I'm going to take a stab at the ontological argument. It's the most intriguing and perplexing of the traditional theistic proofs. Plantinga, Gödel, and E. J. Lowe formulated important versions of the ontological argument, which merit serious consideration in their own right. But these are pretty technical. In this post I'm going to focus on a more Anselmian approach.
This isn't strictly an exposition of Anselm's argument. I'm not sure what he had in mind. Scholars differ on how to interpret his argument.
i) Moreover, anyone writing a millennium later will have conceptual resources at his disposal which were unavailable to Anselm. My primary objective in this post is to consider what kind of argument it is.
In addition, I will attempt to explicate a key principle of the argument: the internal relationship between what is and what is greater than (i.e. between existence and greatness).
ii) It seems to me that the ontological argument takes the form of a dilemma. Even an atheist must begin with a concept of God. Unless he has a concept of God, he can't deny God's existence. (Anselm's target is explicit atheism.)
The idea of God is either greater than the thinker who thinks it or not. If greater, then it must have a corresponding reality above and beyond the thinker. If we can entertain the idea of a greatest conceivable being, then that must be more than an idea.
Anselm's definition of a greatest possible being includes a being who cannot fail to exist.
iii) Anselm's barebones formulation suffers from a superficial equivocation. When he speaks of existing in the mind or existing in reality, he doesn't mean God in himself exists in the human mind. Rather, it's a type/token relation. Our idea of God is a token of the extramental reality. A God who exists in the mind is shorthand for a conceptual token of God.
iv) In Contact, the action builds to the climactic encounter with a superior alien intelligence. However, that climactic scene is anticlimactic. Indeed, it's bound to be anticlimactic.
That's because the alien is just a fictional character. The alien is not a superior intellect. Rather, the alien is just Carl Sagan's idea of a superior intellect. So it was inevitable that the big scene would be a letdown.
The alien character can't be any greater than its creator. It can't be wiser than Sagan. If it's just a human idea, then it can't surpass the source.
That's a problem for SF aliens generally. Since the alien is just a figment of human imagination, it can't rise any higher than the source.
v) Compare that to our notion of the Mandelbrot set. Mathematicians have a partial understanding of the Mandelbrot set. However, the Mandelbrot set vastly exceeds human comprehension. We're dipping our toes into a fathomless fiord. It's far too complex for the human mind to grasp in detail. We can only sample it.
In that case, we have an idea of something greater than ourselves. Something we discover. Because the Mandelbrot surpasses human comprehension, it must in some respect exist apart from finite human minds.
That's a type/token relation. Our idea of the Mandelbrot set is an instance of that greater reality.
vi) In math we also have unproven theorems and conjectures. That means a mathematician can be smart enough to think of a problem that's he's not smart enough to solve.
In principle, a mathematician can devise a provable (or falsifiable) theorem or conjecture which no mathematician will ever be able to prove (or disprove). These conjectures and theorems are true or false independent of whether we can solve them.
But in that respect the concept is greater than the thinker who conceived it. It isn't reducible to human cognition. It has a reality that transcends our efforts to mentally probe it.
vii) We could also relate this to truthmaker theory. Take counterfactuals. Must there be some corresponding reality that makes counterfactual claims true? What's the truth-maker for the truth-bearer? There's a relationship between what's true and what exists. Truth is contingent on being–of some sort.
viii) It seems to me that to succeed, an Anselmian-style argument must demonstrate that the idea of God is suitably analogous to (v) or (vi). That our concept of God is that kind of idea. Once established, that will, in turn, implicate the existence of God.
ix) A potential way to escape the force of the argument is to retreat into conceptualism or nominalism. Of course, that's only as good as the case for conceptualism or nominalism.
Not to stray too far off topic, but since you mentioned math, I had a question. In a post you wrote a long time ago, you stated numbers are internally related. That makes sense: "1 is 3-2," "3-2 is 1," and so forth.
ReplyDeleteMy question is if this implies that knowledge of one number implies implicit knowledge of all numbers. It may depend on what you meant by "internally related," and you may have developed your views since then.
i) If a person has some mathematical aptitude, it might be "implicit knowledge" in the sense by knowing some mathematical truths, he can reason to other mathematical truths. There's that potential. Latent in the knowledge of some numerical truths is the possibility of drawing inferences about other numerical truths.
