Can theists be rational?

[PixyMisa]

Hee-hee.... you said "doe snot"... go get some sleep, CJ!

Ah, doe snot. Takes me back, that does.

Anyone else here used to frequent alt.folklore.urban?

 

[Bri]

As someone else noted, you don't need to posit an infinite number of monkeys. Just a large enough number.

Again, come up with the largest number you can think of and I'll come up with one smaller. It really doesn't make any different how many planets there are, if the chances of any of them going on to develop intelligent life are small enough, it is unlikely that any of them will go on to develop intelligent life.

Why would one assume that the conditions could only be specific to the earth? Are the conditions specific to our sun only specific to the events that caused our sun?

I think I already posted a link to the Rare Earth Hypothesis.

He wrote a book debunking arguments for god.

I stand corrected. I meant that arguing in favor of the existence of gods probably isn't his "thing." Given the subject of the book you referenced, I'd say that's a pretty safe assumption.

-Bri

 

[JoeTheJuggler]

Again, come up with the largest number you can think of and I'll come up with one smaller. It really doesn't make any different how many planets there are, if the chances of any of them going on to develop intelligent life are small enough, it is unlikely that any of them will go on to develop intelligent life.

Again, we know 100% certainly that it is possible for there to be a planet with intelligent life on it.

So "unlikely" here must be a non-zero value. That is, there is at least one. (Remember, the Drake equation is not about probabilities. Its factors are all values that we know to be greater than zero --and could be in the billions--unlike probabilities which can range from zero to one.)

With the existence of God, we don't know that it is not zero. (That is, the answer to "how many Gods are there in the universe?" could be zero.)

When talking about intelligent life in the galaxy (or universe) we start off knowing without a doubt that it exists.

Do you understand this difference?

 

[JoeTheJuggler]

An argument based on Bayes analysis is not a tautology and is not circular reasoning.

Are you suggesting that no argument based on Bayes analysis can be circular?

I don't think anyone here is saying that all arguments based on Bayes analysis are circular.

This one is.

 

[fls]

Are you suggesting that no argument based on Bayes analysis can be circular?

I don't think anyone here is saying that all arguments based on Bayes analysis are circular.

I am.

Bayes' theorem (p(H/E)=p(E/H)p(H)/p(E)) itself is a tautology. That is, if one side of the equation is true, then the other side is true. This means that if we measure or find a way to limit the various components, we can say something useful about the other components.

We do this in medicine all the time. We can measure the sensitivity and specificity of a diagnostic test, estimate the background frequency of a condition in a particular patient population (e.g. the presence of coronary artery disease in 60-year-old sedentary male smokers with uncontrolled hypertension and diabetes), and then use Bayes' Theorem to update the probability that a specific individual has a condition (coronary artery disease) based on a positive test (stress test).

When we talk about using evidence, what we are usually referring to is finding a way to measure or limit one of the components, and updating the posterior probability based on that. You need at least three pieces of information in order to fully define the theorem. If you have less than that, then your posterior probability simply reflects your guess about the missing information - i.e. it's circular.

Linda

 

[Bri]

Again, we know 100% certainly that it is possible for there to be a planet with intelligent life on it.

True, if you felt it impossible for any other planet with life to develop intelligent life, you could take ours into account by giving it a value of 1/n where "n" is the number of planets. Still, the result can be less much lower than 1 depending on what other values you put in (indeed some estimates put the number less than 1).

So "unlikely" here must be a non-zero value. That is, there is at least one. (Remember, the Drake equation is not about probabilities. Its factors are all values that we know to be greater than zero --and could be in the billions--unlike probabilities which can range from zero to one.)

If it were zero, it would be "impossible" rather than "unlikely." They are not zero because they are not impossible.

With the existence of God, we don't know that it is not zero. (That is, the answer to "how many Gods are there in the universe?" could be zero.)

Similarly, we also don't know that the answer to "how many extra terrestrials are there in the universe" could be zero. Nobody is arguing about belief in intelligent life being irrational, after all. The question is whether belief in extra terrestrial intelligent life is irrational.

When talking about intelligent life in the galaxy (or universe) we start off knowing without a doubt that it exists.

Who's talking about intelligent life in the universe? We're talking about extra terrestrial intelligent life (a subset of intelligent life). It's as if we were discussing the existence of unicorns and all of a sudden you start talking about mammals. Does the existence of mammals (of which unicorns would be a subset) somehow give credence to a belief in unicorns? Would an estimate of the probability of unicorns have to be greater than zero since mammals exist?

