Those familiar with creation science know that it is often used as a tool in proselytizing. More times than I would care to remember, a discussion about the claims of creation science would turn into the creationist trying to convert the non-creationist. There was one creationist on CompuServe, Paul Ekdahl, who would post very lengthy messages copied verbatim out of creationist books (so slavishly verbatim that he would even include footnote numbers in the text); when I could finally get him to write something on his own, it would invariably an attempt to convert me.
But there was one incident that stands out in my mind. It happened at The City, a mall in Orange, California, that this year was replaced by a new mall, The Block. In the late-80's, one Scott Alexander opened a creationist fossil shop in The City called "In the Beginning." It was small and laid out like a jewelry store. To his credit, he labeled the fossils with the standard ages, but he also sold creationist books and had a number of exerpts from creationist books blown up and hanging as posters on the walls. It was in response to the poster of the standard creationist misquotation of Darwin concerning the evolution of the eye that started us talking. I informed him of what Darwin actually wrote, though he was skeptical. The next time I was there, I gave him a copy of the misquoted text. He immediately stuck it under the counter, where I'm sure it stayed just long enough for him to round-file it. On that first visit, he asked what I thought of the shop and I told him that the selection of books needed a bit more balance. But when I suggested Phillip Kitchner, he became rather upset at the idea. Guess creationists don't like "balanced treatment" when somebody tries to apply it to them, eh?
Either the first or second time I visited the shop, another customer joined the conversation and soon it was just the two of us, since Scott had work to do. We discussed what the evidence was and I was mainly pointing out the fallacies of creationist claims.
At one point, Scott inadvertantly helped me out. The other guy made a fairly standard claim that the ante-diluvial world did not have any oceans, but was mostly land, plus, that most of the fossilized animals were buried in the Flood. So I asked Scott what kind of fossil is most commonly found. Marine fossils, of course, lots and lots of them. Well, so much for there having been no oceans before the Flood, eh? He quickly changed the subject to something else.
After quite a while, with me doing most of the talking, he suddenly declared that he had been listening to me so now it was my turn to listen to him. Guess what? Instead of discussing creationism, he tried to convert me (gee, where have we seen that before?). But the argument he used was almost classic. I hadn't heard it used before, though I have heard it used a few times since then, so he must have gotten it from somewhere.
He tried to sell me after-life insurance! Though he didn't actually call it that. Rather, he used car insurance as an analogy. He said that we get car insurance just in case we ever get into an accident. If we have an accident, then we are glad we bought the insurance. If we never have an accident, then at least having had the insurance had saved us a lot of worry. Similarly, if Hell exists and we convert, then we are saved, but if we don't convert, then we are damned for Eternity. And if it turns out that Hell does not exist, then we would have lost nothing by having converted but would have gained peace of mind.
Unfortunately for him, I immediately recognized his argument as a rehash of the classic Pascal's Wager. Even more unfortunately for him, I also knew the Wager's problems. It very quickly became obvious that he neither knew Pascal's Wager nor its problems, but he soon learned.
Blaise Pascal postulated that there are two possible conditions, either God exists or He does not, and there are two possible actions you could take, either you believe in God or you do not. Graphing these two possible conditions and two possible actions yields four possible outcomes (green is good, red is bad):
- God exists.
- God does not exist.
- You believe in God.
- You do not believe in God.
|God Does Not Exist
|You Believe in God
|You are saved. You win.
|No loss, but you gain peace of mind and are a better person. You win.
|You Do Not Believe in God
|You are damned. You lose.
|No loss, but also no gain. You do not win; your life was wasted.
Presenting that as a list:You win in these cases --
- If God exists and you believe in Him: then you are saved.
- If God does not exist and you believe in Him: then no loss, but you gain peace of mind and are a better person.
However you lose in these cases --
- If God exists and you do not believe in Him: then you are damned for eternity. This is the ultimate loss.
- If God does not exist and you do not believe in Him: then no loss, but also no gain. You lose by having cheated yourself out of the opportunity to live a good life through faith.
Pascal's reasoning seems to assume that belief in God is needed for a good life. Therefore, with these outcomes if you do not believe in God, then there is a 50% chance of losing really big-time and 50% chance that you would have simply not led a good life. Therefore, you gain nothing by not believing in God and stand to lose everything. However, if you do believe in God, then there is 100% chance you will win, since if God exists then you are saved and if He doesn't exist then you will have at least led a good life. Therefore, choosing to believe in God is a sure bet.
