Ambiguity in the concept of truth

The concept of “truth” is not always as clearly and unambiguously defined as one might think. This essay discusses three possible definitions and illustrates the ways in which they can conflict with each other.

This topic was initially intended here as an example for the article on the motte and bailey fallacy, but the more material was collected, the more it became clear that this topic is too multi-layered and complex to be dealt within the scope of a short example text.

At the same time, the topic is also too important and interesting to be left out completely. As it didn’t really fit into the format of the other articles on this site, this now marks the beginning of a new “Essays” section, where hopefully more articles will be added soon.

The concept of truth is a central philosophical concept that many other important concepts depend upon – including the question of what is “right” and what is “wrong”, or what is a “fact” and what is a “lie”. It is also at the heart of other important concepts, such as “knowledge” (usually defined as “true and justified belief”), how to describe “reality” and many others.

Understanding what interpretation stands behind each use of the term “truth” – or any of its dependent terms – can help to recognise possible ambiguities and avoid falling for intentional or unintentional misunderstandings. This is all the more important as this and the associated terms are used quite frequently - and not always transparently - in political and social debate.

Contemporary discussions about topics such as “alternative facts”, “liar press”, “bullshit” and the implications of the use of generative artificial intelligence (LLMs) depend to a large extent on what we understand to be “true” and “false” or “right” and “wrong“, or “truthful” and “lying”.

As you might expect it from such a central philosophical concept, there have been many different approaches throughout history to defining this term as clearly as possible. And while these approaches are indeed compatible with each other in most cases, this is not necessarily true in all cases.

These definitions can be roughly categorised into the following three groups:

The most straightforward approach to defining the term “truth” is to observe the correspondence of a statement with the reality.

For example:

The statement: “The sky is blue”
is true if we can observe that the sky is indeed blue.

This is probably how most people would intuitively think of the term “truth”: as a representation of reality.

And of course this is also the approach used in many natural sciences. For example in geology:

The statement: “Granite is harder than sandstone”
is true if granite has a measurably higher degree of hardness than sandstone.

Or in biology:

The statement: “Zebras are the preferred prey of lions”
is true if observations show that lions do indeed favour zebras over other prey.

This is a viable approach when it comes to statements that can be verified (or refuted) by simple observation. Lions can be observed hunting, the hardness of rocks can be measured rather easily.

But what if we are talking about statements about something that is not so easy to observe directly?

“The universe began 13.8 billion years ago with a big bang.”

As we cannot directly measure or even observe the creation of the universe, we need a different approach:

Under this approach, a statement is considered true if it can be integrated into an established system of statements without contradiction.

This may not sound very intuitive at first, but it is actually a very common approach. In legal science, for example, it is relevant for the evaluation of new laws or court judgements whether they are coherent with existing laws or previous decisions.

The same applies to mathematics, where we have situations like the following:

The mathematical statement:
$$\sqrt{2}\ne \frac{k}{l} ;k,l\in \mathbb{N}$$ is true if it does not lead to contradictions with the axioms of mathematics.

We find similar approaches, to some extent at least, also in the social sciences and economics. Not to mention special cases, such as theology.

Perhaps the best example of this is physics, in which the two definitions of truth mentioned above are used alongside each other: As a natural science, physics obviously aims to describe reality, and the correspondence of its claims with reality is therefore of central importance.

However, physics is also strongly influenced by mathematics and uses mathematical models to derive statements about reality. This, in turn, is based on a coherence model, as shown above. In most cases, these two approaches lead to the same results … though not always!

For example, many mathematical models tend to run towards infinity – the values or deviations are either infinitely large or infinitely small. In nature, however, “infinity” practically never occurs – there are always limits, both in size and in the accuracy with which measurements can be made.

It is noteworthy that many important advances in physics have time and again resulted from conflicts between mathematical models and reality:

• The realisation that velocities cannot be added up arbitrarily (i.e. to infinity)¹⁾ led to the introduction of a “speed limit” at which causal effects can propagate (somewhat misleadingly referred to as the “speed of light”).
• Conversely, for example, energy states, lengths or time units cannot be subdivided into arbitrarily small quantities, so that the infinite number of decimal places of irrational numbers do not make sense for describing reality (any number with finite decimal places can be represented as a fraction).

