Zach's Ontological Argument in Predicate Logic

Greetings,

It has been quite some time since my last post, due in part to my attending an investment conference called R.I.S.E. in Dayton, Ohio. While there, I found myself attending a 2-hour panel on corporate governance... not the most exciting material, particularly for a philosophy student. However, I had plenty of time to fiddle around with one of my most favorite arguments: the Ontological Argument for the Existence of God.

As an undergraduate in philosophy, it often seems like logic is like a board game without a board—I know the rules, but want a scenario to try my hand with them. So far, the only “board” I’ve learned of that can be played for hours at a time is the Ontological Argument, which is fairly controversial on several grounds. It’s a fun game to play because it’s a challenges to establish a valid argument with true noncontroversial premises, but seems like something where I can consistently make progress.

So, at the conference, here is what I originally came up with:



Where P = …Is the perfection of…, H = …Has the property…, a= A being with all possible perfections, u= The property of existence in the understanding, and r= The property of existence in reality.

The basic argument is that if x is a perfection of existence in the understanding, a being with all perfections and with existence in the understanding must also possess x. As existence in reality is the perfection of existence in the understanding, and a being with all perfections exists in the understanding, a being with all perfections therefore necessarily exists in reality.

This appeared logically valid to me, but I was not satisfied. Premise 1 appears non-controversial to me—if a being has all perfections and has a property, it must therefore have the perfection of that property. However, Premise 2 and Premise 3 seemed more controversial—that the property of existing in reality is more perfect than the property of existing in the understanding (Premise 2), and that a being with all possible perfections exists in the understanding (Premise 3). Thus, I decided to see if I could find non-controversial ways to express these premises.

After playing around with the possibilities, I came up with this argument for Premise 3:



Where H = …Has the property…, A= Can be rationally debated, u= The property of existing in the understanding, and a=A being with all possible perfections.

The basic argument here is that, if any given x does not exist in the understanding, one cannot rationally debate it—for example, if unicorns do not exist in my understanding, then I cannot debate about unicorns. I feel that this should be fairly non-controversial, and thus should make the argument a bit more generally acceptable.

Therefore, my new version of the Ontological Argument (for those who challenge Hau) is:



Where P = …Is the perfection of…, H = …Has the property…, A= Can be rationally debated, a= A being with all possible perfections, u= The property of existence in the understanding, and r= The property of existence in reality.

However, I feel that the new fourth premise—Pru—is still fairly controversial, and wanted to see if I could express it in a less controversial manner. After a bit more exploration (and with the corporate governance panel drawing to a close), I came up with this:



Where P = …Is the purest possible positive property of…, H = …Has the property…, I=…Is a…, n= Perfection, p=Property, …N=Can have a…, u= The property of existence in the understanding, and r= The property of necessary existence in reality.

This is arguing that there’s nothing that exists that is the perfection of existence in the understanding and is not the property of necessary existence in reality. Now, if existence is a property and the property of necessary existence in reality is not the perfection of existence in understanding, then either there exists something that is more perfect existence than necessary existence or existence cannot have a perfection (but not both of these at the same time). As existence can have a perfection, and existence is a property, necessary existence in reality must necessarily be the perfection of existence in understanding.

Plugging this into the original equation would look like this:



Where P = …Is the purest possible positive property of…, H = …Has the property…, I=…Is a…, n= Perfection, p=Property, …N=Can have a…, a= A being with all purest possible positive properties, A= Can be rationally debated, u= The property of existence in the understanding, and r= The property of necessary existence in reality.


So, there you go: Zach’s version of the Ontological Argument in Predicate Logic, plus further argument on Hau and Pru. Also, you may notice that Iep could just as well be left out… I’m trying to anticipate Kant, though. Once I understand his argument better, it’s structured so I should be able to respond and easily plug it in.

Thoughts/comments/suggestions? Think it’s full of crap, think it’s invalid and I missed something, or think there’s a mistaken premise? Impressed with my leet formatting skills on a blog post? Looking forward to any/all comments!

Kierkegaard: Number 10!

Greetings,

Well, just got my PC up and running after frying the motherboard about a month ago... and, a poll on the Leiter Reports with 600 votes found Kierkegaard to be the 10th most important philosopher of the last 200 years!

Ironically enough, Kiekegaard would probably disprove... he's been voted to be important by the anonymous masses in a mass media style of publication... but then again, he was also a fan of irony, so I suppose that's acceptable.

Oh, and I'll have another post up soon with significant content... however, it's long and holds some images which I'll have to format once I'm out of class, so I can't guarantee what time today it'll be up.