Do you understand this difference?

I do understand the difference. Do you?

-Bri

 

[Bri]

Are you suggesting that no argument based on Bayes analysis can be circular?

I don't think anyone here is saying that all arguments based on Bayes analysis are circular.

I am.

Bayes' theorem (p(H/E)=p(E/H)p(H)/p(E)) itself is a tautology. That is, if one side of the equation is true, then the other side is true. This means that if we measure or find a way to limit the various components, we can say something useful about the other components.

Sorry, Linda, but I have to side with Joe on this. Your description of Bayes analysis seems to stem from a misunderstanding of Bayes analysis. It's been around for a long time, it's used often by statisticians and mathematicians, and nobody considers it a form of circular reasoning.

It's also important to point out that Bayes analysis doesn't deal with truth or falsehood except when values for the probabilities are 0 or 1. The most that could be said is that IF you assume prior probabilities of 0 or 1 then the result will be the same posterior probability. That's simply saying that no amount of additional evidence taken into account will change the probability of something that is already true or false. Pretty basic stuff really, and certainly not circular reasoning.

-Bri

 

[RandFan]

Again, come up with the largest number you can think of and I'll come up with one smaller. It really doesn't make any different how many planets there are, if the chances of any of them going on to develop intelligent life are small enough, it is unlikely that any of them will go on to develop intelligent life.

I get your point I really do. I don't think you get mine. Infinite monkey theorem isn't really scientific but it's purpose is to help us understand probabilities when we are discussing infinity. It's been pointed out that infinity isn't needed. Just a very large number. Yes you can keep decreasing the variables to fit your world view against any probability.

 

[Bri]

We're really just talking about intelligent life in this galaxy, of which we are one example.

Imagine my confusion. All this time I thought we were talking about belief in extra terrestrial intelligent life! If we were talking about belief in intelligent life, it would have been a much shorter discussion.

Getting back to a discussion that we were actually having, there is no example of extra terrestrial intelligent life that I'm aware of.

There isn't anything about Drake's equation that excludes Earth.

Except that we were talking about some hypothetical argument for the probability of extra terrestrial intelligent life based on Drake's equation, not Drake's equation itself.

I'm saying that it's rational to look at what we know about elephants when we are wondering whether or not it's reasonable to search for large animals on an as yet unexplored landmass on Earth.

You implied that because extra terrestrial intelligent life is a subset of intelligent life and the fact that we know about another subset of intelligent life (ourselves) in and of itself makes it rational to belief in extra terrestrial intelligent life without regard for the actual evidence of extra terrestrial intelligent life (or lack thereof).

That's the equivalent of arguing that it's rational to believe in invisible elephants because we know something about African elephants.

I understand that is the reason given for bringing up the argument. But there is no direct observation of a fine-tuner, nor is there any hypothesis which makes a fine-tuner necessary.

Nor is there any direct observation of extra terrestrial intelligent life, nor any hypothesis which makes extra terrestrial intelligent life necessary.

However, there is direct observation of intelligent life in this galaxy, plus hypotheses such as the ones I mentioned earlier.

Again, you're changing the subject. Let's stick with something we are actually talking about, which is the belief in the existence of extra terrestrial intelligent life.

I mean, we know that "beings" exist, right? We have direct observation of beings don't we? In fact, WE are beings (human beings to be exact). And we can even make hypotheses such as the ones you mentioned earlier about human beings. So does evidence of beings make belief in supernatural beings rational?

Simply observing that the physical constants have a particular value does not make it necessary that they were chosen capriciously, just like observing that the heavenly bodies moved in a pattern that wasn't immediately obvious meant that their movement was capricious. And as I argued earlier in this thread, the difference between considering a force God or considering it natural is whether or not it is lawful (i.e. not capricious). You don't consider the multiverse explanation 'God', for example.

The jump from "fine-tuner" to "god" is an assumption in the premise. That flaw has already been pointed out and agreed to. Even if there is a fine-tuner, there is no guarantee that it's anything anyone would call "God" (and it could indeed have natural explanations). I've already said that I disagree with the premises of the argument, so you'll get no argument from me there.

The latter three are guesses, not because we are meant to look into our hearts in order to find the answer (like we are when guessing at the prior probability of God), but simply because our information is inadequate at present. The blanks are meant to be filled in by finding opportunities for observation, though.

