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Button T, The Limits of Realism, 2013, pp. 8-9:

For the correspondence theorist, true theories do not aim to copy the world, but aim only at some kind of structural similarity.

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The Correspondence Principle. 'Truth involves some sort of correspondence relation between words or thought-signs and external things and sets of things.'

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But perhaps even the correspondence theory of truth is too ambitious, since it insists that there must be a structural similarity between the subject/predicate distinction of some language and the object/property distinction in the world.

What does the author mean by structural similarity here?

I think I understand correspondence theory. According to correspondence theory, the word "apple" in the English language corresponds to the apple fruit that is mind-, language-, and theory-independent. However, I don't think there is any structural similarity between the word "apple" and the apple fruit. What does structural similarity even mean in this context?

For example, a cow and a horse are structurally similar. However, how can sound waves (words) be structurally similar to a physical substance (apple fruit)?

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    See Structuralism in the Philosophy of Mathematics for the concept of structure in mathematics and I.Grattan-Guinness, Structure-Similarity as a Cornerstone of the Philosophy of Mathematics
    – Mauro ALLEGRANZA
    Jan 4 at 11:58
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    In a nutshell, we have not only a correspondence between objects of A (e.g. language) and objects of B (world) but also a correspondance between relations between objects in the A domain and relations between objects in the B domain.
    – Mauro ALLEGRANZA
    Jan 4 at 13:11
  • The structural similarity is not at the level of words and objects, but rather phrases and states of affairs, and even that, as Peirce put it, "not at all in looks; it is only in respect to the relations of their parts". So there is an isomorphism between world and language where a property red attaches to an object apple in red apple in parallel to grammatic attachment of predicate "red" to subject "apple" in the phrase "red apple". Hintikka explains in detail in Picture theory of language, and extends it to connectives and quantifiers.
    – Conifold
    Jan 4 at 21:49
  • @Conifold "Certain versions of the correspondence theory go further, and insist that each individual sentence must correspond with an individual object of a special sort: a fact, or state of affairs" (Button, 2013). Do you mean this?
    – tryingtobeastoic
    Jan 6 at 12:16

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I'm not deeply familiar with correspondence theory but will try to help interpret what is stated in the question.

a structural similarity between the subject/predicate distinction of some language and the object/property distinction in the world.

Take for example: "The apple is red, sweet and round." Here the apple is the subject, and those adjectives are its predicate. In the world, the apple is object and those adjectives describe its properties. That's the structural similarity between language and the world.

However, how can sound waves (words) be structurally similar to a physical substance (apple fruit)?

Words are not merely sound waves, but concepts. The structural relation posited here is between the concepts represented in language, not the sound waves that represent the language/concepts. There is also no suggestion of a structural similarity between the subject of language and the object in the world. Rather, there is a structure in the world between the object and its properties and that structure is represented in language.

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  • Maybe there is only structure in our heads though. I don't know if there is "structure in the world". When we say "the apple is red", it's just a convenience for us to summarize the model where photons bouncing off the atoms on an apple have a wavelength that we dub "red" when they interact with our retina.
    – Frank
    Jan 5 at 1:15
  • @Frank You know very well that there is structure to the world when multiple observers agree that this object is an apple and looks red. Your comment seems to just be pointing out that the concrete reality underlying that structure is distinct from our linguistic representation of it, which of course is true. Correspondence theory argues they are similar in a certain abstract way, not identical.
    – Brian Z
    Jan 5 at 12:59
  • that was my point - there is agreement on the linguistic representation of something out there, but what exactly that thing out there is, can be (and has been) doubted. What the "structure" underlying "concrete reality" really is may be unknown.
    – Frank
    Jan 5 at 18:40
  • @Frank Right, in other words, you can reject the correspondence principle and posit a different theory. I don't intend to debate or defend correspondence theory, but hopefully I've answered your question.
    – Brian Z
    Jan 5 at 18:50

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