What Part of Speech is 'to' before the verb infinitive?

or the adverb before the split verb infinitive? "To be or not to be; that is the question" "to explore, to seek ... to boldly go" in Star Trek opening mission statement; "Space: The final frontier These are the voyages of the Starship, Enterprise, Its 5 year mission To explore... show more or the adverb before the split verb infinitive?

"To be or not to be; that is the question"

"to explore, to seek ... to boldly go" in Star Trek opening mission statement;

"Space: The final frontier
These are the voyages of the Starship, Enterprise,
Its 5 year mission
To explore strange new worlds
To seek out new life and new civilizations
To boldly go where no man has gone before".
Update: To was a preposition in ME that also took verbs as 'object' of the preposition. The productivity of this rule has been lost in Modern English, leaving many puzzled as to what part of speech 'to' might be in the non-bare verb infinitive construction. One could settle for "to is a fossilised... show more To was a preposition in ME that also took verbs as 'object' of the preposition.
The productivity of this rule has been lost in Modern English, leaving many puzzled as to what part of speech 'to' might be in the non-bare verb infinitive construction.
One could settle for "to is a fossilised form of preposition occurring before verb infinitives" but some prefer to call it a particle, a loose term to refer to all kinds of words that do not neatly fall into any category of well-defined parts of speech.
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