An argument of the form:

1) A implies B
2) B implies A

is a perfectly valid proof of the logical equivalence of the statements A and B. And proving logical equivalence is not a circular argument, it's a proof of logical equivalence. We do this all the time in math (A if and only if B).

Circular reasoning uses the conclusion as a premise in an argument. It's not about "more steps" but about the error of taking the thing you want to prove and using it as justification that the thing you want to prove is true.

In order for you to understand this better, it would be useful if you could explicitly identify the premises and the conclusions of the argument you think I'm making.

Three mutually inconsistent claims, it seems to me. (Not that I see that as a problem - I think the Christian should just reject Q. We can know God's intent at least as far as 'it's for the best').

If you argue "I believe A because B is true, I believe B because C is true, and I believe C because A is true", you have made a circular argument.

The argument I set out above about God:

"The argument that morality is dependent on intent, we can't know God's intent, but God by definition must be good."

is circular:

A requires B.
We cannot know if C has B.
C is inherently A.

Aaron, I can play this same game with Hitler.

Hitler is good.

Everything Hitler does is inherently good.

Your contention that Hitler killed 6 million Jews in the Holocaust is a misreading of the texts. Do you have any textual interpretations that show that? Show your work.

I have nothing to prove, because everything Hitler does is inherently good.

What is it to "murder" and is this what Hitler did?

The neo-Nazis ought to pick up your argument. It would get them out of a lot of debates.

Take the goddamned Hebrew Bible and defend your God. Or stop claiming that the ******* described therein is good. Your choice.

It's a good thing you're not wasteful. Oh, wait...

I hope it's plain to you that these two argument structures are not identical in the slightest bit.

I only really know Catholic stuff, it seemed like something that would be universal.

I reject (1). End of debate.

Whew... that was tough.

?

!

Maybe you think by 'knowing the mind of god' I mean 'knowing that god is good' or 'knowing that god dislikes malice' or something? It's about imputing a specific motive or goal to god without theological justification, or imagining that god is 'OK with it this one time' when about to sin.

This is cool for Protestants?

This is very confusing. I do not see the connection between "imputing a specific motive or goal to God without theological justification" and any of the following statements:

1) hopes for salvation without doing anything to deserve it
2) [hopes] for pardon of his sins without repenting of them
3) hoping to obtain by one's natural powers, unaided, what is definitely supernatural
4) a person might look to have his sins forgiven without adequate penance (this, likewise, if it were based on a seriously entertained conviction)
5) whilst they continue to lead a life of sin, are as confident of a happy issue as if they had not lost their baptismal innocence.

I *DO* see "imagining that god is 'OK with it this one time' when about to sin" as being related to these concepts. But that's not something that was brought up in the original context of the discussion. In particular, it's a claim about a person's understanding of God, and not having anything to do with God's behaviors.

Below is a larger requoted section from the conversation. The bolded in lawdude's post is the specific quote that you were responding to.

But all of those impute specific goals to god...

Edit: Maybe there is an ambiguity to 'Hope' here. I'm of the impression it's not simply the act of wishing it were so.

It's worth taking the time to take a closer look at this for the benefit of understanding how logic works a little bit better.

1) This is not an argument.

http://en.wikipedia.org/wiki/Argument

Primarily, you need to recognize that a (deductive) argument has premises and a conclusion. As presented, neither of these are present. You do have a series of implications:

1) If B is true, then A is true.
2) If C is true, then B is true.
3) If A is true, then C is true.

As argued, this proves the logical equivalence of statements A, B, and C. If any of these are true, then they are all true. Similarly, if any of these are false, they are all false (use contrapositives everywhere). Presumably, you are intending to put a hidden premise of "A is true", "B is true", or "C is true" and a (hidden) conclusion of "A is true", "B is true", or "C is true."

2) Circular arguments

http://en.wikipedia.org/wiki/Circular_reasoning

http://ksuweb.kennesaw.edu/~shagin/l...c-circular.htm

http://www.numeraire.com/download/Wh...rReasoning.pdf

All of these definitions coincide with the characterization I gave:

If we were to inject the hidden premises and conclusion as described above, you would then have a circular argument. You may not be assuming precisely the thing you are trying to prove (for example, using the hidden assumption "A is true" and concluding "C is true") but you are using something that is equivalent to it (ie, repeating the statement in different terms).

For example:

To prove: A is true.
1) If B is true, then A is true.
2) If C is true, then B is true.
3) If A is true, then C is true.
4) One of A, B, or C is true.
5) Therefore, all of A, B, and C is true. (In particular, A is true.)

Step 4 is the step that is the circular reasoning. It is very explicitly asserting the truth of the thing that is to be proven (or something that is logically equivalent to it).

