Similar entities carry information about each other. If you have a copy of Iliad, even if not in the original Greek, you can infer what I could read in my copy in a Polish translation, and vice versa. This is because these translations are similar. Similarly, a painting of Warsaw Castle Square by Canaletto was so detailed that the completely demolished buildings could be rebuilt. Note that the original picture carries information that can be identified in three later photos, even if there are changes of perspective.

While there has been lively research on mental representation and scientific representations as relying on similarity, to my surprise nobody has made the bold move of generalizing it into a theory of semantic information. My own research on mental representation relies on this kind of information. Because there was no previous account on offer, I had to provide it myself.

Jobs for the Theory of Semantic Information

In contrast to Claude Shannon’s ([1948]) theory of communication, which defines information in terms of the probabilities of receiving particular messages, the job of the theory of semantic information is to provide an account of the conditions under which tokens of information are true, accurate, or verisimilar. Thus, a correspondence theory of semantic information should elucidate these satisfaction conditions in terms of correspondence of information and what this information is about. The troubles begin.

First, suppose we understand correspondence in terms of resemblance. Didn’t Nelson Goodman ([1972]) show that anything could be similar to anything else to an arbitrarily large degree? If Goodman is right, then the correspondence account is doomed. Second, even if we could avoid trivialization of resemblance, what is supposed to be similar to what? What are vehicles of semantic information, and how could they be similar to what they are about?

To solve these problems, and remain as general as possible, I rely on two guiding ideas. The first is that the resemblance in question is structural. This implies that the problem of defining correspondence is redefined: one must provide an account of structures that stand in the correspondence relation. The second guiding idea is that theories of information flow are also theories of correspondence.

Building Informational Structures

Finding building blocks of informational structures is relatively easy. Dennis Gabor ([1946]), later awarded the Nobel Prize for his work on holography, defined a ‘logon’ as a unit of information. Any physical vehicle has a number of degrees of freedom: it can vary in a certain number of ways. If you count them, you get logons. Interestingly, these logons are what we’re interested in when we buy computer storage media. It’s not Shannon information; it’s the number of potential degrees of freedom that we’re after: we expect new media to be empty, so there is no Shannon information content when this is the case.

But how do these building blocks come together to form structures? Here’s the second idea that comes in handy. In their important book, Information Flow ([1997]), Jon Barwise and Jerry Seligman provide a logical theory of information flow in distributed networks. They start from the basics to say when information flows. The first step is to understand information vehicles as tokens classified into types.

These classifications are as complex as you wish, which provides a foundation for their analysis of the flow of information in terms of a mapping between classifications. This mapping is dubbed ‘infomorphism’, and as long as it obtains, you could say that information flows from one classification to another. This same mapping could be interpreted as a correspondence that constitutes semantic contents.

The problem is, infomorphism is strict. Unfortunately, Barwise and Seligman do not analyse noisy channels. Compare the Canaletto painting with later photos: there are surely a lot of changes in how things look, but these are still photos that are informative about how the statue of King Sigismund looked. To account for such distortions, I suggest that their definition of infomorphism be relaxed in two ways: First, assume that tokens could be classified as types in a fuzzy manner. Fuzzy set theory is an intuitive solution for this problem, although admittedly correspondences become more widespread. Second, allow for mappings to hold at least some tokens and types of one classification that corresponds to another. I dub this kind of mapping ‘infocorrespondence’.

This is a generic definition of correspondence and many diverse types of correspondence are encompassed by this definition. I do not exclude anti-symmetrical types of similarity, nor do I require that similarity is symmetrical, for example. Depending on the kind of infocorrespondence, one can distinguish different types of correspondence-based semantic information.

An Obvious Objection Arises

Isn’t this kind of correspondence entirely trivial? Aren’t there too many correspondences? My reply is that this isn’t a bug, it’s a feature. Take a simple example: A known trick in cryptography is to use a salient feature to embed a message in another message without any encryption, for example, by embedding the face of a spy in a picture (you cannot even be sure whether I spoofed the painting in a similar manner). The same information vehicle carries multiple messages in its physical structure: one overtly visible (and used for distraction) and another missed by most observers. In such a case, one need not decide beforehand that the huge number of degrees of freedom in a picture must bear similarity to a single target by being part of the same classification. Before we can use semantic information, however, we must ground the classifications we are going to use. If we do, then semantic information becomes available and is no longer trivializable because correspondence is now fixed.

In my article, I abstracted away from pragmatic considerations, although they surely do play a role when semantic information is used as a mental or scientific representation. In my use, semantic information need not have any user or producer; it’s merely an established infocorrespondence. To function representationally for some agent or device, it must be put to use, but that’s a topic for a separate inquiry. With Paweł Gładziejewski (Gładziejewski and Miłkowski [2017]), I defended a notion of structural representation that is compatible with the kind of semantic information introduced here.

The proposed account of semantic information can be further put to use—for example, in measuring semantic information content—but I leave this for another occasion. It also opens exciting prospects of differentiating various kinds of semantic content that rely on diverging kinds of similarity.

Summing up, even though I feel uneasy about proposing a novel account that has its roots in Aristotle’s, Locke’s, and Peirce’s views of meaning constitution, it can serve as a springboard for new insights into the nature of semantic content. Theories of semantic information have never appealed to correspondence before, and it is high time for them to do so. Contra Brette ([2019]), theories of semantic information that rely on the notion of encoding are not at all misguided if we are armed with the correspondence theory of semantic information and an understanding of encoding as a kind of correspondence.

Note

My article is dedicated to the memory of philosopher of information John Collier (1950–2018), who inspired me to seek novel perspectives on information. I am grateful for all our conversations.