Type of Proof
You might like to consider the following examples of different types of "proof":
1. Trust
When someone we trust tells us something we may be inclined to believe what they say because we believe they would not lie to us.
2. Faith
There may be some things we are willing to believe simply as a matter of faith. A belief in a God or gods, for example, may be proved for us on the basis of our faith that a God or gods exist.
3. Personal Experience
We frequently refuse to
accept something is true until we have "seen it with our own eyes". 
Once we have witnessed something we may be inclined to accept it is true,
rather than take it on trust. For example, we may refuse to believe in the existence of
aliens from another world until we see one personally.
4. Logic
It is possible for us to
prove something logically. This is true, for example, of mathematical proofs (a
simple example being 2 + 2 = 4). We accept this as true (or not as the case may be) on the
basis of logic rather than having to be shown it is true. Another example might be the
argument that if there are an infinite number of planets then it is logically true that
somewhere there must be a planet that, just like our own, is inhabited.
5. Empirical Evidence
In this instance we require evidence that we should believe something is true - usually evidence that is something more than simple personal experience. The "aliens" example illustrates this idea.
Even if we personally "see an alien spaceship" we may not accept this as proof of the existence of people from another world since we might be inclined to put it down to "a trick of the light" or whatever.
However, if enough people "saw the spaceship" we might be more-inclined to accept that it existed because our personal observations have been confirmed by others (this does not, of course, mean it has to be true - everyone might have interpreted a stray weather balloon as a spaceship - but it perhaps makes it more likely to be true). Thus, in this instance we have decided that empirical evidence is the only type of proof we will accept, but the level of that proof will also be important.
Empirical means "through the evidence of the senses" but, for our purposes we can consider it to mean factual evidence (in particular, factual evidence we have collected by direct and systematic observation). That is, evidence that has been shown to be true because it has been tested in some way.
The type and level of proof we are willing to accept is important because it relates directly to what we believe we need to do, as sociologists, in order to believe something.
A simple example here is the distinction between common sense and sociological knowledge.
- Common sense ("what everyone knows to be true") requires only a simple level of proof for it to be accepted. If "everyone knows something to be true" then we may be inclined to trust - or have faith - that it is true.
- Sociological knowledge, on the other hand, may require a higher level of proof before it becomes accepted as true. If, for example, a sociologist claims that "what everyone knows to be true" is, in fact, false then they will need to provide evidence (logical or factual perhaps) to support their argument.