation that has not been interpreted, it can be argued that statements of ostensive knowledge are rarefied constructions that are seldom found in real life. The opinions and interpretations that are inevitably interwoven with ostensive statements are all part and parcel of an experience and these latter, along with the generally uncritical way in which they are used and accepted have supplied reasons for some philosophers, beginning with the Ancient Greek, Pre-Socratic philosopher, Parmenides (born around 515 BCE), for being distrustful of them. It is in the case of statements that refer to potential, not-yet become z-facts that Parmenides‘ scepticism of such statements was particularly well-founded. For though we expect the sun to rise everyday, as the Scottish Enlightenment philosopher, David Hume (1711-1776), has shown (1739, 1777) there is absolutely no logical reason or inner necessity that dictates that it will do so. Though the sun’s rising is the result of it following certain laws postulated by scientists, there is no guarantee that stipulates that what these laws say, will always hold true. Hume’s point is that although we detect regularities in nature and evolution has taught us to expect them, there is no underlying logical reason that entails that any regularity observed in the past is of necessity bound to reoccur in the future. All statements that imply or refer to z-facts are therefore to be seen as provisional speculations. Accordingly all human knowledge except for that which pertains to q-facts and some i-facts, is to be seen as being of a provisional nature. For even in the case of a-facts there are usually a host of implicit assumptions concerning the world and how we see it all based on a tacit assumption that there is similarity in the world and that this extends both through time and across place. Though in the above lists the a-facts, b-facts, g-facts, d-facts and e-facts were separated from z-facts, h-facts, q-facts and i-facts, this separation is artificial. To have meaning, many a-facts along with all b-facts, g-facts, d-facts and e-facts depend on the assumption that in the next instant of time that we experience, the similarly in the world that pertains in the immediate present will continue to pertain in future. Apart from the statements referring to the q-facts of mathematics and the i-facts of some philosophical statements, the only statements that appear not to make any assumptions about the future are statements that refer to certain a-facts, these however being, as observed, so simplistic that they have more theoretical reality than actual reality. For this reason Popper argues (1972, p. 42-64), that there are no „primary facts“, no „pure sensations“ and no un-interpretated „bedrock of experience“ from out of which our view of the world is learnt by means of empirical observation. Rather we grow up in a world in which assumptions and theories are so inexorably mixed up with our experience of the world that attempts to separate the three is often lead to confusion. Reasoning and assuming things are so much a part of how we experience the world that it is pointless to search for un-interpretated descriptions of what a subject is experiencing just as it is difficult to try and catch oneself experiencing an un-interpretated sensation. Effectively both are generic generalities of which concrete, specific examples, drawn from life are hard to find. Usually when we eat something we nearly always have and idea what it is that we are about to put into our mouths. Generally we simply know whilst in cases where we do not know, such as at a buffet party, we can infer from the context and appearance whether something will be sweet or sour. Thus even here, our taste buds are anticipating something and our expectations erect a framework which begins interpreting and forming the experience even before we have put anything into our mouths. Nevertheless sometimes we are caught out and one could argue that this is about as close to an un-interpreted sensation as one can get. Another way that we can trick ourselves into experiencing something unencumbered with the expectations of our usual perceptions is through experiencing sensations of colour when we are not expecting them. This can be achieved by making a top, one half of which is black the other half of which is white with black, circular lines of varying length (Kelsey in Hendee and Wells, 1993, p. 39-41).

When spun, faint bands of colour will be seen that no camera can capture because the impression is purely subjective. The effect is due to the fact that between the retina and the brain, the transmission and processing times of signals are different for different colours. Though white light appears colourless, it actually contains all colours so that the eye is in fact seeing colour. This is then made manifest through the black half of the disc in combination with the lines on the other side which, exploiting the different processing times of the different colours, exposes them and makes them perceptible. As this experience of colour goes contrary to our expectations it is again relatively un-interpreted. Here too the emphasis is on word „relative“. Despite the fact that they are hard, if not impossible to find, the notion of un-interpretated sensations does have a use as it can help us in clarifying our ideas about knowledge and truth. As part of a discussion and a process the notion leads to understanding.

