If God Exists, Prove It!

Conversations between theists and skeptics often go like this:

Theist: “God exists.”

Skeptic: “Oh yeah? Well, prove it!”

A thorny problem lies in the term proof. What does it mean to ‘prove’ something? For example, what does it mean to prove the Pythagorean Theorem or prove that a person is not in The Matrix? Answers on the latter will vary more than the former. I have found that people tend to take the term ‘proof’ to mean various things.  For example, many people think that mathematical proofs are paradigmatic. After all, it would be manifestly irrational to deny the Pythagorean Theorem once it was properly explained and demonstrated. Likewise, the skeptic often asks the theist to prove that God exists in the same way. But this unreflective position is not a particularly safe quarter.

Like many of the things we take for granted, there is a great deal of nuance regarding what it means to ‘prove’ something. Some of the greatest minds in history have addressed this question, including Aristotle, Aquinas, Russell, Whitehead, Gödel, and many others. Interestingly, some of these later thinkers, of which Frege, Hilbert, Tarski, and Turing might well be included, spent a great deal of time on mathematical proofs, axioms, and theorems. Their work is breathtaking in scope, and certainly reflects a level of genius achieved by few. This fact alone should give one pause when demanding mathematical proofs for things. Does the demand for such a proof account for the kinds of issues that must be addressed when discussing ‘proof’? Does the demand for this type of proof properly understand the framework in which one might obtain? While it is possible such depth has been accounted for, I do not think the complexity baked into the skeptical demand is usually considered.

The skeptic will generally reply that they do not need a high-level dissertation on proofs, just something simple. Prove God exists like we can prove “2 + 2 = 4.” After all, if God existed, should it really be that complicated to prove? In response, I think we should first note that complexity is not a very good test for truth. Secondly, the higher-level concepts alluded to above are still relevant. Further, such a request betrays a fundamental metaphysical assumption about numbers/mathematics which should be disclosed. Does the skeptic mean that numbers are real? Or sets? Or...? If so, then I think the type of realism implied should enter the conversation.

A skeptic holding to Platonism (perhaps implicitly) would be in a different position regarding the result and underpinning of a ‘proof’ request than a nominalist. The nominalist would be faced with the difficulty of demanding a proof based upon or like things which he does not hold as existing. In essence, the nominalist says, “prove that God exists in the same way you would prove something exists that I do not accept as really existing.” If all we are doing with mathematical proofs is rearranging the furniture of our own (exclusively) mental concepts or linguistic utterances, or winnowing word meaning conventions, then the proof demand of the theist would enter a new (and futile) light. On the other hand, the Platonist assumes abstract objects exist within his request. Thus, he essentially says, “prove that God exists in the same way you would prove that we can know about and reason with abstract objects like Two, Plus, and Four.” Given this rationale, the Platonist does not have much basis to remain in the sort of proof-skepticism from which the request springs.

What has been said so far might seem to smack of the “question the assumptions within the question” notion. This is true to a certain extent. But it is not for purposes of deflection. Instead, we must have clarification about what the interlocutor really wants. And if the interlocutor is unclear, then we risk talking past each other. If the interlocutor makes a request that is unanswerable within even his own framework, the problem remains. And if the interlocutor demands an answer to fit preconceived notions that the theist will not accept, the conversation cannot progress.

It should be said there are some theists who will not use the term ‘proof’ with regard to God’s existence. They will use arguments and present evidence to conclude, usually inductively or abductively, that God exists. To the extent the skeptic demands a proof, some theists will reply that one is not forthcoming or possible, and then explain why the skeptic should not take issue with this. It might be that the skeptic is inconsistent in his demand for proof to have sufficient knowledge for rational belief, or for other reasons altogether. Further, some theists may not even conceive of deductive arguments as ‘proofs’ because they think such a term does not apply within metaphysics. And when discussing the existence of God, we are having a metaphysical discussion. Physical scientific evidence, theories, and so forth might be used in support of premises feeding into the conclusion “God exists” but God is not in principle the proper subject of any physical science. Nonetheless, He is the subject of science (scientia = knowledge) and theists have always held that we can have knowledge of and about God.

Still, the skeptic can respond that all this mumbo-jumbo is well and good for the tweed jacket folks. But he just wants to know why he should think that God exists; he wants to know why the theist can be so (potentially) dogmatic about something so profound. Some thinkers in the past have indeed tried to prove and dissect ‘God’ by geometrical means. Spinoza is probably at the head of this class. Through a labyrinth of axioms and deductions, Spinoza lands what most commentators find to be a type of pantheism (God and nature are identified). I agree with this assessment. While occasionally presenting good food for thought, I think the Lens Grinder shows the theist what to avoid.

