Evaluating the Moral Arguments

This post is meant to be an initial assessment of two forms of the moral argument.  I have taken them exactly as formulated by Tyler.  I want to apologize up front if I come across as overly pedantic.  I like to break things down as much as possible.  Also, it’s my blog… so deal with it.

The Arguments Stated

The Epistemological Argument:

(1) If NE is true, belief in objective moral values and duties cannot be warranted.
(2) But belief in objective moral values and duties can be warranted.
(3) Therefore, NE is false.

Note: “NE” stands for the conjunction of naturalism and evolution.

The Classical Moral Argument:

(1) If God doesn’t exist, objective moral values and duties do not exist.
(2) Objective moral values and duties do exist.
(3) Therefore, God exists.

The Arguments Evaluated

– The Epistemological Argument –

Let’s start by putting this in symbolic form.  Technically, the proposition NE is true is a compound proposition, namely Naturalism is true and evolution is true.

Let n be the simple proposition Naturalism is true and e the simple proposition Evolution is true.  Finally, let b represent the simple proposition Belief in objective moral values and duties can be warranted.  Then the argument can be expressed as

(1) (n\wedge e)\rightarrow \sim b

(2) b

(3) \sim(n\wedge e)

This form of argument is valid (modus tollens), so the first order of business will be to address any ambiguities and then the soundness of the argument.

I’ll start by pointing out that some clarification is needed as to what is meant by “naturalism”, since the term has no precise meaning in philosophy^{1}.  Presumably this term is intended to be a position excluding the supernatural, but then there is the question as to what counts as being super-natural.  For instance, one might subscribe to naturalism, but hold that parallel universes exist or that Platonism is correct, which could be interpreted as “super-natural” in some sense.  Some care also needs to be taken since naturalism is many times distinguished from materialism.

Putting that aside for the moment, let’s examine premise (1) with just a broad understanding of the terms.  Note that the negation of (1) would be \sim[(n\wedge e)\rightarrow \sim b], which is equivalent to n\wedge e\wedge b.  In words, this says that naturalism is true, evolution is true and belief in objective moral values and duties can be warranted.

At this point we need to know more about what it means for something to be warranted.  From what I understand, Tyler uses the term in the same sense as Alvin Plantinga.  It is a technical term given to that which distinguishes mere true belief from knowledge.  In particular, warrant is strongly related to the notion of proper function.  This seems to mean something like our faculties being geared toward forming true beliefs when operating correctly.  Thus, what I’ll need to argue, here, is that our faculties can be geared toward forming true beliefs even if they were not designed by an intentional agent.  However, to prevent excessive length (and because this will be a continued discussion), I shall start by merely giving some general ideas.

Something to note right away is that this argument assumes that morality is objective.  I happen to think that morality can be objectively defined, but I’m not entirely convinced that what counts as moral is objective.  More on this later.  

If we grant for the moment that there is such a thing as objective moral values and duties, then I imagine that these moral facts would exist in the same sense that, say, logical facts do.  As far as we know, what allows us to be able to access such facts is our capacity to think, reason, abstract, and in the case of morality, empathize.  So, it seems reasonable to take it that any creature constructed similarly enough to the way humans are, will be able to access logical and moral facts.  The question then shifts to: how did we come to be constructed in this way?

Certainly one possibility is that God purposefully made us (somehow) this way out of nothing.  Now, one thing we seem to know with reasonable certainty is that our world (and arguably any possible world) is governed by or written in the language of mathematics.  I maintain that the mathematics that underlies our reality exists eternally and necessarily.  So, it may be that there is a multiverse in which all mathematically possible worlds simply exist.  In at least one of them, namely ours, the structure will allow for creatures to exist in a way that they can access the laws of logic and moral laws.  Thus, the need for special creation is eliminated and it is possible that naturalism is true, evolution is true, and yet we can be warranted in a belief in objective moral values.

The last thing to point out is that the conclusion of this argument is not as strong as the theist might intend.  What I mean is that \sim(n\wedge e) is logically equivalent to \sim n \vee \sim e, which simply says that either naturalism is not true or evolution is not true.  Nothing here requires that both are false.

