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Reading my logic textbook, I faced the following two sentences, of which I’m kind of confused.

(1) For given a formula A in Γ, take n so large that …

(2) ... in which P1 takes the value i(P1). For let Δ be a finite subset of Γ. Then ...

In (1), I thought it should have been “for a given formula ...” Isn’t this a normal order for such constructions? Any reason for that?

In (2), I don’t get it what that “for” is for. Was it used as a conjunction, by any chance?

P.S. I’m not sure if I have to put these questions in separate posts. Please let me know, then I’ll follow.

Edit: I attach the page.

enter image description here

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  • Welcome to ELL, Tzetachi. Could you please provide a larger piece of text for each example, so that we can see the full context? Looking at them on their own, I would say that they are typesetting errors.
    – JavaLatte
    Dec 20 '19 at 9:21
  • @JavaLatte Thank you for the comment. I’ll attach a picture of the page; it’s difficult to type those logic symbols.
    – Tzetachi
    Dec 20 '19 at 9:28
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Your question is fine, Tzetachi. And thank you - the picture helps a great deal.

It is true that “for a given formula ...” is - in some contexts - the normal word-order, but not in this context, where the writer is about to demonstrate the truth of the preceding statement.

I think "for" is being used in both (1) and (2) and also in the third marked passage as a conjunction. (A 'subordinating conjunction', to be precise.) It is used to mean 'Because'. Because with at least a comma; maybe even a colon. In fact if you were to put a comma or a colon after all those 'For's I think the meaning would be more apparent.

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  • Thank you for your answer! It helps me to be convinced. I have one additional question: is the “given a formula ...” part of (1) then an adverbial use of a participle phrase? It seems so, but I’m not very sure.
    – Tzetachi
    Dec 20 '19 at 14:24
  • I'm sorry, Tzetachi. Although I'm familiar with "given" in a mathematical context, and I know its meaning, I don't know how it originated or how to analyse it correctly. You could ask in English Language and Usage here on StackExchange. Dec 23 '19 at 10:17
  • It’s totally okay. I’m now quite a bit certain that it is used as an adverbial phrase by the comma and the sentence structure. I couldn’t have realized that without your answer. Thanks again.
    – Tzetachi
    Dec 23 '19 at 10:25

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