Truth

The correspondence theory

A version of what is called the correspondence theory of truth is the following.

A proposition is true iff there is an existing entity in the world that corresponds with it.

Such existing entities are called facts. Facts are relational in that their parts (e.g., subject, predicate, etc.) are related in a certain way.

Under this theory, then, if a proposition does not correspond to a fact, it is false.

This theory of truth is rather intuitive and consistently popular (David 2016).

The coherence theory

The coherence theory of truth is adamant that the truth of any given proposition is only as good as its holistic system of propositions.² This includes (but typically goes beyond) a requirement for consistency of a given proposition with the whole and the self-consistency of the whole, itself—sometimes called coherence.

For parallelism, let’s attempt a succinct formulation of this theory, cast in terms of propositions.

A proposition is true iff it is has coherence with a system of propositions.

Note that this has no reference to facts, whatsoever. However, it need not necessarily preclude them.

The pragmatic theory

Of the neo-classical theories of truth, this is probably the least agreed upon as having a single clear statement (Glanzberg 2018). However, as with pragmatism in general,³ the pragmatic truth is oriented practically.

Perhaps the most important aspect of this theory is that it is thoroughly a correspondence theory, agreeing that true propositions are those that correspond to the world. However, there is a different focus here that differentiates it from correspondence theory, proper: it values as more true that which has some sort of practical use in human life.

We’ll try to summarize pragmatism in two slogans with slightly different emphases; here’s the first, again cast in propositional parallel.

A proposition is true iff it works.⁴

Now, there are two ways this can be understood: (a) the proposition “works” in that it empirically corresponds to the world or (b) the proposition “works” in that it has an effect that some agent intends. The former is pretty standard correspondence theory. The latter is new and fairly obviously has ethical implications, especially today.

Let us turn to a second formulation.

A proposition is true if it corresponds with a process of inquiry.⁵

This has two interesting facets: (a) an agent’s active inquiry creates truth and (b) it is a sort of correspondence theory that requires a correspondence of a proposition with a process of inquiry, not, as in the correspondence theory, with a fact about the world. The latter has shades of both correspondence theory and coherence theory.

States of affairs and facts

When discussing the correspondence theory, we have used the term fact to mean an actual state of things in the world. A problem arises in the correspondence theory, here. It says that a proposition is true iff there is a fact that corresponds with it. What of a negative proposition like “there are no cows in Antarctica”? We would seem to need a corresponding “negative fact” in the world to make this true. If a fact is taken to be composed of a complex of actual objects and relations, it is hard to imagine such facts.⁶

Furthermore, if a proposition is true, it seems that it is the corresponding fact that makes it so; what, then, makes a proposition false, since there is no fact to support the falsity? (Textor 2016)

And what of nonsense? There are some propositions like “there is a round cube” that are neither true nor false. However, the preceding correspondence theory cannot differentiate between false and nonsensical propositions.

A state of affairs is something possible that may or may not be actual (Textor 2016). If a state of affairs is actual, it is said to obtain. The picture theory will make central this concept instead of that of the fact.

The picture theory of meaning (and truth)

The picture theory of meaning uses the analogy of the model or picture to explain the meaningfulness of propositions.⁷

A proposition names possible objects and arranges these names to correspond to a state of affairs.

See fig. ¿fig:picture-theory-of-truth?. This also allows for an easy account of truth, falsity, and nonsense.

Nonsense

A sentence that appears to be a proposition is actually not if the arrangement of named objects is impossible. Such a sentence is simply nonsense.

Truth

A proposition is true if the state of affairs it depicts obtains.

Falsity

A proposition is false if the state of affairs it depicts does not obtain.

Now, some (Glock 2006) argue this is a correspondence theory and others (Dolby 2016) that it is not. In any case, it certainly solves some issues that have plagued the correspondence theory.

“What cannot be said must be shown”

Something the picture theory does is declare a limit on what can meaningfully be said. A proposition (as defined above) must be potentially true or false. Therefore, something that cannot be false (something necessarily true) cannot be a proposition (Dolby 2016). And there are certain things that are necessarily true for language itself to be meaningful—paradigmatically, the logical structure of the world. What a proposition does, then, is show, via its own logical structure, the necessary (for there to be meaningful propositions at all) logical structure of the world.⁸

An interesting feature of this perspective is that it opens up language itself to analysis and limitation.⁹ And, furthermore, it suggests that the set of what is, is smaller than the set of what can be meaningfully spoken about.

