By definition, of being a “STARTING point,” it cannot be deduced. Consider this from a 3 premise syllogism or chain syllogism. Where does the major premise come from that starts the argument? Or if we start with a syllogism and ask where does the major premise come from, one might say, “well it comes from this previous syllogism, or premise.” We can do this for a while, and we will have three options. The first, is to say it is an infinite regress. This ends up in skepticism, and thus denies the law of contradiction. Second, is to say, “I do not know.” This seeming authentic answer hides the fact that you are really saying, “I know that I do not know.” This option is stupid and a self-contradiction, and thus, it has no existence. To know that we do not know is a contradiction. To be true, it must be false at the same time. It ends up in an infinite regress of affirming and denying the same thing. This problem is not limited to thinking; rather, it has ontological implications as well. For example, try saying, “I do not exist”? “You” cannot do it without using “your” existence. This shows the ontological impossibility. That is, reality stops me from doing this contradiction. It does not, and cannot exist. A square circle does not exist in my mind or reality. The law of contradiction is not only a law of thinking, it is a law of reality. If you have a contradiction, you have something that has no existence. Such stupid, non-existence is to be dismissed and tossed in the recycle bins of our minds.
Now though these are called laws of thought, and in fact, we cannot think except in accordance with them, yet they are really statements which we cannot but hold true about things. We cannot think contradictory propositions, because we see that a thing cannot have at once and not have the same character; and the so-called necessity of thought is really the apprehension of a necessity in the being of things. This we may see if we ask what would follow, were it a necessity of thought only; for then, while e.g. I could not think at once that this page is and is not white, the page itself might at once be white and not be white. But to admit this is to admit that I can think the page to have and not have the same character, in the very act of saying that I cannot think it; and this is self-contradictory. The Law of Contradiction then is metaphysical or Ontological.
Since the first & second options are a thinking and ontological impossibility, then consider the other. In this third option, if we keep going back, we must eventually hit the starting point or origin of knowledge. This starting point cannot be deduced, because it is a starting premise and not a conclusion.
There are some irrational comments about this floating around, for some anti-Christian commentaries say that a first principle is not “provable” in any sense. However, provable, in the context of philosophy, logic and doctrine has a strict meaning. It means a deduction. This is true, as far as it goes. However, just because something is not deducible does not mean it is not provable in the sense of giving a logical justification or warrant for why one should pick this first principle over all others. For example, consider the aspect of the self-authenticating principle of the law of noncontradiction, that we just went over. It is not a deduction. It is not circular, because we never left from doing the law of noncontradiction. Yet, it was justified as true because of its necessary and self-authenticating nature.
For a quick comment about this self-authentication of the LoC. It only works because we are only considering it on this narrow slice of reality, and we are ignoring some of the presuppositions that are needed to discuss this in the first place. For example, logic does not even give us knowledge about itself, because it is dealing with the structure of thought, and not the content (terms and premises) of thought. But more on this later.
And so, a worldview or system-of-thinking about the world, must start somewhere. The option of not knowing is implausible with reality. Thus, the next question is if your epistemology is a good one or a bad one. That is, does the starting point of your worldview make knowledge possible or not possible?
Some try to make this point vague or blur it by saying a worldview might be an interconnection of several starting points like a bridge with many supports. This appeal is a red-herring or sleight-of-hand fallacy, to divert attention away that their epistemology is in ruin. It is irrelevant, because even if so, some points would be more foundational than others; thus, if we were to discover one of these foundations were compromised, then the whole structure would fail.
For example, if one attempted to make a dual epistemology with the Scripture and something else “x,” and this “x,” was shown to be faulty, then it would falsify the scripture, which was said to have taught this hybrid epistemology.
Additionally, if one wishes to claim more than one starting point for knowledge, then if one of the epistemologies (K) makes a judgement about one of the other epistemologies (B bible), then in fact this (K) is a higher or more foundational starting point. It is the true starting point that judges the others. If empiricism (or my observations and emotions, or skin color (etc)) gives me additional knowledge that I use to judge the Bible, (if the Bible is correct on this point or that point), then empiricism is a higher starting point over the Bible. Empiricism would be my major premise in a syllogism.
In the quote below, Vincent is using the term “worldview,” but the context is relating more directly to the first principles or the presuppositional level of worldviews. His context is about “how a starting point is completely true versus only partly,” but the overall point addresses our present topic.
Suppose a given system of thought includes the following propositions: (1) X is a man, and (2) X is an accountant. If, in reality, (1) is true but (2) is false, how will a person know to affirm (1) and deny (2), unless he is already acquainted with X? Unless the system is completely true (or false), there is no way to tell which proposition is true (or false) without importing knowledge from outside of the system, and if one imports knowledge from outside of the system, then he would be evaluating the system in question by the second system from which he has gained the knowledge to evaluate the first.
That is, if worldview A is not complete true or false, then there is nothing within worldview A by which we can accurately judge a particular proposition within worldview A as true or false. If we bring in something that we know from worldview B by which we judge something within worldview A, then we are making worldview B to stand in judgment over worldview A. But if one has already obtained knowledge that is accurate, relevant, and extensive enough from worldview B by which to evaluate worldview A, then he cannot meaningfully learn anything from worldview A. He is judging it, not learning from it.
To summarize, even in a so-called multi-structure of starting points, there will be one that is more foundational, and that stands first above the others to judge and evaluate them. The question is, if the starting point of your philosophy makes any knowledge possible? If not, then not only do you not have a worldview to discuss, you do not even have the knowledge to discern “if cats are planets” and “if rocks are clouds.” You have nothing.
 This impossibility of infinite regress will rear its ugly head when dealing with other ontological issues, such as if matter always existed. It is not impossible to progress forwards in time for infinity; however, if matter was eternal, then today would have never reached. You cannot say ‘matter has existed for an unreachable amount of time,’ to then say, ‘it has now reached today’. As said before, a contradiction has no existence. How stupid men become when suppressing God’s truth.
 To affirm the proposition, “Adam is a man” (X), is to deny the contradictory proposition, “Adam is not a man” (Y, or not-X). Likewise, to affirm the proposition, “Adam is not a man” (Y), is to deny the contradictory proposition, “Adam is a man” (X). Now, to affirm both “Adam is a man” (X) and “Adam is not a man” (Y) is only to deny both propositions in reverse order. That is, it is equivalent to denying “Adam is not a man” (Y) and “Adam is a man” (X). But then we are back to affirming the two propositions in reverse order again. When we affirm both, we deny both; when we deny both, we affirm both.
Therefore, there is no intelligible meaning in affirming two contradictory propositions. It is to say nothing and to believe nothing.
-Vincent Cheung. Systematic Theology. 2010. Pg. 21
 H.W.B. Joseph. 1906. An introduction to LOGIC. Pg.13
 “Think about this. If the law of contradiction is the “ultimate” or foundational law of logic, then how can we prove the law of contradiction? Can you prove it without using it? If you can, then the law of contradiction would necessarily be a secondary law. But if you must use it to prove it, then are you being circular? Where is the circle? For something to circle back, you need to move away from it first, but how can you depart from the law of contradiction, so that you can circle back to it to make the fallacy happen? If you can understand this, then you can apply it to biblical apologetics. The only difference is that the law of contradiction has no content, so it is less likely to confuse you. But the principle is the same.”
Vincent Cheung. From his blog post in http://www.vincentcheung.wordpress.com. Sept. 2016.