Thus far, there are no opportunities for observation, and therefore any values placed there are indeed based on "looking into our hearts" or "faith" or whatever you want to call it -- they are NOT based on evidence.

Whether or not Drake's equation is meant to be used that way or not isn't the question -- it's whether it can rationally be used in that way. If you think it can, please explain how similar arguments for a god can't be rational. If you think it can't, please explain some other rational reason for belief in extra terrestrial intelligent life without any evidence.

Or you can concede my point that belief in gods and ET intelligence are both necessarily irrational or neither is necessarily irrational. Then let's go from there.

And I think that illustrates the difference between rational and irrational. Because Drake's equation isn't used to say "I believe in aliens". It is used to say, "looking for evidence of aliens may not be a complete waste of time".

Drake's equation is not only sometimes used to justify beliefs in aliens, but is also used to justify projects like SETI which spend lots of money looking for them even though the equation doesn't even conclude that there are any. The statement "looking for evidence of aliens may not be a complete waste of time" implies that "looking for evidence of aliens may be a complete waste of time."

People believe in God without direct evidence of God, but people don't believe in aliens when we don't have direct evidence of aliens.

...

Exactly. And because of that, we don't have a belief in aliens.

So you think that no people are of the opinion that aliens exist? Really?

Who is "we" in the phrase in bold?

So are you conceding at this point that if someone was of the opinion that aliens exist, that would be an irrational belief?

An informed guess?

What is the guess being informed by if it's not based on evidence?

Exactly. As I said previously, it hasn't occurred to us for several hundred years to say that God controls the movement of the heavenly bodies, because we discovered that this movement is natural, and we don't consider God natural. Prior to that discovery, Christians did consider God responsible for heavenly bodies. They still do now, but in a different way - more like what you mention below.

As far as I know, Christians have always believed in one way or another that God controls nature and often works through nature. So I suspect that discovering natural processes probably isn't going to shake anyone's belief in such a God.

I misunderstood, then. I thought your statement was meant to be sarcastic. In that case, we are back to my point that then gods have already been proven to exist. Since we have discovered forces that fit the definitions of what gods do (Zeus forms thunder and lightning - electromagnetism forms thunder and lightning), those forces are the gods we were referring to with our stories.

If anyone believed Zeus to actually BE thunder and lightning (rather than forming thunder and lightning) then sure the existence of thunder and lightning would mean that Zeus exists. Even so, I don't think anyone would agree with that definition of "Zeus."

My point is simply that that isn't the only way to produce a clearly wrong conclusion.

If you can show that an argument produces a clearly wrong conclusion given correct premises, then you can indeed show that an argument is invalid. That is probably not the case with the argument cj posted, which is why it is usually attacked by objecting to the premises rather than the argument itself.

But since we don't know whether or not this universe we find ourselves in is more or less likely in the presence of a fine-tuner, whether or not the presence of fine-tuning in this universe serves as evidence for a fine-tuner depends entirely on whether or not we assume that it does. That is, we can only get out of this argument the assumptions that we put into it.

A valid objection to the premise in which it is assumed that the universe would be more likely to be fine-tuned with a god than without one.

I think that both beliefs would be irrational. The difference is that, because of that, we don't believe in aliens.

OK, so the first sentence is at least consistent (although it sounds like you're conceding that both are irrational -- correct me if I'm wrong). The second is inconsistent with reality since some people do believe in aliens. In fact, I suspect that some scientists are of the opinion that aliens exist.

If you think you understand Bayesian analysis, then simply argue it for yourself. I can't guess what it is that you think the article says.

I'm not an expert by any means. I have tried to explain it to you as best I can, but the article does a much better job than I ever could.

That is why it is similar to the formula used to estimate whether or not the universe is fine-tuned.

I agree (that's pretty much been my argument all along).

-Bri

 

[Bri]

I get your point I really do. I don't think you get mine. Infinite monkey theorem isn't really scientific but it's purpose is to help us understand probabilities when we are discussing infinity. It's been pointed out that infinity isn't needed. Just a very large number. Yes you can keep decreasing the variables to fit your world view against any probability.

Looking at the equation:

P = A * B​

We know that A is very, very large. Pick any sufficiently large number you want.

B is entirely unknown.

Can we conclude anything about P that does imply a pure conjecture about the value of B?

