AndrewC had a very good answer; however I wanted to add a few things.

When beginning to compare theories it's best to begin by looking at your assumptions. In this case you are assuming that both creation and evolutionary theories are mutually exclusive. The second major assumption is that they have equal probabilities.

Covering the first point, there are creationist theories that do not preclude evolution. There are also evolutionary theories that do not throw out the possibility of initial creation. In other words there is a middle ground between the two which is not accounted for in your application of the Bayes theorem because you are starting from a highly over simplified viewpoint.

Ignoring that, the second issue has to do with assuming that each option has equal probability. This is simply impossible to determine. On the evolutionary side, we have a certain amount of physical evidence which is interpreted to have a certain meaning. This meaning might be correct, it might not be. We've certainly had many instances in history where a scientific "discovery" was made which turned out to be completely wrong as new information surfaced, and we've had many instances where the initial hypothesis has turned out to be as close to "settled" as it gets. However in this particular case, science is still learning about our past: and there are gaps. The gaps don't mean that evolution is any less valid, but it certainly means there are points that need further discovery.

On the creationist side, what "proof" could there possibly be other than the creator coming down and demonstrating in front of a world wide audience how man was formed? Maybe finding a barcode written at an atomic level? Even if either of those happened, it would still be contested. In other words, we have no real way of identifying that which was created versus that which may have "naturally" formed. However, absence of proof is meaningless. Now there are irreducible complexity arguments that, frankly, I'm not even remotely qualified to make an opinion on.

The point is, we can't assume that either option has equal probability initially because there are in fact more than two options and those grey areas are not mutually exclusive. We also can't assume the probabilities are the same because there is a tremendous amount we don't know; which is further ambiguated by the extremes of both sides attempting to narrow the arguments of their opponents.

1. Is this proof correct?
   I'd have to say no as the comparison you are attempting to make is starting from false assumptions.

2. Does this solve the problem of affirming the consequent not only in the case of evolution, but also when dealing with other theories/hypothesis? Again, no. If "other theories" include starting from false assumptions then Bayes won't help you.

AndrewC had a very good answer; however I wanted to add a few things.

When beginning to compare theories it's best to begin by looking at your assumptions. In this case you are assuming that both creation and evolutionary theories are mutually exclusive. The second major assumption is that they have equal probabilities.

Covering the first point, there are creationist theories that do not preclude evolution. There are also evolutionary theories that do not throw out the possibility of initial creation. In other words there is a middle ground between the two which is not accounted for in your application of the Bayes theorem because you are starting from a highly over simplified viewpoint.

Ignoring that, the second issue has to do with assuming that each option has equal probability. This is simply impossible to determine. On the evolutionary side, we have a certain amount of physical evidence which is interpreted to have a certain meaning. This meaning might be correct, it might not be. We've certainly had many instances in history where a scientific "discovery" was made which turned out to be completely wrong as new information surfaced, and we've had many instances where the initial hypothesis has turned out to be as close to "settled" as it gets. However in this particular case, science is still learning about our past: and there are gaps. The gaps don't mean that evolution is any less valid, but it certainly means there are points that need further discovery.

On the creationist side, what "proof" could there possibly be other than the creator coming down and demonstrating in front of a world wide audience how man was formed? Maybe finding a barcode written at an atomic level? Even if either of those happened, it would still be contested. In other words, we have no real way of identifying that which was created versus that which may have "naturally" formed. However, absence of proof is meaningless. Now there are irreducible complexity arguments that, frankly, I'm not even remotely qualified to make an opinion on.

What is the likelihood that evolution is the sole means by which life arose on Earth? Is it still solely "evolution" if it was helped by some external source - even something as innocuous as an asteroid hitting the planet? What if that asteroid was hurled by a super intelligent race (or being) which knew it would be a catalyst to start life? Where do we even draw the line? There are just too many questions here.

The point is, we can't assume that either option has equal probability initially because there are in fact more than two options and those grey areas are not mutually exclusive. We also can't assume the probabilities are the same because there is a tremendous amount we don't know; which is further ambiguated by the extremes of both sides attempting to narrow the arguments of their opponents.

1. Is this proof correct?

I'd have to say no as the comparison you are attempting to make is starting from false assumptions.

2. Does this solve the problem of affirming the consequent not only in the case of evolution, but also when dealing with other theories/hypothesis?

