Who throws the dice for you?

[Heywood]

The existence of such a scientific explanation would make either premise 1 or 2 or both premise 1 and 2 false. If you accept 1 and 2 as true it precludes you from saying there is scientific explanation that we have yet to discover.

I don't think this is the case at all. We understand that any "truth"(*) discovered by science is always provisional in nature, and always subject to revision by later discoveries.

(*) The whole notion of "truth" in this concept is a bit nebulous in the first place. "Truth" is in the wheelhouse of philosophers, not scientists.

If you provisionally accept premise 1 and 2 as being true then it follows that premise 5 is provisionally true. If your atheism depends on a provision that something you think is true....might not be true.....isn't that atheism of the gaps?

[Jackalope]

I don't think this is the case at all. We understand that any "truth"(*) discovered by science is always provisional in nature, and always subject to revision by later discoveries.

(*) The whole notion of "truth" in this concept is a bit nebulous in the first place. "Truth" is in the wheelhouse of philosophers, not scientists.

If you provisionally accept premise 1 and 2 as being true then it follows that premise 5 is provisionally true. If your atheism depends on a provision that something you think is true....might not be true.....isn't that atheism of the gaps?

I suppose that depends on what you mean by "true". As I said, I am uncomfortable using that particular word with respect to science, as "truth" is not something science is concerned with. I think it's conflating two subtly different concepts. I set the epistemological bar pretty high for what I'm willing to call "truth" or "knowledge". I don't think we're on the same page here at all.

Also, given other's reasonable analysis of your premeses, I don't think that we can conclusively say that 5 logically follows. For some values of "true", perhaps.

Incidentally, I don't believe that you have any idea what my position with respect to atheism even is, since as far as I can remember, I haven't stated my position recently - and I can definitely say that it's evolved since I've been here. The closest I can come to describing what my position is would be "ignostic apatheism".

P.S. it's probably not obvious but I'm actually more interested in the meta-issues with such arguments than the arguments themselves.

[Cato]

If you provisionally accept premise 1 and 2 as being true then it follows that premise 5 is provisionally true. If your atheism depends on a provision that something you think is true....might not be true.....isn't that atheism of the gaps?

5 does not follow 1 and 2. I clearly demonstrated why. Are you now ignoring my argument?

[Angrboda]

Premise 4. If our reality is dependent on a supernatural element, then we should observe events which cannot be explained scientifically.
Premise 5. We observe events for which it is virtually impossible to explain scientifically.
Conclusion: Therefore our reality is dependent on a supernatural element.

Where is the fallacy in this argument?

This is a classic example of affirming the consequent, therefore the conclusion doesn't follow. And the reason you've retreated to supernatural causes is because supernatural is defined as the opposite of 'explained scientifically'; if it isn't shown to have a natural, scientific cause, then it's supernatural. You've picked terms which turn your "argument" into a trivial tautology based on the definition of the terms. (You've chosen an excluded middle which is true by definition. Supernatural in this case simply means "not yet scientifically explained," and so it can be substituted for supernatural in your conclusion, yielding the conclusion that our reality is dependent on things that have not yet been scientifically explained. Possibly so, and possibly not. Either way, it's hardly a stunning result.)

Affirming the consequent, sometimes called converse error or fallacy of the converse, is a formal fallacy of inferring the converse from the original statement. The corresponding argument has the general form:

• If P, then Q.
  Q.
  Therefore, P.

An argument of this form is invalid, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).

[Cato]

This is a classic example of affirming the consequent, therefore the conclusion doesn't follow. And the reason you've retreated to supernatural causes is because supernatural is defined as the opposite of 'explained scientifically'; if it isn't shown to have a natural, scientific cause, then it's supernatural. You've picked terms which turn your "argument" into a trivial tautology based on the definition of the terms. (You've chosen an excluded middle which is true by definition. Supernatural in this case simply means "not yet scientifically explained," and so it can be substituted for supernatural in your conclusion, yielding the conclusion that our reality is dependent on things that have not yet been scientifically explained. Possibly so, and possibly not. Either way, it's hardly a stunning result.)

Rasetsu,
At the risk of derailing the conversation, maybe you can help me learn something. I'm struggling to understand the distinction between affirming the consequent and begging the question. The definitions and examples I have sought out are quite similar. Is there a distinction in use based on formal or informal logic? Or am I missing something fundamental?

[Angrboda]

Rasetsu,
At the risk of derailing the conversation, maybe you can help me learn something. I'm struggling to understand the distinction between affirming the consequent and begging the question. The definitions and examples I have sought out are quite similar. Is there a distinction in use based on formal or informal logic? Or am I missing something fundamental?

I'll try to help, but the two seem so distinct to me that I don't know what would untangle the two for you. I'll start by quoting Nizkor's description of begging the question as a preface, so as to contrast it with affirming the consequent.

