When we speak of the 'problem of knowledge,' it is not a question whether man possesses 'knowledge.' That is a fact which no one denies. So we must begin with the idea of 'knowledge.'
Knowledge is a primary fact of human life and experience. Everyone understands what it means 'to know,' 'to have knowledge.' But when we attempt to explain and analyze this idea, we immediately encounter difficulties. Just because it is a primary fact of experience, the idea of 'knowledge' eludes every effort at an exact definition. We can point out certain characteristics of 'knowledge' and adduce definite instances of 'knowledge,' but we cannot really define it. 'To know' is on a par with 'to see,' 'to taste,' 'to touch,' 'to imagine,' 'to will.' Man is simply conscious of these states of his being and gives them a name; and thus he arrives at the idea and the term. It is useless to try to explain to a man born blind what 'color' or even 'seeing' is; just as it is useless to explain to a man born deaf what 'sound' or 'hearing' is.
We can place a man in a certain position and say to him; 'Open your eyes and tell me what you see across the park.' 'I see the Court House.' 'You are sure of it?' 'Yes, I am sure of it.' 'Then you know that the Court House is there.' Or we can say to him: 'Listen; do you recognize the melody?' 'It is the Funeral March of Chopin.' 'Good; then you know the melody.' Again, we may notice that he looks ill and ask: 'What is the matter?' 'I have a headache.' 'Well, then you know what pain feels like.' And so on. It is the experience of this sort which constitutes 'knowing' and 'knowledge.'
Now, there are three elements which enter into knowledge: the knowing subject, the known object, and the mental act of knowing (cognition). The subject is the one who knows; the object is the thing that is known; and cognition or knowing is the mental act which makes this object known to the subject.
The subject, the knower, is man as we notice it in the phrase: 'This man knows his business.' Taken individually, it is the Ego, the 'I myself,' who am the knowing subject, for we say: 'I know this house, this game, this boy.' All our activities are referred to the Ego as the subject. We become aware of this, if we reflect upon the following expressions: 'I walked a mile; I saw an accident occur; I feel a pain in my side; I taste garlic in my food; I smell a pleasant odor in the kitchen; I thought about the depression; I know about the plans of my friend; I was conscious of the act.' Knowledge, then, as a mental activity, belongs to the Ego, the self, as the 'subject' who knows. And it is in this sense that the idea of 'subject' must be taken in the epistemological problem of knowledge, because that is the spontaneous conviction involved in our way of thinking.
The object of knowledge is anything and everything that is, or becomes, or can be, known by man. According to man's spontaneous conviction the objects of his knowledge comprise his own self, various conscious states of his self, and also realities-other-than-self, is a plain fact which he manifests in numberless judgments of everyday life: 'The sun is shining; the wind is blowing; the meal is good; this building is tall; some roses are red.' In all such judgments the ordinary man refers his knowledge to some object, and he is sure that the object is as real as the subject. Whether his common sense view that such 'realities-other-than-self' belong to an exterior world with an independent existence of their own outside man's mind, is precisely one of the problems to be solved. But that every act of knowledge must be 'knowledge of something' and therefore refer to some object is perfectly clear and is disputed by nobody.
The object becomes known to the subject by the act of knowing. This act, of course, takes place in the subject or knower. It is a unitive act, in as much as it brings the object and the subject into contact with each other, thereby rendering the object 'present to' the subject and making the subject 'aware' of this presence of the object. Before being known, the object is merely an 'object-in-itself'; but through and in the act of knowing it now becomes an 'object-to-the-mind.' and it is by becoming an object-to-the-mind that a thing becomes 'known.' Somehow or other, then, an external physical object (if there be such) must become untied to the mind of the subject by means of the cognitional act and be presented to the Ego as an 'object-to-the-mind,' in order that it can become 'known' by the subject; in other words, the object must become intra-mental and intra-subjective, before it can be known. A simple example may make this clearer. I see a burning house and 'know' it to be burning. How do I get to know this fact? The house is perhaps a hundred yards from where I stand.
Surely my mind does not leave my person, cross the intervening space and physically contact the flaming building nor does the burning house leave its foundation, travel over to me, enter my mind and then actually burn inside my person. Nevertheless, the burning house and my mind must become united in some way, or I could not know that the house is burning. Since the house has no physical presence inside my mind, it must have a cognitional presence there by means of sense-perception and thought. An object, then, in order to become known by the subject must acquire an intra-mental and intra-subjective presence or existence, must become an object-to-the-mind, must have a mental objectivity, must become an ideal being.
The very act of knowledge demands this sort of presence of the object in the subject; otherwise no union would take place between subject and object, and knowledge would not be possible. The question, of course, arises: Has this object (for instance, the burning house mentioned earlier) a real, extra-mental existence of its own outside the self and the mind, independent of the cognitional existence which it has in the mind in the act of knowledge? The ordinary man is convinced that it has an objectively real existence outside the mind; idealists on the contrary, assert that we can know nothing but what takes place subjectively in our mind, and that we therefore have no right to affirm the existence of any thing-other-than-self. And so we again are face to face with the fundamental problem of knowledge. Whatever the solution, this much is clear and recognized by all: an object, in order to be known must be cognitionally present in the subject in the act of knowing.
The subject, the object, and the act of knowing are thus the essential elements necessary for knowledge. Whatever pertains to, or proceeds from, the subject is subjective; and whatever pertains to, or proceeds from, the object is objective. The state or condition of being subjective or being objective is then styled subjectivity or objectivity. And anything that pertains to, or proceeds from, the act of knowing or cognition is termed cognitional or intentional. Knowledge will thus be either subjective or objective; viewed from the standpoint of the subject who knows, it is subjective; and considered as referring to the object which is known, it is objective. So much for knowledge as it exists in the knower.