Originally Posted by
Petros Agapetos
Philosophical Atheism: The Logic of Atheism!
Let X = God exists
Then ~X = God does not exist
There are only two possible outcomes: existence and non-existence. If existence is the case, then non-existence is not, and vice versa.
We do NOT assess the truth value of a proposition by entertaining both the positive claim and the negative claim simultaneously:
Positive proposition: God exists.
Negative proposition: God does not exist.
Instead, we assign belief or disbelief to a single proposition separately, as follows: by entertaining each of the positive and negative claims separately, like so:
Positive proposition: God exists.
There are only two possible belief positions here: one of belief (accepting the proposition as true) or disbelief (not accepting the proposition as true).
Negative proposition: God does not exist.
Again, one can only assign belief or disbelief. One cannot both believe and disbelieve a proposition X. One can also not neither believe nor disbelieve a proposition X. One has to choose either belief or disbelief, not neither, and not both! There is no middle option between belief in a proposition and disbelief.
In fact there either is a god or there isn’t. There are only two possible outcomes in reality. However, this true dichotomy (a set of only two options which exhaust all possibilities) refers to the facts of existence (ontology), not what we believe about them (epistemology). When assigning belief or disbelief to each positive and negative propositions, we end up with four possible belief positions:
[+]. God exists:
- I believe: carries the burden of proof!
- I do not believe: the default position in the absence of sufficient evidence to warrant belief; has no burden of proof!
[-]. God does not exist
- I believe: carries the burden of proof!
- I do not believe: has no burden of proof, and is in fact the default position.
Nothing is presumed to exist that does not have sufficient evidence indicating its existence warranting belief.
Failing to become convinced =
failing to believe (fail to accept as true)
The default position is to disbelieve until it has been demonstrated to be the case. The burden of proof is on the claimant (regardless of whether the proposition is positive or negative), the burden of proof is not on the one rejecting a claim.
This is why...
Hard atheism = I believe god does not exist = has the burden of proof! because it is an assertion of god’s non-existence. The hard atheist must meet his burden of proof in order for his belief position to become believable.
Soft atheism = I do not believe god exists = has no burden of proof; is in fact the default position! Notice that there is no burden of proof for rejecting a proposition! The burden of proof is always on the claimant! and not for those who persist in disbelief in the absence of sufficient evidentiary warrant to accept the proposition.
X = God exists
~X = God does not exist
1. I believe X (is true)
2. I do not believe X (is true)
3. I believe ~X (is true)
4. I do not believe ~X (is true)
Either X is true or ~X is true <LEM>
Either X is true or X is false <Bivalence >
LEM = Law of Excluded Middle
Everything must either be or not be.
Bivalence = LEM & LNC
LNC = Law of Non-Contradiction
~(X & ~X)
LNC = X and ~X cannot both be true - nothing can both be and not be.
A proposition X and its negation ~X cannot both be true implies that proposition X cannot be both true and false (simultaneously, at the same time, in the same sense).
If X is true, then ~X is false.
If X is false, then ~X is true.
(1) is equivalent to:
- I believe ~X is false
(2) is equivalent to:
- I do not believe ~X is false
(3) is equivalent to:
- I believe X is false
(4) is equivalent to
- I do not believe X is false
(I) I believe X (god exists)
(II) I do not believe X (god exists)
(III) I believe ~X (god does not exist)
(IV) I do not believe ~X (god does not exist)
Note!
The set (I) is not identical to set (IV).
That is, saying “I believe god exists” is not the same as saying “I do NOT believe god does NOT exist”. The former is an acceptance of a positive claim; the latter is a rejection of a negative claim.
The set (II) is not identical to set (III).
That is, saying “I do not believe god exists is not the same as saying “I believe god does not exist”. The former is a rejection of a positive claim; the latter is an acceptance of a negative claim.
Please note that:
Not believing god exists is not necessarily equivalent to believing god does not exist.
Likewise:
Believing god exists is not necessarily equivalent to not believing god does not exist.
Clarification:
Within the set of people who do not believe ‘god exists’, is a subset of people who believe ‘god does not exist.’
