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Archive for the ‘Logic’ Category

St. Anselm’s Ontological Argument for God’s Existence

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St. Anselm of Canterbury was an interesting guy.  He was born 1033 in Aosta to a well off family.  Though he was a bright and well liked child who stole the affection of his mother, Anselm had a strained relationship with his father.  In his teens, he became intensely interested in religion and wanted to enter the monastery, but was denied.   While in his early twenties, Anselm’s mother died and his relationship with his father became hostile.  Unable to cope with this father, Anselm left his house at the age of 23 and wondered around Burgundy and France for three years.

Around the age of 27 Anselm arrived at a monastery and soon after became a monk.  His brilliance was quickly noticed, and he became popular among his peers.  At one point, they challenged him to prove the truths of scripture by reason alone (i.e. without using the Bible).  Anselm accepted the challenge, and wrote the Monologion.  In this book, Anselm attempted to argue for the existence of God and many of the Christian doctrines without the aid of Scripture. This was no easy task. Ultimately the book is a long chain of arguments that can be tiresome to read.   Anselm would later describe the book as being “knit together by linking of many arguments,” and this fact caused Anselm to be dissatisfied with the work.  It was not that he thought the arguments in the book were false, it was just that they were inelegantly strung together into a long laborious chain of arguments.

As Anselm’s dissatisfaction grew, he became very anxious to discover a new, single, argument that would, in his own words,

require no other for its proof than itself alone; and alone would suffice to demonstrate that God truly exists, and that there is a supreme good requiring nothing else, which all other things require for their existence and well-being; and whatever we believe regarding the divine Being

Anselm desired a single argument that would prove God’s existence and every attribute associated with him.  Anselm took this very seriously to the point that he became obsessed by it.  He lost his appetite and could hardly sleep at night.  At one point his obsession got so bad that he could no longer pay attention in church which lead him to believe the task was a temptation from the devil!  Eventually Anselm finally did discover his “proof,” and he wrote it in the second chapter of his work Proslogion.

So just what was Anselm’s great argument?  Let’s see his own words,

AND so, Lord, do you, who do give understanding to faith, give me, so far as you knowest it to be profitable, to understand that you are as we believe; and that you are that which we believe. And indeed, we believe that you are a being than which nothing greater can be conceived. Or is there no such nature, since the fool has said in his heart, there is no God? (Psalms xiv. 1). But, at any rate, this very fool, when he hears of this being of which I speak –a being than which nothing greater can be conceived –understands what be hears, and what he understands is in his understanding; although he does not understand it to exist.

For, it is one thing for an object to be in the understanding, and another to understand that the object exists. When a painter first conceives of what he will afterwards perform, he has it in his understanding, but be does not yet understand it to be, because he has not yet performed it. But after he has made the painting, be both has it in his understanding, and he understands that it exists, because he has made it.

Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived. For, when he hears of this, he understands it. And whatever is understood, exists in the understanding. And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For, suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.

Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.

Did it convince you?  My guess is you’re probably still trying to figure out just what the argument is!  Well, it can probably be formulated like this,

(1)   God is by definition the greatest possible being.

(2)    The greatest possible being exists in the mind.

(3)   Either the greatest possible being exists in the mind only, or he is exists in the mind and in reality.

(4)   Assume (for reductio) that the greatest possible being exists in the mind only.

(5)   In that case there could be a greater being viz. that very same being existing both in the mind and in reality.

(6)   But then there could a being greater than the greatest possible being (which would be a contradiction).

(7)   Therefore the greatest possible being exists both in the mind and in reality.

Think on that for a second! 🙂  Do you think Anselm was successful?


–All quotations are from the preface of Proslogion except for the main argument which comes from chapter 2 of the same work.


William Lane Craig’s Moral Argument for God’s Existence

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  1. If God does not exist, then there are no objective moral values or duties.
  2. There are objective moral values and duties.
  3. Therefore, God exist.

It seems to me that those who want to reject this argument will do so by denying the second premise.  In that case he’d likely be a non-cognitivist or a relativist.  In response I think Craig would push his point about there being circumstances in which we can just see that certain acts are right or wrong.  We can just see, for example, that many of the acts done by Hitler were immoral.

I suppose some would want to reject the first promise.  So, for example, they might give a naturalistic account of moral properties.  They might argue, for example, that “keeping your promises is good” is equivalent to “keeping your promises is N” (where “N” is some natural property like “maximally conducive to human wellbeing.”).   Or they might give a non-naturalistic account of moral properties, in which case “good” would refer to some irreducible moral property (i.e. a property that could not be reduced to “N”).  I think in both cases Craig’s response would be “So what?  Why should either case create objective moral duties for me?”

