Unpacking an argument

Question

Firstly, I'll admit that this is for a school assignment but is ridiculously abstract. I'm supposed to "unpack" the argument stated below, which is to identify the premises and conclusion of the argument, while also listing down any implicit premise or conclusions to make the argument valid. This is no need to evaluate the argument. The argument is a passage adapted from David Lindberg’s Theories of Vision from Al Kindi to Kepler (pg 10).

A body that is seen does one of two things: either it sends something (an image) from itself to us and thereby gives us an indication of its character, or if it does not itself send something, it waits for some sensory power to come to it from us. The first alternative is unacceptable for it would be impossible to determine the size of an object from an image coming from it to us, for the image of a very large mountain would have to shrink drastically in order to enter the pupil. Since the mountain will not come to the observer, the observer must go to the mountain; he must, that is, send forth his sensory power to perceive it.

Thus far, I've made the following argument diagram/steps and would like to know if they are correct or missing anything (which I believe to be the case):

1. The image of a very large mountain would have to shrink drastically in order to enter the pupil. (Explicit premise)
2. If a very large mountain shrinks itself drastically in order to enter the pupil, then the image we receive is inaccurate. (Implicit premise) (Not sure if this is correct)
3. A very large mountain cannot shrink itself drastically in order to enter the pupil. (Implicit premise) (Not sure if this is correct)
4. It would be impossible to determine the size of an object from an image coming from it to us. (Follows from 1 & 2/3) (Explicit intermediate conclusion)
5. A body that is seen does one of two things: either it sends something (an image) from itself to us and thereby gives us an indication of its character, or if it does not itself send something, it waits for some sensory power to come to it from us. (Explicit premise)
6. The first alternative (it sends something (an image) from itself to us and thereby gives us an indication of its character) is unacceptable. (Follows from 4) (Explicit intermediate conclusion)
7. The observer must send forth his sensory power to perceive an object. (Follows from 5 & 6) (Explicit conclusion)

Answer 1

I rather like this exercise. You are right to say it is abstract and difficult, but that is why it makes for a good test.

.1 This is OK. As you say, it is an explicit premise. It is also scientifically dubious since what is sent from the mountain to us are photons and it is only when these impact the eye and are processed by the visual cortex that an image forms. The photons don't shrink. Nor is it possible to speak sensibly of the size of the image in comparison to the size of the mountain. The mountain has dimensions that might be measured in metres; the image can only be measured as a solid angle in our visual field.

.2 The argument does not say "inaccurate", and I'm not convinced this is really implicit.

.3 I don't think this is implied in any way. I would replace your 2 and 3 with

.2' If the image we have of a mountain is smaller than the mountain itself then there is no way to judge the size of the mountain. Implicit premise. Also false, because as noted above, one cannot compare things and images like this.

.3' If the mountain sends us an image, we would be unable to judge its size. This is your 4, but expressed as a conditional. This follows from 1 and 2' by hypothetical syllogism.

.4' We are able to judge the size of a mountain by sight. Implicit premise. Also false. We can't judge the size of anything by sight unless we know how far away it is.

.4A The mountain does not send us an image. This is your 6. I prefer it here because it follows from 3' and 4' by rule of modus tollens.

.5 This is OK. As you say, explicit premise. Potentially dubious because it may be a false dichotomy: are we sure there are no other explanations of perception?

.7 Again, OK. This follows from 5 and 4A by disjunctive syllogism.

In other words, our 'unpacked' version of the argument shows that it is valid but proceeds from at least three false premises.

Answer 2

Interesting question, particularly the passage which you're asked to parse.

A) Your 3) is slightly inaccurate, in the passage al-Kindi actually says that the 'image ... would have to shrink'; whereas what you write implies the mountain itself shrinks - this is most likely an error of omission.

B) The following is the crux of the argument:

The first alternative is unacceptable for it would be impossible to determine the size of an object from the image coming to us from it

This is true, an image of the mountain is imprinted on the wavefront of light that is incident on it and then reflected back and shrinks as it enters the eye and impinges on our retina.

This image is 2-dimensional; and thus not a proper account of the 'size' of the mountain which is in 3-dimensions, and so has depth.

This is part of what is known as geometrical optics, something that Al-Kindi would have been familiar with at the time.

The detail that al-Kindi is missing is that we have two eyes and they recieve slightly different impressions which is then integrated into a field of vision that has depth; so we can see its true 'size'.

On an entirely separate aside, which may or may not interest you: I find it personally interesting that Al-Kindi is arguing for a sense that goes out to meet the mountain; this suggests that Kants 'Copernican turn' may have roots in the theory of what it means to perceive, and the root of this notion according to a review I just looked at appears to be Galens theory of vision.