I am looking forward to seeing you.
 I want to see you.
In the sentence  we say that to is a preposition. followed by a gerund.
In  we say to is a particle followed by an infinitive.
I here with attach the excerpts of Mr Rod Mitchel for your kind perusal.
No,. "to infinitive" is not a reality if we believe that "to" is an "infinitive particle".
"To" is always a preposition; its core meaning-function is "physical or abstract movement to a goal and arrival there-at".
(An extract in the Prepositons boko I am hoping to publish soon)
Where the infinitive with TO is concerned, what is the core concept? Have a look at the following sentences:
52a. He stopped to talk to the girl. 52b. He stopped talking to the girl. 52c. He stopped working to talk to the girl.
While it is clear that 52a and 52b do have different meanings, this is not obvious to learners of English. 52a shows that ‘he’ stopped doing something (working in 52c) to talk to the girl, while 52b shows that what he stopped doing was talking the girl – after 52b there was no more talking to the girl. For 52a and 52c the answer to the question why did he stop is to talk to the girl, i.e. he wanted to talk to the girl, or needed to talk to her, or had to talk to her. For 52b the answer is something else, like because she bored him or something like that. At the simplest level we could say the TO focuses our understanding on what he WANTS or NEEDS or HAS to do. We can expand 52c (itself an expansion of 52a) in the following way:
52d. He stopped working because he wanted/needed/had to talk to the girl.
The ing-forms in 52b and 52c focus our understanding on what was being done, i.e. the activity ‘he’ was doing. Consider the following:
- The bottle is/was rolling on the table.
- scuba-diving, surfing, sailing, nursing, sky-diving, skiing, teaching
- a sailing ship, running water, an interesting film, a boring topic, a tiring day
The so-called “continuous” or “progressive” aspect in English focuses on the activity of the verb is it is/was (etc.) happening temporarily/short-term. This contrasts with the simple aspect which focuses on a complete action (56) or long-term/permanent action (57). 58, 59 and 60 below further contrast permanent vs temporary.
- The bottle rolled off the table and broke.
- The earth goes around the sun.
- She lives in Seoul, but right now she’s living in Brisbane for a year studying English.
- He is a full-time teacher who works at LSI.
- He is working on a government contract for the next month.
This focus on activity is clear in 54 and 552, where 54 contains the names of activities or jobs, and 55 contains adjectives that focus on activity. Contrast 55 with the list in 61, where adjective forms that focus on result of an activity are used:
- an interested audience, a bored student, a tired teacher, torn paper
Thus, breaking and broken contrast as shown in 62, where breaking shows the activity incomplete at the time of hearing, while broken shows the (later) result of the activity3:
- He heard the sound of breaking glass, and when he went into the room, he saw broken glass strewn about on the floor, and his brother busy breaking up the windows broken by the storm.
The infinitive is simple in aspect. Therefore, the examples in 37 to 51 focus on the action of the verb (in a complete way), not on the activity of the verb. In 37, the understanding is that we want to complete the action of ‘going’, i.e. to be gone, and not just to be in the process of going. The examples in 63 to 65 below further focus on the contrast between activity and action:
- I heard him saying he wanted to be President.
- I heard him say he wanted to be President.
- He was heard to say he wanted to be President
63 shows that the saying was being heard (but the act of saying was not completed before or during the act of hearing), 64 shows that the saying was completed during the act of hearing. 65, on the other hand, focuses our understanding onto a different plane, that of potentiality. That is to say, what the reporter wants us to understand is that ‘he’ said this, but that there is actually no proof within the bounds of the sentence that ‘he’ actually said this. Potentially ‘he’ did say it, but…did he? Such sentences can be found in journalese, for example, where the source (e.g. a government minister, a ‘leak’) or the reality (i.e. truth) of the reported speech is ‘hidden’. It may or may not be true that ‘he’ wants to be president, but the reporter wants us to believe so – he/she is pushing us that way.
