The Logic of Defining Atheism and Atheist

For this discussion the precise meaning of God doesn’t matter as long as the same meaning is used throughout.  There are two different atheisms:

  • Logical Atheism.  Logical atheism (LA) is the proposition that God does not exist.  As a proposition, LA enters into logical relations with other propositions.  If P is some proposition, then LA either entails that P; or is consistent with P; or contradicts P; or etc.  An argument against the existence of God concludes with logical atheism.  For instance: (1) If God exists, then P; (2) however, it is not the case that P; (3) therefore, LA.  The conjunction of (LA & not LA) is a contradiction.
  • Psychological Atheism.  Psychological atheism is the belief that God does not exist.  As a belief, it is the belief of some mind.  Thus psychological atheism is a proposition of the form Believes(x, Logical Atheism), or, for short, B(x, LA).  The proposition B(x, LA) is not equivalent to LA.  Nor does LA entail B(x, LA) nor does B(x, LA) entail LA.  The logic of belief is very complicated, very controversial, and very different from logics that merely involve propositions without intentional operators.

The difference between logical and psychological atheism is significant.  For any believer x, (B(x, LA) & (not B(x, LA))) is a contradiction.   Thus

((x believes that God does not exist) & (x does not believe that God exists)) is a contradiction.

However,  for any believer x, (B(x, LA) & B(x, not LA)) is not a contradiction.   Thus

((x believes that God does not exist) & (x believes that God exists)) is not a contradiction.

It is not a contradiction because B(x, P) does not entail P.

This careful distinction is relevant to the definition of atheist.  An atheist is a person who holds a certain belief.  Thus one may say that

(1)       x is an atheist if and only if B(x, LA).

Now, it is rational to assume that there are no self-inconsistent objects.  That is, there are no objects that satisfy contradictions.  Thus for any property F, there is no object y such that (F(y) & not F(y)).  On this assumption, there is no person x such that

(2)       ((x is an atheist) & (not B(x, LA))).

However, unless you add other assumptions, B(x, not LA) does not contradict B(x, LA), that is, (B(x, LA) & B(x, not LA)) is perfectly consistent.   Hence the following is also perfectly consistent:

(3)       ((x is an atheist) & B(x, not LA)),

which is equivalent to

(4)       ((x believes God does not exist) & (x believes God exists)).

Thus, unless you add other assumptions, it is entirely possible that

(5)       x is an atheist and x believes in God.

The other assumption that has to be added to make (5) contradictory is a principle which we may call No Self-Deception (NSD):

(6)       if x believes P then x does not believe not P.

which is formally

(7)       if B(x, P) then (not B(x, not P)).

NSD is a very strong assumption, and it’s not at all clear why it should be added it to the logic of belief.  Thus consider self-deception.

(7)       x is self-deceived if and only if there is some P such that (B(x, P) & B(x, not P)).

Adding NSD obviously rules out self-deception.  So here is a very diffferent definition of atheism than the one given in (1).  This new and distinct definition is:

(8)       x is an atheist if and only if (B(x, LA) and NSD).

Clearly, NSD is a very strong proposition which is entirely independent of LA and even B(x, LA).  The first definition of atheism in (1) makes no psychological demands of the atheist beyond B(x, LA).  The second definition of atheism in (8) makes an extremely strong psychological demand of the atheist.  It says that an atheist cannot be intellectually dishonest, cannot be self-deceived, cannot be in bad faith, etc. etc.

And all of this lands us right into issues dealing with the ethics of belief.  Since NSD is hardly a logical principle, you might try to argue that it is an ethical principle: for any mind x, for any proposition P, if B(x, P) then it ought to be the case that (not B(x, not P)).  If you believe P, then you are obligated to not believe not P.  But once more, this is a very strong demand.  Anyone who adds it to the definition of atheism has expanded the definition far, far beyond merely B(x, LA).  For now an atheist is a person who believes that God does not exist and who also believes that self-deception is ethically forbidden.

Thus (1) and (8) are very different definitions of atheist.

 

About Daniel Fincke

Dr. Daniel Fincke  has his PhD in philosophy from Fordham University and spent 11 years teaching in college classrooms. He wrote his dissertation on Ethics and the philosophy of Friedrich Nietzsche. On Camels With Hammers, the careful philosophy blog he writes for a popular audience, Dan argues for atheism and develops a humanistic ethical theory he calls “Empowerment Ethics”. Dan also teaches affordable, non-matriculated, video-conferencing philosophy classes on ethics, Nietzsche, historical philosophy, and philosophy for atheists that anyone around the world can sign up for. (You can learn more about Dan’s online classes here.) Dan is an APPA  (American Philosophical Practitioners Association) certified philosophical counselor who offers philosophical advice services to help people work through the philosophical aspects of their practical problems or to work out their views on philosophical issues. (You can read examples of Dan’s advice here.) Through his blogging, his online teaching, and his philosophical advice services each, Dan specializes in helping people who have recently left a religious tradition work out their constructive answers to questions of ethics, metaphysics, the meaning of life, etc. as part of their process of radical worldview change.