My Favorite Books

Ben Bell has been insisting that I list my favorite books on Facebook. I will do that but I thought I would give them here first so that I can explain briefly their significance for me. In truth I have chosen ten books that are not only favorites but which have had a significant place in my intellectual formation. They have made me what I am.

1. Plato, The Republic. The greatest philosophy book ever. It has everything.
2. Lewis Carroll, Alice in Wonderland and Through the Looking Glass. Perhaps the most profound books ever written for a child. The annotated version by Martin Gardner is a delight.
3. Bertrand Russell, Introduction to Mathematical Philosophy. It got me first fascinated by what I'm fascinated by. Though I don't share Russell's views on religion or ethics, he is my model for clarity in thought and writing. A second place goes to his History of Western Philosophy. Not serious historical scholarship but a good place to start.
4. Jorge Luis Borges, Collected Fictions. Very stimulating, lots of fun.
5. Martin Gardner, Fads and Fallacies. My first book on the philosophy of science, though I didn't know it at the time. Chapters on assorted cranks, including flat earthers, anti-Einsteinians, and dowsers.
6. Michel de Montaigne, Essays. The inventor of the essay and one of the most entertaining writers ever.
7. George Gamow, One, Two, Three...Infinity. My father gave me this book written by an eminent physicist when I was about 10. The first chapter, which was my first exposure to Georg Cantor's work on the infinite, simply blew my mind.
8. Edwin Abbott, Flatland. An intriguing combination of science fiction and social satire. It made me question my beliefs about reality at an early age and sent me along the path of philosophy. A version annotated by the mathematician Ian Stewart was published a few years ago.
9. Oliver Sacks, Uncle Tungsten. A memoir of the famed neurologist's childhood that doubles as a book on chemistry. Really good.
10. Liddell and Scott, Greek-English Lexicon. Yes, it's a dictionary! But it is also a comprehensive record of the language and literature of a great civilization. Liddell was Alice's father (see number 2 above).

The Liberal Arts and Belief in God

In my last two posts I discussed the relation of philosophy to the humanities and the liberal arts. I would like to complete my thoughts on these topics by presenting a hypothesis that I have been considering for some time. I am not at all sure if it is correct, so I am eager to receive any responses.

I have settled on an understanding of the liberal arts as any kind of study that is pursued for the intrinsic value of its object. I have presented mathematics as the liberal art par excellence because one's concern at least in pure mathematics is simply with the structures and patterns that one is studying without an immediate interest in the applications that any results about these structures may have. The same holds in the case of the "disinterested" study of the natural sciences, where the sheer beauty and complexity of the world is sufficient motive and reward for the scientist's efforts.

Yet this notion that the world is worthy of study for its own sake entails that there is an intrinsic goodness and value to the world. Absent that, one has no adequate justification of the liberal arts. For if all values are impositions on reality by humans based on their interests and purposes, there is no sense to disinterested study but only to knowledge that advances the interests of man. Hence a narrow, pragmatic focus on the value of education.

Now belief in the intrinsic goodness of the world has usually, though not always, depended on a belief in a benevolent creator-god. I don't mean to suggest that secular scientists and scholars do not have a sense of awe and wonder that is in many ways similar to a religious approach to nature. Nor do I ignore the existence of theists who have no place for the liberal arts. But it does seem to me that one can more readily argue for the liberal arts within a certain theistic framework than from without. So perhaps the present decline in the liberal arts is itself a symptom of a crisis of faith?

Is Philosophy a Liberal Art?

In my previous post, I asked whether philosophy belongs to the humanities. That question is difficult to answer unless one has a clear set of criteria that make a subject a humanistic. But I am more certain about what a liberal art is. And philosophy, as it is normally practiced, is certainly a liberal art.

My principal objection is that many people identify the humanities with the liberal arts. But this is neither historically nor conceptually defensible. The earliest formulation of the liberal arts mainly included what we now would call mathematics (which is usually not considered part of the humanities). But even today math is clearly a liberal art. For I understand the liberal arts to be those disciplines that may be studied simply to enrich one's life rather than to provide a training for a particular profession or occupation.

As an amateur mathematician (with the emphasis on "amateur") I have never used what I've learned in real analysis or abstract algebra to earn my livelihood. But I simply delight in their study! I am a happier person for understanding the fundamental theorem of calculus. And I think I'm a better philosopher for it too.

Now to be sure, math can be used for very practical ends. But that does not make it an illiberal art. For it can and very often is studied simply for its sheer beauty and depth. Philosophy, perhaps, is not so useful, and its charm resides principally in its power to enrich. But the study of both subjects embodies the ideal of a liberal arts education. As does the study of history, language, physics, economics, political science among many others.

