The Problem with ID is Metaphysical
Does Intelligent Design fulfill the necessary criteria to be recognized as a scientific theory?
It depends on who you ask. The fact is there are philosophically two sides to this issue: creationists and neo-creationists who maintain yes, and everyone else, including theologians like the Pope of the Catholic church (who is a trained scientist), who say no. It is the position of the latter, much larger group that a case should be made why creationists calling their belief system 'science' are committing a category mistake. Therefore, the problem with ID is primarily a problem of metaphysics since the implication of supernatural causation cannot be falsified, has no empirical evidence, does not rely on methodological naturalism, is meant to be consilient with theological creationism, suggests a supernatural explanation, and therefore is largely in violation of major consensus within the scientific community.
Naturalism, Supernaturalism, and Equivocation on Science
One of the fundamental philosophical issues going back to the Ancient Greeks is the question of supernatural versus natural causation. Among the Pre-Socratics, the first and greatest philosophers in the West and the fathers of our tradition, there were theologi and physiki, those who admitted, and those who denied supernaturalism. So, it is the primary and fundamental presumption of natural science that there is no supernatural causation. That's built into what science is after thousands of years moving from naturalism introduced by the Pre-Socratics into natural philosophy and natural theology into modern science. According to natural science, there CANNOT be supernatural causes to physical events.
From a metaphysical standpoint, there CAN be supernatural causation. To many (I'd argue everyone before rational powers come to fruition), it seems obvious there can be. And this position is acceptable philosophically because it is generally take that metaphysical necessitation and explanation (SEP) is privileged and foundational. But if one says there is supernatural causation, then one is not doing natural science, which is what most people mean when the use the term science by itself.
The Rejection of Supernaturalism
It is the viewpoint of the majority in this debate, that creation science and theistic science are not natural science:
Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation.5 Mechanisms such as peer review and repeatability of findings are used to try to ensure the validity of scientific advances.
The key to this is the term 'natural phenomena', and it is key because it excludes supernatural causation. Theistic science appeals to natural science to achieve proof of a supernatural agency, attacks the conclusions of natural science (evolution is the obvious target), and uses a term "Designer" which is an obvious synonym for Creator. And yet, the opposite of science isn't religion, because Catholicism is a religion that preaches science, and I'm sure there are atheists out there who believe in supernatural forces. Since conventional Christianity embraces science, this debate is not about religion versus science, but about naturalism versus supernaturalism, which is a core tenet of creationism and religious fundamentalism.
I have no science textbook that starts off, "Now, because we exclude supernatural causation....". It's taken for granted that the methodology of natural science excludes supernaturalism. In Ernst Mayr's This Is Biology, he devotes none of his book to refuting supernaturalism in biology. So, for a creationist to use the term science to describe their views is an attempt to poach the effectiveness of the method of natural science while maintaining a fundamental belief in supernaturalism. It is a category mistake to consider theistic science a form of naturalism. Creation "science" and theistic "science" are attempts (somewhat disingenuous by some) to move have all of the fideist certainty of fundamentalism and literal interpretations of Scripture without having to have the pesky skepticism and fallibilism (IEP) that comes with natural science. It is the viewpoint of many atheists, philosophers, and theologians alike that claiming that theistic science is a natural science is not only bad metaphysics, but is an obvious attempt to craft a pro-creationist doctrine to slip pass by the separation of church and state which is a philosophical prescription in political philosophy arising out of the Enlightenment. The US does not allow the teaching of theology in public science classes.
According to WP:
Methodological naturalism, this second sense of the term "naturalism", seeks to provide a framework of acquiring knowledge that requires scientists to seek explanations of how the world around us functions based on what we can observe, test, replicate and verify. It is a distinct system of thought concerned with a cognitive approach to reality, and is thus a philosophy of knowledge. It is a self-imposed convention of science that attempts to explain and test scientific endeavors, hypotheses, and events with reference to natural causes and events.
It should read "world around us functions based on what we can observe, test, replicate and verify by presuming there are only natural causes". It is a metaphysical necessity of natural science and natural theology that causes, as we understand them, are free of meddling as would be the case with sorcerers, ghosts, goblins, and Greek gods. Christians largely hold that the Christian God doesn't cavort about the earth like Zeus did, using magic, and disguising himself to interact with people. And it is not the claim of natural theology that God cannot do these things, it is the claim that he (or she or it) doesn't do these things.
The philosophical metaphysics of natural science are well articulated. For instance, natural science presupposes a regularity to the universe, affords a special place for induction in reason, and accepts that sometimes the evidence doesn't provide an answer on account of underdetermination. Also, highly influential on natural science is David Hume's views particularly on causality. Natural science embraces the principle of sufficient reason, and and even among natural theologians, who profess faith in God, one just cannot decide a supernatural cause exists even in if the lack of natural explanation is fact. Theistic science specifically attempts to undermine the theory of evolution which is a very durable and more than adequate theory in biology whose scientific controversy ended in the 19th century. It does so by trying to disprove evolution is a naturalistic explanation by engaging in certain details of biology.