This leads me to try and briefly sketch some general precepts by which we might distinguish mathematical and metaphysical proofs. I think that we can hold to a notion of metaphysical ‘proof’ for God. And by ‘proof’ I mean metaphysical demonstration. Such a demonstration is deductive and yields knowledge about something. Aquinas explains it succinctly as follows

I answer that it must be said that demonstration is twofold: One which is through the cause, and is called demonstration "propter quid" [lit., 'on account of which'] and this is [to argue] from what is prior simply speaking (simpliciter). The other is through the effect, and is called a demonstration "quia" [lit., 'that']; this is [to argue] from what is prior relatively only to us (quoad nos). When an effect is better known to us than its cause, from the effect we proceed to the knowledge of the cause. And from every effect the existence of its proper cause can be demonstrated, so long as its effects are better known to us (quoad nos); because since every effect depends upon its cause, if the effect exists, the cause must pre-exist. (ST 1.2.2)

Aquinas argued that we can demonstrate God’s existence from His effects (demonstration “quia”). There was a great deal of debate in medieval philosophy about 'demonstration', how the Posterior Analytics of Aristotle should be understood, and so forth. It is beyond the scope to adjudicate all of these issues here. But I think Aquinas’ position is very defensible, and it provides a clear way forward for all concerned. I would submit that even a skeptic about God should accept this rationale, if for no other reason than to maintain a coherent position on scientific theories and many features of mathematics and logic. Among other helpful attributes, Aquinas’ rendering of demonstration can help us properly cash out mathematical versus metaphysical proofs. Here are some of the basic points:

• Mathematical demonstrations would be akin to the first type alluded to by Aquinas (above). They would be along the lines of “quid” versus “quia,” though not necessarily always so perfectly bifurcated. Mathematical proofs can become exceedingly abstract and require the supposition of axioms and precepts that are not in themselves demonstrated. In a simplified sense, a mathematical demonstration can be shown front-to-back and back-to-front, which a metaphysical demonstration might not admit of, working from front-to-back only. Though, in both cases, we can obtain knowledge (more so in the quia demonstration).

• Mathematical demonstrations are based on abstractions from real things, but the mathematician must take what these things are for granted. So, the mathematician or geometer works from reality taken as it is. But metaphysics concerns what is real, and therefore seems prior to any apprehended mathematical truths. For math and logic to work at all, there must be some objective basis. The world and intellect must be able to connect and relate. And it is just this basis that metaphysical demonstration provides to undergird mathematical demonstration. It should not be surprising that we can have “quid” demonstrations in mathematics and not for all metaphysical demonstrations.

• Quantity and relation are predicated of substance, something that exists through itself. They are accidental and cannot exist in themselves (contra Plato). Quantity and relation are necessary aspects of any mathematical activity. Thus, substance and its nature/being, etc. are antecedent to that which is predicated of it. The higher science is metaphysics, which is one of the reasons Aristotle called it “first philosophy.” Mathematics is downstream from metaphysics, and therefore mathematical demonstrations by their nature yield less science overall compared to metaphysical demonstrations. Mathematical demonstrations are by nature (pun!) narrower in scope and function.

• Mathematical demonstrations allow for more engagement of the imagination, whereas metaphysical demonstrations depart much earlier from possible imagination and revert to intellection only. At a certain point, the mathematician can more easily revert to picturing things in the mind to work out details compared to the metaphysician who often loses this recourse.

Again, this is just a brief sketch. And nothing I write here is meant to impugn or degrade mathematics in any way. The concepts of set-theory, infinity, and even numbers themselves can become exceedingly abstract, often trafficking in notions familiar to the metaphysician. In any event, mathematical and metaphysical demonstrations have important differences. We must note and discuss these differences as they apply to significant conversations, such as those on the existence of God.

If the term ‘proof’ is relegated to an impoverished conception, one that applies only in a mathematical setting, then the theist can only point out some of the issues with this and focus on the attending presuppositions. But if one understands ‘proof’ in a more robust way, such as in the medieval context of ‘demonstration’, then both sides can have a lively discussion about the veracity of the theistic argument and implications of its conclusion. The theist is not obligated to abandon the term ‘proof,’ because metaphysical demonstrations yield knowledge and describe reality, which is the work we should expect a ‘proof’ to accomplish. 

Street Epistemology: A Flawed Approach

In the wake of Peter Boghossian’s A Manual for Making Atheists, the practice and dialogue surrounding “Street Epistemology” (SE) has gained traction, at least in the social/online circles. Evidence of this trend might be found in a simple Google search or looking at Christian apologetic content dedicated to it, such as Justin Brierley’s radio show guests/topics. 