  • Tarentola Mauretanica

    Logical Atheism. Logical atheism (LA) is the proposition that God does not exist.

    Psychological Atheism. Psychological atheism is the belief that God does not exist.

    What about the simple LACK of belief which is the actual meaning of the word by the way.

    • Malatesta

      Lack of belief by itself is meaningless. Bales of hay aren’t atheists, despite their utter lack of beliefs regarding gods (or anything else). As for people who ‘simply’ lack belief, I can only assume this means they’ve never really thought about it or are intentionally withholding judgement. In which case they may functionally behave as atheists, but lumping them in with the rest of us outright rejecters distorts more than it clarifies.

    • http://www.russellturpin.com/ rturpin

      As for people who ‘simply’ lack belief, I can only assume this means they’ve never really thought about it or are intentionally withholding judgement.

      Or they might have listened to believers, thought on their arguments, and concluded that religion is a bunch of poppycock. And still realize that doesn’t constitute evidence there is no god.

  • http://www.legionofreason.com/ HJ Hornbeck

    Hmm, something’s off here. You state “Logical atheism (LA) is the proposition that God does not exist,” which I’d tranlate as “for all X(not IsGod(X)).” The negation of that is “for some X(IsGod(X)).”

    You also state “(B(x, LA) & (B(x, not LA)) is not a contradiction,” however. Isn’t that the same as stating “for some x( Belief(x, for all Y(not IsGod(Y))) ^ Belief(x, for some Y(IsGod(Y)) ).” That seems entirely contradictory.

    HJ Hornbeck

    • http://www.ericsteinhart.com Eric Steinhart

      Yes, the negation of (God does not exist) is (God exists).

      Surely that’s not problematic.

      I can’t follow the rest of your logic.

    • http://www.legionofreason.com/ HJ Hornbeck

      I see my basic point has been beaten into the ground already. Which is fine, because I still have general point left to make.

      By couching your argument in first-order logic, you’re implying all entities within that system obey first-order logic as well. Thanks to your comments, I can see that’s not what you intended; what you were really trying to say was that human beings are not completely rational creatures, and are capable of believing in two contradictory beliefs at the same time.

      You would have generated far less confusion if you’d just talked about “cognitive dissonance” instead, and didn’t mislead with all that irrelevant logic.

      Now: central to your actual argument is the assertion that human beings can have cognitive dissonance over belief and non-belief. However, our ability to rationalize cog.dis is proportional to the excuses we’re able to come up with. “Oh, I only smoke at parties” is a good example, since it justifies the act of smoking as only an occational thing, under strong control and just used as the occasional treat.

      How would someone rationalize away belief or non-belief? Both are completely internal to ourselves, so you can’t get “caught” like you can with smoking. We’ve also had “apostacy = EVIL” collectively pounded into our skulls, as well as “the afterlife is FOREVER;” we’re all quite aware that admitting to non-belief is dangerous and has serious consequences. In contrast, we can easily dredge up our auntie’s friend’s cousin Mildred who chain-smoked yet lived to 142.

      With no way to rationalize, there’s no way to justify cog.dis, and so no human could be dissonant over belief. They’d probably just declare themselves “theist” and be done with it.

      HJ Hornbeck

  • http://florilegia.wordpress.com Ibis3, denizen of a spiteful ghetto

    It is impossible to hold a proposition about reality to be both true and untrue at the same time.Yes a person can lie or be self-deluded or talk themselves into pretending to hold a proposition to be true when they really believe it to be false. None of those options equal actually holding two contradictory propositions to be true. If you believe the world is flat, you can’t simultaneously believe it to be round (i.e. spheroid).

    If a respondent in a survey self-identified as a flat-earther and also answers “yes” to the question of whether they believe the earth is round, we must conclude that they didn’t understand the nature of the question, the definition of flat-earther, or was answering questions randomly or in a deliberately contradictory manner. Why? Because we all know that “the world is flat” and “the world is round” can not both be true.

    • http://www.ericsteinhart.com Eric Steinhart

      Sure

      (P & not P) is impossible;

      but you give no argument that

      (B(x, P) & B(x, not P)) entails B(x, (P & not P));

      nor any argument that

      B(x, (P & not P)) is impossible.

    • http://florilegia.wordpress.com Ibis3, denizen of a spiteful ghetto

      If we *know* P and not P can not both be true, how can we believe both P and not P? You can’t believe something that contradicts your knowledge.

