What is the difference between these two:
Presentation events allow for the sharing of knowledge.
Presentation events allow to share knowledge.
Do they share the exact same meaning?
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I think for the second sentence, what you meant was:
"Presentation events allow sharing knowledge."
"Sharing" is the present participle form and the gerund form of the verb "share." "To share" is the infinitive form of the verb "share." In some languages, the gerund form and infinitive form are exactly the same. That is not the case with English, though.
In the second sentence, the usage is gerundial, that of a gerund. Therefore, the word required is the gerund "sharing," not the infinitive "to share."
As for your question...
The difference between saying "for the sharing of knowledge" and "sharing knowledge" is just semantics. While words with their own meanings are being introduced in the first sentence that technically make the second sentence different, the actual meaning being conveyed by the speaker does not change.
Moving from the first sentence to the second, all that changes is the gerund "sharing knowledge" appears as a noncount noun and direct object of the verb "allow," which a direct object adverbially modifies its verb, rather than "allow" having no direct object but instead a prepositional phrase starting with "for" adverbially modifying it, the gerund "sharing" appearing in that prepositional phrase as a count noun followed by the prepositional phrase "of knowledge" adjectivally modifying it.
In the phrase "sharing knowledge," "knowledge" appears as the direct object of "sharing," the present participle of the verb "share." When the present participle "sharing" is used as a gerund, meaning used as a noun form of the verb, the direct object "knowledge" becomes an adjectival modifier that appears postpositively.
In "the sharing of knowledge," the present participle "sharing" has no direct object. What is being shared is instead introduced by the prepositional phrase "of knowledge." Were "sharing" being used as a verb, the prepositional phrase "of knowledge" would be adverbial, but since "sharing" is being used as a gerund, the prepositional phrase is adjectival.
Brass tacks: There is more than one way to skin a cat.
While the two sentences are mechanically different as far as grammar is concerned, they nevertheless identically use a noun form of the verb "share" followed by an adjectival modifier denoting "knowledge" in a combined phrase that modifies the verb "allow," so their meaning is therefore also identical.
In the 1st sentence, the phrase "allow for" is a phrasal verb, which means it is something that has already been thought of and planned for. Ex. The scientist allowed for drawbacks while computing X. This does not mean that the scientist is letting it happen, it simply means that the scientist thought about the drawbacks while drawing conclusions for his hypothesis.
In contrary, the phrase "allow Y to" means you're granting permission for something to happen.
X - unknown Y - pronoun/noun.
Happy learning, hope you understood.
The difference between these two sentences:
...is that #2 is ungrammatical. You can only use an infinitive after allow when there’s a specific thing named first, usually a person.
The first sentence doesn’t need the for, although it’s not wrong.
I wonder why you didn’t write it more simply:
Your question’s title sentence is also ungrammatical:
...because it is missing determiners. Remember also that below is not a determiner and works best as an adverb. Below is dramatically overused by learners, and usually used in the wrong place, too. In prefix position it should nearly always be replaced by the, this, that, these, or those:
What is the difference between the two sentences below?
What is the difference between these two sentences?
Notice how in the last sentence the word below has become completely unnecessary, and has therefore been omitted.