They do... but in ways completely unrelated to the original context of the conversation.

We've got (1) salvation, (2) forgiveness, (3) attainment of the supernatural, (4) forgiveness, (5) forgiveness (for perpetual sinfulness). But none of these have to do with lawdude's original comment and your response:

It seems that lawdude is referring to passing moral judgment on God by imputing specific motives to the specific behaviors of commanding the Hebrews to kill other people. This is the connection that I do not understand.

Perhaps there is some ambiguity "Hope" is more than "wishing" in that it includes a level of expectation or anticipation.

http://www.catholicreference.net/index.cfm?id=33993

If you want a longer read:

http://www.newadvent.org/cathen/07465b.htm

I'm not sure if this resolves anything.

Aaron, the problem is (1) is the axiom. God is definitionally good. Hitler is definitionally good. Both are unsupported assumptions. If you can assume God is always good you can assume anyone is, even Hitler

The rest of your argument is built on sand, because all I have to do is assume the same thing you do and I can justify anything as moral.

Well I could just be wrong. But googling the problem, I find message boards where Catholics (apparently) characterise presumption of forgiveness as sinful by virtue of the fact that it constitutes presumption to know the mind of god (comment by 'Ender').

I'm familiar with that interpretation (as in, if it's wrong, I'm wrong) so I'm just extrapolating from that.

But that's interesting. Suppose a member of your congregation went around constantly ascribing various mundane events to divine intervention, aimed at producing some particular end. Is that just perfectly kosher?

If you claiming that (1)-(3) cannot be an argument, you are definitely wrong. These are fairly standard conditional statements, and conditional statements have a truth-value. Since having a truth-value is all that is required of a statement in order for it to qualify as either a premise or conclusion, this can be interpreted as an argument. Perhaps you are assuming that conditional statements don't have a truth-value? Because that is false.

Anyway, this should be really obvious, so obvious that I must not understand what you are saying here.

A couple of other points. It is not necessary to use the "is true" locution in logic. There is no difference between "p" and "p is true." But to make my point clear, here is how we would understand (1)

(1) "If B is true, then A is true" is true.

and so on for the other statements.

I'll also note that as presented, (1), (2), and (3) do not show the logical equivalence of A, B, and C. In fact, it isn't even a valid argument. Here's an example to show this.

(4) If it is raining is true, then the streets are wet is true.
(5) If there clouds in the sky is true, then it is raining is true.
(6) Therefore, if the streets are wet is true, then there are clouds in the sky is true.

Obviously (6) is not an implication of (4) and (5).

Perhaps you meant to say this:

7) B is true if and only if A is true.
8) C is true if and only if B is true.
9) Therefore, A is true if and only if C is true.

Now it is a valid, and still not circular, and still can be interpreted as an argument. It has shown A is true whenever C is true and A is false whenever C is false.

I would not consider this a circular argument. Assuming your conclusion is "A," then a circular argument is one where one of your premises is "A." Since that is not a premise in this argument, it is not circular argument. Your parenthetical remark shows where you are going wrong. One of the goals of deductive arguments is can be to show that two different statements are logically equivalent. That doesn't mean that any such argument is a circular argument.

That's totally my fault on the sloppy wording. And that's what I get for posting while tired. I was treating "I believe" as meaning that the statement given was an assumption. I'll admit to not being entirely sure whether "I believe" actually carries content in the structure of the argument. So the statement "I believe X" simply means "X." So that which was presented was merely three assumptions (akin to the three distinct claims in the thing that lawdude is calling a circular argument).

As far as the "is true" goes, I took it out, but then put it back in to try to be more consistent with lawdude's phrasing.

I do have to disagree with you that the following is not sufficient for logical equivalence:

1) A implies B
2) B implies C
3) C implies A

If 1, 2, 3 are true, then A, B, and C are all logically equivalent. If one is true, they are all true. If one is false, they are all false. But I can see that you're treating 6 above as a conclusion, so that could be the source of the confusion.

There might be something distinctly mathematical here. We have tons of proofs where we show various statements are logically equivalent. I suspect you don't do this as much in philosophy. And the conclusion is just the logical equivalence, and we don't care so much about the truth value of any of the statements. It's only important for us to know that it's all the same.

In the logic of a proof (that isn't a trivial exercise), you wouldn't ever be assuming something that you already know is logically equivalent to the thing you were trying to prove. It's just silly.

Prove: A implies B
1) A
2) B (by theorem: A iff B)

Maybe it reads differently in philosophical contexts.

That's fine with me. I never said you have to accept the proposition that God is good. And in fact, to "prove" that God is good under the normal theological constructs is impossible because to bring in the notion of "good" as something distinct from "God" is an error.

