Still, some do not find this answer plausible. In light of what the Bible says about the spiritual condition of most men, this is not unexpected. But in any case, what would be another way we could know that God has revealed Himself? Maybe the reply will be that God hasn't revealed Himself - or if He has, we couldn't know it anyway. Or perhaps there is no God. When these sorts of replies are made, though, I find that the person in question has inevitably not thought through how partial knowledge could be possible apart from revelation of such from one who is omniscient (link). And all other answers suppose that it is more legitimate to evaluate a creator by His creation than creation by a creator. Are any of these options really more plausible than a self-authenticating revelation? Do any of these alternatives have something more substantial than a superficially intuitive appeal? Well, I must leave that to the reader to decide. I would obviously answer in the negative.
Of course, there are perspectives which I would allege attempt to copy the method of knowing God's word, distorting it by substituting in place of Scripture something not of divine origin. And this troubles people, because if revelation is supposed to be self-authenticating, then how is it possible to sift through all these varying claims? Is playing a back-and-forth game of "my source is true and yours is not because my source says so" really the best that a Christian apologist has to offer? Still more troubling, how can our answer to such questions be made without presupposing revelation? After all, if some sort of revelation is necessary, then we wouldn't be able to answer any question without first specifying said revelation.
Well, actually all of this doesn't turn out to be so problematic. For the reply to this last question just is that we can't answer any question without first presupposing a specific, concrete revelation. So what? The reason why some accept and others reject one proposal over against another should depend on what one's revelation has to say about such. In the case of Scripture, while God's word may be self-evident, the only means by or reason for which any sinner would acknowledge it as such is grace.
Even so, we may further note that we are not left without means of distinguishing false claims to divine revelation. Keeping in mind that no necessary condition for knowledge can ground or function to demonstrate a sufficient condition for knowledge (link), there are nonetheless tests we can perform which serve as confirmatory evidences.
Now, necessary truths obviously cannot be falsified. So given that the idea of God, that His revelation is self-authenticating, and that what He speaks cannot be a lie are all necessary truths, the Bible, God's self-attesting word, cannot be falsified. That some do not take these divinely revealed truths as constituting a or the sufficient condition for knowledge does not imply we shouldn't.
Then again, this doesn't imply our belief is arbitrary. In addition to the possibility (indeed, the necessity - link) of self-authenticity, the Bible itself prescribes criteria against which we can test its claims. Prophecy is one example. Internal consistency is another necessary condition for some communication to have been revealed by God. Etc. I have outlined and dealt with numerous such conditions elsewhere on this blog. Once again, no matter how many of these subsidiary conditions we show the Bible must and does satisfy, our trust in it must ultimately be based on its own, self-authenticating claim to be God's word. But by applying these subsidiary conditions to other worldviews, we can falsify them and thereby lend credibility to our own. While this is not demonstration - no first principle can be demonstrated anyway - it is a technique which is seemingly the most plausible means of persuasion available. The rest is left to God.
So, to summarize, Scripturalism - the axiom that the canon of divine revelation in general and the Bible in particular comprises the extant extent of that which men can know - is clearly not the conclusion of a set of theorems, no matter how necessary those theorems may be in order for a system to be true. Axioms must be self-authenticating or self-evident.
But the acceptance of an axiom is not arbitrary. If it were arbitrary, then it would be unnecessary. One of the necessary conditions, however, is that partial knowledge requires self-authenticating communication from one who is omniscient. We may not be able to demonstrate or prove the Bible in particular is said revelation, but this isn't relevant. For the Bible is taken to be the sufficient condition, not a mere necessary condition, and no axiom can be demonstrated, proved, or externally justified. The fact it just is self-authenticating is enough. People may not accept this, but then again, people may not accept that I know myself. I can't demonstrate that either, but is that any reason to think I can't know myself? No. So, to conclude this post on how we can recognize the canon, I cite for consideration the following statement by Gordon Clark from Today's Evangelism, Counterfeit or Genuine? (pg. 113):
But if there is a revelation, there can be no criterion for it. God cannot swear by a greater; therefore he has sworn by himself. One cannot ask one’s own experience to judge God and determine whether God tells the truth or not. Consider Abraham. How could Abraham be sure that God commanded him to sacrifice Isaac? Maybe this suggestion was of the devil; maybe it was a queer auto-suggestion. There is no higher answer to this question than God himself. The final criterion is merely God’s statement. It cannot be tested by any superior truth.