His argument seems good to me, but I suppose I have my own biases.


Written by Tim

January 15, 2010 at 9:58 am

An Argument for the Complexity of God? (Part 2)

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A few posts back I took a look at a critique of the design argument in which the author argued that in order for Intelligent Design to be successful it must be demonstrated that “fundamental complexity” is true.  But since it is extremely difficult or even impossible to demonstrate that fundamental complexity is true, we have good reason for rejecting Intelligent Design.

In response to this I pointed out that the author’s definition of “fundamental complexity” is ambiguous.  Most likely he takes “fundamental complexity” to mean the inability of a phenomenon to be explained in naturalistic terms.  I pointed out, though, that this definition presents no real problem for ID since the ID proponent is not committed to the claim that there can be no naturalistic explanations for a phenomenon; the ID proponent only has to show that ID offers the better explanation for that phenomenon.

With this in mind, here is the author’s argument for the complexity of God:

 (P1) Extremely complex phenomena that cannot even in principle be explained as arising from simpler, more fundamental principles are extremely improbable.

(P2) God is by definition a being that is a) conscious, and b) fundamental in the sense that he is not evolved or derived from anything more fundamental.

(P3) Conscious beings are necessarily extremely complex.

(I1) From (P2a) and (P3), God is extremely complex.

(I2) God cannot even in principle be explained as arising from simpler, more fundamental principles since, from (P2b), God is defined as being fundamental.

Conclusion: The existence of God is extremely improbable [from (P1), (I1), and (I2)].

I don’t think this argument works and here’s why:

(P1) – There are two problems in the first premise.  Firstly, it seems to me to be ambiguous.   Just what does the author mean by “complex phenomena”?  In the opening part of the article, the author says:

“Natural phenomena often seem to be extremely complex.”

Notice the author is talking about natural phenomena.  In other words the author is talking about physical features–cells, flagellums, etc.  This is further evidenced by what the author goes on to say:

“But when scientific explanation is found, the complexity is invariably seen to originate from some simple fundamental principle.  The incredible complexity of the biological world, for example, is beautifully explained by a simple process of random mutations and non-random natural selection.”

Again, notice that the author is talking about physical features; specifically physical features that can be given naturalistic explanations.  Now, it seems easy enough to see why things like cells, fegellem, and car engines are complex phenomena: they all have physical parts arranged in a fashion unlikely to have arisen by chance alone.  But how could it be said that God is a “complex phenomenon”?  That’s the crucial question that needs to be answered.  The engine in my car is pretty complex, and it’d be foolish of me to think it was by pure luck that all the parts randomly and for no apparent reason, formed into the car engine that powers my car.  A more likely story is that a team of engineers designed it, and it was pieced together in a factory. Hence we have a naturalistic explanation for the origin of my engine.   But how might this apply to God? God does not have physical parts that are arranged in some fashion.  It seems really hard to conceive of a way in which God is complex in a way relevant to the author’s argument.  But we’ll examine this a bit more in (P3).

The second problem with (P1) is that with respect to God, it seems likely false.  Suppose we determine that God is complex in a way relevant to the author’s argument.  Why think this would entail that God’s existence is improbable?   There is a strong tradition of Christians who have argued that God is a necessary being.  They have argued that it is not even possible that God not exist.  So even if we discovered that God were complex in some way relevant to the author’s argument, it still wouldn’t follow that God’s existence was improbable.  Now, of course the author might disagree with the claim that God is a necessary being, but then he would actually need to present an argument against this.

(P2a) and (P2b) – I’ll accept.

(P3) – is problematic as well.  The question we’ve got to ask is: How might God’s consciousness be complex in the same way that physical objects (or “complex phenomena”) are complex?   Here’s where the irrelevancy of (P1) comes in.  As pointed out above, in arguing for (P1) the author references physical features.   However, in (P3) the author is appealing to consciousness.   Consciousness itself is not a physical feature because it lacks physical properties.  I might feel pain when I get pricked by a physical needle, for example, but my feeling pain is not a physical event.  I cannot examine or burn, my  feeling pain, for example, because it doesn’t have physical properties.  Now, the author might be holding to a Mind-Brain Identity Theory—the view that mental states are identical to physical brain states.  If so, this would make a wonderful argument for the complexity of human consciousness, but remember, the author is supposed to be arguing that God’s consciousness is complex.  God, if he exists, is not a physical being, thus he has no physical brain for his mental states to be identical with.  So clearly that doesn’t work.