In this case, there is some evidence that B is very, very small. Small enough that P might be very, very small (i.e. that we might very well be alone in the universe).

-Bri

 

[fls]

Sorry, Linda, but I have to side with Joe on this. Your description of Bayes analysis seems to stem from a misunderstanding of Bayes analysis. It's been around for a long time, it's used often by statisticians and mathematicians, and nobody considers it a form of circular reasoning.

I'm going to look at two different kinds of equations in the hope that it becomes clearer.

volume = length X width X height

Pre-op cardiac risk = 11(S3) + 10(MI) + 7(PVC's) + 7(non-sinus rhythm) + 5(70+ age) + 4(emergency) + 3(poor health) + 3(AS) + 3(surgery site)

(reference for the latter: http://www.chiefresidents.net/information_links/risk.htm)

The question becomes, is the conclusion assumed in the premise? If you are given the length, width and height of a box, and you measure the volume of that box, can the volume take on a different value than the (accurate) measures state they should? (No) If you meticulously note the presence or absence of each factor in your risk assessment, and you measure the frequency of peri/post-op cardiac complications in a population undergoing surgery, can the number of complications take on a different value than the measures state they should? (Yes)

I will agree that most of the time, formulas/theorems/equations of the same type as Bayes' theorem are not referred to as circular or tautological, but that is because it is usually a trivial observation, not because it isn't true.

I realize that it is a subtle point, but under certain circumstances, it alters whether or not your conclusion is independent of your premises.

It's also important to point out that Bayes analysis doesn't deal with truth or falsehood except when values for the probabilities are 0 or 1. The most that could be said is that IF you assume prior probabilities of 0 or 1 then the result will be the same posterior probability. That's simply saying that no amount of additional evidence taken into account will change the probability of something that is already true or false. Pretty basic stuff really, and certainly not circular reasoning.

-Bri

Bayes' deals with the probability that something is true or false - like a Bernoulli trial.

Linda

 

[Malerin]

I am.

Bayes' theorem (p(H/E)=p(E/H)p(H)/p(E)) itself is a tautology. That is, if one side of the equation is true, then the other side is true. This means that if we measure or find a way to limit the various components, we can say something useful about the other components.

We do this in medicine all the time. We can measure the sensitivity and specificity of a diagnostic test, estimate the background frequency of a condition in a particular patient population (e.g. the presence of coronary artery disease in 60-year-old sedentary male smokers with uncontrolled hypertension and diabetes), and then use Bayes' Theorem to update the probability that a specific individual has a condition (coronary artery disease) based on a positive test (stress test).

When we talk about using evidence, what we are usually referring to is finding a way to measure or limit one of the components, and updating the posterior probability based on that. You need at least three pieces of information in order to fully define the theorem. If you have less than that, then your posterior probability simply reflects your guess about the missing information - i.e. it's circular.

Linda

If Bayes Theorem were circular, Pr(H/E) would be derived from Pr(H/E). It's not. It's derived from Pr(H), Pr(E/H) and Pr(E/~H).

 

[yy2bggggs]

If Bayes Theorem were circular, Pr(H/E) would be derived from Pr(H/E). It's not. It's derived from Pr(H), Pr(E/H) and Pr(E/~H).

Here's a hint, Malerin. Tautology is spelled starting with the letter "T". Circular starts with an entirely different letter--"C". So if someone uses the "T" word, they probably are not talking about the "C" word.

...unless they don't know the difference.

 

[RandFan]

Looking at the equation:

P = A * B
​

We know that A is very, very large. Pick any sufficiently large number you want.

B is entirely unknown.

I don't think it is. Paulos actually provides some clues in his book.

Can we conclude anything about P that does imply a pure conjecture about the value of B?

I don't know what pure conjecture is. I don't think that the fact that there is a probability of 1 for inteligent life in the universe is of itself insignificant. I don't think that the fact that the elements that are required for inteligent life are common in the universe are insignificant. I also think that as Paulos states that we are unnecassarily limiting the equation to state that the specifics of earth are the only requirements of inteligent life but regardless there is no basis to suppose that the earth is in fact all that rare.

In this case, there is some evidence that B is very, very small. Small enough that P might be very, very small (i.e. that we might very well be alone in the universe).

Not really. No.

 

[Malerin]

Here's a hint, Malerin. Tautology is spelled starting with the letter "T". Circular starts with an entirely different letter--"C". So if someone uses the "T" word, they probably are not talking about the "C" word.