According to StreetEpistemology.com, SE “is the application of epistemology (the study of knowledge) outside of formal academic contexts.” SE casts a wide net but seems very focused on religion. This is natural because questions about the existence of God, life after death, and others have deep and profound significance. For many, these questions are more foundational than questions about politics, the environment, or education. Thus, the focus of SE to date has primarily been to have a respectful and civil dialogue about religious belief. A paradigmatic situation is a non-religious person (e.g. a religious skeptic or agnostic) engaging in a Socratic-type dialogue with a religious (or religious sympathizing) person. I have participated in one of these myself and have witnessed and read about others. The focus of SE as it relates to religious belief is the primary focus of this post.

When I first read about the term “Street Epistemology,” my interest was piqued because of the reference to the study of knowledge. However, as stated above, the method of SE is non-academic. The main thrust of SE is to dig at why a person (P) has a certain belief or set of beliefs (X). Ultimately, the SE practitioner hopes to show that P should not hold X with any confidence or that something is wrong with P holding X. “Officially,” the pure SE practitioner is trying to pursue truth. He accomplishes this in the process of being a good Socratic interlocutor. However, on close analysis, I cannot see how the SE does not bring some serious presuppositions to the dialogue. These presuppositions skew what he wants to accomplish, threatening to undermine the SE project.

SE takes for granted that epistemology is a good starting point for understanding and discussing reality. If this were not the case, the dialogue would not proceed along the lines of belief questioning. The SE wants to know how P came to have an idea or belief X and/or why P continues to believe X. What, if anything, would cause P to hold X less firmly? This is a common SE question. And I think this whole process of inquiry assumes a decidedly idealistic approach. “I have this idea or belief, what explains or is the cause of it?” This hearkens back to Descartes, and I think it ultimately hamstrings the SE.

Consider the following example taken from a blog at StreetEpistemology.com:

Beliefs people hold about reality are not actually reality. Beliefs are simplified abstractions. The fact that these abstractions have the potential to be inaccurate proves that they are, in fact, two different things.

This is a very interesting position. The remainder of the cited SE blog post builds on this by stating things like “When we talk about our beliefs, we are talking about abstract, internal models of how the real world is and works. These models exist only as ideas in our minds.” This position asserts a fundamental disconnect between the mind and the world. It tells us we do not know things but only ideas or abstractions about (hopefully?) things. But if this is true, how do we ever know any thing? How can we properly adjudicate these “abstractions”? The sole answer on this view can be only with other abstractions. So, we must use ideas to judge other ideas. But what organizes and adjudicates these? The problem persists.

We are then faced with the question of what the SE can really accomplish given his starting point. He is being inconsistent with his inquiry by not first subjecting his own method to itself. If the SE is concerned about pursuing truth and knowledge, he should first establish what these things really are before he proceeds, lest he have no objective measure of the beliefs he seeks to question. And there are many other problems with what the SE is taking for granted. For example, he assumes a correspondence theory of truth while simultaneously removing any means of verifying the correspondence. After all, per the SE, it can only be idea versus idea. Maybe the SE can move to a coherence theory of truth, but this also will not help. The SE seems to presuppose that knowledge is justified true belief but then throws shade on justification by alluding to error with no way to properly account for it. The Gettier Problem is also alluded to, and imminently present, but left untouched.

The blog quoted above is, I think, quite representative of the SE framework. This is evident in the holistic focus on attacking beliefs and justification. It is only by assuming a mind/reality disconnect that belief and ideas can be questioned in the way SE does. In the case of religion, the belief is unjustified because it supposedly has no extramental verification or something along those lines. Thus, there is “no evidence” for belief in God, and so on. But SE talks about evidence and empirical observation while still presupposing that the mind is cut off from the world. The SE impugns the believer for unjustified ideas/beliefs but does not see that he is sawing off the branch upon which he sits. The SE loses the means by which to question religious belief (or any other belief/idea). On the SE view, both the SE and believer (if the believer concedes the same starting point) are essentially stuck in the same position as Descartes at the end of his first meditation. Like Descartes, I fail to see any way out for the SE. The demon will continue his torment.

SE tries to get at the truth about reality by not starting with reality. To me, this seems like a futile project for all concerned. A better use of time would be to live in reality and discuss it as such. The SE only wants to focus on the rationality of religious belief. But Plantinga has already helpfully pointed out, albeit using a very different methodology than I am, that de jure objections ultimately reduce to de facto objections. So, even on Plantinga’s epistemology, our time is better spent discussing metaphysics rather than disputations about the rationality of belief. If the SE is truly committed to truth, then epistemology is not the place to start the conversation. 

(Fun!) Brain Teasers

Some accident in an online editorial committee allowed the publication of an article with…yes…Philosophy in the headline. What was neat about this piece is that it contained a few “brain-teasers” that are usually kept within the confines of boring dinner parties or law school library coffeeshops. Included in this Top 10 list are some old-school paradoxes from Zeno, and also some more modern mind benders. I thought it would be fun to briefly cover each one since these types of questions tend to come up in conversations with high-school and college students.

