Friday, April 5, 2019

The What and Why of Logic

Classical education can be thought of as unique both in how it teaches things but also in what it teaches. The subject of Logic is one of those subjects that is unfortunately not found in most schools today, but it is one of the most foundational subjects to a classical education. Given everything else there is to study, why should we spend time on logic? Why not just take more time to study chemistry or literature? 

Logic is the science of good reasoning. It can be thought of as the language of truth. It is the study of proper inference. When someone reasons from a proposition (for example, that ‘God has commanded all men everywhere to repent) to the further proposition that they, indeed, are a man, and therefore should repent, they are being logical. When someone, however, reasons that because an unborn baby is composed of a bunch of cells, it is, therefore, nothing more than a bunch of cells, that person commits the fallacy of composition and reasons illogically. The term logic may sound grey, lifeless, or cold, but it undergirds the arguments of the colorful, the lively, and the emotional human beings made in God’s image. 

Formal logic, such as categorical logic, helps us sort things into proper categories and examine their relationships, such as the syllogism:

All men are mortal
Socrates is a man
Socrates is a mortal

Informal logic helps us see the issues of relevance or ambiguity in everyday arguments, such as the Ad Hominem, or attack on the irrelevant character of the person, rather than the soundness of the argument:

“Ben’s argument about taxes sounds reasonable, but he often yells at his wife, so we shouldn’t take it seriously."

We should study logic because in doing so we can be more human. Part of what it means to be human is to be logical. God created man with the ability to reason. When we reason, we apprehend the truth. This ability allows us to understand rational statements made by others, and to form rational statements ourselves and communicate them. 

The laws of logic actually undergird all communication, and without them, communication becomes impossible. Try making a statement without using the first law of logic, which is that A cannot equal non-A at the same time. Whatever you said, I could easily assert that you said the opposite, unless we both assume the first law of logic. A line can be either curved or straight, but the straight part cannot also be curved. When we make a statement like “the first twelve feet of this line is straight, and the last seven are curved,” we are in fact putting different propositions into categories, and because of the first law of logic mentioned above, when two categories are non-exclusive, they cannot have multiple meanings. We recognize this, and sort things into categories all of the time. When we get up in the morning, we decide to put on our snow boots rather than our flip-flops, and we understand that “snow boot” and “flip-flop” are exclusive items that cannot be the same thing. We then walk into the kitchen and make a distinction between a bowl and a counter, and conclude that based on the construction of those items, we should pour our milk into the bowl instead of next to it. Toddlers sometimes have trouble making these categorical distinctions. 

Perhaps the biggest reason to study logic is to obey the commands of Christ. Jesus Christ is described for us in John 1 as the Truth. In him is perfect and consistent reasoning. He does not think illogically, because He is perfectly truthful. Reasoning improperly is basically lying about reality. When you assert that because both Hitler and your political opponent love dogs, and that this means that they share political views, you are not merely reasoning illogically, but are in fact lying. Jesus does not lie, He commands His followers not to lie; instead He commands them to become like himself. We are commanded to conform to the image of Christ (Romans 8:29). We are also commanded to tear down every argument raised against the knowledge of Christ (1 Corinthians 10:5) and discern between (sort!) good and evil (Hebrews 5:14). 

In a classical school, logic is treated as a distinct discipline because it is of foundational importance, like reading. We teach people how to read because doing so allows them to interpret their world, obey God by reading his Word, and learn any other subject that requires reading. In the same way, we teach logic as a distinct discipline so that the student can interpret their world better, sorting between good and evil, true and false, helpful and unhelpful. By learning logic they will also be able to rightly interpret/exposit God's word after reading it. Lastly, by learning logic, the student will be able to interpret everything else they study! If you want a better math, science, literature, and rhetoric student, teach them how to interpret and sort between propositions in all of those subjects. 

Monday, April 1, 2019

Ontological Argument Paper

This is a reposting of a research paper I wrote for Reformation Bible College in 2013. It was posted on my Tumblr blog (now abandoned) but I don't believe it was ever posted here. It probably isn't my best paper, but it was my first and therefore is special to me. The formatting is going to be wonky as it has been copied and pasted so many times. Enjoy!