DeleteOf course, some people have no capacity to extend their mathematical knowledge that way. They just know how to perform certain manipulations (equations, formulas, or simple counting) to produce certain useful results.
ii) However, I was talking about metaphysics rather than psychology. Implication is a static or timeless relation. The network of mathematical truths is a given totality. A complete (abstract structure). A system of internal relations (in the idealist sense).
And that inheres in the mind of God. At that divine level, ontology and psychology coincide. God is an infinite mind.
This is related to the ontologial status of an actual (abstract) infinite. Stephan Körner had a useful exposition in The Philosophy of Mathematics: An Introductory Essay.
DeleteThanks for the reply. To lay out my concern explicitly, it's that if mathematics is a system of internal relations, then we can't know, in an internalist, infallibilist sense, any mathematical truths. [If you reject that we can know such truths in either or both senses, I guess there is no problem here, but that doesn't work for me.] My working definition of internal relations comes from D. A. Rohatyn's paper on the subject:
Delete“What is the doctrine of internal relations? It amounts to the following theses: (a) that every event, and every entity, in the world is somehow (causally or logically) tied to every other event, and every other object, in the universe, such that (b) to attain complete knowledge of any one thing or state of affairs, is to possess (automatically) knowledge of the whole, i.e. of all states of affairs and of all things.”
I'm a little uncertain what "complete knowledge" means, but Van Til and Clark both make it sound as if for idealists, what a thing is is determined by its context, i.e. everything, so that to know even one thing would be to know everything - metaphysics impacts epistemology. And in our case, we obviously don't know everything, from which Clark concludes internal relations is false and Van Til seems to conclude our knowledge must be analogical to God's rather than univocal.
We can restrict the context here to mathematics and numbers, the point is we'd still know an infinitude of truths. Maybe we could know them dispositionally rather than occurrently, in which case internalist, infallibilist knowledge of mathematical truths, a rigorous theory of mathematical internal relations, and exclusive divine omniscience can be simultaneously coherently maintained?
I'm still working things out. My interest originally stemmed from wondering extent to which internal relations and necessitarianism coincide, as I've been looking for a transcendental argument against necessitarianism.
The position you're sketching is very similar to Brand Blanshard's position in Reason and Analysis. Not coincidentally, Blanshard was a philosopher in the idealist tradition. Not coincidentally, Clark was a big fan of Blanshard.
DeleteI think internal relations apply to abstract objects like mathematical structures, but not to concrete objects. I distinguish between truths of reason and truths of fact. I don't think every fact entails every other fact. Many facts are contingent: they could be otherwise.
This is an old debate. Leibniz wrestled with the same issues. I think he was an idealist. He used logic/internal relations as his model of reality. That, however, entangled him in a necessitarian scheme from which he tried to extricate himself, without complete success.
I don't object to univocal predication in principle, although I don't think that's a requirement for knowledge.
Yes, I recently bought The Philosophy of Brand Blanshard and was immediately struck by similar phrasings Clark used throughout his books.
DeleteI think internal relations apply to abstract objects like mathematical structures, but not to concrete objects.
Understood, I'm just trying to understand whether it is in principle possible to [occurrently] know, in an internalist and infallibilist sense, some mathematical truths without having to [occurrently] know every mathematical truth, an infinitude of truths.
I don't think every fact entails every other fact. Many facts are contingent: they could be otherwise.
I agree. Much of Clark's metaphysical views are wrong, and I believe this is one of them.
"I'm a little uncertain what 'complete knowledge' means, but Van Til and Clark both make it sound as if for idealists, what a thing is is determined by its context, i.e. everything, so that to know even one thing would be to know everything - metaphysics impacts epistemology."
Deletei) Yes, Van Til's theory of knowledge sounds as if it's influenced by an idealist coherence theory of truth. It then adapts that model to facts: every fact is "defined" by God, whose decree assigns meaning to every fact. Every fact serves a purpose in relation to other facts.
That's similar to internal relations, but it's conditional necessity rather than absolute necessity. The teleology of the decree. However, facts could serve a different purpose had God decreed otherwise.
ii) Is there a principled distinction between complete ignorance, complete knowledge, and partial knowledge? Is partial knowledge a distinct, stable category?