    • http://www.ericsteinhart.com Eric Steinhart

      You’re assuming (if B(x, P) then not B(x, not P)).

      And that’s NSD.

      You’re argument depends on NSD.

      Which is exactly the point.

    • http://florilegia.wordpress.com Ibis3, denizen of a spiteful ghetto

      Self-deception is irrelevant. You can believe yourself to be a bathtub if you like. That doesn’t mean you are one.

      Couching a contradiction in symbolic logic doesn’t make it magically possible.

    • sqlrob

      So William Lane Craig is an atheist then?

      Or Francis Collins?

  • http://infinitegames.tumblr.com infinity

    I’m slightly confused….which is probably just not understanding your translation/too much drinking:

    For any believer x, (B(x, LA) & (not B(x, LA))) is a contradiction. Thus

    ((x believes that God does not exist) & (x does not believe that God exists)) is a contradiction.

    Since LA means “God does not exist” and B(x, LA) means “x believes that God does not exist” wouldn’t (not B(x, LA)) mean “Not[x believes that God does not exist”=”x does not believe that God does not exist”

    Does it follow then that “x does not believe that God exists”?

    • http://www.ericsteinhart.com Eric Steinhart

      It’s ok up until your last statement, which does not follow.

    • http://infinitegames.tumblr.com infinity

      Well, that was my question, because that’s what you wrote when you translated:

      (B(x, LA) & (not B(x, LA)))

      to mean

      ((x believes that God does not exist) & (x does not believe that God exists))

    • http://infinitegames.tumblr.com infinity

      Sorry, I’m not trying to be rude, and it may have sounded that way. I just didn’t understand that part of your post.

  • http://verbosestoic.wordpress.com/ Verbose Stoic

    Eric,

    I think the symbolic logic is confusing things here. Translating it to a statement, it seems obvious to me that your:

    B(x, LA) & B(x, not LA) line translates to:

    B(P) & B(~P) (x is irrelevant, and we’re just translating it up to the general statement of believing in propositions).

    Which we then translate to a statement as:

    Believes P and believes ~P or Believes P to be true and believes P to be false. But I’m afraid that IS a contradiction, in the sense that their beliefs form an inconsistent and contradictory set. One does not need to make any sort of strong NSD claim to point out that this is a problem; having a set of inconsistent beliefs is enough to raise all the alarm bells, and one has not had to change the definition of atheist at all to get that (it’s part of a requirement for any rational and reasonable set of beliefs).

    • http://www.ericsteinhart.com Eric Steinhart

      The x is not at all irrelevant, since belief is a relation, not a property.

      Anyway, when you wrote

      But I’m afraid that IS a contradiction, in the sense that their beliefs form an inconsistent and contradictory set.

      you appealed to NSD, and you put the “x” right back in when you said “their beliefs”.

      It is impossible to derive any contradiction in the set of beliefs without NSD; for only NSD allows you to detach P from B(x, P).

      If B(x, P) and B(x, -P), then the set of beliefs is exactly { B(x, P), B(x, -P)},
      whereas the set of propositions believed is { P, -P}.

      Only NSD allows you to derive the set of propositions believed from the set of beliefs.

      Once again, only NSD allows you to derive P from B(x, P).

      That’s the whole point.

    • http://www.ericsteinhart.com Eric Steinhart

      Actually, you’re appealing to a much stronger principle than NSD, namely a principle that goes from B(x, P) & B(x, Q) to B(x, P & Q); then you’re using detachment to go from B(x, P & Q) to P & Q; I should have said that rather than just NSD. Sorry.

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      Well, yes, stronger in a sense, but better supported in another and so weaker: As you seem to accept, what we believe are propositions. Since we believe propositions, I can go directly from the set of beliefs to the set of propositions believed, and that is in fact how I’d determine if the set of beliefs is consistent (since a set of beliefs cannot in and of itself be consistent or inconsistent). Now, you can deny that a set of beliefs has to be consistent, but then you run into issues because of the tight association with propositions; at the end of the day, I would still possess an inconsistent set of propositions that I believe, and there seems little reason to believe propositions if not for their logical power. In fact, it’s hard to see how you could make the association to propositions WITHOUT making certain to maintain the logical consistency required of propositions.

      (As for x being irrelevant, I only said that because it was always the same, so I didn’t need to keep writing it out. It would be presumed that it was about a person’s beliefs).

    • http://www.ericsteinhart.com Eric Steinhart

      Since we believe propositions, I can go directly from the set of beliefs to the set of propositions believed

      No, you can’t go from one to the other without assuming a derivation rule.

      And the derivation rule you’re assuming entails NSD.

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      I’m not sure what you mean here.

