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What is the difference in meaning between "As we have seen" and "As we saw" when occured in a book in the following context:

As we have seen/saw, [a description of a phenomenon that occured earlier in the book] (for example, "As we have seen/saw, method X is faster than method Y" or "As we have seen/saw, application X allows you to send encrypted messages to your friends")

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As is often the case with choice of tenses in English, both are possible, and reflect a choice the speaker/writer is making in how to structure events in time: there is usually no objective difference.

With "as we have seen" the writer is choosing to relate the previous exposition to the present. This might be for various reasons: for example, it might be very recent in the book; they might be further developing an argument from the section they are referring to.

With "as we saw", the writer is choosing to treat the previous exposition as a finished event.

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  • I have been thinking about it. Could we say that the construction "as we have seen, ..." means that a phenomenon has been observed and since then we have understood it, the act of observation ended, but our understanding of the phenomenon has not ended. Therefore, we can easly see the following construction in the literature: "As we have seen in the previous chapter, ...", where we mean that our understanding has lasted since the previous chapter, not only that we saw something in the previous chapter.
    – piter00
    Jun 26, 2019 at 8:52
  • @piter00: yes, that is certainly a possible interpretation.
    – Colin Fine
    Jun 26, 2019 at 22:35

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