In what follows I have edited the stated paradox for relevancy. If you read the original article, you can pick up links to pages with possible solutions and explanations.

#10 – The “Heap”

If a man has zero hairs on his head, we say he’s bald. However, a man who has 10,000 hairs on his head is not considered to be bald. But what if we add a single hair to the head of the man with zero hairs? He would still clearly be bald.

Now let’s say that a man has 1,000 hairs only. But the strands are evenly spaced and really thin. Would this man be bald or not bald? Would you consider a single grain of wheat a “heap of wheat?” Definitely not. How about two grains? Still, probably not. So, when do a few grains or a few hairs end and a whole heap or baldness actually begin? The problem is one of vagueness. Where does one description end and another begin?

This one is more tied up with language and definition than any philosophical principle. We could just say that a man is not technically bald unless he has zero hairs on his head. “Bald” means not one hair. Calling a man bald with any hail would technically be a false statement, or perhaps an inaccurate judgment. We could say the man is “balding” in the sense that he is in the process of becoming bald, and that is probably how the conventional language means it.

In terms of what constitutes a heap, we could also place a rigid definition on this. We could say that 10 or more grains is a heap. The question then becomes why 10 grains and not 2? And this gets at the issue of an arbitrary notion of abstract objects, like “heap,” or even “baldness.” However, baldness is accidental to the man and a heap (or any kind of collection of natural substances) is a technically an artifact. Neither is what an Aristotelian-Thomist would deem a substantial form. Therefore, no anti-realist problem arises. We can make sense out of heap in various cases by being clear what in a given instance is what we mean by ‘heap’.

 #9 – The Liar Paradox

The first sentence of this paragraph is a lie. Stop and think about that sentence for a second. Is it true? Or a lie? A true lie? This is called The Liar Paradox, and it’s also from the time of Eubulides. It’s straightforward and fun and takes the form of one short statement: “This sentence is a lie.” Another incarnation of the paradox is: “Everything I say is false.”        

       

How this one made the list is puzzling. Nothing is being said when a contradiction is uttered. “X is a square circle” does not tell us anything. We do not have any referent in the first sentence of this paradox, so there is nothing to think about. The last statement “everything I say is false” is nonsensical. The examples in this paradox are like saying “it is true that there is no truth.” Such a statement collapses upon itself. Often these “philosophical” paradoxes seem to twist our mind because they violate the principle of non-contradiction somewhere. We know something is amiss even though we cannot always articulate it immediately.

# 8 – Limited and Unlimited

Zeno wanted to show that the idea of a plurality of things (which all exist side by side in time and space) brought with it some serious logical inconsistencies. The Limited And Unlimited Paradox displayed this. Does one thing exist or many? What separates one thing from the next? Where is the line?

This is also called The Paradox of Density, and let’s put it a little differently. This works with multiple objects, but we’ll start with just two. If there are two things, what separates them? You need a third thing to separate the two.

The Paradox of Density takes place on many different scales, but you get the basic idea. So, is there just one massive entity called the universe that contains indistinguishable matter of varying densities (air, the floor, a tree, etc.)? Is all matter perpetually divisible? Or if we divide matter into objects small enough, will we eventually reach the object so small that it cannot be divided?

Zeno was the master of paradox. I think many of his antinomies are good thinking exercises. Before this list, I had not previously seen the paradox of limited and unlimited written in this way. To cash this one out per above, we will first need to unpack it a little more. Take the issue of two things needing something to separate them. First of all, if there are actually two things, then they are distinguishable in some way. In this case, say they have different material constituents. It seems Zeno wants to know what is this “space” thing that we might evoke to explain our separation of them. The “space” between object A and object B cannot be nothing, because then we could not invoke it to explain anything. So, the space between A and B becomes thing C. At least that’s what Zeno thinks. But then he will ask us, what separates A from B and B from C? It seems that a fourth thing must be posited, and so on ad infinitum.

There are probably different ways to address this paradox. On an Aristotelian-Thomist view (A/T), the principles of nature are matter, form, and privation. Thing A is a composite of matter and form. Privation might be thought of as the lack of form that A has. A is what it is, and it is not B because A has the substantial form of A. The same thing for anything B, C, and so on. A and B each can be said to have form, matter, and privation. We predicate these principles of each thing, keeping in mind privation is lack or absence. Zeno’s demand for us to tell him what separates A and B therefore betrays an incorrect view of substances. He wants us to admit that privation is a substance, which it is not.

Still, someone might protest that the “space” between A and B is comprised of various subatomic particles. Space really is “something” if we utilize modern physics. On this view, Zeno’s demand seems to gain traction. First, let us remember what Zeno is trying to establish. He wants to show that if there are many things there must be infinitely many things. But if Zeno just wants to prove that there is an infinite number of things, I do not really see what real problem there is. It seems the specter is predicated on an assumption that if we say there are many things we mean that there is a finite quantity. To me the actual problem with this is unclear. An SEP entry breaks Zeno’s actual paradox down as follows “If there are many things, then there must be finitely many things; and if there are many things, then there must be infinitely many things.” I do not see any reason to think the first conditional has any force such that we need accept it. We could just go this route and let Zeno hit us with another zinger. 

