I did not ignore this, it is a given not open to argument that axioms are inherently true, for us. And as far as we can trust the result of repeatable experiments we can derive constants. Logical truths are one thing, inherent to the structure of our minds. Constants observed in nature are another thing, empirical facts we judge to be inherent properties of the 'real world' around us.
My points were two.
Logic contradicts itself when we accept that something logically impossible is also logically required. (Something: nature's laws and material, coming from nothing).
I think all honest and thoughtful people have recognized that this is an insurmountable obstacle, logically, if not empirically. It certainly happened. That isn't the issue. We can't make sense of it to our minds. The beginning of existence can make no sense, with or without god.
What does this tell us about logic as a whole? Very little, because once we begin to doubt it we lose the ground we're standing on to provide a foundation, even for the doubt. But I think we can say this much: we can only trust logic as a practical guide, not as an ultimate truth, in absence of some other faith.
Logically we know that we cannot make sense of existence merely logically. Anyone who pretends they can is working with a different mind than I have. Do your best to square the circle in a way intelligible to others, see if you can produce a consensus.
We can only trust our logic in the practical sense of observation and experience. We can use it and rely on it without considering it true, outside of our minds. We can say it is true as far as it works. But we wouldn't be having this discussion if the mental structure we both share had no problem comprehending our existence in a fundamental way.
On the empirical side of experiment and observation, we have a similar problem. What appears to us stationary and solid we know to be no such thing on a deeper level. This is simple and old news. But as we dig deeper it gets weirder, as any amateur student of quantum physics knows. Taking things to the most elementary observable level, all of our assumptions about what matter is have been laid flat by our own adhere to the scientific method. Things which should not be possible are observed as we drill deeper into the quantum level.
The closer we try to get to the 'objective' truth, the more we stumble over paradoxes. The whole field of theoretical mathematical physics becomes a tree branching out endlessly with fruits of every shape and color. All is conjecture, beyond proof, beyond experiment, beyond falsification. Only faith in the validity of the mathematical properties of our own minds, for all times and places, can make them plausible, because there can be no test or evidence. Any mathematically consistent model is presumed plausible, but can't be tested proved. So there is no consensus or even move toward consensus. It becomes more and more the theater of the absurd.
Finally, we believe that we are animals in a state no more perfect or objective than any other animal. Our mental and sense apparatus are evolved to suit a particular environment. The whole of present biology gives us no grounds to think our logic or our senses are an actual mirror of reality as it is. It is all we have, so we can work with no other tools. But those tools themselves tell us plainly there is no basis to assume the tools are sound. There is no reason to believe the lens through which we observe and filter the unknown and unseen inputs is anymore accurate or valid for all places and times than for a fish or honeybee.
To have faith in our logic, in our mental apparatus and senses, in our truths and facts, is not justified by that logic, or by that science or those facts. On the contrary, they give us every reason to doubt their validity, beyond mere practical use for the results we desire to obtain. They are no measure of truth, because they make quite clear there can be no objective truth perceived by a subjective consciousness.
To believe our minds and the logical patterns they follow are not mere makeshifts and handy tools, but actually display to us the unadulterated and unadorned play of reality is an immense act of faith that is either vanity, fear, or truth. But in all cases it is faith. It is faith because it is without reason and even against reason, for that is what faith is.
You have to ask yourself, if I really believe my own mind can apprehend truth, why do I believe this? What other than faith can make me believe this? According to the random and purposeless materialism that sits astride the throne of all the sciences, it is not so. Logic, empirical science and applied theory all tell is no.
If you believe it, you're either too afraid to fully accept the implications of what science shows you, you simply don't understand those implications, or you have just put a fig leaf over the god in the machine that runs your universe and makes you the seer of unvarnished truth and reality. In other words, you retain the anthropocentric, objectively true view of the universe that requires a creator, and simply deny the creator as a fashion or afterthought.
I am not arguing for a creator or against it. I am, as ever, just arguing for intellectual rigor and consistency. Accept that you need god for your view, or abandon the view. There can be no faith in the conclusions of our obviously very faulty animal logic, animal senses and animal concepts of what is around us. The limitations can never be overcome as long as we remain the subjective human vessels through which a limited, perhaps tiny spectrum of unknown, infinite inputs is filtered through a perhaps perfectly false lens, to produce a "truth" which is a truth only for us, and nothing more.
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