      My derivation rule, if it can be called one, is no more than the definition of belief, in that I claim that we believe propositions. Given that, having a set of beliefs entails having a set of propositions believed. And that entails that if you want to have a consistent set of beliefs/propositions believed, you can’t be believing contradictory propositions. If you accept that a set of propositions should be consistent, then that means that you should accept that your set of beliefs should be consistent as well. If you deny that, then you deny logic and you really didn’t need to make the move to beliefs.

    • http://infinitegames.tumblr.com infinity

      I guess I’m not sure that, strictly speaking, being an atheist implies that one has a consistent and rational set of beliefs. Plenty of people hold irrational or contradictory beliefs (look at all the religious folk) which means we know it is possible. Certainly, being a skeptic or a rationalist implies consistency, but I think you have to argue more thoroughly to demonstrate that being an atheist does. I mean, obviously any x such that B(x,p) and B(x,~p) holds irrational views, but I’m not sure you can say, logically, that that means they aren’t an atheist unless you require all atheists to be rational.

    • http://infinitegames.tumblr.com infinity

      Sorry, Eric, you replied while I was writing, making my comment redundant.

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      This argument, though, would be used against the original logical definition as well. If you don’t care about being consistent, then why would you care about the logical definition either? But the post, it seems to me, distinguishes between the two cases by saying that the logical argument would be a problem but the psychological would not, and my reply is basically to show that yes, indeed, we have a contradiction even in the psychological case — ie where we only refer to beliefs — that’s pretty much the same one as the logical argument.

    • http://infinitegames.tumblr.com infinity

      No, because LA as defined in the post is the proposition: God does not exist. I don’t think the argument that the definition of atheist does not require that every atheist has completely rational belief sets can be extrapolated to an argument that logical propositions don’t need to be consistent.

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      You have my argument backwards.

      If there is a problem of having a contradictory set of propositions in the logical argument, then I argue that there is still that precise problem of having a contradictory set of propositions at the psychological level because what we believe are propositions. Therefore, either there is a problem at the psychological level as well or there never was any problem at the logical level; the charge that we don’t need to expect all atheists to be rational would apply at the logical definition as well.

      Unless, of course, the whole point was to show that it is logically and psychologically possible to have such conflicting beliefs, at which point we didn’t need all of that symbolic logic to prove that since, well, psychology already has [grin].

    • http://infinitegames.tumblr.com infinity

      @Verbose Stoic here.

      Ah. Okay. Sorry, I read through your posts too quickly. I think I understand what you are saying better now.

  • http://verbosestoic.wordpress.com/ Verbose Stoic

    Well, let me refer back to your previous post to try to make something make sense here:

    You can use a psychological argument to say that by our psychological make-up it is possible for us to hold contradictory beliefs; you may indeed find people who have that. What, then, would it mean if you found someone who claimed to be an atheist and yet claimed to believe in a personal God?

    One way out would be to say that they are an atheist, but have some work to do in clearing out the underbrush to have a completely consistent set of beliefs.

    Another way would be to say that you don’t know; you’d have to examine their reasons and rationales to see which is what they believe and which are irrational, inconsistent, or outdated beliefs.

    The problem is that I don’t really think anyone would deny that, even those who answered A in the previous post. That we can have inconsistent sets of beliefs is undeniable psychologically. That we shouldn’t have them and so it is not a legitimate situation to be an atheist who believes in a personal God also seems well-supported.

    Ultimately, you’d be right in saying that it is not logically impossible to be an atheist that has a belief in a personal God, either directly or as a consequence of other beliefs, but I’m not sure that those situations are interesting in any way except to show that people who are in that situation have some work to do.

  • http://www.ericsteinhart.com Eric Steinhart

    @ibis3 -

    You can believe yourself to be a bathtub if you like. That doesn’t mean you are one.

    Correct: if B(Bob, (Bob is a bathtub) it does not follow that (Bob is a bathtub).

    And so B(Bob, (Bob is a bathtub)) does not contradict (Bob is not a bathtub).

    So your reasoning is in error and the contradiction you mention does not occur.

    And that’s exactly the point.

    • http://florilegia.wordpress.com Ibis3, denizen of a spiteful ghetto

      This whole conversation is ridiculous. Being an atheist consists of believing that “Gods do not exist” is a true statement. As long as Jane is of sound mind, if she truthfully describes herself thus: “I believe Gods exist” she has opted out of conforming to the definition. It doesn’t matter if she’s self-deluded or misunderstanding the question or the definition. Just like Bob and his bathtub claim. It doesn’t matter why he thinks he conforms to the definition of “bathtub”. Why is this so difficult for you to grasp?

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      Well, think of this question:

      A person has become an atheist, meaning that they do believe that gods do not exist. However, they have not cleaned up all of their inconsistent beliefs yet, and so maintain some beliefs that either directly or indirectly force them to assent to at least one god does exist. Is it wrong to call them an atheist until they’ve purged their belief system of all inconsistencies? Especially considering that if we also consider indirect beliefs there may be no way of determining when that is?