...unless they don't know the difference.

Well aren't you just the smarmy little jerk lately. Hmm, where would I get the idea fls thinks Bayesian arguments are circular?

I don't think anyone here is saying that all arguments based on Bayes analysis are circular.

I am.

Edit:

Oh, and fls comes right out and says it at one point:

I will agree that most of the time, formulas/theorems/equations of the same type as Bayes' theorem are not referred to as circular or tautological, but that is because it is usually a trivial observation, not because it isn't true.

 

[fls]

Imagine my confusion. All this time I thought we were talking about belief in extra terrestrial intelligent life! If we were talking about belief in intelligent life, it would have been a much shorter discussion.

Getting back to a discussion that we were actually having, there is no example of extra terrestrial intelligent life that I'm aware of.

Me neither. So what gave us the idea that there may be extra-terrestrial intelligent life if it wasn't the presence of terrestrial intelligent life?

Except that we were talking about some hypothetical argument for the probability of extra terrestrial intelligent life based on Drake's equation, not Drake's equation itself.

I do not understand the relevance of your comment.

You implied that because extra terrestrial intelligent life is a subset of intelligent life and the fact that we know about another subset of intelligent life (ourselves) in and of itself makes it rational to belief in extra terrestrial intelligent life without regard for the actual evidence of extra terrestrial intelligent life (or lack thereof).

If that's how you read it, then you misunderstood. I meant that we got the idea that intelligent life may be present in this galaxy from our own presence (unless you have another suggestion), so we start by considering what we can learn from our own presence. It doesn't mean that we believe that there is life elsewhere without evidence, but it sets a higher prior probability than if we weren't here (leaving out the inherent contradiction in that ).

That's the equivalent of arguing that it's rational to believe in invisible elephants because we know something about African elephants.

That doesn't even make any sense. At no point have I suggested that we should start believing in entities with imaginary and previously undiscovered qualities. I actually thought I was arguing the opposite.

Nor is there any direct observation of extra terrestrial intelligent life, nor any hypothesis which makes extra terrestrial intelligent life necessary.

Right. Otherwise we wouldn't be having this discussion.

Again, you're changing the subject. Let's stick with something we are actually talking about, which is the belief in the existence of extra terrestrial intelligent life.

I mean, we know that "beings" exist, right? We have direct observation of beings don't we? In fact, WE are beings (human beings to be exact). And we can even make hypotheses such as the ones you mentioned earlier about human beings. So does evidence of beings make belief in supernatural beings rational?

I don't think the sticking point is 'beings', rather I think it is 'supernatural'. If we haven't ever come across any observations that are necessarily capricious or unlawful, why would we have any expectation of doing so in the future?

The jump from "fine-tuner" to "god" is an assumption in the premise. That flaw has already been pointed out and agreed to. Even if there is a fine-tuner, there is no guarantee that it's anything anyone would call "God" (and it could indeed have natural explanations). I've already said that I disagree with the premises of the argument, so you'll get no argument from me there.

Is there any point to the argument, then? Otherwise, aren't we just saying something like, "this observation is not fully explained, therefore it suggests our explanation is incomplete"? It seems a trivial insight, since it can and is said about pretty much everything we're trying to study.

Thus far, there are no opportunities for observation, and therefore any values placed there are indeed based on "looking into our hearts" or "faith" or whatever you want to call it -- they are NOT based on evidence.

Whether or not Drake's equation is meant to be used that way or not isn't the question -- it's whether it can rationally be used in that way. If you think it can, please explain how similar arguments for a god can't be rational. If you think it can't, please explain some other rational reason for belief in extra terrestrial intelligent life without any evidence.

Or you can concede my point that belief in gods and ET intelligence are both necessarily irrational or neither is necessarily irrational. Then let's go from there.

What do you think is more plausible - that I will discover a new species of insect in my backyard, or that I will discover a new species of large hominid in my backyard (given that it mostly consists of pool, deck and some small plants and grass)?

Drake's equation is not only sometimes used to justify beliefs in aliens, but is also used to justify projects like SETI which spend lots of money looking for them even though the equation doesn't even conclude that there are any. The statement "looking for evidence of aliens may not be a complete waste of time" implies that "looking for evidence of aliens may be a complete waste of time."

I agree.

So you think that no people are of the opinion that aliens exist? Really?

I think people's beliefs are qualified by information as to how likely it is that they exist.