 -The Classical Moral Argument-

This argument is another example of modus tollens.  Since it is valid, let’s consider the premises.  I’ll be a bit shorter with my analysis of this argument to start.

First let me say that I see no reason to accept (1).  As alluded to above, moral facts may exist in the same way that logical facts do.  Second, I contend that (2) is undecidable.  Morality is of such a nature that we cannot tell if it is truly objective.  It certainly feels this way, but this is largely built on intuition deriving from how we are made up as humans.  At best, I think one could only maintain that morality is what I call “locally objective”.  That is, there is a certain set of moral laws M associated with humans (based on how we operate) such that any creature c that is sufficiently similar to humans will be subject to M.

Okay, at this point I don’t want to take much more time, so I’ll pass it over to Tyler.  Upon receiving his critique, I will then expand on my thoughts where needed.

1. http://plato.stanford.edu/entries/naturalism/


A Friendly Discussion on the Moral Arguments

I am a mathematician.  But as many of you know, the topic of God’s existence is also of great interest to me.  This is in large part due to my desire to understand the ultimate nature of reality.  Some might reckon that pursuing the question of theism is a waste of time.  It has been debated for millennia with seemingly little progress.  While perhaps true, I tend to be a bit more optimistic.  Even if the question is ultimately undecidable, some very interesting ideas and philosophy have come out of the discussion, which have shaped many areas of our thought.

There are many different types of arguments for the existence of God, and even if they ultimately fail, there is no denying that evaluating them has led to great progress in various philosophical topics.  The notion of morality happens to be one of these.  In fact, the moral argument is one of five or so major types of arguments for God’s existence.  I personally find the topic of morality to be one of the most difficult to analyze and nail down.  Because of this, I find the moral argument to be the weakest of all theistic arguments.  Others, like my friend Tyler Dalton McNabb, assess it as among the stronger arguments.

So, this is what I would like to do: Tyler and I have agreed to have a friendly discussion on the moral argument.  He has presented the basic arguments on his blog.  I will give an initial assessment of these arguments on my blog and he will then address my criticisms back on his blog.  It should prove to be a fruitful exchange, so follow along and enjoy.  Comments are also welcome.

Christian “Trump Cards” – Part 2

Recently I began compiling something of a list of, what appear to be, commonly appealed to “trump cards” by certain Christians during attempts at rational dialogue.  While I certainly don’t intend to implicate all Christians (or even only Christians), I have noticed a regular occurrence of these “moves” in a multitude of discussions.  In Part 1 I briefly discussed the appeal to faith.  From my own experience discussions seem to either begin or end with this “trump card”.  For part 2 I would like to analyze what seems to be a background assumption of many Christians.  This “trump card” isn’t necessarily appealed to directly; it most often operates behind the scenes, but has noticeable effects.  Here it is:

A: If one does not believe that Christianity is true, then that person hates God and rejects “His” gift of salvation.

The difficulty with this background assumption is that it goes to the heart of the Christian message.  Humans are the creation of God, but are separated from “Him” because of sin.  Ultimately, this means that humans are headed for one of two fates: eternal heaven or eternal hell.  Those who repent and accept Christ are granted eternal heaven, while those who do not get eternal hell.

Now, eternal hell (which is generally taken as never-ending punishment) is rather harsh.  So, to alleviate the uncomfortable dissonance, it is my opinion that many Christians are driven to hold A.  It is much easier to believe that unrepentant God-haters who despise “His” sacrifice deserve never-ending punishment than it is to accept that honest seekers and skeptics could somehow “miss the boat” and end up in eternal torment.

The problem, of course, is that A is a completely unwarranted assumption.  More than that, it is unfalsifiable in the sense that all counter-examples can be dismissed.  Since no one can expose his or her first person perspective to direct analysis, we must always go off of what people report about themselves.  The person who accepts A, however, can simply maintain that the non-believer is deceiving himself or herself by suppressing the truth (more on that at a later time).