    • http://florilegia.wordpress.com Ibis3, denizen of a spiteful ghetto

      This: “they do believe that gods do not exist” is contradictory to this: “assent to at least one god does exist”. These are statements of fact and both can not be simultaneously true.

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      But, to repeat, would it be wrong to call them an atheist until they have eliminated all inconsistencies in their belief system?

    • http://florilegia.wordpress.com Ibis3, denizen of a spiteful ghetto

      Why call Bob a bathtub if he isn’t one? Aren’t you then just making the word “bathtub” mean something other than what is the accepted definition? That makes for awfully confused communication. Now we can sit down and all agree that from now on, “bathtub” will include in it’s definition “people like Bob” but maybe we’ll have to come up with a new word to describe “a vessel designed for people to bathe in”.

    • Josh, Official SpokesGay

      Stoic, don’t move the goalpost. This is not about subtle and changing inconsistencies. It’s about a thing being the exact opposite of another thing. Black is not white. Fire is not freezing cold. People who believe in God are not atheists.

      I cannot believe grown adults are spending time here debating this. Have you gone completely mad?

    • Josh, Official SpokesGay

      It certainly is ridiculous. In fact, it’s just wankery at this point. Honestly – if this is professional philosophy it’s embarrassing.

    • http://www.ericsteinhart.com Eric Steinhart

      Either prove a contradiction or accept the logic.

  • http://www.ericsteinhart.com Eric Steinhart

    @VerboseStoic -

    You’re appealing to this principle: if (B(x, P1) & B(x, P2) & . . . B(x, Pn)), then B(x, {P1, P2, . . . Pn}). And you’re saying that B(x, {P1, P2, . . . Pn}) is impossible if the set {P1, P2, . . . Pn} is inconsistent. Which, remarkably, entails that either every human has an entirely consistent belief set, or no human has any beliefs. Both of which are false.

    But let’s move on to your larger point — yeah, we already know from psychology how inconsistent people really are. I’ve been trying to say that for several posts now…

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      Actually, I never said it was impossible. At best, I said it was problematic. In short, it’s just as inconsistent at the logical level as at the belief level since as we believe propositions we have the exact same consistency issue with them at both levels.

      If all you wanted to say was that it is possible for us to have inconsistent beliefs, then fair enough. What that would mean for the definition of atheist is not altogether clear. The natural reaction would indeed be to say that any belief in a personal God means that you are not really an atheist. If you bring in the idea of inconsistent or outdated beliefs, then I do think someone could argue that someone could be an atheist and hold that belief but we would expect that to be transitory, not something that impacts the definition of atheist. And, as stated, it still wouldn’t be clear if you should call them an atheist in that case.

    • Josh, Official SpokesGay

      For God’s sake Eric, stop it. People have engaged you in good faith and clearly, explicitly explained that their objection is NOT to the fact that people are inconsistent but to the fact that you cannot sensibly say a person who believes in God is an atheist. Maybe it’s not intentional but you’re not playing fair on the rhetorical field here and it’s rude.

      If you want to say people are inconsistent, then say. Stop conflating that with the reasonable objection about terms meaning their exact opposite. Gah – that this even has to be said.

  • John Morales

    Eric:

    An atheist is a person who holds a certain belief.

    Can’t do that to a privative definition.

    The prefix a- indicates [absence of | without | lack of | not] — thus, an atheist is someone without theism.

    Expressing that in your logical format, if theism (T) is the proposition that God is believed to exist and B predicates belief, then a theist is x:B(x, T) and an atheist is xB(x, T).

    • Ben Finney

      Exactly so.

      Eric, please accept that when someone calls themselves an atheist, they are *not* bound to your insistence that they are making any proposition.

      Atheism is not any proposition about the facts of God. It is not “the proposition that God does not exist”; it is not “the belief that God does not exist”.

      Rather, an atheist is someone *who is not a theist*. Atheism is not a proposition, it is a position that one is unconvinced by *someone else’s* proposition.

      It’s weird that we need a term for that, when we don’t need a term for the absence of just about any other belief on the planet. But its weirdness doesn’t reduce the fact that the term *is* needed, to describe the minority of people who are free from a particularly pernicious class of belief.

      While you continue with your straw man definitions of atheist that we reject, you will continue to make nonsense of what we believe. Please accept that your definition of us is false, and that we have a perfectly working, sensible, sound definition.

    • John Morales

      [meta]

      Obviously, I think your comment is a damn good one! :)

  • http://eternalstranger.com drawswithpens

    I’m a bit confused here. You state:

    The difference between logical and psychological atheism is significant. For any believer x, (B(x, LA) & (not B(x, LA))) is a contradiction. Thus

    ((x believes that God does not exist) & (x does not believe that God exists)) is a contradiction.

