What does isomorphism between language and reality mean? [closed]

Question

I came across the sentence "isomorphism between language and reality" in a dissertation at http://sammelpunkt.philo.at:8080/2168/1/ghenea.pdf. What meaning does the use of isomorphism mean?

In context:

According to these philosophers, language must not be opposed to reality, but it must be seen as a part of it and, thus, the philosophy of language must be the study to describe the different functions of the language. ... On the one hand, in his early philosophy Wittgenstein sustains the existence of an isomorphism between language and reality, and in his late philosophy, on the contrary, he states that our language is made up of a series of language games.

Answer 1

In simple terms, the context is indicating that language and reality are directly related, further supported by the context that follows the source text that implies heavily that if language is understood, so is reality.

The fact that this question is being asked is meta to the document. The fact that the question is being answered without referencing well the source documentation is actually validating the source documentation with respect to the language games.

If a phrase is written in another context, and nobody is around to read it, does it make any sense?

Answer 2

A mathematician's complicated way of saying language gives a picture of reality using words. Some specialists are unable to translate their specialist terms into normal language. But the use of the term isomorphism sounds enormously scientific and raises a banality on the level of high science. And the speaker knows that most readers have no idea of what isomorphism means. And if you read a definition where a mathematician explains the term you understand nothing. A phenomenon you often find in linguistics as well.

By the way, there are similarities between language and mathematics as mathematics is a special language about numbers and similar concepts. But often it is no use transfering mathematical concepts to language. Mathematics is a strict one-dimensional language where there are no ambiguities. Language is on a much higher level and one could say it is multi-dimensional. One of the causes why computers have difficulties with translating languages.

Answer 3

From en.wiktionary, sense 2 of isomorphism is “A one-to-one correspondence”. The three specializations within that entry (to the word's uses in “group algebra”, computer science, and category theory) are essentially equivalent. For example, in algebra, a bijective relation – an isomorphism – is both injective, or one-to-one, ie each domain element maps to a single range element, and surjective, or onto, ie every range element has a domain element that maps to it.

Applying sense 2 to the example in question, we have that “isomorphism between language and reality” refers to a direct correspondence, or a direct and complete matchup, between elements of language and elements of reality, such that each element of each sphere – language or reality – maps uniquely to a single element of the other.

Note – The answer above explains the meaning of the phrase “isomorphism between language and reality”. The answer neither implies nor claims that “isomorphism between language and reality” can actually exist. I think it's self-evident to practically everybody that real languages often are ambiguous (while reality typically is not), and that a real language often can describe the same bit of reality several different ways. In other words, the concept of “isomorphism between language and reality” is nonsense.