Justification for Foundational Belief

[Skepsis]

Why look for sensory experience (perception and thought) to validate your trust in sensory experience then? How would philosophical justification escape classification as a sensory experience?

Can there be no verification for this belief other than intuition?
I'm fine with that because I have judged trusting my memory and senses as integral to interacting with the world with any meaning.
You make a fine point.

---

Your question doesn't make mush sense. If you are capable of asking "am I justified?", it means you have already accepted certain beliefs based on which you determine that justification might be required. Like you said - these are a-priori beliefs. A question even more basic, i.e., if any justification is possible, already has some axioms at its basis. These beliefs are inherently unjustifiable since any justification provided would lead to circular reasoning.

This is what I suspected. I had to ask if there were ways to show the truth of foundational beliefs without using the belief because I really didn't know.

However, there is an indirect test for validating these axioms. As you've said, these are foundational beliefs, i.e. ones which lie at the basis of every other belief that you hold. Therefore, in order to have a rational and logical world-view, all your beliefs must satisfy two conditions a) all of them can be logically derived from the foundational beliefs and b) none of them may contradict the foundational beliefs. If you can find a single belief in your system that logically follows the foundational one and still contradicts them, you have a good reason to question your assumption.

I understand, but this still presumes the truth of the beliefs. I think this is a fair justification, however, because these beliefs have no base justification and cannot have a base justification.

Let's see if I can help you with that. As an evidentialist, I assume that the following three would be the foundational axioms of your worldview.

1. I exist.
2. Reality exists.
3. I am perceiving reality.

The first one is pretty simple. The proposition "I don't exist" is self-defeating since the "I" here is referring to an entity that does exist. This doesn't come under the purview of validation or justification because its a statement that cannot be false.

You hit the nail on the head up until here. After this, I have a few questions.

In the second, reality refers to everything that exists around you. Now, since you are looking for the "truth" of this belief, you have to ask - what does "truth" mean. Suppose I point in a direction and say "there is a tree over there", what determines if my statement is true or not is whether there actually is a tree over there. It wouldn't matter is I were blind, if there is a tree, I'm telling the truth.

Truth is determined by whether the statement corresponds to reality of things as they are. If the statement "reality exists" isn't true, then the very concept of truth has lost its meaning. The statement "reality does not exist", therefore, is automatically false.

The truth of the statement doesn't change, it just loses all value. It isn't false, it is meaningless.
... Right?

The third is the trickiest - the most common argument against it being the "brain in the vat" scenario, or in today's date, the matrix scenario. What if all of you sensory inputs are constructs of another intelligence. First of all, this statement would not contradict any of the previous axioms - you still exist and reality still exists - there is simply a perceptual disconnect between your reality and the actual reality. However, in that case, the rules would change significantly. You don't exist in the actual reality and the actual reality doesn't exist for you. Any statements you make regarding "truths" or "justifications" or "validations" would be based on your reality. The intelligence feeding you the sensory data would bear the responsibility of making your reality consistent and non-contradictory - even if that intelligence is your own. For example, in your dreams, "your" reality is often confusing, contradictory and therefore unlivable. While this does not solve the philosophical dilemma, it still gives a handy test for making answering the question.

This sounds a lot like solipsism. You know you exist and reason that reality does too by its non-contradiction, but you can't know if anyone else shares your reality.
You make this easier to understand and have given the best explanation in my opinion. I would love to hear more from you.

---

I guess my question would be what is the purpose of this search for foundational beliefs?

I had hoped to find the basis for my belief structure. I feel it is wise to try and find answers to things that are pressing issues to you, take in those answers and determine whether or not they are satisfactory. If they aren't, I look for more answers. If those answers aren't satisfactory, then I keep looking.
If there is no satisfactory answer that I can find, I give up the propositions.
In this case the answers being given are very, very informative and are pertinent to the question.