There is still might be a physicist demanding an answer to this quandary without “appealing to the outdated physics of Aristotle.” The A/T view will still look at substances A and B, where the privation in substances could simply be termed matter in potency to something we know not what. Or, if we broke things down to the subatomic level, we would just identify other distinct form/matter composites filling the “space.” After all, “space” on this analysis is something of a placeholder for substances not observable by the senses. If the subatomic particles exist in the way we think they do, they would be form/matter composites with essences/ natures. Responding to Zeno, we would not necessarily need to say that what exists within what we call ‘space” is infinite, though I cannot see the problem if were (and we would need to know a little more about how ‘infinite’ is being used – e.g. potential or actual, etc.).

The second part of the paradox above seems odd to me. It makes little sense to say the universe could just be one thing with indistinguishable matter of various densities because densities and other properties are just what distinguishes matter. And there is the example of trees and air, which have distinct material constituents. Here it seems “matter” is used in something of an equivocal sense, which we need not accept. It seems to be used in both generically and specifically. To say, “everything that exists is material” is not the same thing as saying, “everything is ultimately the same thing.” To ask if all matter is perpetually divisible is a benign question because even if matter is infinitely divisible it does not follow that substances, comprised of matter and form, are.

#7 – The Dichotomy Paradox

Let’s say that you decide to walk to the store and buy a soda. For you to get there, you’ll have to cross the halfway point. No problem, this makes sense. But from the halfway point, you’ll have to next cross the halfway point of the halfway point (three-quarters of the way from your house to the store). Then you’ll have to cross the halfway point of that distance and the halfway point of the next smaller distance.

So wait a minute. If you keep dividing your trip into halfway points, you’ll never actually be across the halfway point . . . ever. How is this possible? You know that you can go to the store and get a soda. But when do you actually cross the last halfway point (where there are no more halfway points)

This one has gotten a lot of attention. Most of the time people try to solve this mathematically, which is fine as far as math is concerned. I will not attempt nor really address that type of resolution. For what it’s worth, the disputations in higher level math about infinite sets as they apply to this paradox are just doing metaphysics in a different way. In any event, I think Zeno’s false assumption is that extrinsically denominated measurements like “halfway” have substantial reality instead of having accidental being and leading to mental abstractions and subsequent judgments which start from reality and then fold into other concepts which do not have extramental existence. [yes, that last sentence was long]

Zeno’s paradox, in this case, rests upon substantive predication of place and time, which on the A/T view are only accidental to substances. A substance undergoes accidental change by going from place A to place B. Zeno is ultimately saying that it takes an infinite time to get from A to B. This is based on an infinite divisibility of the walking distance. But, as Aristotle pointed out, the infinite divisibility of the sidewalk only exists for the one measuring, not necessarily the one traversing. This sounds like a cop-out, but if we think about it, the sidewalk is not actually divided as such, but only so divided by abstraction/calculation of the one measuring it (or the one creating the paradox!). There is no actual problem for the unreflective guy just walking to get a soda. Zeno treats “halfway” and other measurements as though they are real things, which they technically are but only in a derivative and/or abstracted way. Time itself is an extrinsically denominated accident. What is time if not that which tracks/measures change? The very notion of there being any time measurement on the paradoxical journey in question presupposes that change is real. Zeno needs to assume change is real to disprove change, so his argument does not work.

I am not an anti-realist about time or measurement, they are not mere constructs. But they are of and about substances. And we must agree that substance undergoes change, or the paradox does not get off the ground.

Consider what happens to the paradox if there is an earthquake and ground collapse into a black hole oblivion behind Zeno as he travels to get a soda. On his finite journey, Zeno has gone 1 mile out of the 5 it is supposed to take him infinity to traverse. The 1 mile behind him is gone. His “line” of travel has shrunk by 20%. By the rationale in the paradox we can then have an earthquake happen on all ground in front of him as well. Zeno is just left standing on one plot of soil, say it is 2 feet across. Still, poor Zeno is apparently looking at an infinite amount of time to even kneel in prayer for rescue. For him to kneel, he has to move just 1 inch.  But the space cutting infinity still must happen. The result of Zeno’s paradox is that change, or motion, just cannot happen at all.

Another way to look at this is to borrow something from the mathematical side. Zeno is admittedly traveling between two finite points. He is not traveling an infinite distance. How does it even make sense in principle that it would take infinite time to cross a finite distance? The distance is fixed, and not expanding. Zeno seems to be predicating a finite and an infinite accident of substances which are at the same time and same relationship. But this can only occur by an error of our judgment or the pressing of a mental abstraction onto reality.