    But wouldn’t (B(x,LA) & (not B(x,LA))) actually translate to ((x believes that God does not exist) & (x does not believe that God does not exist)) ? After all, you can’t turn LA into “God exists” for your translation of the second half, can you?

    • http://infinitegames.tumblr.com infinity

      Yeah, I pointed this out in comment #4 and he seems to agree, but hasn’t changed the OP.

    • John Morales

      But wouldn’t (B(x,LA) & (not B(x,LA))) actually translate to ((x believes that God does not exist) & (x does not believe that God does not exist)) ?

      No.

    • http://infinitegames.tumblr.com infinity

      …Can you explain?

    • http://eternalstranger.com drawswithpens

      I’d be interested in an explanation as well. It’s been a while since I’ve had formal logic, so if I’m missing something, I’d like to learn.

    • John Morales

      It literally translates to it, but it doesn’t mean it, as Eric has set it up.

      I can’t explain it any better than Eric did: it is a logical contradiction, but (given the empirical fact that people apparently can hold contradictory beliefs) is not a psychological one.

      (It’s similar to a paraconsistent logic)

    • John Morales

      Um. But yes, that’s the transliteration into natural language.

      (Sorry, I am too terse at times)

  • Josh, Official SpokesGay

    I’d really like to know what you think, Daniel Fincke. Does this conversation look reasonable to you? Am I the only one who sees this as pure through the looking glass nonsense? Is this the sort of thing any respectable philosopher would defend as precise argumentation? Frankly it’s an embarrassing spectacle.

    • http://florilegia.wordpress.com Ibis3, denizen of a spiteful ghetto

      It’s actually quite similar to the inanity of the ontological argument. You can’t define even a superlative god into existence. Even if you want to pretend you can by using symbols instead of plain words. It’s just equivocation and wordplay (aka bullshit).

      Eric, if you still think you have a case, explain in plain English, not symbolic logic, how Jill can be a flat-earther (defined as someone who believes “the earth is flat” to be a true statement) and can also simultaneously believe the earth to be spheroid. Given that Jill is an adult of at least average intelligence and sound of mind.

    • http://freethoughtblogs.com/camelswithhammers Daniel Fincke

      I’d really like to know what you think, Daniel Fincke. Does this conversation look reasonable to you?

      I’m not sure yet. I won’t have the time to look it all over and think about it carefully for a couple of days.

  • http://verbosestoic.wordpress.com/ Verbose Stoic

    Josh and ibis3,

    Before going on about my “shifting goalposts” (Josh) or simply talking about calling someone something they’re not (ibis3) both of you might have been better served reading what my actual OBJECTIONS were to Eric’s point, as I suspect you’d find that they were quite similar to yours.

    What I’m objecting to in your comments is the insistence that there’s no possible issue here, which is why I asked — multiple times, never answered — at what point of consistency would it be okay to call someone an atheist? Now, you can argue — and I’d be inclined to agree — that an explicit statement of a belief in God likely counts one out as an atheist, but that does not mean that the only other option is just something derived indirectly through a long and subtle chain of reasoning from existing beliefs. For example, someone might be inconsistent in thinking that God does not exist but we were intelligently designed, which by implication would claim that God exists. That’s not all that subtle, but then are they an atheist, a theist or what?

    Again, at what point can you say that someone has that sort of inconsistency in their belief system but it is still acceptable to call them an atheist?

    So, would you care to address this point, or concede it, or what?

    • Josh, Official SpokesGay

      Again, at what point can you say that someone has that sort of inconsistency in their belief system but it is still acceptable to call them an atheist?
      So, would you care to address this point, or concede it, or what?

      Sigh. I’ve addressed this. Over, and over, and over. A person cannot simultaneously say “I’m an atheist,” and “I believe in God,” and be considered sane. This is, if we’re to take the survey in question seriously, precisely what a portion of respondents said. This is nonsensical. It indicates a lack of understanding of the question, of the terms, or a conflicted internal state.

      It does not indicate there’s something sensible about saying “I believe in God and I also don’t believe in God.”

      Once again, in very small words, spoken very slowly: black is not white. Freezing cold is not searing hot.

      We’re talking the most basic, primary logical constructs. Are you really debating these?

    • http://freethoughtblogs.com/camelswithhammers Daniel Fincke

      I still have yet to read carefully but I take it the point may be that one part of one’s mind may believe one thing while another part of it believes another and that this is pretty common. Hence, the phenomenon of self-deception. Just today I had a creationist make a bunch of true comments that are only true if evolution is true. Creation and evolution were not part of the discussion so there was the easiest acceptance in the world of basic genetic concepts that in another concept, framed another way, he would most certainly start denying. It’s this kind of thing that I think Eric may be getting at. But, again, I’ve not read through all this yet.