Within the set of people who reject god’s non-existence, is a subset of people convinced of god’s existence.
Examples to drive the point home!
Example 1.
Flip a coin!
The only two possible outcomes are “heads” and “tails”. However, belief is not limited to only these two options:
- I believe “heads”
- I do not believe “heads”
- I believe “tails”
- I do not believe “tails”
In the absence of sufficient information to assess the probability of “heads” and “tails”, it is conceivable that one could find himself in no better position than to disbelieve either claim:
Claim 1. The outcome is “heads”
Claim 2. The outcome is “tails”
One can be forced by rationality to disbelieve both possible options (due to insufficient information to assess probability), even though one of these options has to actually be the case!
Not believing the coin is going to land “heads” is not necessarily equivalent to believing the coin is going to land “tails”.
Example 2.
The number of blades of grass in my backyard is either even or odd. If the number is not even, it must be odd (and vice versa). Here are the possible belief positions:
The only two possible outcomes in reality:
Claim A. The number is “even”
Claim B. The number is “odd”
The four possible belief positions:
- I believe “even”
- I do not believe “even”
- I believe “odd”
- I do not believe “odd”
In the absence of sufficient evidence warranting belief on either proposition one can be forced by rationality to disbelieve either one of only two possible options: one may be rationally justified to disbelieve either claim (even though we know, one of them has to actually be the case).
Notice again!
Not being convinced the number is even is not the same as being convinced the number is odd. One can disbelieve both the claim that the number is even as well as the claim that the number is odd.
Similarly,
Not being determined to be true is not equal to being determined to be false.
Example 3 - The Courtroom Analogy!
Either the defendant is guilty (committed the crime) or the defendant is innocent (did not commit the crime). However, failing to find the defendant guilty does not in any way establish the defendant’s innocence!
In court, we assess the proposition
“The defendant is guilty”. We do not assess innocence!
Proposition: “The defendant is guilty”.
The only two possible belief positions for this single proposition are belief and disbelief.
- Belief (The defendant has been found guilty)
- Disbelief (The defendant is “not guilty” = has not been found guilty).
The set of people who are in fact innocent is a subset within the set of people who have not been found guilty.
Similarly, the set of people who believe ‘god does not exist’ is a subset within the set of people who do not believe ‘god exists.’
Among those who have failed to be proven guilty, there are those who are in fact innocent (a subset of the “not guilty”).
Similarly,
“I believe god does not exist” implies
“I do not believe god exists”.
However...
“I do not believe god exists” does not necessarily imply that “god does not exist.” Just as not being found guilty does not imply a demonstration of innocence, not being convinced that god exists does not imply belief in god’s non-existence!
How can you preach atheism and know your logic is correct when you do not even know the proper notation ? The proper notation is P, ~P, P v Q, P ^ Q , P ==>Q etc. and truth tables.Second of all, you say the burden of proof is on the believers however you fail to comment that truth only exists in mathematical world. For instance, go try to prove that all crows are black ! Sure, you might get lucky and find a crow with a non-white feather in the beginning of your search but that is unlikely ! The real world is a place for wonderful things--sunsets and flowers and poetry. It surely is a place for love. But truth lives somewhere else. Truth lives in the mathematical world. Therefore, I propose a Bayesian analysis of the situation. Most believers in god try to use the Reductio ad unlikely but that does not always work so in this case I better draw a Bayes Box which I will do after explaining the priors.
The first difficulty is to understand the priors. This is a hard thing to get your head around. For the roulette wheels, we were asking: How likely do we think it is that the wheel is rigged, before we see any of the spins? Now we’re asking: How likely would we think it was that there was a God, if we didn’t know that the universe, the Earth, or we ourselves exist?
At this point, the usual move is to throw up one’s hands and invoke the charmingly named principle of indifference—since there can be no principled way to pretend we don’t know we exist, we just divvy up the prior probability evenly, 50% for GOD and 50% for NO GOD.