Further, even if we take Zeno’s bait and start “slicing” the line, why should we think that it is infinitely divisible? The infinite time traversing the line seems to be predicated on no stopping point to the slicing. But if there is a stopping point, a measurement or fundamental block of reality by which the line could be sliced no more, then traversing it is no longer logically problematic. The line folds or is halved into infinity only if we agree with Zeno that this is possible in principle. Yet, Zeno’s position then seems to imply an infinite regress of material constituents; that we can just keep going forever and never get at the ultimate “stuff” of physical reality. If there is nothing foundationally physical, then it presents some significant problems for how we would have anything physical at all to start slicing. To take another tack, it seems that for Zeno the house of quarks, bosons, leptons, etc. would just be based on a sinking foundation of nothingness unless we posit that the physical gives way to the metaphysical and ultimately just lands on pure Being itself. And if Zeno wants to land here, great. I think that would relieve the tension in his paradox.

Much more could be said on this. And much brighter minds than me have presented ways to escape from Zeno that probably make this short attempt seem inconsequential. But the whole point is to try and have some fun, right?

#6 – Achilles and the Tortoise

In this puzzle, Achilles races a tortoise. To be a nice guy (demigod), Achilles gives the tortoise a 100-meter (328 ft) head start because Achilles is an extremely fast runner and the tortoise is . . . well . . . a tortoise. As soon as the gun fires and the race begins, Achilles quickly closes in on the slow-moving tortoise. In no time, Achilles has crossed the 100 meters (328 ft) of the head start that he gave the tortoise. Simultaneously, the tortoise has traveled 10 meters (33 ft). So Achilles still hasn’t caught the tortoise. But again, Achilles will quickly close in, crossing the additional 10 meters (33 ft). During this time, however, the tortoise has traveled another 1 meter (3 ft). By this logic, Achilles can never truly catch the tortoise, can he? How can this be possible? Every time he gets closer, the tortoise goes further. Does this mean that motion itself is impossible even though we experience it daily?

The resolution to #7 (above) applies equally to this one. Zeno is denying that change/motion is possible, but the same flawed assumptions and problematic conclusions await. Achilles should feel good about his speed.

#5 – The Paradox of Inquiry

As Meno said, “And how will you inquire into a thing when you are wholly ignorant of what it is? Even if you happen to bump right into it, how will you know it is the thing you didn’t know?” Socrates rephrased the paradox this way: “A man cannot search either for what he knows or for what he does not know. He cannot search for what he knows—since he knows it, there is no need to search—nor for what he does not know, for he does not know what to look for.”

This paradox seems to betray a fundamental misunderstanding of knowledge. It treats knowledge as if it is this “thing” that we look for like lost car keys or El Dorado. How do we even look for something if we do not even know what “it” is?

One way to address this is to take the empiricist (in the classic sense) tack. What man knows are things in the world, composites of form and matter. The intellect apprehends the form of the object and an identity/relation obtains between the knower and object known. The intellect can form abstractions from the things it encounters, and can organize, arrange, and make judgments about them. To borrow from Aristotle, nothing is in the intellect that was not first in the senses. We can understand this as the starting point for knowledge. Man encounters, learns, and interacts with the world. This is a progressive process. We did not start out asking “where can I find an automobile?” Instead, by living and operating in the world of things, man begins to ask questions and seeks to solve problems. Still Plato would persist “how do you know what questions to even ask?” To which we might reply that such a question presupposes an understanding of human nature that we need not accept, an understanding that goes against reason. Man can “know” what to look for in many instances because He has a true grasp of the world as it is. We can understand by the very nature of what we are, what natures are, and that something is out of order and seek a way to properly order things. To argue in the way of the Meno paradox is to simply assume a certain philosophical anthropology that is unnecessary.

Of additional note is that the Meno paradox is predicated on the idea that we do not really come to know things, only to remove the scales covering what we already possess in some way. Via the philosophical dialectic, we recall the really real things that we grasped before our soul was imprisoned in our body. Plato’s theory of reminiscence is, I think, implicit in Meno and need not be accepted.

#4 – The Double Liar Paradox

Let’s move up to more modern times and toy with a fun extension of The Liar Paradox called The Double Liar Paradox. First dreamed up by mathematician P.E.B. Jourdain, this brainteaser goes as follows: Take a flash card or a piece of paper. On one side, write: “The sentence on the other side of this card is true.” Now flip it over and write on the other side: “The sentence on the other side of this card is false.” If the second sentence is true, then the first sentence is false. (Flip the card.) Here, you end up moving into an indefinite changing of sides—side A to side B on the card. But if the sentence you first wrote is false, as the second sentence claims, then the second sentence would also be false. Thus, both sentences are right and wrong at the same time. Have fun with that one.