Fair enough. I went back and read lawdude's post and I suspect my confusion comes from a difference in how we convert his argument example into syllogistic form.

Well, I'm not sure we disagree. Your original interpretation of lawdude's example as "If A is true, then B is true," would most commonly be interpreted as a material implication, i.e as "A ⊃ B." Under this interpretation, A is not logically equivalent to B. However, you seem to be interpreting it as "A ≡ B," in which case you are correct that A is logically equivalent to C.

This all sounds correct and similar to philosophy. I thought you were arguing that (1)-(3) were circular. Anyway, I have a fairly literal view of a circular argument. I would only say that an argument is a circular argument if the exact conclusion is a premise in the argument or used as a premise in an argument justifying one of the premises. So, I agree with you that your example is not a circular argument:

3) A ≡ B
4) B
5) ∴ A

A is not a premise in the argument. I was confused by this:

I would not consider this a circular argument as stated. The conclusion is

(6) A is true.

and this is the same as any of (1)-(5). In fact, it isn't even logically equivalent to any of (1)-(5).

As for lawdude's original example:
Here's how I would interpret it:

10) B ⊃ A.
11) B
12) ∴ A

13) C ⊃ B
14) C
15) ∴ B

16) A ⊃ C
17) A
18) ∴ C

Here I would agree with him that while all three of these arguments taken in isolation are completely unobjectionable, taken together they constitute circular reasoning.

For instance, let's say you want to prove C. If you present as your argument (16)-(18), then the natural response will be to ask for a proof of A. We would then prove A using (10)-(12). If asked for a proof of B, we would then use (13)-(15). But that is illegitimate. Since (14) simply asserts the original conclusion, we are using our conclusion as a premise.

Ahhh... I'm not yet saying that A is logically equivalent to B. I'm saying that after you have all of the implications (A implies B) and (B implies C) and (C implies A) that you have shown logical equivalence of all the statements. As I re-read the conversation, I think I'm starting to see what's going on.

In the way that I try to teach students to write mathematical proofs, I try to instill in them the idea that the argument is what happens in between the true statements, and that the argument is where all of the interesting stuff happens.

----

To prove: Given A, prove C.

Proof: Assume A.

1) Argue that A implies B.

You now know B is true.

2) Argue that B implies C.

You now know that C is true. QED.

----

But for you, this would read something like:

1) A
2) A implies B
3) B implies C
4) Therefore, C.

Yes, I agree that this formulation leads to circular reasoning. To go back to my original fatigue-induced post and to clean it up (more for me than anyone else):

I see this as three statements which are independently proven (or assumed to be true).

1) Argue (assume) that B implies A
2) Argue (assume) that C implies B
3) Argue (assume) that A implies C

The consequence of having shown all three of these results is that A, B, and C are logically equivalent. Putting this in the same language as above:

To prove: A iff B iff C.

Proof: Assume B.

1) Argue that B implies A.

Assume C.

2) Argue that C implies B.

Assume A.

3) Argue that A implies C.

You now know that A iff B iff C. QED.

[We do this often enough in math that we've even got an almost universal abbreviation for it. TFAE (the following are equivalent): A, B, C.]

And in the context of whether this is a circular argument, there is no actual conclusion that A, B, or C is true. And this would be the type of thing that lawdude needs for this to be a circular argument. You would have to assume something that is shown to be equivalent to the thing you're trying to prove.

It depends on what is being said whether I would say it's a "sin" (a violation of some moral principle of God) or just an "error" (a misunderstanding of the situation). Or sometimes, that person might actually be right.

But I think that people who say that sort of thing aren't clear about the theological implications. To claim that a certain event is God acting is to assert something about God (edit: beyond that which has already been revealed). This essentially raises one up to the level of being a prophet for God. If God actually had nothing to do with it, then it's a sin. If God had something to do with it, but the interpretation of the event is wrong, then I would just call it an error (unless it's just grossly wrong, then it's like a false teaching, which is again a sin). And if the person is speaking truthfully about God's action, then it's simply truth.

The thing that people tend not to realize is that the responsibility to God when you are a prophet is significantly "higher" than that of just an average follower. You are given a higher level of responsibility, and so you are held to a higher standard of accountability. I don't think people really want that, and so they probably should not declare God's intentions on trivial matters.

(The same applies to statements like "God told me to tell you..." Do you really want to be in a position where you stand before God and he says, "I never said that"? So if you're going to say stuff like that, you'd better be very, very sure about it. Edit: And this is why I have such a hard time conceptualizing how I would respond if I believed that God told me to do such and such, especially when such and such is a bizarre statement. The question asks me to abandon or skip the entire assessment of the statement, which is an integral part of the process.)