If NO GOD is true, then complex beings like humans must have arisen by pure chance, perhaps spurred along by natural selection. Designists then and now agree that this is phenomenally unlikely; let’s make up numbers and say it was a one-in-a-billion-billion shot. So what goes in the bottom right box is one-billion-billionth of 50%, or one in two billion billion.
What if GOD is true? Well, there are lots of ways God could be; we don’t know in advance that a God who made the universe would care to create human beings, or any thinking entities at all, but certainly any God worth the name would have the ability to whip up intelligent life. Perhaps if there’s a God there’s a one in a million chance God would make creatures like us.
So the box now looks like this:
At this point we can examine the evidence, which is that we exist. So the truth lies somewhere in the bottom row. And in the bottom row, you can plainly see that there is a lot more probability—a trillion times more!—in the GOD box than in the NO GOD box.
This, in essence, is the famous William Paley’s case, the “argument by design,” as a modern Bayesian type would express it. There are many solid objections to the argument by design, and there are also two billion billion fighty books on the topic of “you should totally be a cool atheist like me” where you can read those arguments, so let me stick here to the one that’s closest to the math at hand: the “SIMs” objection.
You probably know what Sherlock Holmes had to say about inference, the most famous thing he ever said that wasn’t “Elementary!”:
“It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth.”
Doesn’t that sound cool, reasonable, indisputable?
But it doesn’t tell the whole story. What Sherlock Holmes should have said was:
“It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth, unless the truth is a hypothesis it didn’t occur to you to consider.”
Less pithy, more correct. The people who inferred that God either exists or does not exist were considering only two hypotheses:
The argument by design suffers from much the same problem. If the only two hypotheses you admit are NO GOD and GOD, the rich structure of the living world might well be taken as evidence in favor of the latter against the former.
But there are other possibilities. What about GODS, where the world was put together in a hurry by a squabbling committee? Many distinguished civilizations have believed as much. And you can’t deny that there are aspects of the natural world—I’m thinking pandas here—that seem more likely to have resulted from grudging bureaucratic compromise than from the mind of an all-knowing deity with total creative control. If we start by assigning the same prior probability to GOD and GODS—and why not, if we’re going with the principle of indifference?—then Bayesian inference should lead us to believe in GODS much more than GOD.*
Why stop there? There’s no end to the making of origin stories. Another theory with some adherents is SIMS, where we’re not actually people at all, but simulations running on an ultracomputer built by other people.* That sounds bizarre, but plenty of people take the idea seriously (most famously, the Oxford philosopher Nick Bostrom), and on Bayesian grounds, it’s hard to see why you shouldn’t. People like to build simulations of real-world events; surely, if the human race doesn’t extinguish itself, our power to simulate will only increase, and it doesn’t seem crazy to imagine that those simulations might one day include conscious entities that believed themselves to be people.
If SIMS is true, and the universe is a simulation constructed by people in a realer world, then it’s pretty likely there’d be people in the universe, because people are people’s favorite things to simulate! I’d call it a near certainty (for the sake of the example, let’s say an absolute certainty) that a simulated world created by technologically advanced humans would have (simulated) humans in it.
If we assign each of the four hypotheses we’ve met so far a prior probability of 1/4, the box looks something like this:
Given that we actually do exist, so that the truth is in the bottom row, almost all the probability is sitting in SIMS. Yes, the existence of human life is evidence for the existence of God; but it’s much better evidence that our world was programmed by people much smarter than us.
Advocates of “scientific creationism” hold that we should argue in the classroom for the existence of a world-designer, not because the Bible says so—that would be unconstitutionally naughty!—but on coolly reasonable grounds, founded on the astonishing unlikelihood of the existence of humanity under the NO GOD hypothesis.
But if we took this approach seriously, we would tell our tenth graders something like this: “Some have argued that it’s highly unlikely for something as complex as the Earth’s biosphere to have arisen purely by natural selection without any intervention from outside. By far the most likely such explanation is that we are actually not physical beings at all, but residents of a computer simulation being carried out by humans with unthinkably advanced technology, to what purpose we can’t exactly know. It’s also possible that we were created by a community of gods, something like those worshiped by the ancient Greeks. There are even some people who believe that one single God created the universe, but that hypothesis should be considered less strongly supported than the alternatives.”