    • http://freethoughtblogs.com/camelswithhammers Daniel Fincke

      Here’s another example. Someone who fears an authority figure’s punishments theoretically will not misbehave in egregious ways with the authority figure present. Let’s say there is a Christian who sincerely believes that God is always present watching and generally fears God’s punishments to the extent that he alters his behavior frequently to get God’s approval. Yet, despite this genuine belief, there are other times at which he acts in ways he never would if an authority who would punish him were in the room. He does things he wouldn’t even do if he thought it was only his boss or his wife who knew it. So, to do this action is to evince in practice a disbelief that he is being monitored by any authorities. And therefore, he also is acting in a way that indicates practical disbelief in God. So, he oscillates between belief and disbelief or both belief and disbelief operate in the same, very sane, cognitive dissonance afflicted mind.

      So, the question I think Eric is getting at is whether there are scenarios where someone with such an oscillation might be called an atheist or whether someone who is primarily an atheist could hold similarly incompatible beliefs.

      Maybe here’s an example. Say a convinced atheist in a moment of panic has fears that God is punishing him arise or say the atheist has the thought flash through his mind that he should pray to God for help. The atheist may remind himself that he has plenty of good reasons to dismiss those irrational fears or impulses but nonetheless some part of him still believes and is tempting him.

      In this context, consider THIS crazy brain: http://freethoughtblogs.com/camelswithhammers/2010/06/06/of-two-minds-about-the-existence-of-god/

    • danielrudolph

      That makes sense. If he had said that, we could have had a discussion.

    • http://www.legionofreason.com/ HJ Hornbeck

      I have two issues with that. First, the dissonance doesn’t persist; the atheist “accidentally” calling on a god will go “whoops, old habits die hard” and goes right back to non-belief. I doubt a never-believer could make that mistake, and from personal experience I know I’ve never made it without tougue firmly planted in cheek. A former believer might do it, sure, but over time the remembered behavior will fade away.

      Secondly, split-brain patients are called that for a reason: they functionally have two brains instead of one. Even Ramachandran himself clearly implies that person is best thought of as two seperate persons. If you need to abuse the very definition of “person” in order to create two conflicting beliefs about X, that’s a good sign we should doubt dissonance about X is even possible in normal circumstances.

      HJ Hornbeck

    • http://verbosestoic.wordpress.com/ Verbose Stoic

      Josh,

      No, you actually haven’t answered my question at all, which charitably means that you haven’t understood it. However, I think I can take on your example and explain Eric’s point, as I think that your strong reaction is the sort of reaction that he’s reacting against.

      Take this part of your comment:

      “Once again, in very small words, spoken very slowly: black is not white. Freezing cold is not searing hot. ”

      Eric doesn’t deny this. He accepts these sorts of things. What his argument is, though, is that when you are talking about beliefs this sort of argument doesn’t hold, because in these cases we are talking about the things themselves, in reality, and so by definition they can’t be in both states. But when we’re dealing with beliefs, is it possible for a person to be in two contradictory belief states? Well, presuming that you accept — as I think you must — that someone is still an atheist or theist even when they aren’t actually directly acting on those beliefs, then if someone has some cases where they act on “God doesn’t exist” and some cases where they act on “God exists” then it is possible for someone to be in contradictory belief states. And so Eric does not deny that atheism means that someone doesn’t believe God exists, but denies that being in a theistic belief state must mean that you can’t be an atheist.

      Let’s take the survey example. You claim that someone who would answer on that survey both that they are an atheist and that they believe in a personal God is not sane. I retort that all that means is that they have an inconsistent belief set. Their belief — take the strong atheist stance in this case because it’s clearer — that God does not exist comes to the fore when they answer “I’m an atheist”, but later, when examining the personal God question, their belief in a personal God comes to the fore. Since, however, having an inconsistent belief set is not in any way abnormal for humans — we do it all the time, and I’d bet that even you have an inconsistent belief set that we could reveal under similar circumstances over different propositions — it seems odd to call them insane. But it is inconsistent, and if we pointed it out to them they’d notice that and presumably try to resolve it. Perhaps we can say that they believe that God does not exist and believe that God exists, but don’t believe that they believe that God does not exist and that God does exist at the same time. Due to the circumstances, they are unaware of this inconsistency.

      Now, to the actual question: at what point in this, then, do we say that they are not an atheist?

