I'm going to look at three different worldviews and what they say about this. Let's start with the eastern worldviews.
Hinduism, New Age
All eastern thought teaches right off the bat that the world is nothing but an illusion and nothing we experience can be trusted to be true. What's more is that if I were to believe that, I would also have to believe that the person telling me this is an illusion too. Why should I trust the word of an "illusion"? Not only that, I should not trust the logic I used to conclude that I shouldn't trust the "illusion". Eastern thought is not very compelling for someone that is looking for truth, because it basically teaches that truth cannot be known, no matter how hard to try to find it.
Naturalism, Atheism
Naturalism is quite deceiving when it comes to this question. Naturalism relies on our senses and logic to form its worldview, but at the same time defeats the reason to trust our senses and logic. Naturalism relies on the theory of Evolution for the emergence of man, his senses, and his logic. Evolution is strictly concerned with survival not truth. With senses that are tuned (by natural selection) for survival, we cannot trust them to provide us with truth. That is not to say that everything we experience and discern is false, it is just to say that Naturalism demands that we can't trust that it is true.
Christianity
There's a couple of ways to look at this question from the Christian worldview.
The first is what is referred to as "Total Depravity of Man" (will be discussed in a later post). If misunderstood (as is the case for many Christians), this doctrine states that when Adam sinned in the Garden of Eden, that sin entered the world and clouded man's judgment of everything, so that it is impossible for him to know or find truth. The only way for man to discern truth is by God's Spirit, which man must accept first. My concern with this is that if man cannot discern truth without God's Spirit then how can man recognize God's Spirit as the Truth? If this doctrine is adopted, then even Christianity undermines man's ability to know truth.
The second is to see that The Fall in the garden clouded man's heart rather than his mind. Man can experience and discern truth. As long as man is truly searching for truth, then he will find it. What keeps people from recognizing ultimate truth and its implications is the clouding (hardening) of his heart by his sin against God. If people are willing to follow the evidence where it leads, they can find the ultimate truth (Jesus Christ is the Way, the Truth, and the Life).
The reason that I bring up this topic is two-fold:
1. The Christian worldview is the only of these that allow for man to actually know truth. So many Naturalists claim that their worldview is superior to Christianity because they are more "scientific" and Christianity is based on "blind faith". When the opposite is actually true. The reason they can get away with this is because many Christians hold the first view that I presented, thus have no way to rebut the Naturalist.
2. The Eastern/New Age view of truth makes no sense. If it is true, we have no reason to trust that it is and we also have no way of finding out until we die, and even then some of the eastern religions teach that we won't learn anything, we'll just be thrown back into this world of "non-knowledge".
So, the Naturalist is living inconsistently, and the New Age believer is living in denial. Christianity is the only one that offers consistency and confidence in knowledge of truth. In fact, Christianity even takes it a step further and explains why people accept the other two options; even though they lead to logical absurdity and inconsistency.
For more about how to discern truth within the Christian worldview, see my post "Nature vs Scripture".
I also recommend:
Online Articles
Alvin Platinga's essay "Evolution vs. Naturalism".
Kenneth Samples' article "Darwin's Doubt".
Kenneth Samples' article "Do False Beliefs Promote Survivability?"
Books
A World of Difference- Kenneth Samples
Come, Let Us Reason- Norman Geisler
Podcasts
Just Thinking
Let My People Think
Straight Thinking
Stand to Reason