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Author
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Topic: Metaphysical Truths as Irreducibly Complex Systems, and their Non-Computability
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Danpech
Member
Member # 163
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posted 17. August 2003 19:50
It is my contention that the truth of any matter is irreducibly complex. You must in some sense know, and apply, all of the basics of a given matter in order to have an accurate, or correct, understanding of the matter. This would hold for metaphysical truths as for anything.
One of my favorite sources of metaphysical argument is the account of the life of Abraham as found in the Christian Bible, and of this account as focused on the test given to Abraham by God. The words recounting this test are as follows.
quote:
1And it came to pass after these things, that God did tempt Abraham, and said unto him, Abraham: and he said, Behold, here I am. 2 And he said, Take now thy son, thine only son Isaac, whom thou lovest, and get thee into the land of Moriah; and offer him there for a burnt offering upon one of the mountains which I will tell thee of. 3 And Abraham rose up early in the morning, and saddled his ass, and took two of his young men with him, and Isaac his son, and clave the wood for the burnt offering, and rose up, and went unto the place of which God had told him. 4 Then on the third day Abraham lifted up his eyes, and saw the place afar off. 5 And Abraham said unto his young men, Abide ye here with the ass; and I and the lad will go yonder and worship, and come again to you. 6 And Abraham took the wood of the burnt offering, and laid it upon Isaac his son; and he took the fire in his hand, and a knife; and they went both of them together. 7 And Isaac spake unto Abraham his father, and said, My father: and he said, Here am I, my son. And he said, Behold the fire and the wood: but where is the lamb for a burnt offering? 8 And Abraham said, My son, God will provide himself a lamb for a burnt offering: so they went both of them together. 9 And they came to the place which God had told him of; and Abraham built an altar there, and laid the wood in order, and bound Isaac his son, and laid him on the altar upon the wood. 10 And Abraham stretched forth his hand, and took the knife to slay his son. 11 And the angel of the LORD called unto him out of heaven, and said, Abraham, Abraham: and he said, Here am I. 12 And he said, Lay not thine hand upon the lad, neither do thou any thing unto him: for now I know that thou fearest God, seeing thou hast not withheld thy son, thine only son from me. 13 And Abraham lifted up his eyes, and looked, and behold behind him a ram caught in a thicket by his horns: and Abraham went and took the ram, and offered him up for a burnt offering in the stead of his son. 14 And Abraham called the name of that place Jehovahjireh: as it is said to this day, In the mount of the LORD it shall be seen.
15 And the angel of the LORD called unto Abraham out of heaven the second time, 16 And said, By myself have I sworn, saith the LORD, for because thou hast done this thing, and hast not withheld thy son, thine only son: 17 That in blessing I will bless thee, and in multiplying I will multiply thy seed as the stars of the heaven, and as the sand which is upon the sea shore; and thy seed shall possess the gate of his enemies; 18 And in thy seed shall all the nations of the earth be blessed; because thou hast obeyed my voice. 19 So Abraham returned unto his young men, and they rose up and went together to Beersheba; and Abraham dwelt at Beersheba.
KJV
For me personally, the entire account of Abraham's life is one of the top five most important pieces of literature in existence, and one of the reasons I think it so important is because I see it as a prime example of an irreducibly complex system - a metaphysically irreducibly complex system. In this portion of the account, there is a piece missing: the rest of the account prior to this point in Abraham's life.
Now, from a Christian point of view, the correct basic understanding of this test is spelled out in Hebrews 11:17-19. But, there are still plenty of good questions that arise about this test; Here are a few of many: Why did God think to put Abraham through this test in the first place? Could this same test rightly be put to any random person living today in America? What impact did the test have on Isaac?
The most striking thing about this test is that it seems that God requested Abraham to do something that one would be right to think is abominable: taking the life of a person not worthy to be put to death. The account gives no hint that Isaac was worthy to be put to death. But, the account does give far more than a hint of a rather different interpretive framework. It is this framework that begs for our attention.
(What is so interesting about metaphysics is that a computing machine lacks the ability to appreciate what can be called, simply, 'significance'. A computer would never be able to identify any significance in the account of Abraham's life, and could no more care that God had asked Abraham to kill his son than the fact that Abraham likely had hair on his head.)