So let the humanities die if they must! They seem to be a recent development in human history. But the ancient and hoary liberal arts--may they live on forever.

Positive Science, Negative Theology

Last night's talk, “Positive Science / Negative Theology,” by former Berry physics professor and current Emory theology student appealed to a broad audience.

Dr. Wallace argued something to this effect: Science is at its best when making positive claims. For example, platypuses lay eggs, the earth is (generally) spherical, and that wavelength equals wavespeed divided by frequency.

Theology, however, is best served when making negative “claims”, although “claims” is perhaps not the correct word. Negative experiences, in accordance with the apophatic tradition, edifies true religious experiences, according to Dr. Wallace. For example, experiences of “emptying” or of realizing one’s insignificance would appear to fall under the status of apophasis. While much could be said about apophasis, I'll leave that to subsequent posts. Instead I want to take up the positive/negative distinction between theology and science.

Dr. Wallace originally claimed that proper science is positive and proper theology is negative. It was unclear whether or not “negative science” could even exist, and positive theology—such as ontological proofs for God—are not edifying as is negative theology. However, Dr. Wallace also argued that, by science, he meant a vast collection of facts—but facts ought really to be interpreted as very well educated opinions, that might not correspond to actual reality and might end up being wrong. While the intention of science is to tell us what is, it can only do so through telling us what it definitely is not (for example, that Aristotelian physics fails, or that Newtonian physics are irrelevant to objects moving at speeds comparable to that of light).

Let us then, make this distinction: Science is positive in its intention but negative in its method. Science cannot tell us that all platypuses lay eggs or that wavelength equals wavespeed divided by frequency; rather, it can tell us that this has been the case for all observable phenomena, and we see no logical basis for assuming that these trends will not apply universally. However, what it can absolutely do is determine when things are inadequate (such as Aristotelian physics), and narrow down the choices accordingly. Perhaps Popperian, but nevertheless seems consistent.

Now, in terms of negative theology, Dr. Wallace argued that one should approach God negatively—at least, through a negative method. However, the intention of theology is to know and form a relationship with God; it does not have a negative relationship to God in intention, or else one may as well watch television for hours, since you’ll have just as much negative knowledge about God.

So, science has positive intentions and negative methods. Theology has positive intentions and negative methods. Therefore, positive science and negative theology don’t refer to the same thing—one refers to intention, while the other refers to method.

What are the implications of this?
Is the positive/negative dichotomy right?
Is there a third option here—not merely a gradient scale, but an actual third option?

Is Philosophy Part of the Humanities?

I've been reading a number of articles recently that discuss the fate of the humanities. A couple of days ago someone put a copy of a New York Times article "In Tough Times, the Humanities Must Justify Their Worth" in my box. And the literary critic Stanley Fish has posted several comments on the same site on the topic of the value of a humanities education. His entry on the "Last Professor" discusses the book with that title by Frank Donaghue, who argues that the humanities don't so much face a crisis but rather are already on their deathbed as the university becomes driven by purely practical concerns. "...all fields deemed impractical, such as philosophy, art history, and history will henceforth face a constant danger of being deemed unnecessary" writes Donoghue, according to Fish. Fish himself notes wistfully that he was lucky to get into the humanities business when things were still good, but otherwise seems to think Donoghue's pessimistic prognosis is correct.

I am not by inclination pessimistic. I also tend to think that the present is not that different from the past, and that in some sense the humanities have been dying and coming back to life (sometimes in new forms) as long as they have been around. What may appear to us as imminent demise may just be another stage in development.

But I'm not so interested in all that. I'm more interested in the question of whether philosophy is one of the humanities. I'm not so sure it is. According to Berry's general education classification, it is, but that is just a result of an arbitrary bureaucratic classification. Certainly it would be hard to make the case that the kind of philosophy I do has much in common with the other disciplines lumped together as humanities. I suppose that the humanities are concerned with the study of humanity. But my current research interest in philosophical logic is not principally (or, at all, for that matter) concerned with humans. And many sciences (biology, economics, political science) not usually considered humanities study humans. So such a characterization of the humanities as the study of humans is not very helpful.

There must be a special method or approach that distinguishes the humanities from other disciplines. But there again I think that much of philosophy would fail to be humanistic. Except for the more historical/literary approaches to philosophy, a lot of philosophy, especially the analytic sort, resembles more in its approach the formal methods of mathematics and linguistics than what usually goes on in literature or history departments.

So help me out here. What makes a discipline humanistic? And does philosophy as a whole (as opposed to just some forms of philosophy) count as humanistic?