The SIMs hypothesis
The simulation hypothesis or simulation theory proposes that all of reality, including the Earth and the universe, is in fact an artificial simulation, most likely a computer simulation. Some versions rely on the development of a simulated reality, a proposed technology that would seem realistic enough to convince its inhabitants the simulation was real. The hypothesis has been a central plot device of many science fiction stories and films.
...
Simulation hypothesis
Nick Bostrom's premise:
Many works of science fiction as well as some forecasts by serious technologists and futurologists predict that enormous amounts of computing power will be available in the future. Let us suppose for a moment that these predictions are correct. One thing that later generations might do with their super-powerful computers is run detailed simulations of their forebears or of people like their forebears. Because their computers would be so powerful, they could run a great many such simulations. Suppose that these simulated people are conscious (as they would be if the simulations were sufficiently fine-grained and if a certain quite widely accepted position in the philosophy of mind is correct). Then it could be the case that the vast majority of minds like ours do not belong to the original race but rather to people simulated by the advanced descendants of an original race.
Nick Bostrom's conclusion:
Nick Bostrom in 2014
It is then possible to argue that, if this were the case, we would be rational to think that we are likely among the simulated minds rather than among the original biological ones.
Therefore, if we don't think that we are currently living in a computer simulation, we are not entitled to believe that we will have descendants who will run lots of such simulations of their forebears.
— Nick Bostrom, Are you living in a computer simulation?, 2003[2]
Ancestor simulation
In 2003, philosopher Nick Bostrom proposed a trilemma that he called "the simulation argument". Despite the name, Bostrom's "simulation argument" does not directly argue that we live in a simulation; instead, Bostrom's trilemma argues that one of three unlikely-seeming propositions is almost certainly true:
"The fraction of human-level civilizations that reach a posthuman stage (that is, one capable of running high-fidelity ancestor simulations) is very close to zero", or
"The fraction of posthuman civilizations that are interested in running simulations of their evolutionary history, or variations thereof, is very close to zero", or
"The fraction of all people with our kind of experiences that are living in a simulation is very close to one"
The trilemma points out that a technologically mature "posthuman" civilization would have enormous computing power; if even a tiny percentage of them were to run "ancestor simulations" (that is, "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor), the total number of simulated ancestors, or "Sims", in the universe (or multiverse, if it exists) would greatly exceed the total number of actual ancestors.
Bostrom goes on to use a type of anthropic reasoning to claim that, if the third proposition is the one of those three that is true, and almost all people with our kind of experiences live in simulations, then we are almost certainly living in a simulation.
Bostrom claims his argument goes beyond the classical ancient "skeptical hypothesis", claiming that "...we have interesting empirical reasons to believe that a certain disjunctive claim about the world is true", the third of the three disjunctive propositions being that we are almost certainly living in a simulation. Thus, Bostrom, and writers in agreement with Bostrom such as David Chalmers, argue there might be empirical reasons for the "simulation hypothesis", and that therefore the simulation hypothesis is not a skeptical hypothesis but rather a "metaphysical hypothesis". Bostrom states he personally sees no strong argument for which of the three trilemma propositions is the true one: "If (1) is true, then we will almost certainly go extinct before reaching posthumanity. If (2) is true, then there must be a strong convergence among the courses of advanced civilizations so that virtually none contains any individuals who desire to run ancestor-simulations and are free to do so. If (3) is true, then we almost certainly live in a simulation. In the dark forest of our current ignorance, it seems sensible to apportion one's credence roughly evenly between (1), (2), and (3)... I note that people who hear about the simulation argument often react by saying, 'Yes, I accept the argument, and it is obvious that it is possibility #n that obtains.' But different people pick a different n. Some think it obvious that (1) is true, others that (2) is true, yet others that (3) is true."
As a corollary to the trilemma, Bostrom states that "Unless we are now living in a simulation, our descendants will almost certainly never run an ancestor-simulation.
https://en.wikipedia.org/wiki/Simulation_hypothesis
How to address claims of god’s existence rationally
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