Nevertheless, let’s take a look at A itself and see if it makes better sense to adopt its negation.  Note that A is a conditional statement.  Let  stand for the simple proposition A person P believes that Christianity is true.  Let H represent the proposition P hates God and rejects “His” gift of salvation.  Then the assumption A can be expressed as

\lnot C\rightarrow H

The negation of this is therefore

\lnot(\lnot C\rightarrow H)\equiv \lnot C \wedge \lnot H

In English this would read

\lnot A: Person P does not believe that Christianity is true, but does not hate God or reject “His” gift of salvation.

Let’s see why \lnot A is more likely true than A.  If we look again at the component propositions \lnot C and H we run into an immediate problem.  Notice that \lnot C is a proposition that refers to the noetic status of a person.  It makes a claim about what a person believes.  In other words, it reports that some person takes the Christian system of belief to be false or not to correspond to reality.  The proposition H, by contrast, refers to a directed feeling or emotion of a person.  So, the assumption A claims that a certain state of unbelief with respect to some propositions implies an associated emotion with respect to the content of those propositions.  This is a very queer claim indeed.  Generally, the status of one’s belief has no connection to how one feels about the content of the belief.  For instance, I don’t believe in fire-breathing dragons.  In other words, I take it that they do not exist.  But this says nothing of how I feel about fire-breathing dragons.  In fact, I think fire-breathing dragons, while scary, are pretty awesome.  So, if this connection fails to hold in general, why should we believe it holds in the specific case of Christianity?  It is true that some people hate the idea of the Christian God, but there is no evidence to suggest that every non-believer does.

The underlying issue here is that many Christians conflate two types of “rejection”.  Let’s call the first type of rejection relational rejection and the second type propositional rejection.  Relational rejection involves rejecting a person or something a person is offering.  It involves a negative feeling toward the person or thing offered by the person.  For instance, if a boy asks out a girl and she says “no”, then she has relationally rejected the poor boy.  She is saying that she does not like the idea of having a particular type of relationship with him.  Propositional rejection, by contrast, is simply to not accept a proposition as being true.  For example, suppose a girl is asked whether she thinks that some boy will ask her out.  Suppose she says “no”.  Then in this case she is engaging in propositional rejection.  That is, she is rejecting the proposition that some boy is going to ask her out.  Notice that this rejection says absolutely nothing about whether she wants the boy to ask her or not.

The confusion arises from a failure to see the distinction between the proposition that one thinks is either true or false, and the content of the proposition that one may or may not have a feeling about.  For the Christian, the content of the belief is so central and personal that disbelief is automatically taken to be personal.  But there is no reason to think that disbelief is always (or even often) of a personal nature.  Thus, the Christian who holds A is going to have to summon some really compelling evidence.  Next time I’ll address one such argument claiming that truth is a person and hence rejection of the “truth” amounts to rejecting the person.

Some Common Christian “Trump Cards” – Part 1

Talking with Christians (and religious people in general) is a mixed bag.  Sometimes you get awesome intelligent people along with a really great discussion (even if you end up disagreeing).  Most of the time, however, the discussion ends up in frustration.  Having quite a bit of experience, I have put together a list of some of the most commonly used discussion killing “trump cards” played by many Christians.  I’d like to address each one in a separate post.  In analyzing each, I hope this will be useful to both skeptics and believers to promote more fruitful dialogue.  But before I get to the list, I’d like to give an explanation as to the root of these “trump cards”.

Controlling Assumptions

While there is no doubt that humans are rational beings, there is also no doubt that humans are emotional beings.  Unfortunately, at the conscious level, we are much more influenced by the latter than the former.  Emotions and other psychological effects are so powerful, that humans have to work quite hard to be rational in the midst of them.  This is not completely bad, since our drive, hope, and motivation are essential aspects our success.  The problem is striking a correct balance, which is obviously fairly difficult.

Here lies one of the difficulties with Christianity.  Not only is Christianity a system of belief, it is a system of belief saturated in emotion.  It is a system designed to address the core of human longings: purpose, meaning, forgiveness, justice, belonging, love, hope, peace, etc.  It provides a complete mental framework from which to operate.   This, of course, is not a bad thing, but the practical effects of adopting it can make it rather difficult to maintain objectivity.  One is easily blinded to the cold matters of truth when it just feels right.

