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Here are two statements:

  1. The first statement is:
    To every action there is always an equal and opposite reaction.

  2. The second statement is:
    For every action there is always an equal and opposite reaction.

Now, can anyone explain what the actual difference is between these versions?

Actually the first statement is known as Newton’s Third Law of Motion. But the question suddenly came to mind: Would there be any difference if I were to replace To with For?

And for this reason only I thought for asking this question in this community.

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  • 2
    It's oversimplified per Wikipedia. To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. Commented Nov 5, 2023 at 8:42
  • 3
    @HippoSawrUs Plus what Newton actually wrote was: “Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.”
    – tchrist
    Commented Nov 5, 2023 at 18:04
  • At school I’m sure I learned the second version. Means the same as far as I’m concerned but suspect it was taught as more modern English usage. First version seems weird to me. And as, of course, Newton wrote in Latin, the first form would seem to have little justification.
    – David
    Commented Nov 5, 2023 at 21:04
  • Well, the first isn't really grammatical, so there's that. Commented Nov 5, 2023 at 22:25
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    @AzorAhai-him- If only one of them's grammatical, it's certainly the first! Commented Nov 6, 2023 at 2:01

4 Answers 4

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The normal usage is for, not to (though to can be used in some contexts).

This is just mathspeak (also logic), as the way to pronounce the Universal Quantifier , pronounced as "for all" (or "for each" or "for every"), in formulas like

  • (∀x ∈ A) f(x), pronounced as "For all x in A, f of x"

Note that f (x) is always pronounced with of, just as ∀ x   is always pronounced with for. These prepositions don't mean anything, any more than the to in I want to leave means anything; they're just grammatical markers.

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    It's not a simple exchange of prepositions. In the second example , with for, the prep for means per. The PP for every action is an adjunct (read adverbial) there. However, in the first example, with to, the PP to every action is presumably the complement of the noun reaction. And it's been fronted. So the original unmessed-around-with sentence in that case is: There is always an equal and opposite reaction to every action. Commented Nov 6, 2023 at 2:06
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    Could you combine them both, as in "For every action there is a [...] reaction to it"? In my mind this shows nicely the different functions of "for" and "to". I'm not a native speaker though, so I can't judge if this is grammatically correct or not.
    – Christoph
    Commented Nov 6, 2023 at 14:02
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    Let this be a salute to Prof. Lawler, since this is his last answer on this site. May we be so fortunate as to have again another contributor so knowledgeable as he.
    – Robusto
    Commented Dec 7, 2023 at 0:18
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If you reposition the adjunct/prepositional phrase to the end of each sentence, the result is:

  • There is always an equal and opposite reaction to every action.

  • There is always an equal and opposite reaction for every action.

Clearly, react and reaction strongly collocate with to but not with for (reaction to / ?reaction for).

This does not mean that For every action there is always an equal and opposite reaction is ungrammatical. There are many constructions along the lines of For every A there is a B.

It seems to me, however, that To every action there is always an equal and opposite reaction connects the reaction more directly to the action than does For every action there is always an equal and opposite reaction.

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    +1 See my comment to John! The for-PP is an adjunct, the to-one is a complement licensed by the noun reaction.. Commented Nov 6, 2023 at 2:11
  • @Araucaria. Thanks. That's a useful differentiation of the functions of the two prepositional phrases.
    – Shoe
    Commented Nov 6, 2023 at 7:54
  • From the perspective of a native speaker "reaction to" functions a lot like a single word hers. Whereas "reaction for" functions more like two separate words, "reaction" and "for". There could be "a meal for every child" or "a car for every family", but you would never use "to" in the same way. I don't know if there is a formalized name or framework for this kind of thing. Commented Nov 6, 2023 at 13:33
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    @shadowtalker. I think the word you are looking for is collocation: thoughtco.com/what-is-collocation-1211244
    – Shoe
    Commented Nov 6, 2023 at 13:50
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There is always an equal and opposite reaction to every action.

To = that can be paired with, that is [contextually] associated with.

Compare "The key to the door"; "The solution to the problem."

There is always an equal and opposite reaction for every action.

For = that is applicable to. (Often demonstrating purpose of the complement noun, or by which the complement noun is affected.)

Compare "The present for John is on the table"; I have bought a tyre for the car."

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For a simpler explanation, both are the same.

  1. An action has something that reacts to it... the reaction.

  2. Each action has a reaction for it. Two things that go together, or the reaction belongs to the action.

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  • Yes… I suspect there is no useful difference in either English or Physics Commented Nov 7, 2023 at 18:25

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