It looks deceptively simple ... because it is both deceptive and simple. The most basic problem is with that basic implicit assumption the God is needed to lead a good life, which is false (that is addressed below by the Atheist's Wager). But that's not the least of Pascal's Wager's problems.
First there is one very basic question which never gets asked here: which god? Just because some of the gods may exist, does not mean that they all exist. Which one do you choose? Remember, if you choose the wrong one, the outcome will be the same as for not choosing any (ie, #3 and #4). Each god has roughly the same probability of existing as any other (ignoring some of the pantheon package deals out there), or that none of them exist. So choosing the right god is not 100% as presented to us, but rather is a fraction of 1%.
Even worse, you not only need to choose the right god, but you also need to choose the right theology. Some gods have a variety of theologies associated with them, each one considering itself the True Faith and the others heresies; e.g., the various sects of Christianity. So even if you choose the right god, if you choose the wrong theology, then you are just as out of luck as if you had chosen the wrong god, some times even more so. Pascal was a Catholic, so he was talking about choosing to be a Catholic. The Protestants using his Wager in vain have already chosen the wrong theology and so picked the losing side of the Wager and are trying to make losers out of everyone they proselytize to. To choose none of the gods actually turns out to be the safer bet, because, unlike the Christian god, a lot of the gods couldn't care less whether you believe in them or not.
And what happens if you choose a god and it turns out that none of them exist? Pascal naively assumed that being a Catholic had an inherent benefit of making you a better person, which you could not achieve as a non-believer. While there may be some room for argument in the first part, the last part is blatantly untrue.
Pascal maintained that believing in his god and theology costs you nothing, but that is not true of his own theology, nor of most of the theologies that exist. What if you could not pursue your dream career because your chosen god forbade it? Or marry your one true love (your "media naranja", or "half orange", as my wife's grandmother had put it) because your god forbade you to marry that kind of person? Or learn the sciences because your god forbade you to study the truth? Or to think for yourself because your god forbade it? Or had to suffered from a horrible disease or injury or had to watch your child die horribly of a treatable disease because your god forbade the medical treatment for it? For many of us, that would be too great a cost to bear.
So I told my after-life insurance salesman that his after-life insurance was a rotten deal (unfortunately, I didn't think of that name for it until the next day, but that poor guy was already hurting too much). We had to pay an exorbinant price for a policy that would only pay in the most restricted and oddest of circumstances. By the car insurance analogy, it would only pay if you were hit by a green Edsel -- on the northbound side of the Santa Ana Freeway -- while it was exceeding the speed limit -- backing up -- at night -- with its lights off -- being driven by a one-armed Lithuanian midget.
He had been so self-assured that his argument was flawless and unassailable. He couldn't understand what had just happened. I think he still doesn't know what had hit him.
Which goes to show that it does pay to read the classics.
Recently while following links through Wikipedia, I encountered this variation on and response to Pascal's Wager. The article appears to be based on American philosopher Michael Martin's description of it in his 1990 book, Atheism: A Philosophical Justification, with which I am not familiar. Searching around a bit, I have found another use of this Wager, which I will discuss below briefly. Indeed, the article seems to allude to there being multiple versions of this Wager, as indicated in the quotation below.
The Atheist's Wager is used to prove that the results of leading a good life has nothing to do with whether any gods exist. Gods or no gods, leading a good life has a positive outcome. Furthermore, it can be used to show that atheism is a more rational position than theism is.
According to the article, the assumptions of one version of the Atheist's Wager are:The article proceeds with the assumption that should a god exist, it would be a benevolent god. I feel that this leaves out the situation of an arbitrary and/or malevolent god, in which case all bets would be off. More on that below.One version of the Atheist's Wager suggests that since a kind and loving god would reward good deeds – and that if no gods exist, good deeds would still leave a positive legacy – one should live a good life without religion. Another formulation suggests that a god may reward honest disbelief, a reward which would then be jeopardized by a dishonest belief in the divine.
Let's examine the Atheist's Wager more formally by following the format from the discussion of Pascal's Wager above.
Remember that Pascal's Wager used one set of conditions (either God exists or He doesn't) and only one set of actions (either you believe in God or you do not), which results in four possible outcomes (22). The Atheist's Wager uses the same inputs as Pascal's Wager (albeit redefining the condition slightly to be the existence of a benevolent god) plus an additional set of actions (either you lead a good life or an evil one). Thus the Atheist's Wager has three sets of binary inputs in contrast with Pascal's Wager's two, thus the Atheist's Wager ends up with eight possible outcomes (22).