The Ontological Argument is one of the most highly debated theistic proofs in Apologetics today. Some philosophers have dismissed it as nothing more than a & charming joke, yet philosophical giants throughout history such as Scotus, Descartes, Spinoza, Leibniz, and Plantinga have risen to defend it. Popular Apologists seem to be sharply divided over how useful this argument really is, however. For example, one of the most prominent Apologists today, William Lane Craig, devotes less than a single page to it out of the 415 that comprise his signature work Reasonable faith, and the well known Catholic Apologist Peter Kreeft takes 3 pages to outline the ontological argument and writes; “We include [the ontological argument] not because we think it conclusive or irrefutable, but for the sake of completeness.”
Yet, on the other hand, Alvin Plantinga, one of the most well-respected Christian philosophers alive today has written an entire book on this argument and has even formulated a version of it that has gained wide acceptance among the philosophical community at large. Douglas Groothuis, another prominent apologist who writes and speaks frequently of the ontological argument, gives us an idea of why the argument is so captivating: 

Imagine a philosophical argument that has been engaged by some of the most stellar minds in the history of thought about the greatest controversy ever engaged: the existence and nature of God. This line of reasoning requires no empirical premises; it works from sheer rational concepts. Now imagine that the conclusion of this argument announces that a Perfect Being exists–a superlative entity in who rests all possible perfections and in whom no defect can be found. Is this an apologetical fantasy? No, it is the ontological argument.

This paper will seek to analyze the versions of the ontological argument that Anselm developed, in order to determine whether or not it is a useful argument to employ in the Christian Apologetical discipline. Anselm developed two arguments, and both will be assessed. Special attention will be paid to the logical structure of the arguments, and to the truth of the premises. An emphasis will be given to represent and interact with the primary sources, both in the positive arguments and the critiques by those such as Gaunilo. 
The originator of the ontological argument was St. Anselm of Canterbury, though he derived his inspiration of the argument from Augustine of Hippo. Anselm, (1033-1109), was a Benedictine monk, the second Bishop of Canterbury, and philosophical theologian known as the ‘Father of Scholasticism’. His ontological argument is found in his book Proslogion, which he formulates not to further convince himself or others that God exists, but to come from the viewpoint of one who already believes that he exists yet wants to know more about God (i.e. “Faith seeking understanding”). Anselm’s express purpose: 

But when I reflected on [The Monologion] and saw that it was put together as a long chain of arguments, I began to ask myself whether one argument might possibly be found, resting on no other argument for its proof, but sufficient in itself to prove that God truly exists, and that he is the supreme good, needing nothing outside himself, but needful for the being and well–being of all things.

It is in this context that we will look at Anselm’s two similar arguments, both of which are based on the same idea. The contemporary philosopher Richard Taylor suggests in his introduction to The Ontological Argument: From St. Anselm to contemporary philosophers that embedded within Anselm’s Proslogion are two similar arguments, though Anselm might not have realized this himself. The first one argues that God can be proven to exist simply from the concept of God; the second makes the stronger claim that God is the only being that exists necessarily. We will look at what Anselm says about both arguments in his own words: 

Now we believe that thou art a being than which none greater can be thought…But when [a fool] hears what I am saying–”A being than which none greater can be thought”–he understands what he hears, and what he understands is in his understanding, even if he does not understand that it exists…Even the fool, then, must be convinced that a being than which none greater can be thought exists at least in the understanding, since when he hears this he understands it, and whatever is understood is in the understanding. But clearly that than which a greater cannot be thought cannot exist in the understanding alone. For if it is actually in the understanding alone, it can be thought of as existing also in reality, and this is greater. Therefore, if that than which a greater cannot be thought is in the understanding alone, this same thing than which a greater cannot be thought is that than which a greater can be thought. But obviously this is impossible. Without doubt, therefore, there exists, both in the understanding and in reality, something than which a greater cannot be thought.