Coffee and Philosophy: Brewing the “Good Stuff”

Greetings,
Coffee is everywhere—from cheap office brewers to a pricey cup at Starbucks, it is a phenomena that persists in many forms and fashions. Of course, there are many methods of brewing coffee; one person might the boldness of coffee brewed from a French Press, while another prefers the simplicity of an auto-drip. Still, others care less about the taste than about the convenience, and are content with a $2.00 cup from Starbucks. An interesting analogy can be drawn if one compares the methods of brewing coffee with the methods of “brewing” philosophy, that, whether you know about your tastes in coffee or philosophy (or both), might spark some interest in your mind.

One way of brewing coffee is the Percolator. This is the device one sees in generic Western movies, a simple pot with a filter inside that one heats over an open stove or fire. This generally makes a poor pot of coffee, but requires no electricity, and can generate vast quantities of the drink. It’s extremely hard to know when it’s time to pull it off the heat, and is unlikely to make something tasty—but it’s useful for excursions and low-budget western movies.

Percolators are a method similar to amateur philosophy, such as that from much of the blogosphere and from those who enjoy talking about intellectual matters, but who have never read or studied philosophy in their life. People often make fun of those who expound their views as “philosophies”, cheap knockoffs of the real thing as they all, but nevertheless enjoy it for cheap entertainment value. The people who resort to this generally don’t know that something better exists—or don’t have the intellectual bravery to live someplace with electricity (interpret that as you wish).

The Auto-Drip is another method of brewing coffee. By this method, hot water automatically drenches ground coffee beans from a small reserve tank. There exists a lot of variety among auto-drip makers—options can include everything from pre-programmed brewing to single-cup brewing to brewing for large amounts of people. Those who want can brew a cheap cup in a minute from pre-packaged grounds, while others might carefully grind their own beans, take care not to let the coffee burn, and produce a wonderful cup of coffee.

Similar to the auto-drip in philosophy is the mainstream historical material. After all, who hasn’t heard that the Greeks taught moderation, the medieval philosophers tried to prove that God exists, or that Nietzsche argued that God is dead (and we have killed him)? Of course, for those who are willing to take the time and study the material, they’ll find a lot more depth—the Greeks were about more than moderation, the medieval philosophers made some intriguing points on human nature (Augustine, anyone?), and even Nietzsche’s ravings on a dead God might have more subtlety than meets the eye. In fact, those who are willing to take the time, do the work to grind the beans, and make sure that the pot doesn’t burn may find themselves with a genuinely delicious, distinctive cup of Joe—or of existentialism, whichever’s your cup of tea… eh, enough with the silly puns; back to the analogies.

The French Press is the method of brewing coffee for the connoisseur, involving labor and time, as well as attention to detail. It’s important not to grind the beans too finely, not to pour too much water in, and let the coffee steep before you sift the grinds out via a screen. However, those “in the know” will tell you that, if you’re looking for the best, this is where it’s at. It’s not accessible to many people, and takes a good deal of time and energy, but the payout—if you can make it—is certainly worth it.

The French Press loosely corresponds to genuine philosophic study. This generally involves, for those who choose to partake, a lot of time, effort, and mental energy. One must carefully read sources in their original language to catch their true meaning. One must analyze the criticism of peers and, a harder critic, one’s own scrutiny. One must be willing to dedicate hours of difficult, intellectual exercise that needs to always be aware of itself. Essentially, this will allow one to enjoy coffee—or philosophy—in its purest form, and find the most long-lasting pleasure. You may still be able to enjoy the lesser forms, such as the auto-drip, but you’ll know what you’re missing, and won’t be able to consider it with quite the merit that you perhaps once did.

The $2.00 Cup of Starbucks is suave, sexy, and unbearable without large doses of sugar, cream, chocolate syrup, and whipped cream. It boost your feelings of self worth—I’ve seen people who’ve filled old Starbucks cups with coffee from an auto-drip just so others can see them drink from it. However, if you really take the time to stop and think about what you’re drinking, you’re going to be disappointed; you wasted your money on a $2 cheap of burned coffee, so best to pretend like you don’t see its flaws and wait until you have something better to drink
I couldn’t possibly imagine what this could emulate in philosophy… do as you will with that.

Lastly, there are many more methods of brewing or making coffee, such as espresso machines and vacuum pots. However, they tend to be a bit less common, and I’m not familiar with them enough to comment.

At any rate, I hope you enjoyed the article. I’m personally an auto-drip kind of guy; I’d like to get into the French Press one day, but I’m not ready for it yet, and will wait until I have the knowledge to use it properly. What about you?