Take an illustration: Suppose I know nothing about Mark Twain until I read an encyclopedia article about him. I now know something about him that I didn't know before reading the article. That makes a difference regarding my prior state of knowledge in relation to my subsequent state of knowledge. Something that makes a difference is a genuine distinction.
But, of course, there's still a lot that I don't know about Twain.
iii) Context can certainly improve our understanding. If I read Tom Sawyer and Huck Finn, and if I then read his boyhood reminisces in Twain's autobiography, that supplementary info about the author may improve my understanding of his semiautobiographical novels.
iv) However, just knowing more doesn't necessarily illuminate one's understanding of a particular issue. For instance, Hannibal was a port town on the Mississippi. Having some background info can aid one's reading of Huck Finn and Tom Sawyer. Likewise, knowing about antebellum slavery can aid one's understanding of Huck Finn.
Now, at a metaphysical level, in terms of natural causes and historical causation, past, present, and future range along an interlocking continuum.
However, knowing about Hannibal in 2015 doesn't necessarily improve my understanding of Mark Twain's novels, because Hannibal in 2015 isn't Mark Twain's Hannibal. That's not the Hannibal of Twain's boyhood. Antebellum Hannibal was a very different place than 2015 Hannibal. Likewise, the condition of the Mississippi river in 2015 isn't directly germ to understanding Huck Finn.
It's the wrong context. In fact, using the future to interpret the past is misleading. That's because many things that are true of 2015 Hannibal are false of 1850 Hannibal. The more you know about the modern town of Hannibal, the more that may interfere with your understanding of Twain's novels. Even though past and future are linked by a chain of cause and effect, to understand more about Twain's novels, we need to know more about the past, not the future. More about the period when Twain was a boy.
Cont. v) In math, you have a network of logically implicated truths. So, in principle, you could start anywhere, and reason your way to the whole. To the extent that mathematical relations are mutually inclusive, you can infer everything from something.
DeleteNow I'm not sure if that's true between different branches of math. I don't know if geometry entails number theory, or vice versa.
vi) However, contingent truths are different from necessary truths. For instance, historians think we can better understand the present by better understanding the past. Knowing the past explains the present. Because the present is the result of past actions, past choices, if you want to understand why and how we got to this point, just retrace the chain of events. So goes the argument.
Yet if that's true, it ought to be reversible. We should be able to predict the future–which lies along a common trajectory:
Past>present>future.
But, of course, our ability to extrapolate from the present to the future is limited and unreliable. Projections become less certain the farther out we go.
That's in part because the very effort to anticipate the future can influence our future actions. It becomes a moving target. We change the object of knowledge in the very process of contemplating the outcome.
In addition, every present cause has branching effects. Branches of branches of branches the farther out we go. It's too complicated for humans to track.
Finally, even if human decisions are predetermined, that doesn't necessarily mean they are predetermined by historical factors. Although human decisions are predestined, that doesn't necessarily mean they are the product of intramundane causation. Although the agent's character is a factor, although his situation is a factor, the ultimate reason for his choices is the purpose that serves in God's master plan for the world. In principle, a human agent's choice could be independent of his environment or even his character traits. It just can't be independent of the decree.
History is like a well-written novel. Motivated actions. Ends and means. But there are different possible pathways to the same destination. So we don't know in advance which one God has foreordained. That's something we find out by living through time.
Consider another comparison:
Deletei) Appearances to the contrary, Pi is not a random number. It has a subtle pattern, even if that eludes human detection.
Pi has no give. The decimal expansion of Pi must be in that exact sequence every step of the way. Not a single digit can be different. Not a single transposition.
So we might say the internal structure of Pi is very tight.
ii) Let's compare that to a contingent state of affairs. If the Titanic didn't hit the iceberg, that would change the future in many ways. But what change or changes in the past would be necessary for the Titanic to avoid colliding with the iceberg?
There are different ways that could be accomplished. One way is if the captain changed his mind, if he changed course an hour before.
And what would be necessary to prompt the captain to change his mind? Well, it could be something as simple as God causing the captain to change his mind.
His change of mind needn't be the result of a preceding chain of events. It could be a discrete mental event that's discontinuous with the past. It needn't be linked to a causal continuum extending back in time.
On that scenario, it would only take a single change in past to change many things in the future.
In that respect, a contingent state of affairs isn't tight in the sense that Pi is tight.