This one is just like #9. There is nothing to it because there is no actual referent to the propositions. The words on the paper are not conveying anything about reality.  It is like saying “married bachelor.” A “sentence” that has no content is essentially vacuous, the words are said but have no signification. I could just write something like “there is no meaning except that there is no meaning about meaning…” and it would be non-sensical. Contradictions are not things. We can talk about them abstractly only because we know the non-contradictory nature of reality.

#3 – The Monty Hall Problem

This one can be seen on game shows everywhere. Let’s say there are three doors. Behind each of two doors is a brick, but one door masks $1 million. You get to pick a door and see if you win the million. Let’s suppose you choose Door A and hope for the million. Then the game show host opens another door at random to see if you won or lost. The host chooses Door B, and it reveals a brick. With Door B out of the way, the one-third odds just got a lot better. You’re left to choose between Door A and Door C. You can even switch to Door C now if you want. Since you don’t know what is actually behind your door, you’re still picking between two doors. So your odds are 50/50, right? Door A, Door C . . . it’s one out of two . . . can’t get any simpler than this. Wrong. At this point, it sounds counterintuitive to say that you have a two-thirds chance of getting the $1 million if you switch doors and a one-third chance if you stay put. But it’s true. Can you figure out why?

Since this is more of a probability related problem, I will leave it to those more inclined in that direction. But this is certain a fun question to think about in case you ever need it.

#2 – The Barber Paradox

The puzzle is simple: A barber says he’ll shave any man who does not shave himself and all men who do not shave themselves if they come to be shaved. The question is: Does the barber shave himself? If he does, then he no longer shaves all men who do not shave themselves because he shaves himself. If he does not shave himself, then he does not shave all men who do not shave themselves.

By including himself in the “bargain,” the statement of the ambitious barber results in a contradiction. If he maintains his deal, the falls on his own sword (or really sharp scissors). We have no reason to accept the bargain as having any meaning as it is presented.

#1 - Schrodinger’s Cat

Moving on to the best brainteaser, which is arguably not a paradox, let’s talk about Schrodinger’s cat. It begins with the idea that we take a cat and place it in a soundproof box. Now, without lifting the lid to observe the cat, how do we know whether the cat is alive or dead?

In a nutshell, every time you look at something (a chair, for instance), you get a definite answer as to its state. (It is there.) When you turn your head, you can only get probable chances of whether it is still there or not. Yes, it’s safe to say that the chair didn’t get up and walk away. But without observation, you’ll never really know. So, at what point can the things we observe be certain to exist (or exist in the state we observe them)?

In the early 1700’s, Bishop George Berkeley is credited with arguing “esse est percipi” (“to be is to be perceived”). Schrodinger’s Cat has always seemed to me a lot like Berkeley’s position. Berkeley solved this problem by positing that things existed when we were not thinking about them or perceiving them because God was thinking about them. The modern science from which Schrodinger’s Cat springs would not offer such rationale.

To think that nothing exists until we perceive it is of course an absurd claim. Science could not work if this was true, because science takes for granted in one observation all kinds of unseen/unperceived things. Further, this way of understanding reality is impossible because it presupposes a knowing subject in order for a known object to exist. But our actual interaction with the world is the exact opposite. We only know ourselves because the external world first impinges upon us. To ask, “how do I really know that the chair exists when I am not in the room” betrays a skepticism rooted in a false understanding of what knowledge is and what things are (e.g. having natures, substantial forms, etc.). The idealist undertones of this paradox/dilemma need not be accepted. If knowledge is of things and not ideas or beliefs about things, and if things exist as substantial forms having certain natural operations, etc. then Schrodinger’s Cat does not present any real problem. There may be other ways around this as well, such as the fact that we simply have no good reason or evidence to think that the chair should have moved, so we are rational or warranted in thinking that the chair is still there. In any event, I hope no animals were harmed in the formulation of this paradox. 

Is God a Person?

In recent months, I have seen the question come up numerous times of whether it is correct to say, “God is a person.” Many Christians do not care nor think much about this. For most believers, it probably boils down to one of those “not a salvation issue” deals. But I think this issue is important. It speaks to one’s conception of God and His nature. And the nature of God is something every Christian should care and think about often.

I have argued that it is incorrect to say that “God is a person.” At least, one errs in using such phraseology in almost all contexts in which it is said. In the absence of extensive qualification that for all practical purposes eliminates the basis by which we might use “a person,” Christians should not say “God is a person.”

It is, of course, unproblematic to say "person" of God if by that you mean “God the Father is a person,” or “the Person of the Holy Spirit is God,” or “there is the Person of God the Son.” But when someone says, “God is a person,” they are making a statement about the Divine Essence itself. If you say, “Socrates is a person,” you mean that Socrates is an individual substance of a rational nature (or pick any definition of person you want). But when we press “a person” onto God, we run into myriad problems.

