Russell
According to Russell, knowledge by acquaintance is obtained through a direct causal (experience-based) interaction between a person and the object that person is perceiving. Sense-data from that object are the only things that people can ever become acquainted with; they can never truly KNOW the physical object itself. A person can also be acquainted with his own sense of self (cogito ergo sum) and his thoughts and ideas. However, other people could not become acquainted with another person's mind, for example. They have no way of directly interacting with it, since a mind is an internal object. They can only perceive that a mind could exist by observing that person's behaviour.
To be fully justified in believing a proposition to be true one must be acquainted, not only with the fact that supposedly makes the proposition true, but with the relation of correspondence that holds between the proposition and the fact. In other words, justified true belief can only occur if I know that a proposition (e.g. "Snow is white") is true in virtue of a fact (e.g. that the frequency of the light reflected off the snow causes the human eye, and by extension, the human mind, to perceive snow to be white). By way of example, John is justified in believing that he is in pain if he is directly and immediately acquainted with his pain. Not if John makes an inference regarding his pain ("I must be in pain because my arm is bleeding"), but feels it as an immediate sensation ("My arm hurts!"). This direct contact with the fact and the knowledge that this fact makes a proposition true is what is meant with knowledge by acquaintance.
On the contrary, when one is not directly and immediately acquainted with a fact, such as Julius Caesar's assassination, we speak of knowledge by description. When one is not directly in contact with the fact, but knows it only indirectly by means of a description, one arguably is not entirely justified in holding a proposition true (such as e.g. "Caesar was killed by Brutus").
The acquaintance theorist can argue that one has noninferentially justified belief "that P" only when one has the thought "that P" and one is acquainted with both the fact that P is the case, the thought "that P", and the relation of correspondence holding between the thought "that P" and the fact that P is the case. So I must not only know the proposition P, and the fact that P is the case, but also know that the fact that P is the case is what makes proposition P true.
Read more about this topic: Knowledge By Acquaintance
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