That would require a three-dimensional table, but since my skills for rendering 3-D tables in HTML is limited, I will follow the Wikipedia article's lead and split it into two 2-D tables. Each table represents one of the two conditions and presents the outcomes of the two sets of actions (again, in the graphs green is good and red is bad):Possible Conditions:Looking at the tables, we can see that the only factor that really matters is what kind of life you lead; the existence/non-existence of and belief/non-belief in any gods are simply not factors and have no real bearing on the outcome.
- A benevolent god exists.
- A benevolent god does not exist.
- You believe in a god.
- You do not believe in a god.
- You lead a good life.
- You lead an evil life.
A Benevolent God Exists You Believe in It You Do Not Believe in It You Lead a Good Life Heaven (infinite gain) Heaven (infinite gain) You Lead an Evil Life Hell (infinite loss) Hell (infinite loss)
A Benevolent God Does Not Exist You Believe in It You Do Not Believe in It You Lead a Good Life Positive Legacy (finite gain) Positive Legacy (finite gain) You Lead an Evil Life Negative Legacy (finite loss) Negative Legacy (finite loss)
Presenting that as a list (copied from the Wikipedia article):
- You may live a good life and believe in a god, and a benevolent god exists, in which case you go to heaven: your gain is infinite.
- You may live a good life without believing in a god, and a benevolent god exists, in which case you go to heaven: your gain is infinite.
- You may live a good life and believe in a god, but no benevolent god exists, in which case you leave a positive legacy to the world; your gain is finite.
- You may live a good life without believing in a god, and no benevolent god exists, in which case you leave a positive legacy to the world; your gain is finite.
- You may live an evil life and believe in a god, and a benevolent god exists, in which case you go to hell: your loss is infinite.
- You may live an evil life without believing in a god, and a benevolent god exists, in which case you go to hell: your loss is infinite.
- You may live an evil life and believe in a god, but no benevolent god exists, in which case you leave a negative legacy to the world; your loss is finite.
- You may live an evil life without believing in a god, and no benevolent god exists, in which case you leave a negative legacy to the world; your loss is finite.
But to make that more clear, I will apply some of my professional training (computer logic) and present the above as a truth table from which we will derive a Boolean Algebra expression which we can then simplify down to the minimal logical expression.
If you are not familiar with Boolean Algebra or with designing digital logic circuits, here are a few definitions:
Now let's apply those ideas to expressing the Atheist's Wager as a truth table, which we can then simplify to its minimal form, eliminating extraneous inputs in the process:
- Many of the rules of algebra also apply to Boolean Algebra. The differences are:
- Boolean variables have one of two values: true or false. True is often expressed as one(1) and false as zero (0).
- Addition represents the OR function, which yields a true result if any of the inputs are true.
- Multiplication represents the AND function, which yields a true result only if all the inputs are true.
- The third function is inversion, AKA "NOT", which is represented in various ways such as with the symbol ¬. It takes only one input with the output being the inverse; ie, a true input produces a false output and a false input produces a true output.
- A Boolean function produces a single true/false output based on several inputs.
- A truth table is a common tool for displaying all the possible values of the inputs of a Boolean function along with the corresponding output. For n inputs, there are 2n possible combinations of input values and hence 2n possible outputs; eg, 2 inputs -> 4 outputs, 3 inputs -> 8 outputs, 4 inputs -> 16 outputs, 10 inputs -> 1024 outputs. In the data sheet of almost any digital circuit you will find a truth table for that circuit's logic.
- Any combinatorial logic circuit can be expressed as a Boolean function. The process of designing a logic circuit includes using Boolean algebra to simplify the circuit's Boolean expression down to a minimal form using the least number of components. That minimization can also serve to eliminate inputs that are simply not needed by the circuit.
- A common first step in circuit design involves creating a truth table of all possible inputs and their corresponding outputs, which can then be expressed as a Boolean function. That would be the initial Boolean function which you will then simplify.Boolean Variables:Therefore, the only meaningful factor is how you live your life. If you lead a good live, then the outcome is positive and if you lead an evil life then the outcome is negative. The existence of any gods has no bearing in the matter, nor does whether you believe in them.