It is not incorrect to attribute “person” to God in the sense that He is one (not divisible) subsistent, and rational. Naturally, this is dependent upon whether you affirm such a definition of person. But even on other views of “person,” most Christians would say that God is one, that He is self-existent or exists necessarily. To say that He is subsistent means that His very nature is to exist. To say that He is rational is to predicate reason, intelligence, and so on. [I will leave the problems I see with other theistic conceptions of God relating to divisibility and subsistence for another time.] 

  

As alluded to above, there is a major theological issue in the question of whether we should say God is a person. The Christian faith holds that God is three Persons. What God is, as revealed to us from the pages of Scripture, just is three eternally distinct yet cosubstantial Persons; Father, Son, and Holy Spirit. Christians claiming that “God is a person” must reconcile this position with Trinitarian doctrine on pain of heresy. And I wonder in what sense a Christian holding to orthodoxy can essentially say “God is a Person that is three Persons.” This seems like a flat contradiction. For example, on my preferred definition of person, one would say “God is a subsistent individual of a rational nature that is three subsistent individuals of a rational nature.” Or, on a different view, you might say “God is a continuous center of consciousness that is three continuous centers of consciousness.” The main problem might be in the univocal predication of “person.” So, perhaps we should take “God is a person” and “God is three persons” in an equivocal sense. But this seems to kick the can down the road. For, which statement is making a true predication of the Divine Essence? If we say “both,” the difficulty remains.

Consider the idea of saying, “God is a person” and “God is three persons” in an equivocal sense. In so doing, one would affirm that “God is a person” and “God is three persons” mean completely different things. Like “my car is red” and “Enron was in the red.” This is a different issue than reconciling various anthropomorphic depictions of God in the Bible (e.g. that God has arms, hands, feet, etc.). The question here pertains to the Divine Essence, not descriptions of God’s activity in human history, man’s relationship to God, etc. It just does not work to make a direct predication or description of the Divine Essence in completely different senses. Either one says something about the Divine Essence and the other does not, or neither says anything. And the Christian must say that "God is three persons - a trinity." What, then, of the other statement "God is a person"?

Perhaps one could say that the statements “God is a person” and “God is three persons” should be understood analogically. That is, in a basic sense there is something similar and something different in the term “person” between the two statements. Returning briefly to what was said above, “person” is undivided, subsistent, and rational. To say that God is these things is true. But can we really say that these things are different between the first and second statement? I do not think so. There is no way to deny these predications in any meaningful sense to either side; to what level and in what way would they be partially the same and different? And if this is the case, it seems the analogy option goes away, or is muted for practical purposes.

It seems that a major compilation, or perhaps even the root of the whole issue, concerns the article in “God is a person.” When the indefinite article “a” or “an” is used it signifies an instance of a kind. To say, “Socrates is a person” or “Euthyphro is a person” signifies that Socrates and Euthyphro are species (man) within a genus (animal). We know that problems arise when somebody tries to tell us “a house is on fire.” To which we reply, “which house!?” It is implicit in the term “man” that we signify an instance of a kind. And in any other term preceded by “a” or “an” we are faced with the same conclusion. “Rocky is a dog” means that Rocky is one of many (however you cash out the problem of the one and many). Yet, in what way might God be an instance of a kind? I submit there is no way if we want to maintain a correct view of God.

God cannot be an instance of any kind without reducing Him to an inferior ontological status. To say that God is an individual requires one to say what kind He is an individual of. And this at least in principle places God alongside other things, even if a different order of magnitude. Christians should reject this notion; God is not one among any others.We can say that God is individual (i.e. He is apart from all else, He is indivisible, etc.) but not an individual. Instances of kinds have properties, are composite (of at least act/potency, existence/essence, etc.), can fit within a taxonomy, and so forth. None of these things can be said of God, though they may be said of lesser deities or other substances.

We must drop the article to maintain a correct view of God. Thus, what seems to be left is to say, “God is person” and “God is three persons.” But the first of these does not make much sense. There needs to be an article, plurality, or complete change for it to be intelligible, and we have just seen that the article fails. We can say, for example, that “God is personal.” Such a statement is true and reflects conclusions from both revealed and natural theology. Yet, this is radically different than saying “God is a person.”

I understand that many Christians object to the classical view of God that I am defending. One primary objection is that such a depiction does not square with the Bible. But nowhere does Scripture maintain that “God is a person.” God is described and reveals Himself to be personal, and in fact tri-personal. Each Divine Person acts in human history in perfect harmony. If Christians believe that the Father sends the Son in the power of the Spirit, then they should reject the statement “God is a person” unless they are merely trying to describe God’s personal activity or His loving nature. To describe the Divine Essence as “a person” should be avoided.