In 66, on the other hand, it is clear that the subject of the sentence (the naughty boy) does not have the goal of being spanked; rather, spanking is thought necessary or wanted in the situation. Wanted itself merely shows that something is desired in a pretty definite way (in 72, for example, the customer would not be happy to be brought a cup of tea instead). The presence of TO shows the goal the subject is aiming to reach, while the ing-form in 66 shows that this is not the goal of the subject; rather, the activity that is wanted (= needed, lacking1).
67 to 71 further refine this contrast. 67 and 71 focus our understanding on the activity of the verb, that is to say the redecorating that is necessary but not necessarily wanted in 67 and the activity that is pleasant in 71 but not necessarily done with a goal in mind. 70 shows that the swimming is actually done with a goal in mind, which is to keep fit, and further, the ultimate goal is ‘fitness’. Similarly, 68 and 69 give us to understand that the goal is to redecorate the flat – someone actually has this in mind as a goal rather than simply an activity.
- That naughty boy wants spanking.
- The flat needs redecorating.
- The flat needs to be redecorated.
- I need to redecorate the flat.
- I like to swim to keep fit.
- I like swimming. It’s a pleasant activity.
- I want to drink a cup of coffee.
66 to 72 further contrast (a) the activity of the ing-form with (b) the movement-and-arrival [that is to say, goal orientation] of the TO+infinitive by (a) withdrawing focus from concepts circling around intention or need by focusing on the activity (66, 67, 71) and (b) highlighting these concepts by using the TO+infinitive in 68, 69, 70 and 72, albeit at times ever so subtly.
The picture on this page this illustrates the concept of TO with infinitives. The man is saying I want to drink a cup of coffee. In his mind is his goal (the cup of coffee), and the aim of his speech act is for him to get to his goal. The goal is the reference point which the subject of the preposition wants to or needs to or has to get to.
In short, the TO+infinitive shows that there is a goal, while the bare infinitive or the ing-form shows that the focus is not on a goal, but on complete or permanent action (the infinitive) or activity pure and simple (the ing-form).
So - in summary - we only use "to" with the infinitive when there are goal-reference semantics. In all other cases, the infinitive does not take "to". Goal-reference is the semantics-function of the preposition "to".
[...] if you have always been taught that TO marks the infinitive and that therefore that "to go" and the like are verbs, you might even ‘instinctively’ feel that this is true. It isn’t. It’s just been ‘hammered in’ from a tender age. " To go" is not an infinitive, nor is it a verb. It is the infinitive "go" (which is actually a noun) used with the preposition TO. [...]
The concept of ‘’split infinitive’’ (e.g. "to bravely go where others fear to tread" instead of "to go bravely where others fear to tread"), where TO and the infinitive are ‘split’ apart, was a mistake based on the translation of Latin grammar to English grammar. In Latin infinitives are single words formed by adding -E or -RE to the verb stem (thus ESSE be/being, MIRARE look/looking). Being single words, it is impossible to break up an infinitive in Latin. BENE MIRARE look/looking (at something) well can not be changed to *MIRA-BENE-RE – just as in English phrases like "looking well" cannot be changed to *look-well-ing.
For those of you who speak or who have studied French (infinitive in -r/ -re), German or Dutch (infinitive in -(e)n), Italian (infinitive in -re), Spanish (infinitive in -r), Old English (infinitive in -(a)n) and so on will know that the same is true for these languages; the infinitive can’t be split because it is a single word. And in such languages, prepositions like TO can be used before the infinitive to show the relationship between a ‘subject’ and the infinitive, not to form the infinitive; in fact, in the Latin languages, Dutch and German and many other languages, a variety of prepositions can be used with the infinitive.
It was felt to be logical by grammarians brought up on Latin grammar to assume that English also must have an “undetachable” addition to show the infinitive; this was already evident in the 1600s and 1700s. TO seemed to be the logical choice, and so the technical terminology of the type “the verb to be” and “the verb to look” was invented. The technical terminology is inaccurate. The verb in the sentence "We go to school" is not “to go”; it is simply "go". Also, "to bravely go" in English is as correct as "to go bravely". It is not a mark of ’illiterateness’ or ‘Americanism’ or anything such like, but rather shows a difference in meaning focus.
Does what Rod Mitchel say is correct or is there a flaw in his argument?