The values of the result (the function f(G,B,L) as read from the 3-D table above) will be:
- G = a benevolent god exists -- T = exists, F = does not exist
- B = belief in a benevolent god -- T = believes, F = does not believe
- L = leads a good life -- T = good life, F = evil life
- T = positive outcome (ie, heaven or positive legacy)
- F = negative outcome (ie, hell or negative legacy)
Now we can read the Boolean expression straight off the table:
Truth Table Inputs Outcome G B L f(G,B,L) T T T T T T F F T F T T T F F F F T T T F T F F F F T T F F F F
- For every T result, we write that term.
- Every term of the expression is a combination of the variables G, B, and L:
- If the input variable was a T, then we simply write that variable.
If it was an F, then we invert it; ie, if G is an F, then we write ¬G for "not-G".
- The meaning of the term is that we are AND-ing those variables together (AND is logical multiplication).
Eg, G¬BL means "G AND NOT-B AND L", which will be true (T) if G=T, B=F, and L=T; if not, then the term will be false (F).
- The terms are all OR'd together (logical addition).
- The entire expression will be true (T) if any one term is true. If all terms are false (F), then the entire expression is false.
The expression is (using parenthesis to make clear which variable is NOT-ed):Outcome = GBL + G(¬B)L + (¬G)BL + (¬G)(¬B)LMost of the rules of algebra apply for grouping and factoring. Please also note the following identities that are used for simplifying:NOTE: in order to avoid confusing T and F for variables, T = 1, F = 0Applying those rules to our expression above:
A + ¬A = 1
A(¬A) = 0
A( 1 ) = A
A + 1 = 1
A( 0 ) = 0
A + 0 = A
Outcome = GL(B + ¬B) + (¬G)L(B + ¬B)
Outcome = GL( 1 ) + (¬G)L( 1 )
Outcome = GL + (¬G)L
Outcome = L(G + ¬G)
Outcome = L( 1 )
Outcome = L
For completeness sake, let's return to the truth table and simplify it by introducing a third possible input state: X. Where you see an X input, then that means "don't care"; the output is the same whether that input is true or false. BTW, that is the notation that you will see in the truth tables in datasheets for digital logic circuits.That simpler truth table also shows that the input values for G (existence of a god) and B (belief) have no bearing on the outcome. The outcome depends entirely on how you live your life.
Truth Table Inputs Outcome G B L f(G,B,L) X X T T X X F F
As an additional exercise, we should note that that simplification could have been performed entirely through the truth table. If we rearrange the rows we can pair up rows that are identical except for one input, which we can then combine and replace that input with an X. For example, rearranging the rows of the truth table above:Combining the adjacent rows which are the same regardless of the value of B (belief):
Truth Table Inputs Outcome G B L f(G,B,L) T T T T T F T T T T F F T F F F F T T T F F T T F T F F F F F F
Rearrange to pair up rows based on G (existence of a god):
Truth Table Inputs Outcome G B L f(G,B,L) T X T T T X F F F X T T F X F F
Combine the "don't care" rows based on G (existence of a god):
Truth Table Inputs Outcome G B L f(G,B,L) T X T T F X T T T X F F F X F F
And we get the same minimal truth table as above.
Truth Table Inputs Outcome G B L f(G,B,L) X X T T X X F F
So again we find that the input values for G (existence of a god) and B (belief) have no bearing on the outcome. The outcome depends entirely on how you live your life.
As I already mentioned, I feel that the argument presented on the Wikipedia page for the Atheist's Wager is incomplete because it only considers whether a benevolent god exists. But if a benevolent god does not exist, then that would mean either that no god(s) exist (which is what I assume is supposed to be implied) or that a malevolent god exists. Or if not actually malevolent, then at the very least very arbitrary. Like the god described by that subset of Christian sects that includes fundamentalists and evangelicals.
Frankly, with a god like that all bets are off. As Dan Barker says in his song, You Can't Win with Original Sin: "Any god that would damn me will just as certainly damn you too." It's like being in a very bad marriage (been there!) with a spouse who is impossible to please: damned if you do, damned if you don't, damned no matter what! Even when she describes explicitly what would please her and you do exactly what she tells you, you're still damned.
Similarly with the malevolent god of that set of Christian sects, even when you do everything you're told to in order to be saved, you still don't know whether you're saved -- I have read countless testimonials and anecdotes of former and current believers who have suffered those agonizing doubts. Remember that each of those sects believe that all the other sects have gotten it wrong, so you have to believe that your particular narrow sect is the one that had gotten everything right. Because if it had gotten wrong anything part of the requirements for salvation, regardless of how minute, then your arbitrary god will damn you for it. Or, being absolutely arbitrary, He'll damn you anyway even if you met every single arbitrary requirement, because ... arbitrary.
