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In many languages that I know morphology plays a role in creating words. And, as much as I know, in morphology we have a root, which is the most important part.

Now, in seimitic languages (like Arabic, Hebrew, Aramic, ...) this process is extremely flexible and creates lots of words. I see that people give different meaning to different words coming from the same root.

Can we argue that, words with the same root must necessarily be related in meaning? Can we reject different meanings for words with the same root?

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    "Related in meaning" is a very hard concept to specify, since "meaning" is even more difficult, and "related" seems to mean something different but equally vague. If you have loose constraints, everything is related in meaning to everything else.
    – jlawler
    May 4 at 14:48

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First, we different words in general have different meanings, even when they are derived from the same root. The whole reason for having different words is to express different meaning, full synonyms are rare to non-existent (depending on how narrow you can define the meaning of a word).

Second, roots and derivations organize meanings. So it is to be expected, that words derived from a certain root are also related in meaning. This is the general rule.

Third, while usually roots have one (broad) meaning, this is not without exceptions, there can be root with two or even more different unrelated meanings, and some derived words relate to one meanings and others to the other. This can happen by different processes such as sound merger of roots that were different, or through borrowing.

Fourth, while having a general rule of related meanings, it is not without exceptions. Some word forms may acquire completely unrelated meanings due to different processes, e.g., metaphoric use or loan translation (a nice example of the latter is the Arabic word for "zero", see this question and its answers: How often are dictionary etymologies wrong?).

Fifth, don't underestimate time depth. Meanings of related words can drift apart over centuries or even millenia, obscuring the original linkage in meaning. Of course, analogy tends to correct this process, it happens nevertheless.

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    This makes deciphering the true meanings of old texts extremely difficult. One good way of finding the original meaning is cross-checking. One root in another more clearer part meant that, thus it might mean this in the current context. But with what you said, we lose this. May 4 at 10:29
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    Reading old texts is indeed a very difficult task, and there are even more things to factor in: Readability of the text, blurred or missing parts, and scribal errors. When you are lucky you have multiple copies of the same text, but they may show differences (in fact, they will show differences, mostly minor, but they are there). May 4 at 11:39
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    In general, the meaning of a word in one period tells you nothing reliably about the meaning of even the same word in a different period. Often, the meanings are similar, or even the same, but you can never rely on this without knowing about the particular word. Consider what has happened to the English words nice and silly over a fw cernturies, and how operation acquired a surgical meaning four hundred years before procedure did.
    – Colin Fine
    May 4 at 16:21
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You have identified a existing premise of morphological theory, so yes, one can say that words which share a morpheme also have shared semantic properties. That premise is not necessarily accepted by all theorists, but it is very widely accepted. It follows from the theory of compositionality, that morphemes have some form *(e.g. -k, -veg- etc.), and a syntactic and semantic function, signalling tense, case, number, gender agreement etc. or some lexical property.

The position that each morpheme makes a semantic contribution (including indirect semantic contributions in the form of syntactic signalling which itself contributes a bit to semantic interpretation – such as case marking) is a pretty weak claim, in light of the fact that we see many cases where the full meaning and use of a word cannot be computed from the purported meaning properties of the constituents. Semitic root derivation as you mention is an example. The pertinent question that theorists ask is, to what extent can decomposition into morphemes be justified when the meaning of a combination is not regularly computable from the meaning of the sub-parts? That has been a long-term unresolved squabble in linguistics.

English has a number of verbs (ultimately taken from Latin) that are treated as being bi-morphemic, for example submit, remit, transmit, permit, emit, admit, commit; subsume, resume, assume, consume, presume. The analogous word *transume is lexicographically treated as "archaic" (meaning, "there used to be such a word"), and "exume" is a spelling variant of exhume which involves a different supposed root. The Latinate prefix-plus-root constructions are sufficiently unpredictable in terms of possible combinations and semantic interpretation that many people treat subsume, resume, submit, remit as monomorphemic roots. The extent of required predictability is an fundamental variable in theories of language. Under the rubric of "Lexical phonology and morphology", many linguists found a way to have their cake and eat it too, so that the desiderata of transparent shared meaning and productivity were subordinated to the desiderata of maximally identifying "patterns", and thus it became acceptable again to say that per-mit is bi-morphemic, even though the meaning of "permit" cannot be computed from the meaning of "per" and the meaning of "mit" – the meaning itself must be stored in the lexicon. That theory encompasses both bimorphemic words whose meaning is semantically compositional, and bimorphemic words whose meaning must be stored. In that theory, there is not necessarily a computed semantic relationship between words that have a stared morpheme.

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There are at least a few mechanisms by which words may be formed from a root without sharing any meaning with it.

The one that first came to mind is rhyming slang, where a root is used because of its sound rather than because of its meaning.

For a relatively famous example, the word raspberry has two common meanings: a small fruit and a noise made with the mouth, possibly while pressing it to a piece of skin. The latter is chiefly used in the phrase "to blow a raspberry". The etymology is that the sound is reminiscent of a fart, rhyming with raspberry tart, shortened to simply raspberry.

More examples can be found at the Wikipedia page.

Another example, which might or might not properly count depending on how you intended the question, is the practice of arbitrarily choosing names for things, for instance through brand names.

Mercedes happened to be the name of daughter of an engineer making cars a hundred years ago, and now "the first Mercedes I've seen with my own two eyes" is either a person or a car.

You might even include words like Shakespearean, as shake and spear where chosen as parts of a personal name without any connection to the words modern meaning.

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