The second most striking thing about this test is that God does not let Abraham go through with the act. But, without the context for this test - the missing piece - it would seem that God had, just out of the blue, asked Abraham to kill his son. As if Abraham had met God for the first time just seconds before, and then suddenly asks him to simply take up his sword and kill his son where he is standing. No reason given, just do it. Why do it? Because God said so, and God is the Big Boss. This is an application of what is called the Divine Command theory, usually applied to the origin of common sense ethics (all of which come under the Golden Rule). The question, then, is, did God expect Abraham to simply obey? Was that the significance of this test?
The context for Abraham's test, namely everything that God had said and did in Abraham's life up to that point, was something that Abraham would have seen like a flashing neon sign right in his face. If you can put yourself in Abraham's place, by imagining that everything told in the account of Abraham's life had happened to you (assuming you already understand the cultural significance of those portions of the account that reflect the cultural practices particular to Abraham's culture), then you will not be able to keep from seeing this test in terms of this context. God had set up the context.
If we take the account at face value, then we would have to conclude that God had not once told Abraham what to think of the test: "Abraham, I am going to ask you to sacrifice your son, but I want you to know that I do not mean for you to actually go through with it. Just act like you are going to go through with it, and at the last moment I will stop you."
You can't input this account into some 'Philosophically Neutral Computing Machine' and have the Machine give an output that has any common sense to it. It will simply tell you what the text already spells out. But, some people read the portion of the account that tells of Abraham's test as if there is no context for it. Just do what God says. You don't need to care about significance, God will make sure that you learn the significance of everything in the end, so long as you ignore the question of significance for anything that God has not specifically told you to pay attention to regarding the question of its significance. The only significance is what God spells out, so, if God says to do something and doesn't say why, then all you need to know is that you must comply. Even if it is to kill your own son.
Sounds a little too much like Basic Training in the Armed Forces. Now you know what a real soldier is, and that is very significant. Metaphysics as irreducibly complex systems demand every part of you. The truth swears allegiance to no one, so we are required to swear allegiance to it, and only to it. And, the truth is, we are not computing machines, much less obedience machines. We must think things through. Finally, we must keep from conflating word, thought, and object when computing someone else's words. Especially if those words are thick with metaphysics.
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Noel Rude
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Member # 516
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posted 18. August 2003 18:16
“It is my contention that the truth of any matter is irreducibly complex.” An intriguing thought! though perhaps the moderator isn’t too pleased that you chose the Hebrew Scriptures to illustrate your point, this because you then open yourself to the accusation that you are arguing for a particular truth rather than your point which is that “the truth of any matter” is irreducibly complex.
But you get me to thinking. Is reality itself irreducibly complex? Yes, according to the mathematical Platonist. There are aspects of reality that are contingent (the laws and constants of physics, perhaps, and the fact that I am scribbling these lines), and there are aspects of reality (logico-mathematical truths) that could be no other way in any possible world. Thus, I would say, for the mathematical Platonist reality is irreducibly complex (IC).
And so this brings up the question: Must philosophers always begin with IC? Or, put another way, can IC come from non-IC? (This is not quite the same as the issue of whether IC originates only with intelligence.)
Thus our scientific theories deal with how we get from a prior state to a later state, or simply with how things work (not why they exist).
We begin with God, the materialist's eternal cosmos, the anamist's eternal cosmos, a CTMU, and/or life as a given – whatever it is we begin with IC … except … except that I believe there are those attempting to get something for nothing, such as the Big Bang arising from fluctuations in the fabric of nothing (or however they may phrase it). And, we must note, not everyone is a Platonist.
Anyway this is all very interesting. If IC can come only from IC, is there then no novelty? I propose that there is, and that agency is involved and is one aspect of the IC of ultimate reality, but maybe that is another topic for another brainstorm.
[ 18. August 2003, 18:58: Message edited by: Noel Rude ]
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Mark
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Member # 888
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posted 24. August 2003 13:53
Very interesting posts.
With respect to the Abraham story, Dan, you may already be familiar with it, but a famous eulogy on that story is "Fear and Trembling", by Kierkegaard. Kierkegaard views the story through the metaphysic of faith, rather than the metaphysic of obedience. I suppose he would say that obedience is embraced by faith, that faith is somehow "larger," more global. If you are interested in that story, and the existential dynamics at work, I recommend it.
But back to your original question, Is truth irreducibly complex?
I understand the term "irreducibly complex" as a descriptive term (an adjective) for a functional system, with emphasis on the term, "system." I don't understand a monolith as irreducibly complex; obviously, if you remove the one element present in a monolith, the function is gone, but this is a tautology. An irreducibly complex system would require at least two "parts," each of which had an origin, identity, and function independent of the other parts, and when combined (in the "correct" way) produce a function distinct from any function produced by the elements independently (or in any other possible combination). Further, if any element is removed from such a system, the system "fails," that is, it no longer functions (for any purpose).