Formal methods

A set of tools was developed for exploring theories of truth, especially correspondence theories.¹⁰ Focus turned from beliefs to sentences, which are akin to propositions. (Recall that the above theories have already been recast in the more modern language of propositions.) Another aspect of these sentences under consideration is that they begin to be taken as interpreted sentences: they are already have meaning.

Beyond this, several technical apparatus are introduced that formalize criteria for truth. For instance, a sentence is given a sign \(\phi\). A need arises to distinguish between the quotation of sentence \(\phi\) and the unqoted sentence \(\phi\), which is then given the quasi-quotation notation \(\ulcorner \phi \urcorner\). For instance, let \(\phi\) stand for snow is white; then \(\phi \rightarrow\) snow is white and \(\ulcorner \phi \urcorner \rightarrow\) ‘snow is white’. Tarski introduces Convention T, which states that for a fixed language \(\bm{L}\) with fully interpreted sentences, (Glanzberg 2018)

An adequate theory of truth for \(\bm{L}\) must imply for each sentence \(\phi\) of \(\bm{L}\)
\(\ulcorner \phi \urcorner\) is true if and only if \(\phi\).

Using the same example, then,

‘snow is white’ if and only if snow is white.

Convention T states a general rule for the adequacy of a theory of truth and is used in several contemporary theories.

We can see that these formal methods get quite technical and fun! For more, see Hodges (2018; Gómez-Torrente 2019; Hylton and Kemp 2019).

Deflationary theories

Deflationary theories of truth try to minimize or eliminate altogether the concept of or use of the term ‘truth’. For instance, the redundancy theory claim that (Glanzberg 2018):

To assert that \(\ulcorner \phi \urcorner\) is true is just to assert that \(\phi\).

Therefore, we can eliminate the use of ‘is true’.

For more of less, see Stoljar and Damnjanovic (2014).

Language

It is important to recognize that language mediates truth; that is, truth is embedded in language. The way language in general affects theories of truth has been studied extensively. For instance, whether the truth-bearer is a belief or a proposition or a sentence—or something else—has been much discussed. The importance of the meaning of truth-bearers like sentences has played another large role. Theories of meaning, like the picture theory presented above, are often closely intertwined with theories of truth.

One of the most popular theories of meaning is called the theory of use:

For a large class of cases of the employment of the word “meaning” – though not for all – this word can be explained in this way: the meaning of a word is its use in the language. (L. Wittgenstein, Hacker, and Schulte 2010)

This theory is accompanied by the concept of language-games, which are loosely defined as rule-based contexts within which sentences have uses. The idea is that the meaning of a given sentence is its use in a network of meaning that is constantly evolving. This view tends to be understood as deflationary or relativistic about truth.

Metaphysical and epistemological considerations

We began with the recognition that truth is intertwined with metaphysics and epistemology. Let’s consider a few such topics.

The first is metaphysical realism, which claims that there is a world existing objectively: independently of how we think about or describe it. This “realism” tends to be closely tied to, yet distinct from, scientific realism, which goes further, claiming the world is “actually” as science describes, independently of the scientific descriptions (e.g., there are actual objects corresponding to the phenomena we call atoms, molecules, light particles, etc.).

There have been many challenges to the realist claim (for some recent versions, see Khlentzos (2016)) put forth by what is broadly called anti-realism. These vary, but often challenge the ability of realists to properly link language to supposed objects in the world.

Metaphysical idealism has been characterized as claiming that “mind” or “subjectivity” generate or completely compose the world, which has no being outside mind. Epistemological idealism, on the other hand, while perhaps conceding that there is a world independent of mind, claims all knowledge of the world is created through mind and for mind and therefore can never escape a sort of mind-world gap.¹¹ This epistemological idealism has been highly influential since the work of Immanuel Kant (Kant, Guyer, and Wood 1999) in the late 18\(^\text{th}\) century, which ushered in the idea of the noumenal world in-itself and the phenomenal world, which is how the noumenal world presents to us. Many have held that phenomena can be known through inquiry, whereas noumena are inaccessible. Furthermore, what can be known is restricted by the categories pre-existent in the knower.

Another approach, taken by Georg Wilhelm Friedrich Hegel (Redding 2018) and other German idealists following Kant, is to reframe reality as thoroughly integrating subjectivity (Hegel and Miller 1998; Žižek 2012); that is, “everything turns on grasping and expressing the True, not only as Substance, but equally as Subject.” A subject’s proposition is true inasmuch as it corresponds with its Notion (approximately: the idea or meaning for the subject). Some hold that this idealism is compatible with a sort of metaphysical realism, at least as far as understanding is not independent of but rather beholden to reality (Žižek 2012, 906 ff.).

Clearly, all these ideas have many implications for theories of truth and vice versa.