idioms - In ‘have to’, does ‘to’ have the obligation meaning?

When I come upon this sentence: I have to do something, I thought have to of it acts like a phrase, where the meaning is having an obligation. And have to is an auxiliary verb like must. But after bring its question and negative sentence: do I have to do something?, I don’t have to do something, something was wrong, I thought, and looked up CGEL. They say have is not an auxiliary but a catenative verb that takes non-finite complement.

From all this, I get the question: which one, have or to, has the meaning of the obligation? From OLD (to as an infinitive marker,#7), to has the obligation meaning when it gets along with be verb. Then is it still valid that in have to to has the obligation meaning?

Answer

Have to [VERB] is an idiom, a collocation whose meaning cannot be derived from the meanings of the components.^† It is the entire have to [VERB] collocation which has the meaning, not any one component.

Typical characteristics of an idiom are described in SIL's glossary

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  Its individual components “can often be inflected in the same way individual words in a phrase can be inflected. This inflection usually follows the same pattern of inflection as the idiom's literal counterpart.”

  
  

  Thus, although the collocation has the same meaning as the modal auxiliary must, have plays the syntactic role of a lexical verb. Like other lexical verbs it has the finite forms and non-finite forms (an infinitive and participles) which modals lack. Consequently, it is inflected for person and number as well as tense, it can enter into verb constructions such as perfects and progressives, it can be employed in non-finite phrases and clauses, and (to address the specific issue you raise) it can act as the complement of other verbs, including catenative/auxiliary verbs like do. This greater flexibiity is no doubt part of the reason why it has gone a long way toward replace must.

  
  


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  It “behaves as a single semantic unit.” Specifically,
  

  
  
  
  
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    “It tends to have some measure of internal cohesion such that it can often be replaced by a literal counterpart that is made up of a single word”—viz., must.

    
    
  
  
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    “It resists interruption by other words whether they are semantically compatible or not.” For instance, although we accept an adverb between have to and the complementary [VERB], the connection between have and to is so strong that it is never interrupted and in fact has unique pronunciations, usually spelled hafta and hasta.

    
    
  
  
  • “It resists reordering of its component parts.” For instance, we don’t break up have to in cleft constructions:
    

    
    

    ^okI have to go, but not
    ^∗ It is to go I have or
    ^∗ What I have is to go.

    
    

    
    
  
  
  
  
  


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  It “has a non-productive syntactic structure. Only single particular lexemes can collocate in an idiomatic construction. Substituting other words from the same generic lexical relation set will destroy the idiomatic meaning of the expression.” Thus, we cannot substitute possess or obtain for have and keep a similar meaning; even with get, which we can substitute, there is no trace of the have to meaning:

  
  

  
  

  ^∗ I possess to go.
  ^∗ I obtain to go.
  ^okI get to go.

  
  

  
  

  But it must be acknowledged that I have got to go, in which have got means have, does mean the same thing as I have to go.

  
  

  Still, 4½ out of 5 is a pretty high score.

  
  
  

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^† Historically, to be sure, the idiom arose out of a construction whose meaning can be derived from its components, and doubtless there was a time when its use was sufficiently narrow that its meaning was not idiomatic. But that was long ago.