      You can insist that they are not an atheist because they contain a belief that God exists. But as myself and Dan have pointed out, we can and do claim that someone believes X because it is the logical conclusion of other beliefs and behaviour they exhibit. If that’s the case, then what we see in examples like the creationist who holds beliefs that you can’t justify at least unless they believe in evolution mean that they are both creationists and evolutionists. What should we call them, then? Surely you’d want to argue that they aren’t actually both. So at some point we can put someone into one of those two categories even if they seem to hold some beliefs inconsistent with that category, which then should apply to the term “atheist” as well. And it is this question that you continually refuse to answer, despite claiming to have answered it multiple times.

      Now, one way out is to argue that in the cases Dan and I have been citing, there is no actual belief in the contradictory problem. While logically we should believe all the consequences of our beliefs, in practice it turns out that we don’t. So despite believing those things that seem to indicate that they must believe two contradictory propositions, they actually don’t; they simply haven’t worked out all the consequences of the beliefs they hold yet. There’s still an inconsistency, but we can still say that they don’t actually believe the specific inconsistent belief because they haven’t worked out the logical consequences yet. The survey case, though, seems to be a case where they do have the specific belief, and that wouldn’t be allowed.

      None of this would indeed prove them insane; they’d merely have an inconsistency. And one can question whether the survey case really does reveal separate specific beliefs. So it is possible that you are right and that the people in the survey should not be called atheists. But look at all the work we have to do to get there without running into massive issues that you simply could not see and so could not address. It’s not as trivial as you make it sound, and what Eric said in his initial post about a distinction between the logical contradiction and beliefs seems to be right, unless you have something to say that can contradict that as opposed to simply saying that it’s stupid.

  • ElGatoCello (@ElGatoCello)

    Eric,

    I like the argument you are trying to make, and generally agree with your conclusions and people who are still struggling coming to terms with their atheism still need to be welcomed into our community, but I think that there is a little bit of notation abuse (I mean this in the “mathematical sense” of the term.)

    The way you have defined LA, in the context of translating into everyday language,

    B(x, LA) ~B(x, ~LA)

    are indeed semantically identical.

    Put another way, if I redefined our terms where, without loss of generality x = Xavier because I enjoy descriptive variables,

    B(x, LA) == Xavier burrows to Los Angeles

    then

    ~B(x, ~LA) would mean

    ~(Xavier burrows to ~(Los Angeles))

    ~(Xavier burrows to someplace other than Los Angeles)

    Xavier did not burrow to someplace other than Los Angeles

    Which would mean that either Xavier did not burrow at all (our vacuous case which we may ignore for the same reason we discard “nobody believes anything”), or he burrowed to Los Angeles. Thereby implying B(x, LA). The if direction follows the same way.

    Whether or not {B(x, LA), A, A –> B(x, ~LA)} is logically consistent, in the end, has no bearing on how we should be interacting as a community.

    • http://infinitegames.tumblr.com infinity

      I don’t quite buy your argument. Most importantly, you substitute Los Angeles for “God does not exist” — the latter is a proposition, the former is not, so your analogous case will behave completely differently. So the negation of the latter is different from the negation of the former. (“someplace other than Los Angeles” compared to “God exists.”)

    • ElGatoCello (@ElGatoCello)

      I don’t see how that is a problem, though.

      In this particular case, as far as I can see, we are devolving our statement B(x, LA) into “x believes LA” right?

      I’d feel more comfortable agreeing with you if LA and “~LA” was actually a binary statement.

      In actuality, it isn’t.

      ~LA subsumes a number of different propositions with very different properties.

      i.e. ~LA could mean “Zeus exists” or “Yahweh exists” etc…

      Any person who is sufficiently desirous could certainly come up with some X such that X—>B(x,~LA) iff ~LA means “Zeus exists” but not when ~LA means “Juju On The Mountain exists.”

      If we’re going to define our statement in terms of our logical calculus, we should probably define it more strictly. As we’ve discussed it informally, it should probably translate to (Ax)(B(y,~Rx)) [For all gods x, y does not believe x exists.]

      Where B(x,y) means “x believes y” and Rx means “x exists” (Note that I would have used “Ex” but I didn’t want it to get confused with the existential quantifier.)

      That way, we could define rejection of our statement to be (Ex)(B(y,Rx)) [There exists a god x such that y believes x exists.]

      We could then say that the negation of our statement would result in ~(Ax)(B(y,~Rx)) or (Ex)~(B(y,~Rx)) [There exists a god x that isn't one that y believes doesn't exist.]

      From there, the argument still follows and still, (Ex)~(B(y,~Rx)) iff (Ex)(B(y,Rx)).

  • Steve Schuler

    “Do I contradict myself?
    Very well, then, I contradict myself;
    (I am large—I contain multitudes.)”

    From “Song of Myself” by Walt Whitman

  • http://thecanberracook.blogspot.com Alethea H. Claw

    Have you established that such people actually exist yet? I haven’t seen convincing evidence for that.


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