The Details of Biology Are Irrelevant
Theistic science muddies the water philosophically by casting doubt on the conclusions of natural science. In increasingly sophisticated attacks using the language biology, mathematics, and chemistry, it marshals details to cast doubt on evolution, which is non-controversial within natural science. But metaphysically (and legally in Kitzmiller), the primary motivation of theistic science is to convince people it is a (superior) form of science leading people back to the supernatural claim of a Designer or Creator. In this way, it not only equivocates on the term 'science' taking people's confusion or ignorance for granted, and not only rejects the supreme presumption that there are no supernatural causes, but goes on to cloak itself by adopting the actual practices of natural scientists (poorly as many critics maintain).
And yet, even if one attempts to use naturalism to discredit certain naturalistic findings, one cannot then arrive at a supernatural conclusion and continue to call one's theory natural science since it natural science excludes supernaturalism as a presumption. This is the metaphysical inconsistency in theistic science which makes it theological and not scientific in the primary sense of the word. It claims that the findings of natural scientists support a supernatural conclusion. Obviously, the logical contradiction is apparent.
This is not happenstance. A number of prominent philosophers of science maintain that theories are laden with metaphysical presumption. Therefore, theistic scientists arrive at different biological conclusions than natural scientists precisely because they philosophically start with presumptions about the viability of supernatural causation. In modern parlance, their theory arrives at different conclusions because scientistic theories (be they creationist or natural with scientistic indicating the superficial practices as distinct from the fundamental metaphysical presumptions) are theory-laden:
In the philosophy of science, observations are said to be "theory-laden" when they are affected by the theoretical presuppositions held by the investigator. The thesis of theory-ladenness is most strongly associated with the late 1950s and early 1960s work of Norwood Russell Hanson, Thomas Kuhn, and Paul Feyerabend, and was probably first put forth (at least implicitly) by Pierre Duhem about 50 years earlier.
Modern philosophers of science have argued that rather successfully (and contributing to the defeat of the programme of the logical positivists) that scientific theories are intimately bound to the nature of psychological observation. In other words, observation sentences fail to be objective, because observers are by definition subjective, and that attempts at objectivity are at best idealized (philosophical) intersubjectivity. I suspect this is less of a problem for Continental philosophers of science, than analytic philosophers who are used to carving the observer out of the theory. But language is normative, conventional, and teleological, if you believe latter Wittgenstein. (Philosophical Investigations is of course open for interpretation, but see language-games and the private language argument for a start.)
Summary of Why ID Isn't Natural Science
So, now let's put ID in the proper philosophical context. ID is a both a philosophical theory and a political agenda (addressed elsewhere, but in the words of the ID folks themselves the Wedge Strategy) that is promulgated almost entirely by theistic scientists (there are outliers, of course). Setting aside the political agenda for replacing natural science with theistic science, stand the metaphysics of the theory itself.
Theistic science and the ID it advocates is theology and NOT natural science because while it pays lip service to methodological naturalism, it is inherently hostile to naturalism by way of the belief of the reality, truth, or adequacy of supernatural causation. It conflates two important theological statements: 'God CAN intervene in the universe because He is all powerful' with 'God DOES intervene in the universe because He is all powerful'. Catholicism, as a prominent example, rejects this (as I understand Catholic doctrine with little effort to master the nuance of the encyclicals or history being non-Catholic).
Intelligent Design is a research methodology, but it is not one of natural science. In fact, it is has been crafted to replace natural science. It may call itself science, wear the lab coat, get degrees in natural science, talk like natural science, and apply to the local public school to "teach the (non-existent) controversy". But it is not natural science, because natural science rejects supernaturalism in causation and has done so in increasingly better language from Thales to Bacon to Carnap. It may efface the Christian God, and even spawn an Islamic and ET version, but the concepts, under the lamp of philosophical analysis, ID can't conceal the clear fingerprints of fundamentalist theology that begs for supernatural forces to run amok through the union of naturalism, materialism, and physicalism that undergird natural science today.
The Dream of Reason by Anthony Gottlieb
Early Greek Sciences: Thales to Aristotle by G.E.R. Lloyd
Greek Science after Aristotle by G.E.R. Lloyd
The Origins of Modern Science by Herbert Butterfield
Husserl and the Sciences by Richard Feist
This is Biology by Ernst Mayr
Causality by Judea Pearl
A Companion to the Philosophy of Science edited by W.H. Newton-Smith
Abusing Science: The Case Against Creationism by Philip Kitcher
Why Intelligent Design Fails: A Scientific Critique of the New Creationism by Young and Edis (with the caveat I only poked around in Google Books, and Amazon still has it on the way).
Kitzmiller v. Dover, Robert T. Pennock, and John F. Haught