But let’s move on here…  How might we say that God’s consciousness is complex?  Well, says the author,

To see that consciousness itself is complex, consider that consciousness requires the ability to store and access information that is linked together in many intricate ways as well as the ability to process that information and to reason. The web of intricately interconnected data that consciousness requires is extremely complex.

But notice, he hasn’t argued for this point at all.  He just asserts it.  What’s worst is we never find out just what “intricately interconnected data” amounts to or why it should be considered “complex phenomena.”  Plus, when we take into account the fact that God is not a physical being, it becomes really hard to see how any part of him could be considered “complex phenomena.”  

Now, I suspect that ultimately what the author is attempting to argue is that mind has an organization about it that seems unlikely to have arisen apart from a designer (whether that designer be God or evolution).  Since God displays this ‘mental organization,’ and since God is not designed, then it is unlikely that God exists.   But then, again, he’d need to reply to the long tradition that God is a necessary being.  So on the whole, his argument seems to fail.

Written by Tim

January 14, 2010 at 7:03 am

You Can’t Prove a Universal Negative!…Or can you?

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Now don’t get me wrong here, I’m a Bible thump’n evangelical Christian, but I have to point out bad arguments when I see them…even when they come from Christians.  In fact, I think I ought to be harder on Christians then I am non-Christians.  After all, we are supposed to be in possession of the most complete and cogent world view.  So why would we need to propound bad arguments?  So here’s a bad argument that I’ll seen thrown around a bit.  It goes something like this: 

Atheist: God doesn’t exist.

Theist: But you cannot prove a universal negative, so you cannot know that God doesn’t exist.  In order to know that God didn’t exist, you’d have to examine the whole universe.  But you cannot do that so you cannot know that God exist 

My dear Christian brothers and sisters, if you are using this argument, STOP!!  Do not pass go, do not collect $200…  It’s a bad argument.  Why?  Because you can prove a universal negative.  How?  By showing that it’s falsehood involves us in an inconsistency. Here’s an example: 

Universal negative: There are no four-sided circles. 

Now, let’s suppose, for a second that the above sentence were false.  In that case there would be at least one object in the universe that was a four-sided circle.  But how could there be a four-sided circle?  What would it look like exactly?  Try picturing it in your head… Don’t feel bad if you can’t.  In fact you shouldn’t be able to conceive of four-side circle because the concept is contradictory.  By definition circles don’t have sides.  So the existence of a four-sided circle would be inconsistent, hence the above is true. 

Now, in the past atheists have argued that believing in God’s existence is like believing the existence of a four-sided circle.  They argued that God—were He to exist—would be a ‘walking’ contradiction just as our four-sided circle proved to be.  So, for example, atheists argued that God’s omnipotence is contradictory.  You’ve seen the fruits of this argument if you’ve ever been asked the question “Can God create a stone so large he cannot lift it?”  This question shows—or at least it’s supposed to show—that God’s omnipotence is contradictory, thus such a God cannot exist.  Or consider this: 

  1. God is omnipotent, thus He has the power to rid the world of evil.
  2. God is omniscient, thus He knows how to rid the world of evil.
  3. God is omnibenevolent, thus He does not want there to be evil in the world.
  4. There is evil in the world.
  5. Therefore God does not exist 

Again, this is meant to show an inconsistency.  In this case we are told that God’s existence is incompatible with the existence of evil.  Thus either God exists, or evil exist, but not both.  Since we know evil exists, then God cannot exist…or so goes the argument.

 In any case, the point is that atheists have tried to show that God doesn’t exist, and that the whole “you can’t prove a universal negative thing” response simply ignores this fact.

Written by Tim

January 13, 2010 at 11:09 am

Plato the friend of Atheists?

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There’s been a few occasions now where I’ve asked an atheist how they explain things from their naturalistic world view and I’ve been told “We can just appeal to Plato’s Forms as an explanation.”  I’m not sure if this is an ongoing trend, or just a few isolated instances.   One of the atheist even appealed to Plato’s Forms as an explanation for the cause of the universe…I’m not sure how that would work exactly, and unfortunately I didn’t stick around long enough to find out.  In any case, if they are going to appeal to Plato’s theory of the Forms, I suppose they should deal with the problems surrounding it.