So to break Anselm’s first argument down: Anselm is positing that”
 1. God is defined as a being than which nothing greater can be conceived, and of which everyone has an idea of, even if only in their understanding.
2. A thing exists either in the understanding only, or in both the understanding and in reality. 
3. It is greater to exist in reality than to exist merely in the understanding. 
4. If God only existed in the understanding, then he would lack a perfection, and then he would not be the greatest possible being. 
5. But the definition of God is that he is the greatest possible being (from 1). 
6. Therefore, God exists not only in the understanding but in reality as well. 
What Anselm means by a being “than which nothing greater can be thought” in premise 1 may be summed up in this definition: “A Perfect Being is a being who possesses every property it is better to have than to lack and who possesses this array of compossible excellent properties to the utmost degree (or to their intrinsic maximum value)”. Another part of this argument that needs further explaining is the assumption within premise 3 that existence is a perfection; in other words, it is assumed by Anselm (and by Descartes later) that it is plainly better to exist than to not exist. But think of it this way. Any god who didn’t exist would actually be less worthy of worship than anything that did exist, because of all the things needed for something to be in any sense powerful, glorious, and worthy of worship, actual existence is the first! As Taylor writes, “God, whatever else he may be, must be a reality as the very minimum condition of being thought of as God.” Or so it would seem…Though for some it is common sense that existence is an attribute of perfection, Immanuel Kant disagreed, as we will shortly see. Anselm’s first argument is logically valid, so in order to refute it the truth of the premises must be undermined (and there are no shortage of those who try!). Two men in particular have critiqued this argument of Anselm’s, and their concerns will be looked at in turn. The first was a contemporary of Anselm, a monk named Gaunilo, who though affirming the existence of God as strongly as Anselm did, he nevertheless thought that the major flaw with Anselm’s argument was that if you followed the same logic, but substituted “God” with any other object, you could come to the same conclusion that based on that objects definition, it must exist. Basically, Gaunilo accused Anselm of defining God into existence. He used an example to demonstrate this: “…it is said that somewhere in the ocean is an island…and they say that this island has an inestimable wealth of all manner of riches and delicacies…it is more excellent than all other countries…Now if someone should tell me that there is such an island, I should easily understand his words, in which there is no difficulty. But suppose that he went on to say, as if by logical inference: ‘You can no longer doubt that this island which is more excellent than all lands exists somewhere, since you have no doubt that it is your understanding. And since it is more excellent not to be in the understanding alone, but to exist both in the understanding and in reality, for this reason it must exist.
His obvious purpose in illustrating his island example was to draw a similar argument following the same logical lines, and then by showing how absurd his argument was, to also show how absurd Anselm’s was. The Oxford Illustrated History of Western Philosophy sees an exact correspondence between the two examples: “The arguments are exactly parallel…Gaunilo’s argument is formally exactly like Anselm’s.” The authors clearly agree with Gaunilo as well: “Since Gaunilo’s [argument] plainly does not [work], neither does Anselm’s.” But not so fast. What drives Anselms’s argument in the first place is that there can be thought a being who is the greatest possible being in every way possible. There cannot be two perfect beings, only one, which means that contrary to the Oxford Illustrated History of Philosophy, Anselm and Gaunilo were talking about two different types of beings; Anselm was talking about the greatest possible being while Gaunilo was merely describing the greatest possible island. He was taking an object (an island); predicating all of its desirable attributes to infinity, and then positing that he could do this with any object. But there is only one being that is the perfect being, logically speaking. Which means that if this island Gaunilo is talking about is really the epitome of perfection in the same way Anselm’s is, and not just perfect as to its own properties, then the island would in fact be the greatest possible being–proving Anselm’s argument! Gaunilo takes a contingent being and tries to make it into a necessary being. The second critique of Anselm’s first version of the Ontological argument is by the philosopher Immanuel Kant, who charged Anselm with assuming that existence is a predicate of perfection. He is right, as we see in premise 3: “It is greater to exist in reality than to exist merely in the understanding”. Douglas Groothuis summarizes Kant’s concern in his chapter on the Ontological argument in Christian Apologetics: A Comprehensive Case of Biblical Faith

“For Kant, existence is merely a logical predicate, not a genuine predicate. A genuine predicate adds significant information regarding the subject, as in ‘The tree’s leaves were dark green.’ but contrariwise, a logical predicate adds nothing significant to the subject, as in, ‘The trees leaves are leaves.’…A real predicate ‘enlarges’ a thing in Kant’s terminology.” 