This is an example of something I call a controlling assumption.

Definition [Controlling Assumption]A controlling assumption is an assumption that once adopted sets a mental framework that interprets all data to be consistent with the assumption, even data contrary to the assumption itself.

One might describe a controlling assumption as a self-preserving assumption.  It is intimately related to the idea of confirmation bias.  For example, consider the famous psychological experiment where several researchers checked themselves into a mental hospital.  Once admitted, they acted completely normal.  One would hope that the doctors of the hospital would be able to recognize that these “impostors” were completely sane and free of mental illness.  In other words, the healthy should be distinguishable from the sick.  The problem, however, is that the doctors were under the influence of a controlling assumption, namely People who enter the hospital as patients have a mental illness.  Because of this, the doctors interpreted the researcher’s normal behavior as symptomatic of their supposed “neuroses/psychoses”.  Even as the researchers documented these things with meticulous notes, the doctors recorded in their charts that “Patients engage in note taking behavior” as if it was pathological.  Ironically, those who were actually mentally ill caught on to the researchers almost immediately.

Although not always the case, the Christian belief structure can operate much like a controlling assumption, and part of the self-preserving nature of the belief structure manifests itself in various “trump cards” when being challenged.  I address the first of these below.

“Trump Card” 1  -[You just have to have faith]

Generally, the very first response to any rational challenge is an appeal to faith.  How “faith” is being used, however, is not generally very clear.  When pressed for a definition, most respond by quoting Hebrew 11:1, which says, “Now faith is the assurance of things hoped for, the conviction of things not seen.” (NAS)  Using this as a definition, what the Christian is saying is that one just needs to have assurance.  My initial thought is, “Oh, is that all I need?”.  Of course, even if Christianity is something I hope for, the problem is that I don’t have assurance.  This is what I am seeking, but not finding.  It strikes me a bit like saying to an addict who is asking how to stop, “Well, you just need to stop.”  That won’t be received well, because that is the very problem that needs addressing.

The go to response from here is generally to deny that faith has anything to do with the intellect, but is a matter of the heart.  Again, it isn’t at all clear what this is supposed to mean, nor is it clear where such an idea is expressed in the Bible.  In fact, the Greek word for “heart” in the New Testament is καρδια or kardia, which was taken to include the whole self, including the faculty and seat of the intelligence.  Thus, to say that faith is a matter of the heart and not the mind is an artificial and incorrect distinction even measured against the Bible.

Finally, telling someone that faith is required only pushes the problem back a step.  Why is faith required?  How does one know this?  And what guides where I place my faith?  After all, many religions appeal to the very same requirement.  So, which does one choose?  I think the issue clearly reveals that faith is not an epistemological tool that yields knowledge.  This can be more rigorously demonstrated as follows.

(1) Suppose that faith provides a means of knowing something.

(2) The Christian has faith and so knows Christianity to be true.

(3) Therefore, from the definition of “know” it follows that Christianity is true.

(4)  The Mormon has the same sort of faith and so knows Mormonism to be true.

(5)  Therefore, Mormonism is true.

(6)  Christianity and Mormonism are incompatible systems of belief.

(7)  Therefore, either Christianity or Mormonism (or both) is false.

(8)  If Christianity is false, then we get a contradiction with (3).

(9) Thus, Christianity must be true and Mormonism false.

(10)  If Mormonism is false, then we get a contradiction with (5).

(11)  Thus, Mormonism is also true, which contradicts (7).

(12)  Therefore, since our initial assumption leads to a contradiction, it must be the case that (1) is false.

Of course, one could deny that Christians and Mormons have the same faith, but then one would have to wonder how we could possibly distinguish between “real” faith and “fake” faith.  One would then have to appeal to something other than faith anyway.

