It is imperative to remember that the goal in epistemology is to properly identify objective truth criteria. "Truth criteria" which can only pertain to an individual's subjective experience is of very little value in attempting to know and understand the objective nature of reality. Mistaking one for the other makes a very profound difference -- it is ultimately the difference between objective rationality and functional solipsism.
If certain knowledge is only obtainable through empirical means - i.e. by means of perceptual observation; i.e. by means of personal experience - then "certain knowledge" is reduced to subjective knowledge, and there is no objectivity to speak of. I can not perceive your perception - and neither can you perceive mine. Your "truth" is entirely built upon your own subjective perception - to which I have no access. And vice-versa. Everyone has their own (subjective) truth, but there is no access to truth which transcends personal experience; no access to truth which transcends individual perception; no access to objective truth.
Of course, adherents to this doctrine can (and must) make exceptions in order to play in the world of objectivity -- but they are exceptions; exceptions which necessarily step outside of this doctrine in order to borrow from an other, more rational, more objective epistemological principle: Logical Necessity.
Logical necessity grants to the realm of empirical observation, perception and experience that element which is necessary to break free from the tyranny of the subjective, into the world of objectivity: logic - and with it, objective identity.
Of course, peddlers of various forms of empiricism can also believe in logic and identity - but not consistently. Only as exceptions. They can believe that "A is A" regarding everything which they have perceived, but according to their epistemological principles, there is no way to know that it is true about that which they have not perceived - it can be (and is) assumed - but it certainly cannot be certain. Therefore, to them, the "law" of identity is not so much a law which is and must be true about everything in reality. It's more of a general rule about everything that they have experienced, and it's assumed to be true about everything else. 2+2 equals 4, not because it must, but because we've never experienced an instance of 2+2 equaling anything else -- it could equal 5 somewhere in the universe, or with some object which we have yet to discover. Contradictions don't exist - but not because they can't. Rather, it is because we simply haven't found any. There could be contradictions out there that we simply haven't observed yet. Thus, there are no laws - whether mathematical or logical. Only pragmatic generalizations. Such is the end of that doctrine which attempts to skirt around logical necessity.
The alternative: accepting that there are some things which are simply true whether we have experienced them or not (i.e. accepting objective truth!) "How do we know that such things are true though, if we don't experience them!?". You think. You think about reality, consider alternatives, and realize that sometimes, there is only one option. For instance, you think about the question of contradictions. You consider the alternativses: either contradictions exist or they don't. You realize (hopefully) that the former idea is, itself, contradictory and ultimately destructive to all knowledge, truth, reality and life; that if it is true, then it is false; that it cannot be true. Therefore, the only other alternative - that contradictions do not exist - is necessarily true. It must be.
Notice that I am not claiming that this thought process makes these things true. I am claiming that this thought process is the method (the only method) of discovering these things to be true. The law of identity is universally true about all of reality. It always has been and always will be - and it always would have been even if none of us ever knew about it. My thought process in discovering it no more "makes it true" or "creates it into reality" than the scientist's perception in discovering a new bacteria "makes it true" or "creates the bacteria into reality". This is not "primacy of consciousness" as Objectivists are in the habit of claiming. This is simply another form of discovery - performed by the mind rather than the senses; a form of truth criteria which is analytical rather than empirical.
Apart from this form of truth criteria, the modern empiricist (regardless of the name he wishes to go by) is stuck in his own subjective fairytales. The key - the only key - to accessing the realm of objectivity is to understand that we know some thing to be true simply because of the fact that they must be true - they are logically necessary.