The most famous exponent of the theory of incommensurability is Thomas Kuhn. To state his theory in the simplest form, incommensurability is simply the idea that theories within science are not compatible, and that the languages they use are, at least in part, mutually untranslatable. This is also linked with the idea that theories cannot be meaningfully compared with each other, because if two theories use different languages that cannot be translated from one to the other, then it seems the theories cannot be compared in any normal way.
[...] To go into more detail, the advocates of the incommensurability thesis do seem to say that they can understand the meaning of expressions in an untranslatable language, but if the meanings are known, then it means that the language can be translated. From this it seems that the advocate of incommensurability has an incoherent view. The second of the arguments is that it makes no sense to say a person or organism has ideas unless they have a language that can be understood, for a language that cannot be understood could really be seen as not being a language at all. [...]
[...] It seems to me that if you go on this view of incommensurability and the idea that most forms of the argument proposed by Kuhn involve examples, then the direct incoherence theory is very appealing as an objection to the idea of untranslatability, and therefore the supposed incommensurability of theories due to this untranslatability. However, I will now look at some indirect arguments against untranslatability to further undermine the thesis. These are the ideas that: it is incoherent to profess to understand ideas expressed in an untranslatable language because they must be incomprehensible, and it is incoherent to think of someone who uses an untranslatable language as having a language at all. [...]
[...] This is because it seems not to apply to arguments of untranslatability where the language of argument and the untranslatable language are distinct. However, I find this hard to grasp because surely if you are using one language to argue that another language is untranslatable, then you must in some way use terms from both languages, or how can you even mention the so-called untranslatable language in a way that can be understood? However, I will concede that the argument does not cover forms of the untranslatability argument where examples are not used. [...]
[...] To conclude then, it seems that the idea that theories are incommensurable due to the untranslatability of languages seems false in my opinion. I have shown that the arguments made by the advocates of incommensurability are incoherent. This has been objected to heavily, but I believe these objections have also been shown to be fruitless. It seems the advocates of incommensurability such as Kuhn and Feyerabend seem to be unclear as to what they are saying, or try and change the meaning of what they say to suit them at the time. [...]
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