Chuck Missler and the Existence of Infinity

Along with my (slow) endeavor of exploring and critiquing the ideas undergirding intelligent design, I want to resume a project I started a while back that involved addressing the claims of Chuck Missler.  As I have previously mentioned, Chuck Missler is a well educated man.  That being said, I also get the strong impression that Missler pretends to know a lot more than he really does.  What annoys me the most is that he seems to present himself as an expert in, well, just about everything.

In his Bible studies, Missler lectures his flock on everything from cosmology to quantum mechanics to information theory and beyond.  Missler has everything figured out it seems, and, while he might deny it, presents himself as having just about everything figured out.  It’s shocking that he hasn’t been awarded a Nobel prize.  Listening to his talks, one cannot help but be impressed by the depth and breadth of his knowledge.  However, once one gets over the dazzle of Missler’s apparent expertise in everything, one begins to pick up on very questionable claims and ideas.  Most of the time Missler alludes to very deep ideas, but glosses over them to spare his audience the details.  OR, maybe Missler really doesn’t know or understand the details.  This is my suspicion, which is motivated by several cracks in his intellectual veneer amounting to questionable claims on his part.

The first issue I’d like to address regards the size of the universe.


Missler is fond of proclaiming there are two central mathematical concepts that we don’t find in nature: Infinity and randomness.  I’ll save randomness for another post.

Does Infinity Exist?

Certainly infinity exists conceptually, but the question is whether it describes anything real.  In particular, Missler focuses on size.  This can go in two directions: (1) small scale infinity, and (2) large scale infinity.

Small Scale ∞

Most people are familiar with number lines.


For our purposes we can focus on the interval [0,1].  We can cut this interval in half and get [0,\frac{1}{2}].  This can be cut in half again to get [0,\frac{1}{4}].  In fact, we could carry out this cutting procedure indefinitely, always obtaining a new interval [0, \frac{1}{2^{n}}].  This means that we can make the interval as small as we like.  Put differently, we can cut the interval infinitely many times in the sense that there will never be a limit to the number of times we can cut the interval in half.

Now suppose that our interval [0,1] models a length in space-time, say an inch.  If the correspondence were true, then it would follow that space could be indefinitely halved.  According to Missler, this is actually not true.  It turns out that there is a limit to smallness in space-time.  In other words, there is a smallest distance.  This distance is known as the Planck length, which is defined by

\ell_{p} = \sqrt{\frac{\hbar G}{c^{3}}}

where \hbar is Planck’s constant, G is the gravitational constant, and c is the speed of light.  This length is exceedingly small, a mere 1.6\times 10^{-35} meters (approximately).  Missler is fond of saying that if at any point you divide a distance into lengths smaller than \ell_{p}, then you lose locality, the thing you are cutting is suddenly everywhere all at once.  What he concludes is that our reality is actually a “digital simulation”, terminology he uses purposely to insinuate that our world is created by God.  Such loaded language seems to be characteristic of Missler.

So, what is the nature of this mysterious length?  Where does it come from and how do we know it is the smallest length?

The Planck length has profound relevance in quantum gravity.  Put differently, it is at this absurdly tiny scale that quantum effects become relevant and the question regards how gravity behaves or should be understood at this scale.  Both general relativity and quantum field theory must be taken into account.  The definition of the Planck length now makes sense since the speed of light c is the natural unit that relates time and space, G is the constant of gravity, and \hbar is the constant of quantum mechanics. So the Planck scale defines the meeting point of gravity, quantum mechanics, time and space.

Theoretically, it is considered problematic to think of time and space as continuous because we don’t appear to be able to meaningfully discuss distances smaller than the Planck length.  Unfortunately, there is no proven physical significance to the Planck length because current technology is incapable of probing this scale.  Nevertheless, current attempts to unify gravity and QM, such as String Theory and Loop Quantum Gravity, yield a minimal length, which is on the order of the Planck distance.  This arises when quantum fluctuations of the gravitational field are taken into account.  In the theory, distances smaller than \ell_{p} are physically meaningless.  Two “points” at distances smaller than \ell_{p} cannot be differentiated.  This seems to suggest that space-time may have a discrete or “foamy” nature rather than a continuous one.  Unfortunately for Missler, however, we just don’t know at this point.  Thus, the declarative nature of his claims are hasty.