Groothuis also notes that “If existence does not function as a genuine predicate, this is fatal to Anselm’s argument, since he is arguing from the very concept of God (plus logical principles) to the existence of God…If Kant is right, Anselm is wrong…” Philosophers have debated Kant’s question quite independently of the ontological argument, but the short answer is that it is quite legitimate to predicate existence to something, if that something demands existence to complete its definition. in other words, if it is really better to exist than not to exist, then to predicate this attribute to ones definition of anything is rationally justifiable. In conclusion, this first argument of Anselm’s is the most popular overall, though mostly because of its criticisms. The two major criticisms are 1. It defines God into existence, which leaves open the absurd idea that one can do so with any object of their choice (I am thinking of the worlds greatest blonde girl. This blonde girl is the best possible blonde girl ever; i.e., the most beautiful, greatest personality, best character, and madly in love with me. Thus she must exist in real life, because it is better for her to exist in real life than merely in my imagination.) The refutation to this refutation of Gaunilo’s is that to properly conceive of the definition of a perfect being means that there is only one being suitable to posit in this argument, and this is the best, most perfect being, not the most perfect version of any being you please. However, this is where Kant’s criticism comes in, because in order to soundly refute Gaunilo it must be true that it is rationally justified to 1. Attribute existence to something, and 2. That it is better to exist than to not exist. This idea of a “necessary being” is what will be assessed next, because if it is possible that this being not exist, then the first argument falls. This argument, though formulated by Anselm in the 11th century, was significantly developed by Charles Hartshorne and Norman Malcolm in the 1960’s. Here is Anselm’s second argument in his own words, which, though similar to the first, is subtly different: And certainly it exists so truly that it cannot be thought of as nonexistent. For something can be thought of as existing, which cannot be thought of as not existing, and this is greater than that which can be thought of as not existing. Thus, if that than which a greater cannot be thought can be thought of as not existing, this very thing than which a greater cannot be thought is not that than which a greater cannot be thought. But this is contradictory. So, then, there truly is a being than which a greater cannot be thought–so truly that it cannot even be thought of as not existing.
As was intimated earlier, the difference between Anselm's first argument and this one is with the idea of "necessary existence", as Groothuis writes: "The difference with this argument is the employment of the concept of what later philosophers call 'necessary existence.' God does not simply happen to exist as 'a being than which nothing greater can be conceived to exist.' Rather, God exists as a matter of logical necessity." The premises, taken from Groothuis, are as follows:
1. God defined as a maximally great or Perfect Being. 2. The existence of a Perfect Being is either impossible or necessary (since it cannot be contingent). 3. The concept of a Perfect Being is not impossible since it is neither non–sensical nor self–contradictory. 4. Therefore (a) a Perfect Being is necessary. 5. Therefore (b) a Perfect Being exists. The argument basically goes that there is a being that possesses a necessary existence, and then it makes the jump that because this being is necessary, it must also of course exist. According to Richard Taylor, the key to understanding Anselm’s second argument is to understand first a distinction between two senses of existence. The first kind of existence is that which exists in the understanding only, and the second is that which exists in reality. Again, as with the prior argument, the downfall of this one is that it is not clearly demonstrable that existence in reality is necessary for a Perfect Being.
The logic surrounding the ontological arguments is very complex, in part because the arguments themselves are a priori and purely conceptual. No side has a clear victory on whether or not existence is a predicate or whether actual existence is “greater” than nonexistence, and one of the downsides of this argument is that this logic is very confusing. Groothuis notes: “The rather abstruse reasoning of the ontological argument may make it intellectually inaccessible to many.” The overall goal of this paper is not to see if the Ontological argument is logically sound (though that plays a large part), but instead whether it should be used in Apologetics. My contention is that the complex nature of the argument severely hinders its recommendation for use even if it is logically sound. When I use this argument in apologetical dialogue, it is so confusing both to explain to the audience that many can’t refute it simply because they are so baffled and confused by it! Even if we restrict ourselves to the realm of natural theology and all of the theistic arguments within, there are so many other arguments that one could use. When Anselm was developing his first argument, after he had gone through most of his argument, he said this: “And thou art this being, oh lord our God.” Anselm made the huge leap of the being that resulted from his argument and the trinitarian God of the Bible. The ontological argument is usually considered a “theistic” proof, but when the word “theistic” is taken in its accepted definition, that is, a personal deity, then the ontological argument is actually a “deistic proof”, because the being that results from a successful inference of the argument is an abstract concept that is Perfect in every way. Yes, this is what God is, but that is only part of what God is. He is much more than that. I would argue that using the ontological argument in apologetical dialogue helps little in trying to win people to Christ, because even if they understand what you are trying to argue, they are far from the redeeming God of scripture, in whom they must place their faith in for salvation through Christ.