I am not going to rag on you too much for this, because I really do think that we've brought out the crux of our disagreement and I actually appreciate it when you are clear and not vague (as you sometimes can be).

But the problem with this is it is basically like the people who oppose gay marriage because they say that marriage is definitionally between a man and a woman and gay marriage would change the definition.

What they want to do is the same thing you want to do-- avoid consequentialist analysis. They want to say that gay marriage should be prohibited even if it could be shown that allowing it would do no harm, because gay marriage simply is not marriage and can never be marriage.

The problem with this, in my mind, is that you are basically using language to do something that language cannot do. Language cannot fix the meaning of an underlying concept. It can only label it.

In other words, it doesn't matter if you, Aaron W. (and again, I am not REALLY bagging on you here, because your position is taken by LOTS of reasonable religious people), define God as good, that doesn't mean that God has to be good. Because God is just a word and a different group of people can argue just as vehemently that their definition of God is different, and since "God" is just a word, there's no way to say that one group is right and one group is wrong. Just like just because Pat Robertson may believe that the concept of "marriage" can only, definitionally include opposite-sex unions does not mean that a same-sex couple who participated in a wedding ceremony in Boston isn't married.

Saying "the definition of God is that God must be good" is a meaningless, unwarranted bit of language-twisting. And nonbelievers-- and indeed many believers-- have different definitions of God. So to have a conversation, you have to get to consequences, just like you have to get to consequences in the marriage debate. A person who thinks that gays can't be married and a gay married couple are just never going to agree on what a marriage is; so too lots of people are never going to agree with your conception of the inherent concept of God.

But it seems to me that you're trying to do precisely this when you use the word "good." That is, you're saying "God is not good because good is something else." Well, what is that something else? Are you appealing to universal sense of good?

If you are, then I can play the same game with your label of "good." Why is what you call "good" the thing that's actually "good"?

If not, then you're appealing to a relativistic sense of good. But if you're appealing to a relativistic sense of good, then your sense of good is just as good as my sense of good. (Intentional play on words.)


And that's okay. The end goal is not to get everyone to think exactly like I do.

The answer is that there's a difference between agreeing on the general notion of what "good" means (which I think most people do agree on) while disagreeing with whether specific actions fit within the definition, and disagreeing about a fundamental aspect of the definition.

In other words, I think I can argue at least on a basic level about what is moral and what isn't moral with anyone who shares my general notion that "good" refers to things that one should do, or which are generally beneficial to humanity, or which are commanded or recommended by traditional or commonly-accepted conceptions of morality. We might disagree on the specifics of whether a given action is "good" or not, but we have in mind the same concept.

But if I am talking to someone who has a very extreme version of Ayn Rand-style objectivist philosophy and who believes the sole definition of "good" is "whatever benefits me", I basically cannot have that conversation. In the first instance, we disagree about the details. In the second instance, we disagree about the entire concept.

Now, I understand that's a fuzzy distinction. There are going to be some borderline cases where you could classify a particular disagreement to be about either the details or the concept. But I would still say that it delineates the difference between people with a generally shared conception of a notion and people with incommensurate conceptions of a notion.

What I am saying is that people who believe that goodness is an inherent aspect of the definition of God fall in the second category when they are speaking with those who do not. Just as people who believe that marriage is inherently opposite-sex fall in the second category when they are speaking with those who think that the concept includes same-sex marriages.

If you think God is good by definition, then, yes, as I conceded upthread, you basically can't evaluate the goodness of God's actions. Argument over. (This is also true of Hitler's actions if one thinks Hitler is good by definition, which is the point I was making earlier.) If you think that God is not good by definition, then you can evaluate them based on whatever metrics one uses for determining if an action is good.

The point I would make about this is "e pur si muove", i.e., that while it ends the DISCUSSION because the participants have two different definitions of what God is, it doesn't change whatever the actual nature of God is. God either has this characteristic of being always good or She doesn't; the fact that we can't have a conversation about it because you assume that She does have that characteristic doesn't change that fact and if, you are in fact wrong, wouldn't invalidate moral critiques of God made by others.

In other words, relativistic versus absolute notions of good. You're arguing from a relativists' perspective (good is that which we have agreed is good).

I don't think I've ever portrayed the critiques as "invalid." I have attempted to show that they are meaningless if you use the theist's terms. Going back to Hitler, I can list reasons for me to reject claim (1) because I'm bringing a different understanding of "good" into the conversation. This does not invalidate your position (in that you have a consistent understanding of your own terms), but it does show that we're not speaking the same language.