To summarise: there are certain properties of mathematics that are not reflected in reality. Infinity and irrationality are just two examples of many.

This insight is of course not new, and at least for more experienced physicists it should be self-evident that the mere fact that something can be derived from a mathematical model is not enough evidence to assume that it actually describes reality. Further experimental evidence would be necessary in order to verify the finding first. Without these, one should first assume that they have found a mathematical artefact and not discovered a new aspect of reality.

And of course, despite certain possible problem cases, mathematics has proven to be an enormously powerful tool for describing physical reality, which in most cases can also provide correct findings.

The ability to build up an at least superficially coherent worldview and to avoid cognitive dissonance is one of the most important cognitive abilities of every human being.

An important aspect of this capacity is the ability to judge new information according to whether and how it can be fitted into the existing worldview. New information that is not so easy to integrate or may even contradict it requires at the very least a higher degree of mental effort to process than those that fits in easyly.

What is often considered “difficult” fields of knowledge such as quantum mechanics or probabilistics are so inaccessible precisely because they do not seem to fit so neatly into a naïve understanding of physics or maths.

We (all!) also find it more difficult to accept new information if it contradicts our existing political, religious or general social view points. When confronted with such information, we tend to initially view it as less relevant and/or less credible than information that seems to confirm our existing positions. This effect is known as a cognitive bias called confirmation bias.

As with all cognitive biases, these are not laws of nature that we cannot avoid. People are perfectly capable of deciding for themselves which new information they want to accept and which they don’t – and ideally we even do this according to rational criteria and not just based on a “gut feeling”. However, in the case of ideas that contradict our existing beliefs, this is associated with a rather high mental effort, so that we use this ability mainly for particularly important questions – for example for important business decisions – while otherwise psychological effects such as those described above play a more important role.

One particular aspect of social groups is that they establish certain norms that apply within this group. This can happen by tacit agreement, as well as by regulation or at least influence by an authority (e.g. legislature, clergy); in any case, these norms are specific to the respective group or society. In other contexts, they may be defined differently.

Such definitions can refer to a broad spectrum of different normative standards: They range from simple rules of daily coexistence (e.g., “stand on the right and walk on the left on the escalator”) via codified rules (e.g., statutes or laws) to the framework in which phenomena of daily life are interpreted – for example, is a lightning storm understood as an electrostatic discharge, or the expression of an angry God? (See also: social narrative).

To take a simple example of such a social norm, which is codified both by convention and by law, one could state:

“In traffic, everyone must drive on the right side of the road.”

The arbitrary nature of such a definition is often only apparent when confronted with an alternative definition that applies in a different context. In other parts of the world – such as the British Isles, Cyprus or Japan – the following applies instead:

“In traffic, everyone must drive on the left side of the road.”

The very same questions can even be answered differently by the same group at different times. For example, Sweden changed from driving on the left to driving on the right in 1967. There are also other social narratives that can change over time:

Until the early 20th century, the question of who held souvereign power in a country was generally answered by the principle of divine mandation. This could be summarised (somewhat simplified) as follows:

“The king is the sovereign appointed by God.”

Since then, this role has changed completely. Even in (European) countries that have retained a constitutional monarchy, the principle of popular sovereignty now applies. To put that into an (again somewhat simplified) phrase:

“The people are the sovereigns from which all power is derived.”

Social determinations of this kind are doublessly also a form of “truth”. One is justified to say that it was true for people of the Middle Ages that their ruler was mandated by the grace of God, just as it is true for us today, that we the people are (or should be) the souvereign power of a state.

It is not difficult to imagine situations in which the different definitions of “truth” can be conflated. In the worst case, this can be used as a rhetorical confusion tactic, namely by establishing a “truth” according to one definition and then pretending it is the other.

This is akin to what is referred to here as the “motte-and-bailey fallacy”, which describes a situation where two similar (but not identical) positions – in this case two different definitions of truth – are substituted for one another in the hope that the debate opponents, or at least part of the audience, will not notice (see also: (Argumentum) ad Captandum (Vulgus)).

