So...Do we have a prolepsis for numbers?
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That was truly interesting. Thank you for sharing it.
I’m reminded of the tribe I learned of many years ago that had just four numbers: One, Two, Three, and Many. -
Very good video! And while we're still searching for ways to say it precisely, I'd have to say that Yes "prolepsis is involved with numbers - and it seems to involve something "inmate" as in the example of the babies used in the video.
Before they have seen the first example of a difference in quantity, they have some kind of "etching" that tells them that difference in quantity is significant to them.
And I think that "before they have seen the first example" is where we need to focus as we try to describe a faculty of prolepsis. Not on how it gets more accurate with practice, but how and why it is there in the first place, just like pleasure and pain and the other faculties are also there at birth. Focusing on adults forming conceptions of oxes after seeing more and more of them is not the place to look.
I think this video illustrates the best way forward is to look again at babies, just like with pleasure and pain, at a time period when Nature is fully in control and there is no possiblity of corruption through mistaken opinion.
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Thinking of gods, and looking at babies:
A baby's parents and/or caregivers would be the model of a godlike being. But this model is more in line with the common conception of gods, providing food, clean diapers, a social model and a model of language &c. It's a very fortunate baby whose parents provide a model of blessedness and imperturbability!
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But this model is more in line with the common conception
I agree, Godfrey. Also, of course, given the word "conception" is appropriate here is itself an indication that this is an idea and is past the point of preconception.
And I think that "before they have seen the first example"
As you say, "adults forming conceptions" is too late to be anticipations, because it involves thinking.
"Before they see their first example" is too early to have an anticipation, as the anticipations are a sense just like the others. We cannot see anything until we have something to look at.
Our anticipation of numbers is just like our vision of numbers: just as we can see 2 apples on a table with our eyes (if they are near) we can also see 2 apples on a table with our mind (if we think about them).
Different versions of D.L. 10.38
[Hicks] For the primary signification of every term employed must be clearly seen, and ought to need no proving; this being necessary, if we are to have something to which the point at issue or the problem or the opinion before us can be referred.
[Yonge] In fact, it is absolutely necessary that we should perceive directly, and without the assistance of any demonstration, the fundamental notion which every word expresses, if we wish to have any foundation to which we may refer our researches, our difficulties, and our personal judgments.
[Bailey] For this purpose it is essential that the first mental image associated with each word should be regarded, and that there should be no need of explanation, if we are really to have a standard to which to refer a problem of investigation or reflection or a mental inference.
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I agree, Godfrey. Also, of course, given the word "conception" is appropriate here is itself an indication that this is an idea and is past the point of preconception.
Great way to state it Bryan!
"Before they see their first example" is too early to have an anticipation, as the anticipations are a sense just like the others. We cannot see anything until we have something to look a
And that's a great clarification too. It's not like an innate idea of numbers is encoded at birth, what we're searching for is a description of a mechanism that swings into action as soon as it is exposed to ________, just like the eyes swing into action when they open and are exposed to light.