I like the Wright Flyer as a good example of such a system. We see a variety of systems (wings, motor, controls, horizontal stabilizer, etc.) combined in a way to produce a novel function -- flight -- that none of those systems could produce alone (or in any other combination or permutation). We also see that, should one of those systems be removed, the function of stable, directional flight would be lost (I emphasize "stable"). Since wind power is unreliable (and sometimes an enemy of both stable and directional flight), I view the motor as essential (hence, a glider doesn't qualify; and, as an aside, I note that birds also have "motors," although they use wind energy when convenient -- birds are "smarter" and more efficent than airplanes). I won't go into the fact that the motor on the Wright Flyer can itself be viewed as an irreducibly complex system.
A response to your question about metaphysical truth requires some common understanding of the term "metaphysical truth." A logical positivist would say: "No metaphysical truth can be empirically verified, therefore we talk nonsense." A Platonist would say: "The universe and everything in it are merely physical expressions of universal forms, and hence the universe and everything in it necessarily embody and express underlying metaphysical truths." A naturalist (or a Cartesian) would say: "I can't verify, or even infer, metaphysical truths by observation of the material world, and since my observational universe is limited to the material world, I have nothing to say about the matter." A Buddhist would say: "All matter and energy proceed from the same source, are fundamentally identical, regardless of material expression, and we all share equally in this original source and hence are all of a piece." A Christian would say: "A creating, good, and rational God made the universe, and its laws, for the purpose of (?) the goodness of the act of creation itself, an arena for kindred spirits ("in his image") to live and flourish within the protective embrace of innately beneficial "laws," and/or to share his love with kindred spirits in the joy of a good and fecund universe."
It should be noted that those (like logical positivists) who deny the very existence of metaphysical truths are themselves asserting a metaphysical position, both in their commitment to their method, in their inferences, and in their ultimate conclusion. The logical positivists can't verify the truth of their claims (or more importantly their assumptions), and that's why some highly intelligent people continue to disagree with them.
Actually, I think most metaphysical systems, at some bare-boned level, are irreducibly complex. If you remove the ideal forms from Platonism, the system collapses (this has happened for many people in modern culture, who find themselves in an atomist universe, devoid of connecting or interpretive symbols, forms, customs, or moral systems; they experience themselves as disconnected in an "anything is possible" universe -- Note that a positive spin is sometimes put on this state of affairs with the worship and glorification of personal "freedom," which is merely the introduction of a new metaphysic that attempts to make sense of the new state of affairs, sans organizing Platonist forms).
Other examples would be the Christian metaphysic: remove the diety and the system fails to function.
The term "irreducible complexity" was introduced into the vocabulary to describe certain biological systems that seem to be analogous to the Wright Flyer -- that is, remove any identifiable part and the functionality is lost; the system "crashes."
Then, other claims are made about IC systems (assuming they exist).
The first claim is that a Darwinian mechanism could not have produced an IC system.
As I understand the reasoning underlying this first claim it is based on both logical and emprical grounds.
First, the logical argument applies only to direct Darwinian pathways -- gradual, step-by-step change and development over time, without change in function. The claim is made that it is logically impossible, under the Darwinian paradigm, to construct an IC system in a direct, step-by-step pathway (that is, the function does not change throughout the pathway -- for example, once an eye, always an eye.) Change in function throughout the process is not admitted in this argument.
The second argument -- the emprical -- answers the proposal of an indirect Darwinian pathway, that is, a change in function at some or all the steps, co-option of functions, and so forth. The claim is made that there is no empirical evidence to support this position (in the form of a demonstrable, testable hypothesis of how an indirect Darwinian pathway could have assembled a specific IC biological system).
The ID Conclusion: Neither a direct nor an indirect Darwinian pathway could, or did, assemble an IC system.
Then, the argument takes one more step: The very existence of IC systems implicates intelligence in their design.
So,we have 3 questions:
1. Do IC biological systems exist? This question reflects the arguments over whether a mousetrap or a flagellum or an immune system are "really" irreducibly complex.
2. If they exist, can Darwinian mechanisms -- either a direct or indirect pathway -- explain them? By defintion, a direct Darwinian pathway cannot explain them; the only alternative is an indirect pathway. This question reflects the discussions about various hypotheses for the indirect construction of various biological systems, like the flagellum ("certain TTS secretory systems share proteins with the flagellum system and are therefore precursors, etc, etc!")
