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I won't argue. Mathematics could be defined as a science if you define science quite generally.

I also don't think Creationism is unscientific. I just think it is bad science.

You cannot demonstrate that faith in God is less rational than the belief that the symmetric axiom of algebra is true (i.e. reflective of the way the real world operates). You also cannot demonstrate that the "kind" of faith is different.

No I can't but that isn't what makes the assumptions different. My point is that faith in these basic axioms, and faith in several philosophical axioms (such as I exist, I am not just a brain in a jar, the universe has patterns that can be observed, etc) is a necessary prerequisite to logic. Without them you simply cannot have logical reasoning. Anyone who tries to "do" science is going to need to assume that kind of thing.

But assumption of an intelligent designer is not one of the basic assumptions needed to reason logically. Just as the assumption of aliens, the assumption that my next door neighbour is a vampire, or an assumption of the tooth fairy is necessary to reason logically.

Evolutionists do not have any consensus among them about the fundamental essential axioms that are needed for the theory to be true. For example, is time constant? Have the basic forces (gravity, elctro-magnetic, strong and weak) always existed in their present form? Are the laws of physics constant in all places in the universe and at all times in history? If so, does that necessitate that matter has always existed only in its present form?

Replace "evolutionists" with "scientists" because your criticism above is levelled at all scientific fields. All sciences assume certain constants extend back in time. Yes perhap gravity has not always been constant, but as far as we know nothing can change the gravitational constant, in fact it is likely to cause problems with planet orbits if it had been significantly different in the past.

However, the idea that all living creatures have a single common ancestor defies logic on the face of it.

That is irrelevant considering that the fossil record is clear evidence that common descent has occured. The pattern of the fossil record is compatible with common descent against the odds - high odds. If we were to create a random fossil record every second for a billion years the chances are that not one of them would have a patter that supports common descent. Yet the fossil record on Earth does. So many conveniences, a complete lack of fossil cases that would immediately destroy the idea of common descent (where are the mammals in the cambrian? etc)

Common ancestry would imply that the genetic information (diversity) existed in simpler life forms in ancient history.

No it wouldn't. Common descent simply implies that species today are derived from earlier species in the past. Common Descent was accepted by science before genetics was even discovered. And the theory of evolution as it stands today does not require genetic diversity of today's species to exist in past species. Populations can increase in diversity one generation to the next.

Evolution proposes that life forms were both simpler and less diverse - an idea that is self-contradictory.

Well that is what the fossil record shows as well - simpler and less diverse.

" I also don't think Creationism is unscientific. I just think it is bad science."

At least you are expressing it in a more logical way here.

"But assumption of an intelligent designer is not one of the basic assumptions needed to reason logically."

You are still confusing the need for axiomatic faith with the particular axioms. You do not need to believe in the algebraic axiom of symmetric equality in order to think logically, but you do need to define what your axioms are in order to begin a logical framework.

Evolutionists have not done this to my knowledge. I have asked for it repeatedly and gotten nothing. It is unfair to engage in a debate without defining the terms.

"All sciences assume certain constants extend back in time. Yes perhap gravity has not always been constant, but as far as we know nothing can change the gravitational constant, in fact it is likely to cause problems with planet orbits if it had been significantly different in the past."

Whether it causes problems with planetary orbits is irrelevant (unless you mean to say that planetary orbits somehow prove that gravity has always been constant). The issue is what bearing it has on evolutionary theory since billions of years are so essential to this theory.

"The pattern of the fossil record is compatible with common descent against the odds - high odds."

Age measurements amount to massive finger pointing and circular reasoning. If a new archaeological discovery is made that does not fit within the parameters of evolutionary theory, the theory evolves (which is not unscientific in and of itself). The fossil record is interpreted by evolutionary theory rather than being the foundation of it. At what time in history was there less diversity of living things than today? And how do you know? What non-living time indicators exist that correspond to your historical arrangement of the complexity of living things? (We need to know this because if you are using other living things for time indicators you are engaging circular reasoning by referencing your own theory for a time indicator.) How do you know these nonliving things are the age you claim (without referencing your own theory)? What assumptions (either axioms or logical extensions of them) are made when estimating the geological changes that have occurred during Earth's history? How would possible cataclysmic events effect your model of predicted historical patterns and events? How are your predictions more reliable than the ability to predict future weather patterns?

The lack of a logical connection between more fundamental axioms implies that evolutionary theory itself is axiomatic. I cannot argue against a premise when there is none. This is what evolutionist hypocritically accuse creationists of.

We know for certain that time does not flow at the same rate when measured at different velocities. So when you claim the earth or universe is a certain age (always stated as fact) where is the measurement valid? What parts of the universe are older or younger? How much variation is there? .02%? 100,000%? If you admit that the universe did not always exist in its present form, what effect did the formation have on the time indicators we now use to measure the age of the universe and earth?

"But assumption of an intelligent designer is not one of the basic assumptions needed to reason logically."

Two things:

1) just for clarification, the assumption of an intelligent designer is a feature of creationism, not intelligent design. In intelligent design, it is deduced from information theory.
2) I have trouble seeing, though, how the assumption of an intelligent designer is not needed to reason logically. For instance:

If the world is simply a collection of particles, and we are the result of unguided but deterministic (or even non-deterministic) sequence of events, it is not logical to trust our conclusions, as they are only guided by physics and not by logic.

To put it another way, if I say "you only believe he is innocent because you are his mother", I am saying that your thoughts are unreasonable, that there is an outside force causing you to believe something that is contrary to fact, and that you are bull-headed in your position only on the basis of external forces beyond your control. However, if I say "you believe he is innocent because of the facts of the case" I am saying that you have made a logical deduction and have used reason to do so. In a purely materialistic world, however, the former is all one has available to them. Therefore, the entire ability to reason is unfounded without the assumption of a metaphysical reality beyond materialism.

"That is irrelevant considering that the fossil record is clear evidence that common descent has occured. The pattern of the fossil record is compatible with common descent against the odds - high odds."

Was the pattern of common descent determined before or after looking at the fossil record? I agree that the fossil record is highly patterned, but that does not imply common descent. In fact, the ordering of the fossil record makes implying descent from it very difficult. We have found living species of plants and animals that were missing from the fossil record for tens and even a hundred million years. Had we not found them alive, we would have assumed on fossil evidence that they had gone extinct.

While I agree with the heavy ordering of the fossil record, I don't think it agrees with an evolutionary explanation, because it has disparity preceding diversity in the cambrian, while the theory of evolution predicted the opposite. Likewise what we find in the Cambrian are not simple creatures. Some of these creatures have very complex systems and mechanisms surpassing what we find today.

The only reason that the order of the fossil record matches the order of evolution is that the order of evolution was deduced from the fossil record. Had the fossil record had birds before reptiles, evolution would have no problem explaining that I'm sure. My point isn't that evolutionists are pulling a fast one, but rather that evolution doesn't predict the specific ordering of the fossil record. If the ordering was due to a physical process you may very well get the same ordering (for example, the buyancy of carcasses -- I know this is true for the general ordering but not aware of the specifics -- but this is one example).

"Well that is what the fossil record shows as well - simpler and less diverse."

Not really. Some of the cambrian fossils are remarkably advanced. Likewise, as far as diversity, there were more phyla present in the Cambrian than exist today.