Description of Begging the Question

Begging the Question is a fallacy in which the premises include the claim that the conclusion is true or (directly or indirectly) assume that the conclusion is true. This sort of "reasoning" typically has the following form.

• Premises in which the truth of the conclusion is claimed or the truth of the conclusion is assumed (either directly or indirectly).
  Claim C (the conclusion) is true.

This sort of "reasoning" is fallacious because simply assuming that the conclusion is true (directly or indirectly) in the premises does not constitute evidence for that conclusion. Obviously, simply assuming a claim is true does not serve as evidence for that claim. This is especially clear in particularly blatant cases: "X is true. The evidence for this claim is that X is true."

One thing to note about begging the question is that it is not a formal fallacy, which is to say that the logical form isn't necessarily invalid, the structure of the logic may be acceptable, but it still begs the question because there is a circular dependence between the conclusion, and something that was assumed or claimed in one of the premises (or implied, but not explicitly stated). Thus it isn't a structural property per se. This circularity is what makes it fallacious, as, if the conclusion, or the substance of the conclusion is already in one of the premises, one can throw away all the other premises without destroying the argument, as the argument consists solely of whatever was (illicitly) claimed in the premise.

On to affirming the consequent. Affirming the consequent is a formal fallacy, which means that the structure of the syllogism is actually invalid. The structure is as noted before:

• 1. If P, then Q;
  2. Q;
  Conclusion: Therefore P

An example of such would be the following:

• 1. If I purchase this car, I obtain title to it;
  2. I have obtained title to this car;
  Conclusion: I purchased this car.

In this case, I might have purchased the car to obtain the title, but there are other ways that I might have obtained title to the car, such as by a gift or an inheritance. If I purchased the car, it is necessarily the case that I obtain title to the car; however, it isn't necessarily the case that if I obtained title to the car, I did so by purchasing it. The entailment flows from P to Q, but not the other way around (from Q to P). In order for P to be implied by Q, "If Q, then P" — the converse — would have to be true, but that premise isn't anywhere stated ("Q --> P").

It may help to look at why a person might make this mistake. Basically, "If P, then Q" states that anytime P is true, it entails that Q will also be true, or in symbolic form, "P --> Q". It can be noted that if Q is not true, then P cannot be true, because if P were true, then Q could not be false. This is stated as "If not Q, not P", or stated symbolically, "not-Q --> not-P". Q being false implies that P is also false. This is known as the contrapositive of "P --> Q", and it does follow logically because the original entailment and it's contrapositive have equivalent truth tables. However, it's easy to mistake that the contrapositive is valid, "not-Q --> not-P", with the converse of the original, which is "Q --> P". The converse sounds similar to the contrapositive, but its truth isn't guaranteed by the original premise, "P --> Q", whereas the truth of the contrapositive is guaranteed by the truth of the original. It's possible this similarity is what confuses people.

Well, let me know if this has been helpful or if you have further questions. I didn't explain begging the question much. I'll think on it more. Hope it helps.

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ETA:
It's worth noting that in an example syllogism given by Heywood earlier, the converse was implied by the way it was stated.

• 1. Unexplained events occur, only if God exists;
  2. Unexplained events occur;
  Therefore: God exists.

The structure of this syllogism is:

• 1. Q, only if P;
  2. Q;
  Therefore: P.

or less clumsily:

• 1. If and only if P, Q; ("If and only if God exists, there will be unexplained events;")
  2. Q ("There are unexplained events;")
  Therefore: P. ("God exists.")

This seems superficially similar to the affirming the consequent example, except that the first premise, "If and only if P, then Q" actually implies both "if P, then Q" and "if Q, then P" in the same premise because of the "if and only if" (symbolically P <--> Q; meaning P --> Q and Q --> P). So both the premise P --> Q and its converse (Q --> P) are included in that one premise. [There were people claiming that he was begging the question, but I think most of those complaints were a result of people not understanding exactly what begging the question means. Ben suggested something else, but I never got clarity on his argument. The main fault I saw was that premise 1 was not obviously true, and therefore the syllogism was unsound.]

[Heywood]

The conclusion of God invokes the supernatural and in your argument God is only true if the supernatural is assumed. This is begging the question.

I don't have to accept 5. The alternative that I proposed is that there is a scientific explanation that we have yet to discover. As an illustration: God did not make the solar system work until Newton had an opportunity to ponder skydiving fruit.

The problem with this argument is that if there is a scientific explanation that we have yet to discover, then premise 1 or 2 or both is false. You cannot invoke this argument if you accept premise 1 and 2 as true.

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Premise 4. If our reality is dependent on a supernatural element, then we should observe events which cannot be explained scientifically.
Premise 5. We observe events for which it is virtually impossible to explain scientifically.
Conclusion: Therefore our reality is dependent on a supernatural element.

Where is the fallacy in this argument?

This is a classic example of affirming the consequent, therefore the conclusion doesn't follow.

I agree with your criticism that the affirming the consequent fallacy exist and therefore the argument is invalid. I got sloppy.