A little late, don't you think? I mean, 800 years after Christ...
Logic itself relies on presumptions, self-evident truths, axioms, etc. It cannot even begin a solid "proof" without one. So, presumption alone is not a disqualification for knowledge or proof.
Unless it is trying to prove something real. Outside of geometry, I can't think of too many self-evident truths that would apply to the real world with certainty, but I am saying this wihtout giving it much thought, so I may be wrong, but that's my gut feeling.
Besides, pure logical "proofs" are not real proofs but theorems or working models.
But we are not only physical beings. We also have intellect and consciousness
They are not sui-generis existence, but epiphenomena of the nervous system.
Whether it be the taste of strawberries or a logical proof or a moral axiom.
Talk about mixing categories and lumping them all in one basket! What is a moral "axiom" anyway?
Some things we can only know subjectively. It's still knowledge
You are using "knowledge" as awareness. What we are aware of are called "feelings." A strawberry "tastes good" because its meat gives us a pleasing/satisfying feeling (meaning we want to extend it or repeat it ad nauseum). We don't know why a strawberries "taste good." It's not knowledge (as in rational knowledge); it's awareness.
Like trying to describe a taste or logically prove "strawberries taste good." It's interesting but you're not going to get there from here IMHO.
Behavior that repeats itself is defined as "feels good." It's an inference, not a proof. The only way to "prove" something tastes good is to ask an individual if it does. And that is an investigative proof rather than logical.
I'm sure you're aware of the Orthodox objection to applying logical proofs to this and the Eucharist for example.
Yes, of course. The Orthodox would never postulate something like 'transubstantiation.' To them, divine mysteries are God's secrets not meant to be understood by humans. In other words, Orthodoxy firmly believes, without going into the details and mechanics as to how, that the bread and wine are ontologically changed by the Holy Spirit following the humble petition of the priest. (See epiclesis).
Certainty, again, depends on what level of knowledge you're after. You can apply logic to physics or philosophy. In general, the level of certainty in this direction goes down; in particular, it can vary. Understandably, at both end, the very big and the very small, certainty decreases.
However, your certainty is not a requirement for reality. For humans, certainty is a quality of knowledge, but not an limit on reality.
Besides, pure logical "proofs" are not real proofs but theorems or working models.
No, they're real proofs. That's what the tool of reason is best used for. Above pure empiric measurement, if you want to prove something is logically true - according to reason - you're required to have a tight, valid, deductive syllogism for it. Else your statement is unproven. You can have evidence, inference, beliefs, strong feelings, etc., but not proof in the strict requirements of formal logic.
My main point in our discussion is that this is the case with your philosophy, which could be described as your strict empiricism. It is not proven.
Worse it is logically inconsistent. You have a big logical contradiction in your position. The statement "only that which can be proven using science or logic alone is true" cannot be proven using science or logic alone. This is a performative contradiction. It's a point of failure for your axiom.
You can still hold to it of course, but no one else is required, logically, to hold it or be bound to treat it as true or proven.