What clear and precise arguments can be worked out from the excerpt on 'the only proof capable of being given' from Mill's Utilitariansim?
The only proof capable of being given that an object is visible, is that people actually see it. The only proof that a sound is audible, is that people hear it: and so of the other sources of our experience. In like manner, I apprehend, the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it. If the end which the utilitarian doctrine proposes to itself were not, in theory and in practice, acknowledged to be an end, nothing could ever convince any person that it was so. No reason can be given why the general happiness is desirable, except that each person, so far as he believes it to be attainable, desires his own happiness. This, however, being a fact, we have not only all the proof which the case admits of, but all which it is possible to require, that happiness is a good: that each person’s happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons. Happiness has made out its title as one of the ends of conduct, and consequently one of the criteria of morality.
The only clear and precise argument that can be made from the idea that "the only proof capable of being given that an object is visible, is that people actually see it" is best stated by Mill. Given that something must be able to "be acknowledged" in order for it to be so.
For some, they are unable to acknowledge the fact that certain things exist based upon the fact that the, personally, have never seen it or had any experience with it. For many people, they must be able to hold, taste, touch, experience something to admit (comfortably) that something does exist.
For example, many people fail to believe in UFOs based upon the fact they they have never seen a UFO. People who think scientifically feel as if they need the satisfaction of seeing something to admit that it actually exists. Without seeing, or experiencing it, they fail to acknowledge the realness (or existence) of the object.
As for those abstract "objects", or ideas, these things manifest themselves in ways that are physical for the person (like love, happiness, fear). A person can hold a person whom they love and the love, therefore, manifests for them.