In the light of the above considerations, one may summarise by saying that apart from some truths of mathematics and some philosophical statements that arguably amount to tautologies, such as such as Parmenides‘ „that which is, is“, all objective knowledge is to be seen as „as if“ formulations that assume that there is similarity in the world that extends both through time and across space. As abstractions of abstractions q-facts and i-facts, though raised above the assumption that there is similarity in the world and thus nominally exempt from the proviso of a provisional status, nevertheless are part of the apparatus that assumes similarity and indeed manages it. In this sense their exemption is really only apparent. As the case of a-facts indicates, philosophical facts are part of a dialogue concerning our place in the world and how we see things, that changes with time so that the philosophical problems of one age are often very different from the philosophical problems and reflections of another. With the passing of time some philosophical problems fade in importance and drift into irrelevance, whilst others are solved. Within the tenets of what has be expressed above, the sum total of true statements expressing facts that range from b-facts through to q-facts constitute „objective knowledge“ or „objective truth“. In endeavouring to understand „The Way of the World and the Way Things“, both in science and in daily life, we reach out toward and endeavour to cognitively grasp something. This means separating it out of its context within the whole and so inevitably it becomes distorted. Thus within the world as a whole truth is perpetually by turns hidden and by turns revealed. In the diagram below, a subject at any given point can never see the whole but instead, depending on his or her position within the diagram can only ever see one facet in its entirety or alternatively, has a glimpse into a limited number of facets of the whole, represented by the concave enclaves that represent truth revealed. Seen from another standpoint however, these self-same curved shells hide and shield truth.

Objective truth is always a matter of frames of reference, of parameters and of resolution. Accordingly in the diagram above there is no single point from which a subject has access to all truths — for this point is blocked out by the oversize dot in the middle. The dot, which represents the theoretical standpoint from which any interaction made is conducted, is a fixed and stable anchor point for the purposes of the interaction concerned. Another frame of reference requires a different anchor point and whilst it may well result in new things being seen, at the same time other things become invisible or are only vaguely detectable. In the next diagram, the image has been given a fractal dimension, and the oversized dot has been replaced by a modified copy of the whole that reflects the continually shifting boundaries of applicability within which truth both manifests itself and hides itself. This new image thus not only reflects the fractal nature of reality but also the never-ending task of interpretation that is synonymous both with life and with any scientific endeavour that has not abandoned the ideal of advancing through falsification and of truth as a regulative idea. The diagram can therefore be seen as an image of subjective thought, forever honing in on contexts of thought and perception and forever stumbling on new things — whilst inevitably overseeing others.

This modified diagram corresponds with what Popper calls „modified essentialism“ — a practical and pragmatic essentialism in which the fundamental properties of the world are, layer by layer (or theory by theory), successively exposed and explored by science and through the sincere practising of the critical, experimental method that is the only benchmark for genuine scientific endeavour (1972/1986, p. 196-197):

… although I do not think that we can ever describe, by our universal laws, an ultimate essence of the world, I do not doubt that we may seek to probe deeper and deeper into the structure of our world or, as we might say, into properties of the world that are more and more essential, or of greater and greater depth.

Continuing he says:

Every time we proceed to explain some conjectural law or theory by a new conjectural theory of a higher degree of universality, we are discovering more about the world, trying to penetrate deeper into its secrets. And every time we succeed in falsifying a theory of this kind, we make a most important discovery. For these falsifications are most important. They teach us the unexpected; and they reassure us that, although our theories are made by ourselves, although they are our own inventions, they are none the less genuine assertions about the world; for they can clash with something we never made.

 

References

Heidegger, M., Parmenides, translated by Schuwer, A., and Rojcewicz, R., Indiana University Press, Bloomington and Indianapolis, 1992/1998

Hendee, W. R. and Wells, P. N. T. (editors), The Perception of Visual Information, including Detection of Visual Information by Kelsey, C. A., Springer Science and Business Media, New York, 1993

Hume, D., A Treatise of Human Nature, Edinburgh, 1739/Everyman Library by A. D., J. M. Dent & Sons, London/ E. P. Dutton & Co., New York

Hume, D., An Enquiry Concerning Human Understanding, 1777/The Open Court Publishing Co., Chicago, 1930

Kirk, G. S., Raven, R. E., Schofield, M., The Pre-Socratic Philosophers, A Critical History with a Selection of Texts (second edition), Cambridge University Press, Cambridge, 1983

Popper, Karl R., Conjectures and Refutations, Routeledge and Kegan Paul, London and Henley, 1963/1972

Popper, Karl R., Objective Knowledge, Oxford University Press, Oxford, 1972/1986

Popper, Karl R., The World of Parmenides, Routledge, London, 1998/Routeledge Classics, Abingdon, 2012

Popper, Karl R., Autobiography by Karl Popper, in The philosophy of Karl Popper, in The Library of Living Philosophers edited by Schlipp, P. A., Open Court Publishing C., La Salle, 1974/Unended Quest, Routeledge, Abingdon/New York, 2002

Tarski, A., Logic, Semantics, Metamathematics, Papers from 1923 to 1938, translated by Woodger, J, H., Oxford University Press, Oxford, 1956/Hackett Publishing Company, Indiania, 1983