What follows is an excerpt from a paper I had to wrote on the criticisms of Plato’s theory of the Forms as presented in his dialogue Parmenides.  This was the place in the paper where I discussed the problem called the “Third Man Argument.”  Sorry I know it’s a bit techinal, I’m just to lazy to rewrite it for the blog right now 🙂  Also the references at the bottom are what I used for the entire paper, not the excerpt…once again I am too lazy to take out the ones that weren’t used in the excerpt (man I’m feeling lazy today!).  In anycase, this represents one of the problems these atheists would have to deal with if they are to make Plato a friend of atheists.



The Third Man Argument

     The third man argument is probably the greatest (or at least the most popular) problem for Plato’s theory of the Forms.  As mentioned above, the primary role of the Forms is to explain predication.  The statement the Statue of Liberty is large” is supposed to mean that the Statue of Liberty participates in largeness.  But what exactly is it supposed to mean for the Statue of Liberty to participate in largeness, or, for that matter, anything at all to participate in largeness (or in any other Form)?  Plato’s gives the following answer in Parmenides 132c12 – d4:

In my opinion, the ideas are, as it were, patterns fixed in nature, and other things are like them, and resemblances of them-what is meant by the participation of other things in the ideas, is really assimilation to them.


 Plato’s view (given through the mouth of Socrates) is that the Forms are patterns, and insofar that an object resembles a Form, it participates in that Form.  Forms, then, are like paradigms and participation just is resemblance, i.e. resemblance of an object to the Form(s) it participates in.  Judgments of the sort x is F mean precisely that x sufficiently resemblances F.  Hence, the judgment “the Statue of Liberty is large” means that the Statue of Liberty sufficiently resemblances the Form of the Large.  For a person to make the Judgment “the Statue of Liberty is Large,” it involves that person being acquainted with the Form Largeness and seeing that the Statue of Liberty sufficiently resembles that Form (Rickless, 2007).  In fact, according to Plato, not only does the statue of liberty resemble Largeness, but every single large object resembles that Form as well.   This is true not only of Largeness, but of every other Form as well.  Plato’s assumption is that anytime there is a group of things that share a common nature (largeness, beauty, goodness, etc) there exists one Form “over” all the like things. This assumption has been called “One Over Many” (OM):

OM   – For any collection of things (a, b, c, etc) that are F, there exist a single Form by virtue of which they are all F.  (Cohen, 2006)

     A second assumption made by Plato is that a Form can be predicated of itself.  In the case of largeness, not only are the Statue of Liberty, Jupiter, and Great Danes large, but Largeness itself is large.  The same holds true for all other Forms as well.  The Beautiful is itself Beautiful, The Good is Good, Equal is Equal, etc.  This assumption has been called “Self-Predication” (SP)

            SP        F-ness is itself F (Cohen, 2006)

     At this point Plato’s theory runs into a difficulty. If predication is supposed to be explained by participation in the Forms, how does one explain predication with regard to the Forms themselves? Must the Form of the Large participate in itself?  Or does it participate in a different Form of the Large?  Is The Beautiful, beautiful in virtue of itself or some other Form?  Is the Good, good by virtue of itself or another Form that it participates in? On this issue, Plato assumes that Forms cannot be what they are by virtue of participating in themselves.  This assumption has been called “Non-identity” (NI)

            NI        F-ness is not F by virtue of participating in itself (Cohen, 2006)

     With these three assumptions in place a major problem arises for Plato’s theory as illustrated in Parmenides 131e8 – 132b2:

—And what now? What do you think of this?

—Of what? —I presume you believe that in each case there is one form because of [ej k ] something like this: whenever you think several things to be large, perhaps you think, looking at them all, that there is some idea, one and the same; hence you suppose that the large is one.

—You speak the truth, he said. —And what about the large itself and the other large things?

Whenever you look at them, with your soul, in the same way, will there not appear again one large thing [e{ n ti au\ mevga], by which [w| / ] all these appear large?

—So it seems. —So, another form of largeness will turn up besides the largeness itself that has come to be and the things that participate in it; and over all these again another, by which [w| / ] all these will be large; and thus you will no longer have one of each form, but an indefinite plurality. (as cited in Scolnicov, 2003). 