Again, no. If "other theories" include starting from false assumptions then Bayes won't help you. Honestly we may as well substitute "my big toe" for 'E' and a "can of spam" for 'C' and be able to derive the exact same amount of meaning from the equation.

AndrewC had a very good answer; however I wanted to add a few things.

When beginning to compare theories it's best to begin by looking at your assumptions. In this case you are assuming that both creation and evolutionary theories are mutually exclusive. The second major assumption is that they have equal probabilities.

Covering the first point, there are creationist theories that do not preclude evolution. There are also evolutionary theories that do not throw out the possibility of initial creation. In other words there is a middle ground between the two which is not accounted for in your application of the Bayes theorem because you are starting from a highly over simplified viewpoint.

Ignoring that, the second issue has to do with assuming that each option has equal probability. This is simply impossible to determine. On the evolutionary side, we have a certain amount of physical evidence which is interpreted to have a certain meaning. This meaning might be correct, it might not be. We've certainly had many instances in history where a scientific "discovery" was made which turned out to be completely wrong as new information surfaced, and we've had many instances where the initial hypothesis has turned out to be as close to "settled" as it gets. However in this particular case, science is still learning about our past: and there are gaps. The gaps don't mean that evolution is any less valid, but it certainly means there are points that need further discovery.

On the creationist side, what "proof" could there possibly be other than the creator coming down and demonstrating in front of a world wide audience how man was formed? Maybe finding a barcode written at an atomic level? Even if either of those happened, it would still be contested. In other words, we have no real way of identifying that which was created versus that which may have "naturally" formed. However, absence of proof is meaningless.

The point is, we can't assume that either option has equal probability initially because there are in fact more than two options and those grey areas are not mutually exclusive. We also can't assume the probabilities are the same because there is a tremendous amount we don't know; which is further ambiguated by the extremes of both sides attempting to narrow the arguments of their opponents.

1. Is this proof correct?
   I'd have to say no as it does not answer the question you are attempting to form.

2. Does this solve the problem of affirming the consequent not only in the case of evolution, but also when dealing with other theories/hypothesis? Again no. The comparison you are attempting to make doesn't fit this theorem and others of a similar nature are likely to not fit as well.

AndrewC had a very good answer; however I wanted to add a few things.

When beginning to compare theories it's best to begin by looking at your assumptions. In this case you are assuming that both creation and evolutionary theories are mutually exclusive. The second major assumption is that they have equal probabilities.

Covering the first point, there are creationist theories that do not preclude evolution. There are also evolutionary theories that do not throw out the possibility of initial creation. In other words there is a middle ground between the two which is not accounted for in your application of the Bayes theorem because you are starting from a highly over simplified viewpoint.

Ignoring that, the second issue has to do with assuming that each option has equal probability. This is simply impossible to determine. On the evolutionary side, we have a certain amount of physical evidence which is interpreted to have a certain meaning. This meaning might be correct, it might not be. We've certainly had many instances in history where a scientific "discovery" was made which turned out to be completely wrong as new information surfaced, and we've had many instances where the initial hypothesis has turned out to be as close to "settled" as it gets. However in this particular case, science is still learning about our past: and there are gaps. The gaps don't mean that evolution is any less valid, but it certainly means there are points that need further discovery.

On the creationist side, what "proof" could there possibly be other than the creator coming down and demonstrating in front of a world wide audience how man was formed? Maybe finding a barcode written at an atomic level? Even if either of those happened, it would still be contested. In other words, we have no real way of identifying that which was created versus that which may have "naturally" formed. However, absence of proof is meaningless. Now there are irreducible complexity arguments that, frankly, I'm not even remotely qualified to make an opinion on.

The point is, we can't assume that either option has equal probability initially because there are in fact more than two options and those grey areas are not mutually exclusive. We also can't assume the probabilities are the same because there is a tremendous amount we don't know; which is further ambiguated by the extremes of both sides attempting to narrow the arguments of their opponents.

1. Is this proof correct?
   I'd have to say no as the comparison you are attempting to make is starting from false assumptions.

2. Does this solve the problem of affirming the consequent not only in the case of evolution, but also when dealing with other theories/hypothesis? Again, no. If "other theories" include starting from false assumptions then Bayes won't help you.