Who is "we" in the phrase in bold?

People generally. I don't think people 'believe' in aliens in the same way that they 'believe' in elephants. I think it's more like the way in which we 'believe' in the possibility of undiscovered rodent species (except more exciting).

So are you conceding at this point that if someone was of the opinion that aliens exist, that would be an irrational belief?

I think the problem is with trying to consider it as an all-or-none type of situation.

What is the guess being informed by if it's not based on evidence?

Information.

As far as I know, Christians have always believed in one way or another that God controls nature and often works through nature. So I suspect that discovering natural processes probably isn't going to shake anyone's belief in such a God.

Yes.

If anyone believed Zeus to actually BE thunder and lightning (rather than forming thunder and lightning) then sure the existence of thunder and lightning would mean that Zeus exists.

Not the existence of thunder and lightning - the existence of something that forms thunder and lightning.

Even so, I don't think anyone would agree with that definition of "Zeus."

Right. That's what I said.

If you can show that an argument produces a clearly wrong conclusion given correct premises, then you can indeed show that an argument is invalid. That is probably not the case with the argument cj posted, which is why it is usually attacked by objecting to the premises rather than the argument itself.

So these 20+ pages attacking the argument itself don't count?

OK, so the first sentence is at least consistent (although it sounds like you're conceding that both are irrational -- correct me if I'm wrong). The second is inconsistent with reality since some people do believe in aliens. In fact, I suspect that some scientists are of the opinion that aliens exist.

I'm just saying that we're talking about opinions qualified by scientific inquiry. We aren't certain about aliens, but there is something in between certainty and no-idea-whatsoever.

I agree (that's pretty much been my argument all along).

-Bri

I misunderstood then. I thought you were agreeing that the results of the formula made it more likely that a fine-tuner was present.

Linda

 

[fls]

Here's a hint, Malerin. Tautology is spelled starting with the letter "T". Circular starts with an entirely different letter--"C". So if someone uses the "T" word, they probably are not talking about the "C" word.

...unless they don't know the difference.

Well, a tautology is a type of circular argument. Unless you mean a circular argument is necessarily fallacious...

Linda

 

[fls]

If Bayes Theorem were circular, Pr(H/E) would be derived from Pr(H/E). It's not. It's derived from Pr(H), Pr(E/H) and Pr(E/~H).

Which are entirely dependent upon p(H/E).

The problem with circular arguments is that you can't always recognize that you've said the same thing twice when it's put into a form that superficially looks different, but is actually equivalent.

Linda

 

[yy2bggggs]

Well aren't you just the smarmy little jerk lately.

Well, it's been explained to you before--and understanding the difference is critical in order to understand what people are really saying.

Hmm, where would I get the idea fls thinks Bayesian arguments are circular?

Bayes Theorem, qua this:

If Bayes Theorem were circular, Pr(H/E) would be derived from Pr(H/E). It's not. It's derived from Pr(H), Pr(E/H) and Pr(E/~H).

...is not a Bayesian argument. It's an equation.

And so far I haven't actually seen, including in your quote, a clear indication that fls has stated that Bayes Theorem was a tautologycircular. Though there seems to be something to address now.

Well, a tautology is a type of circular argument. Unless you mean a circular argument is necessarily fallacious...

No. A tautology is a statement that is necessarily true; i.e., true in all possible worlds. A circular argument can be a tautology, but not all tautologies are circular arguments.

Example 1
1=sin²x+cos²x
Example 2 (consider only the argument itself for this example)
Prove A. Proof: Assume A. Then A=>A.
Example 3
A=>A

All three examples are tautologies. But only example 2 is circular, because only in example 2 is there a conclusion that assumes the premise. Example 3 is worth noting because the truth of A isn't ever assumed or concluded--the statement A=>A is true even when A is false. In example 2, only the true case is focused on, and a not necessarily true suggestion is made that A is true (i.e., certain to be true; it so happens that in this example, if the premise "A" is false the conclusion is false, but that's not a necessary property of circular arguments). In example 1, there's only an equation that is necessarily true.

Circular arguments are in particular problematic because they ignore the conditions under which the argument may not be true.

 

[fls]

No. A tautology is a statement that is necessarily true; i.e., true in all possible worlds. A circular argument can be a tautology, but not all tautologies are circular arguments.

Ah, I see what you're getting at. I was thinking of tautologies in the context of an argument.

Linda