     The problem can be put this way:  If one considers a collection of large things—say, the Statue of Liberty, Jupiter, and a Great Dane—according to OM, there must exists one Form “over” them by virtue of which they are all large.  Hence the Statue of Liberty, Jupiter, and Great Danes will all be large by virtue of participating in the single Form of the Large.  However, according to SP, Forms can be predicated of themselves.  Hence the Form of the Large itself is Large, and the collection of large things will now consist of the Statue of Liberty, Jupiter, Great Danes, and the Form of the Large.  Since OM demands that there exist a Form “over” any collection of things with a common nature (in this case largeness), then there must exist a single Form over the collection of large things, i.e., there must exist a single Form over the Statue, Jupiter, Great Danes, and the Form of the Large, by virtue of which they are all large.  Lastly, by NI a Form cannot participate in itself, hence the “new” Form of the Large that exists over the “new” collection of large things must be numerically distinct from the Form of the Large.  But then there will be a new collection of large things, viz., the Statue of Liberty, Jupiter, Great Danes, the Form of the Large1, and the Form of the Large2.  By OM, there must be a new Form that exists over the new collection, and the process repeats itself ad infinitum. (Rickless, 2007)

Cohen, S. (2006). Criticism of Theory of Forms. Retrieved 2008

Copleston, F. (1946). History of Philosophy: Greece and Rome. Paulist Press.

Graham, D. (2007, Feburary 8). Heraclitus. Retrieved November 2008, from The Stanford Encyclopedia of Philosophy:

Plato. (n.d.). Parmenides. Retrieved December 2008, from The Internet Classics Archive:

Plato. (n.d.). Phaedo. Retrieved December 2008, from The Internet Classics Archive:

Plato. (n.d.). Sophist. Retrieved December 2008, from The Internet Classics Archive:

Rickless, S. (2007, August 17). Plato’s Parmenides. Retrieved Decemer 2008, from The Stanford Encyclopedia of Philosophy.

Russel, B. (1967). A History of Philosophy. Touchstone.

Scolnicov. (2003). Plato’s Parmenides. University of California Press.




Written by Tim

March 10, 2009 at 11:39 am

Rationalism to the Extreme?

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I’m always amazed when I find someone who holds logic and reason above everything else. Coming from someone like me, this may sound like quite a shock since I’m an incredibly logically minded person. However, I do realize the importance of personal feelings and emotions even if I’m not always so adept at showing them. In fact, I would place emotions on the same level of important as logic and reasoning; it’s just that I think the two serve different purposes.

In any case, I’m fascinated by people who hold logic and “rationality” on a pedestal far above anything else. Feelings are of no value to them, and personal perspectives don’t matter either; the only thing that matters is the cold, hard facts. These people trust their rational intuition more than anything else, thus they subject everything to logical scrutiny. If something doesn’t make sense to them logically then it’s not worth believing. We can call these people “rationalists.”

Perhaps one of the best known examples of a consistent rationalist is a man by the name of Parmenides who lived about 2,500 years ago. Parmenides was a rationalist to the extreme. He believed that the world was one eternal, unchanging whole. He didn’t believe there was any sort of change whatsoever. He thought change was illusory.

One has to wonder how in the world he could come to such a conclusion? We see change everywhere! The seasons change, the sun sets and the stars rotate around the night sky, children grow older, water rushes about in rivers, etc. In fact, your body will have undergone numerous changes by the time you finish reading this post. The world is full of change! So, how could Parmenides have come to such a ridiculous conclusion? Contrary to what his odd view of the world may suggest, he was actually extremely bright, and he drew his conclusions from a rather logical and impressive string of arguments:

1. Anything we can think or speak about either exists or doesn’t exist

2. Anything that doesn’t exist is nothing

3. We cannot think or speak about nothing

4. Hence, we cannot think or speak about what doesn’t exist

5. Therefore anything we can think or speak about exists. [1]

In other words, to think or speak about nothing is to not think or speak at all. So the object of thought and speech must be something. Parmenides identified this “something” with what he called “Being” and then he drew out several conclusions regarding Being. For example, he wondered if Being began to exist at some point. If Being did begin to exist then it must have come either from something or from nothing. If from nothing, then it would not have come into existence since no thing can come from nothing. But on the other hand, it could not have come from something either, since something can only be what it is and nothing else—it cannot become something that it is not already. Hence being never began to exist; being is eternal. Furthermore, being cannot change, for that would mean that it has become something else, but that has been proven to be impossible. Thus for Parmenides, being is eternally what is, and it can neither be nor become anything else. There is no change whatsoever …Chew on that for a bit!

Anyway, the next time one of those rationally minded people has you frustrated by their unyielding adherence to logical reasoning, just take a deep breath and remember it could be worst…they could be Parmenides 🙂


[1] Lawhead, W. (2006). Voyage of Discovery: A Historical Introduction to Philosophy. Wadsworth Publishing.

Written by Tim

January 5, 2009 at 1:48 pm

Posted in Logic, Philosophy