Nevertheless, even if this turns out to be the case, the question becomes: what follows from that?  As mentioned above, Missler is fond of saying that the universe is a “digital simulation”.  Certainly the term “digital” would be apropos, but his use of “simulation” seems loaded and dubious.  “Simulation” suggests that this world isn’t the “real” world.  It suggests that our world merely imitates some meta-world.  Of course, Missler purposely uses the term as a way to smuggle in a simulator.  That simulator is God, and the meta-world is the spiritual world.

Large Scale ∞

The more questionable of Missler’s claims regards the size of the universe.  He brazenly declares that we have discovered the universe to be finite.  This is just flat out false, and such carelessness makes me question his credibility.  It is likely that he is simply confusing the observable universe with the universe proper.  There is no doubt that the observable universe is finite.  It is estimated to have a radius of 46 billion light years and due to expansion grows ever larger.  However, this does not necessarily imply that the universe proper is finite in size.  Sir Roger Penrose, one of the most respected mathematical physicists in the world, says, “it may well be that the universe is spatially infinite, like the FLRW models with K = 0 or K<0.” (see The Road To Reality, p. 731)

Note: FLRW models refers to  Friedmann–Lemaître–Robertson–Walker models and K is a density parameter governing the curvature of the universe.

Even a quick search on Wikipedia reveals that, “The size of the Universe is unknown; it may be infinite. The region visible from Earth (the observable universe) is a sphere with a radius of about 46 billion light years, based on where the expansion of space has taken the most distant objects observed.”

In fact, the possibility of an infinite universe is the stuff of some multiverse models.  Max Tegmark, a mathematical physicist at MIT puts it this way:

If space is infinite and the distribution of matter is sufficiently uniform on large scales, then even the most unlikely events must take place somewhere. In particular, there are infinitely many other inhabited planets, including not just one but infinitely many with people with the same appearance, name and memories as you. Indeed, there are infinitely many other regions the size of our observable universe, where every possible cosmic history is played out. This is the Level I multiverse.

Tegmark goes on

Although the implications may seem crazy and counter-intuitive, this spatially infinite cosmological model is in fact the simplest and most popular one on the market today. It is part of the cosmological concordance model, which agrees with all current observational evidence and is used as the basis for most calculations and simulations presented at cosmology conferences. In contrast, alternatives such as a fractal universe, a closed universe and a multiply connected universe have been seriously challenged by observations. Yet the Level I multiverse idea has been controversial (indeed, an assertion along these lines was one of the heresies for which the Vatican had Giordano Bruno burned at the stake in 1600†), so let us review the status of the two assumptions (infinite space and “sufficiently uniform” distribution). How large is space? Observationally, the lower bound has grown dramatically (Figure 2) with no indication of an upper bound. We all accept the existence of things that we cannot see but could see if we moved or waited, like ships beyond the horizon. Objects beyond cosmic horizon have similar status, since the observable universe grows by a light-year every year as light from further away has time to reach us‡. Since we are all taught about simple Euclidean space in school, it can therefore be difficult to imagine how space could not be infinite — for what would lie beyond the sign saying“SPACE ENDS HERE — MIND THE GAP”? Yet Einstein’s theory of gravity allows space to be finite by being differently connected than Euclidean space, say with the topology of  a four-dimensional sphere or a doughnut so that traveling far in one direction could bring you back from the opposite direction. The cosmic microwave background allows sensitive tests of such finite models, but has so far produced no support for them — flat infinite models fit the data fine and strong limits have been placed on both spatial curvature and multiply connected topologies. In addition, a spatially infinite universe is a generic prediction of the cosmological theory of inflation (Garriga & Vilenkin 2001b). The striking successes of inflation listed below therefore lend further support to the idea that space is after all simple and infinite just as we learned in school.

So, it seems that unless Missler knows something all other physicists don’t, he is being much too hasty and cherry picking possibilities to support what he wants to be true.