The use of the term “alternative facts’, with which Kellyanne Conway, then advisor to former US President Donald Trump, attempted to justify a claim by press spokesperson Sean Spicer, who had made a factually incorrect (in the sense of “not corresponding with reality”) statement about the number of people attending the president’s inauguration ceremony, can be understood as such an equivocation. What she was probably trying to suggest was that the statement was “true” according to one of the other definitions of truth – either in the sense of coherence with her world view, or as a social truth in her or the president’s social environment.

In principle, there is nothing to be said against using such an “alternative” definition of truth – provided that it is communicated transparently. However, this was not the case in this situation. Rather, Ms Conway tried to present her “social truth” as equivalent to contradictory statement, for which she was (probably deservedly) accused of trying to tell a lie.

One possible solution to such definitional conflicts might seem to be to define a hierarchy - for example, by considering correspondence truths to be “more correct” or “more true” than coherence truths and then considering possible social truths to be less significant than the other two forms.

This approach is the logical consequence of a naïve assumption that the correspondence with reality represents the “natural” definition of the term, while the other forms are rather “redefinitions”, i. e. rhetorical tricks to be able to utilise the term outside its normal field of application.

However, it must be countered that each of the above definitions of truth has an area of validity in which it is “more correct”, or at least “more meaningful” than the others. To name just a few examples:

• Even if mathematical concepts such as the imaginary number i or irrationality have no correspondence in reality, they are still useful concepts that can help to describe real-world phenomena better than would be possible without them. In other words, a coherence approach is much more useful in these cases than relying on correspondence alone.

• When historians write about the worldview e. g. during the time of the Chinese Han dynasty, it makes little sense to point out that the earth was actually already a sphere in the 3rd century AD. The important aspect here is that the social truth for people in this society was of a flat world.

Instead of establishing a general hierarchy of truth definitions, it makes more sense to choose the most appropriate definition for each specific context and – this is the important part: to also make this transparent!

One type of argument that crops up time and again in public discourse on a variety of topics is that a “scientific consensus” exists on a particular issue. This means that the vast majority of experts (or scientists) who deal with a topic hold a certain position, which thus represents the current state of science.

Examples of such topics of discussion include climate change, a range of issues surrounding the classification and treatment of COVID-19 – and, of course, the aforementioned shape of our planet.

The reference to a “consensus among experts” as a rhetorical device is certainly debate-worthy on many levels. In this context, however, it should only be pointed out that this is again a truth based on social consensus, i.e. an agreement within a community to interpret a phenomenon in a certain way (even if this is of course usually based on correspondence with reality [research] and/or coherence with existing knowledge about the research object).

Conversely, critics of such positions often try to argue with supposed “common sense”, with arguments that seem plausible enough to non-experts to be compatible with their existing world view. These are all aspects of a “coherence truth” which appeals more to the target group’s confirmation bias or, in some cases, perhaps even wishful thinking.

Which position is the “more correct” one will have to be decided on a case-by-case basis. What is important for us is that classification according to the different types of truth as described above is not in itself a sufficient indication of which side should be believed.

A number of problems can arise when different concepts of truth are used in a way that makes them indistinguishable. In extreme cases, different definitions of truth can be used in parallel in the same context, or even in the same statement.

In some cases, this kind of ambiguity leads to a form of motte and bailey-situation in which the different concepts are indistinguishably intermixed.

However, one should not automatically assume that this is always a deliberate rhetorical confusion tactic. The differences between the definitions used are not always as clear and recognisable as in the examples here. It is more likely that the reason for this kind of ambiguity is genuine confusion.

This makes it all the more important to know and recognise the possible implications that arise from the various concepts of truth and, if necessary, to have them clarified by all discussion parties.

And of course one should avoid such ambiguities oneself. This can be achieved by clarifying the definition(s) used, or by using qualifying attributes, i. e. terms like “social truth” versus “correspondence truth”. In some situations, it may also be sufficient to simplay mark the different levels of abstraction of truth versus “truth” typographically (e. g. by using quotation marks for a “meta”-usage of the term).

• Alternative facts
• Confirmation bias
• Motte and bailey fallacy

• Truth on Wikipedia
• Truth on Stanford Encyclopedia of Philosophy