What if only I want to show that a statement is true? To do so, I could present a sound argument. It's both the least and the most I need to do.

If I want to convince someone that a statement is true, then presenting a sound argument may be either insufficient or unnecessary.

So, I guess a refrigerator has both a function and a purpose.

Yes. There are exceptions. That's not a problem. I said primary function, not essential function (a function that it cannot lack).

Does anything that cannot think have a purpose?

That is a really interesting question. We have this situation in current philosophy where the idea of purpose or intention is only comprehensible as the conscious activity of an individual mind. In fact one of the principle tenets of scientific naturalism is that 'nature acts without purpose' - therefore no 'telos' or tendency, not only 'religious' terms but even in terms of 'progressiveness' in evolution (i.e. Herbert Spencer et al).

The paradox is that existentially this means that the human ego is left with the task of devising purposes in a universe where there is none.

of course, in all traditional (i.e. pre-modern) societies, nature is alive with purpose, and the diety or dieties have purposes in which humans even feature in some ways.

it is really out of scope for this thread but I think I will put together a post on it separately.

A good argument is one we find persuasive.

The evidence is overwhelming for you, but not for Abmadinejad. You and your consensus will mock him, and he and his consensus will mock you.

And the string theorist may mock you for seeing the Earth as a sphere, when for them its obviously a 12-dimensional object. It's the same old human animal, patting itself on the back for its prejudices. It's the same old role-play, identification with God, or the Truth, or common sense, or the majority, or individualism. It's a cape that comes in many colors.
To say that one's view is a truth for everyone is the new version of religious superstition. I think I prefer religious superstition which is explicitly based on faith.

For him it does not weigh more than a large building.

But this is to slide away from the pressure point. It's where men disagree that arguments are necessary in the first place.

From a practical point of view, I believe in the truth of physics. But such belief is so justified that it makes comes across as a dodge of the issue.

It's still just your opinion that the Holocaust happened. I happen to agree with you. Maybe you would bet your life on it. But others disagree. And perhaps they would bet their lives on it. Yes, it more to persuasive to appeal to the Lord or objective reality, depending upon your audience, but that is not proof of your connection to some transubjective entity. You have your faith/justification and certain consensus behind you. Nothing else.

But that is enough, for we get by on our prejudices all the time. Myself included.

This issue is that right and wrong are decided subjectively. When many subjectivities agree on something (like the relative weights of buildings and basketballs), they experience a strong sense of objectivity. But when it becomes less obvious, the subjective root of existence becomes more obvious. Morality, politics, a murder trial, first date conversation, the tact or tactlessness of a eulogy, this discussion we are having right now....

All that is experienced is real. A dream is real. Feelings are real. Misunderstandings are real. All consciousness is reality. We tend privilege objectivity for practical reasons, but subjectivity is the source, root, and ground of objectivity. And the individual genius in art,philosophy, and science is where we honor subjective visions. But these visions must be assimilated before anyone finds them honorable.

When many subjectivities agree on something (like the relative weights of buildings and basketballs), they experience a strong sense of objectivity.

You mean intersubjectivity. But, I think that you think that intersubjectivity = objectivity, don't you? Why, again, do you think we don't have access to the objective, just because we are experiencing subjectively?

I am not sure what you have in mind by "intersubjectivity", but I would say that intersubjectivity amounts of objectivity in some cases, but not in other cases.

This is what I have in mind by intersubjectivity.

You typed this in another thread:

Objective: What is true no matter what anyone believes.
Subjective: What is believed to be true.

And to this I will add intersubjectivity:

Intersubjectivity: What is believed to be true by two or more people.

What I implied is that intersubjectivity does not equal objectivity. This means, like you noted, that just because we have intersubjectivity for something, it does not follow that that thing is objectively true. But, it could mean we have access to the objective. For instance, if everyone agrees that they see and feel this rock here, there would be intersubjectivity that the rock exists, and I think we can safely assume that the rock objectively exists. This is not to say I'm absolutely certain that the rock objectively exists, but that I do find it much more likely.

The two people may be equally insane. You can't mean that. It would depend on who the people were who agreed the rock exists. But yes, strong evidence for the existence of something is agreement among people. But, remember, lots of people have agreed on having been abducted by space-aliens. I think that evidence is pretty weak. In fact, the United Kingdom has recently stopped its research program into the existence of UFOs.