Quote:
Originally Posted by Ken G
The truth I refer to is not meant to be an absolute concept of truth, as I've said in the past it is strictly the concept of "scientific truth"-- the objectively repeatable footprint left by some far more inscrutable beast that science has no way to define or address. I'm not sure if you are objecting to my ruling out of other forms of truth, which I did not intend (truth vs. scientific truth is another thread), or if you feel that scientific truth can be extended outside of what is observable.
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I do feel that scientific truth may be extended beyond what is observable, or, as I prefer to put it, I feel that the concept of "observable" should not be restricted to "physically observable". The way you phrased another part of this post showed the crux of our difference of opinion so far:
Quote:
Originally Posted by Ken G
There is indeed a tendency in mathematics to start with some familiarity, work backward to the axioms that give it, then work forward from those axioms to see how you did-- much like in science. But if you started with a familiarity based on observation of reality, you are in effect doing science not pure mathematics. The distinction isn't really between "physics and math", it's more between whether you start with axioms you like, or start with familiarities you wish to make contact with. What ends up happening is often a kind of combination, so the distinctions are not so cut and dried as I may have suggested.
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You're using a notion of "science" that excludes mathematics (let's reserve that term for "pure mathematics", here), because math is not based on physical evidence. This is a common definition used by many people, but I wish to challenge it, because, in the context of these discussions we've been having, I am convinced that making such a distinction contributes more to cloud the issues than to clarify them.
The notion of "science" you used, while common, is not the only one. There are also authors, as you must know, who would include mathematics among the sciences. Although pure math is not subject to the veredict of physical evidence, I would argue that it
is subject to a different standard of proof, which comes from elementary logic. I would also argue, as some authors do, that elementary logic is no less objective than physical evidence. In fact, even in the day to day practice of the experimental sciences it's often difficult to disentangle the one from the other, as observations are also to some extent theoretical constructs (you've agreed to this in previous discussions).
In short: I reject the dichotomy between
objective natural sciences on one hand, and
arbitrary theoretical mathematics on the other. I say that mathematics is every bit as objective as the natural sciences, except that it is grounded on a different kind of evidence (logical, rational, or intuitive).
I won't claim that this point of view is better than yours, or that I can prove it is truer, but I put it to you that this philosophy, that regards evidence and logic as the two sources of objectivity, is no less defensible than the philosophy that sees physical evidence as the only possible route to objective knowledge. I put it to you as well that, in any case, the latter philosophy
is no more than a philosophy: a good scientist may accept it, but he is not required to.
Quote:
Originally Posted by Ken G
But the process (4)-(5)-(6), those "rules of logic", were also built on the backs of observation. Your position only works if you view those rules as separate from the axioms, as though given to us separately from the process of choosing axioms. I view the rules of logic as just more axioms that we chose because they work, just like the other axioms. We are not born with the ability to be logical, it is our experiences, our observations of reality, that train us to do it. [...]
All our minds can do is organize our familiarities, the idea that we can do something more fundamentally separate from reality is hard to support. Even if one attributes "instinctive" logical capabilities to our minds, they would have been "chosen" by natural selection, i.e., chosen to conform to the observational tests of who survives. If we count "death of an illogical brain" as a kind of "observation of how reality works", then it's still all grounded in observations.
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Not every one agrees with that. Many thinkers throughout the ages have argued the opposite, that logic is indeed an innate ability of our species.
While I personally find very plausible the
conjecture that much of our thought processes are a result of our biological evolution, I am not sure I would extend that assumption to our entire intellect, including basic logic. As such, for the purposes of this discussion, I will reject that extension, on the grounds that I have never been shown any conclusive evidence that the whole edifice of logic, from top to bottom, is merely a tool molded by our environment through evolution in a contingent fashion.
As an alternative, I offer a different conjecture: that the rational part of our minds is not a mere product of our environment, but rather the environment itself has been conditioned by the rules of logic, because we live in a logical universe. This is why we've been so successful at using reason to understand the world. It was not natural selection which chose our logic, but logic which chose our universe.