That is the Universe of Hurt that you let yourself in for by believing in a god who is not benevolent.
On the Philosophy of Religion website (copyright by Tim Holt), is a discussion of Pascal's Wager and on the Atheist's Wager. The author refers to Michael Martin (links to a Philosophy of Religion biographical web page) and starts out paraphrasing him, so I would assume that this page is a paraphrasing of what Michael Martin had written.
He points out a major problem of Pascal's Wager being that it ignores other possible entrance criteria for heaven and that those other criteria would depend on what kind of god exists (hence the earlier discussion's assumption of a benevolent god as opposed to my discussion of an arbitrary and possibly malevolent god). For example:We literally cannot analyze or discuss the outcome of our actions in any meaningful manner if a god or gods exist. Therefore, in order to work out the consequences of our actions and what actions are in our interests, we must remove the existence of the gods from such analysis; we must assume that atheism is true in order to develop any kind of meaning discussion.Consider anything that you might do in order to get to heaven. Whether it is believing in God, or performing good works, or converting heathen, there are always two possible outcomes if there is a God. There are possible gods that would admit you to heaven because of what you have done, and there are possible gods that would consign you to hell for what you have done. Any action, then, could either lead to heaven or to hell. We therefore cannot decide what to do based on what consequences that course of action would have if there were a God.
So, to believe or not to believe. What are the costs versus benefits when the gods do not exist?Through experience and real-world observation, it is obvious that belief is of dubious benefit and is the source, or at the very least an enabler, of far more evil than good. By their fruits we do know them. As the author of the page points out, in an atheistic universe it is better to be an atheist and any successful pragmatic argument is successful will be an argument for atheism, not for theism. And if a god or gods exist, then we have nothing to go by and we cannot formulate any successful pragmatic argument.
- Even if God does not exist, it could be that religious belief brings sufficient happiness to those that possess it that it is better to be a believer than it is to be an atheist. If that is the case then we are pragmatically justified in believing in God.
- If God does not exist, it is plausible to think that the cost of religious observance outweighs its benefits. If that is the case, then it is better to be an atheist.
That page then presents a revised version of the Wager:This revised version of the Wager would go something like this:
- It is possible that God exists and it is possible that God does not exist.
- If one believes in God then if he exists then one either receives an infinitely great reward or an infinitely great punishment and if he does not exist then one loses little or nothing.
- If one does not believe in God then if he exists then one either receives an infinitely great reward or an infinitely great punishment and if he does not exist then one gains little or nothing.
- It is better to either receive an infinitely great reward or an infinitely great punishment or gain little or nothing than it is to either receive an infinitely great reward or an infinitely great punishment or lose little or nothing.
- It is better not to believe in God than it is to believe in God.
- If one course of action is better than another then it is rational to follow that course of action and irrational to follow the other.
- It is rational not to believe in God and irrational to believe in God.
Did you also find Item #4 confusing and difficult to parse? Let me take a crack at it:Michael Martin is quoted indirectly as saying that if any pragmatic argument of the form of Pascal’s Wager is sound, then it is an argument for atheism, rather than for religious belief. I think that that point has been well made."It is better to either receive an infinitely great reward or an infinitely great punishment or gain little or nothing than it is to either receive an infinitely great reward or an infinitely great punishment or lose little or nothing."
Let's substitute some of the wording with place-holders:
Performing that substitution, we get:
- Statement-A = "receive an infinitely great reward or an infinitely great punishment"
- Statement-B = "gain little or nothing"
- Statement-C = "lose little or nothing""It is better to either Statement-A or Statement-B than it is to either receive an Statement-A or Statement-C."Remember that we are comparing the outcomes of believing or not believing. If any gods do exist, then the outcome is the same whether we believe or not: "receive an infinitely great reward or an infinitely great punishment". Remember, just believing is no quarantee of an infinitely great reward because of the arbitrary nature of a malevolent god, just as not believing is no quarantee of an infinitely great punishment because of the possibility of a benevolent god. Therefore, since Statement-A is a possible consequence in both cases, it can be safely removed from the analysis; it makes no difference whatsoever and hence is useless.
That reduces Item #4 to the following (text re-substituted in awkward either-or wording edited out):"It is better to gain little or nothing than it is to lose little or nothing."We can see that that statement is true, because a gain is better than a loss.
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First uploaded on 1999 March 05.
Last updated on 2017 March 27.