3. If they exist, and Darwinian mechanisms can't explain them (at least right now), are we warranted to infer design?
This last question implicates metaphysics, and hence the emotionality of some of the discussions surrounding ID. The design inference, at least to some, violates the "science metaphysic," and therefore cannot be admitted to the discussion.
The ID proponents object: "No, it doesn't violate the science metaphysic! Many sciences infer design in their investigations, and some scientific endeavors exist exclusively for the purpose of discovering and inferring design (for example, SETI)."
Science has its own metaphysic, and some of its proponents seem to be claiming that this metaphysic is irreducibly complex: to wit, if you add a foreign element (Intelligent Design), you change the very function of science; science is a closed system and ID cannot be admitted into its function, or else it function would "crash."
What do you think? Am I misreading the situation?
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Danpech
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Member # 163
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posted 26. August 2003 18:57
First (implicit) point: Metaphysical truths, whatever are these truths, demand every part of you ---especially in a world where there is strict disagreement over what to reject as metaphysical falsehoods.
Second (explicit) point: in order to rightly determine metaphysical truths (say, human origins) from things 'evident' ('the evidence') requires knowledge of all the fundamental facts/principles of the matter.
That's what the controversy over ID is about:
1)those who strickly oppose ID are confident that they know all of the fundamentals of the matter in order to be justified in their strict opposition to ID.
2)some Id'ers believe that those who are in strict opposition to ID are lacking some pieces of the puzzle (or are 'simply' unwilling to admit significant pieces already evident).
Of course, we have the option of taking a particular position on a given metaphysical question while cognizant that we have knowledge of less than all of the fundamentals pertaining to that question. But, it seems as if the most basic metaphysical questions cannot be held at arm's length once you are aware that there is very severe disagreement over what are the answers to these questions--over what are the most basic metaphysical truths.
And, to have proved what are metaphysical falsehoods requires knowledge of all the most basic pieces of the puzzle regarding the thing judged false. It is possible to make the mistake of thinking we have all the pieces when we really don't, and this happens because we are just that ignorant of some of the pieces.
Such ignorance is sometimes the result of pure lack of knowledge. But, it is also sometimes the result of having the wrong framework. Reductionism is a useful tool, but are there not also other useful tools? There are. What we hold as metaphysical truths depends on what we expect one of more of our favored tools to accomplish.
Popular science-based views of basic metaphysical questions must account for the basic fact that these views are built upon a collection of other basic empirical and logical facts. There aren't many basic facts that a given view requires. But, take away any one of these facts and the only thing left is the option to hold a particular position while cognizant that one has less than all the pieces of the puzzle.
I don't think that IC, applied to metaphysics, is a tool. I think it is as inescapable as logic itself. Something is what it is. Our problem, in some cases, is often more about determining what something isn't, than in pinning down exactly all that it is. What so often happens is that we look for a 'magic pill', as it were, to all questions. Reductionism seemed, to some people, to be the one framework for everything. It seemed to them that life could be fully defined in terms of mechanical function. They were so intoxicated at the seeming possibility that reductionism was the One Great Answer that they at first missed both the fact of their own 'subjective personal experience' and the fact that it is precisely by way of this 'subjective' experience that they possessed the notion of objective knowledge (neither of which they believed that a rock possessed).
So, what's the missing piece of the puzzle? Answer this question for yourself: Are you the ground of being?
Mechanical reductionism, by assuming that one can know the nature of the knower (oneself), is the effective presumption that oneself is the ground of being. I think this presumption is the wrong framework, and I also think that most of those who hold to reductionism are unaware of their own presumption: they are too intoxicated with reductionism in their efforts to oppose what they are convinced are grievous metaphysical errors. For me to say this is to risk being charged with making ad hominem attacks, but that's just the nature of basic metaphysical concerns. As I said, the most basic metaphysical matters demand every part of you in this world: somebody is in serious error.
How much greater a thing is there than the knower? Surely not a rock. How, then, can the knower come from non-knowers? The reductionist says that the knower comes from non-knowers by way of non-knowing mechanics during millions of years of very slow development under harsh conditions. But, a rock knows nothing of harshness. A rock lacks a 'subjective' sense of the significant. ...or, does it?
[ 26. August 2003, 19:15: Message edited by: Danpech ]
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