Gödel's theorems mean that no matter how complete the formal system, it will always leave a semantic residue: semantics cannot be reduced to syntax, meaning to grammar, reality to mathematics, quality to quantity, etc. This seems intuitively obvious, but it's nice to have logic on one's side.
The bottom line is that man will never arrive at a theory of everything, but will be perfecting it until perishing from global warming in a few years.
At the moment, I'm cross-referencing our favorite logician, Gödel, with our favorite biologist, Robert Rosen.
As Gödel was a "meta-logician," I suppose we could say that Rosen was a meta-biologist, although he would no doubt object to the characterization, since it might imply an element of woo-woo or oogily-boogily.
Rather, he believed that he was the one pursuing hard science, while pulling no metaphysical punches. It's the reductionists who are the softheads. Rosen was a real scientist, proof of which is found in the fact that I don't understand half of what he says. I do, however, get the big picture.
Indeed, the big picture is the meta-picture, precisely. I won't say it's the only thing that interests me. Then again, it does seem to be my default setting, and indeed the default setting of any philosopher properly so-called. Now, to even call oneself a "philosopher" strikes me as unbearably pompous, for what is philosophy but error on a grandiose scale, with no hope of arbitrating between this doozy and that whopper?
If I actually believed that, I would despair, for it would mean that the bOb is pointless in a double sense, or nihilism squared. It would of course mean that life -- anyone's life -- is utterly meaningless. But it would also mean that my life in particular is not even meaningless, what with its meta-preoccupation with universal truths.
The moment I began studying psychology, I couldn't help thinking about metapsychology, i.e., the larger system of which one's psychological theories must be a part -- both the truths entailed in one's psychology, and the axiomatic truths it presupposes.
Moreover, without consciously realizing it, I was always on the lookout for logical and meta-logical inconsistencies in this or that system or paradigm. In general, the only way to harmonize such inconsistencies is with recourse to a higher truth in a vertical spectrum. Once you do this, you realize that, for example, mind cannot be a material process for the same reason that physics cannot describe reality. Again, there is always a semantic residue in such attempts at reducing one level to another.
For Rosen the duality of quantity and quality is not the same as that between hard and soft science, respectively. Rather, it rests on "presuppositions about the nature of material reality and on how we obtain knowledge about it." The duality between syntactics and semantics goes to "what is true by virtue of form alone, independent of any external referents, and what is not."
Which raises an interesting question: can formal truth be true in anything other than a trivial sense? In other words, is mathematics true only within its own system, or does it disclose real truth about the actual world? If one says Yes to the latter, this has enormous metaphysical (because meta-mathematical and trans-human) consequences.
The reductionist is guided by the conviction that "Qualitative is nothing but poor quantitative." Given this presupposition, "everything we call a quality or a percept is expressible in terms of numerical magnitudes, without loss or distortion.... therefore, every quality can be quantitated, and hence, measured or computed." Thus, "Everything else we call science is ultimately a special case of physics."
Put that way, it sounds almost like a straw man. And yet, it must be the metaphysical underpinning of science, so long as science is "true." If reductionism is not the case, then what is the foundation of the world? Not in some airy-fairy way, but precisely? What are the ultimate truths that must be and cannot not be, in order for mundane science to be true (at least as far as it goes)?
Now, some people couldn't care less about such questions: "most practicing mathematicians, like most practical (empirical) scientists, go on about their business, indifferent to such matters, convinced to the depths of their soul about the reliability of what they do."
Wait a minute -- depths? Soul? How did these contaminants get into the lab?! I suppose we can say that wherever the reductionist goes, he goes there too and spoils it.
In Hilbert's formalistic school of thought, semantics can "always be effectively replaced by more syntactic rules." That is to say, "any external referent, and any quality thereof, could be pulled into a purely syntactic system."
But a syntactic system is "a finite set of meaningless symbols" guided by a finite set of rules for combining them. Such a system is necessarily consistent, but is it complete? Yes, if you and I are machines. But if we were machines, could we ever know it? If math is just about more math, where's the inscape hatch? And if math is about the world, what is the world about?
Well, thanks to both Gödel and common sense, we know that whatever the mind is, it isn't a machine or computer.
But if reductionism is obviously wrong, does this imply that the opposite approach is the correct one? I don't think so. Rather, I suspect a kind of eternal complementarity between the extremes of empiricism-idealism, subjectivity-objectivity, quality-quantity, etc.
The ancients began at the other end -- the other end of reductionism -- in that for them
life simply was; it was a given; a first principle, in terms of which other things were to be explained.
To us this may seem naive, but is it any more naive than for a conscious lifeform to declare itself to be absolutely contingent? Whence this absoluteness? How did it sneak into the lab? Must have been smuggled in by Soul and Depth.
We are told that biology reduces to physics. But what if physics is an entailment of metabiology or something? Well, stranger things have happened.
On the one hand, biologists have convinced themselves that life is somehow the inevitable necessary consequence of underlying physical (inanimate) processes.... But on the other hand, modern biologists are also, most fervently, evolutionists; they believe wholeheartedly that everything about organisms is shaped by essentially historical, accidental factors, which are inherently unpredictable and to which no universal principles can apply.
In short, "they believe that everything important about life is not necessary but contingent."
That's what you call meta-irony, only without the self-awareness necessary to generate a guffah-HA! experience.
I'm running out of time, so I'll end with this thoughtlet: biology is indeed reducible to physics at one end, while referring to life at the other. But what does it mean to be "about" life? For that is life?
I'm going to go out on a limb and suggest that what we call life is ultimately rooted in the principle of Life Itself, just as the mind is grounded in the principle of Consciousness Itself, and persons in the principle of Divine Personhood. Above that it goes dark. Which is not to say that we can know nothing about it, only that it exceeds our puny models. Call it the principle of Divine Overflow.