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1) If many individuals experience the same thing, in a consistent and reproducible way, there is an underlying reality to that experience.
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That may be, but the reality is that invariably the experience is had by one and the revelation of that experience merely believed by many. Religion is a prime example: Islamic believers hold that Mohammed received the word of God when the book called the Koran literally came down from the sky, actually fell from the sky according to some. So there is ostensibly an established reality, that the prophet received the word of God from the heavens. However, a review of the nature of non-believers before the time of that event with reference to the historical context even to the present reveals that were a man of that time to claim to have written this book and presenting it to people for their approval he would probably have been lynch-mobbed and stoned to death, so the story was a safe form of self-preservation so that he could stay alive, after all, there were certain lessons to be learned from the life of Christ. So reality is or is not truth, or religion is or is not reality, you decide, for it is obvious that Mohammed was a literate and gifted genius whose study of writing compelled him to use what he had learned to make an attempt to teach an ignorant people how to live and whose imagination allowed him the time wherein to do this.
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2) If a set of foundational assumptions are taken to be true and logical deductions made from these assumptions, then the later stages of logical deduction are correct.
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Elementary logic: on the one hand, mathematics is an indispensible utility to explain theory but a mathematical conclusion cannot be allowed to initiate theory. I trust that you agree.
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3) There is an underlying consistency to reality which can be apprehended.
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The attribute of empathy may be an evolutionary throwback to the true wonder of reality, the birth of babies, the evolution of life, the beauty of nature, the warmth of the sun, the cleansing and sustenance of the waters - wonder has its roots in bewilderment, the apprehension of one's environment, one's reality. Reality is like a complex discipline, like the science of chemistry. It doesn't change, once the facts are learned, they form the basis for the acquisition of new knowledge, and empiricism is the consistency that rules.
Real science is truth. Truth leads to understanding. Tolerance is acceptance of the truth. Intolerance is denial.