On Chess, But Applicable to Anything

"Its not enough to be a good player; you must also play well" - Tarrasch

James 4:11-12

Brothers, do not slander one another.  Anyone who speaks against his brother or judges him speaks against the law and judges it.  When you judge the law, you are not keeping it, but sitting in judgment on it.  There is only one Lawgiver and Judge, the one who is able to save and destroy.  But you--who are you to judge your neighbor?

the argument from universals.

An argument for platonic realism regarding universals (that abstract entities exist and can do so without dependence on their instances) takes the following form:

(1) There is a possible world where there are no particular things colored red.

(2) Despite the fact of (1), the following propositions are true, and necessarily so; that ‘necessarily, red is a color (there is no possible world where red is not a color)’, and ‘necessarily, red resembles orange more than it does blue, (there is no possible world where red doesn’t resemble orange more than it does blue’, and also that ‘necessarily, no single indivisible entity can be both red and green at the same time (there is no possible world where a single thing can be both red and green).

(3) Since the propositions expressed in (2) are necessary truths, they are also true in the possible world expressed in premise (1). But (1) stipulated that that there is a world where no particular thing is colored red. So the question is, if propositions are true or false in virtue of the content they express, how can it be the case in the possible world where there are no instances of red that propositions expressed in premise (2) are true? The way it out is to assert (4).

(4) In a possible world where nothing in particular is colored red the necessary propositions expressed in (2) are true because they refer to the form of red, which is an uninstantiated universal. Therefore,

(5) Platonism in true.

The only way out of this consequence, it seems, is the denial of the last part of (3); namely, that propositions can only be true or false in virtue of the content they express and refer too. To say it another way, one must deny that propositions need not have intention to be true or false. But this seems crazy, and I cannot even begin to conceive of what this might look like, so pending further enlightenment by some sneaky Aristotelians, I must declare (5).

Well, assuming everything I’ve articulated adds up, consider the following proposition:

(6) Necessarily, to be a person is to have rational faculties (either dormant or otherwise).

If (6) is true, then so is

(7) There is a possible world where there are no instances of persons, but since (6) is necessarily true, it’s also true in such a world. But if (6) is true (and necessarily so),

(8) (6) is (necessarily) true in virtue of the fact that it expresses, namely, that a person necessarily has rational faculties (dormant or otherwise). If this is a fact, then there is at least one person, and He must necessarily exist, since (6) could only be true in virtue of this fact. And if there is a person that exists necessarily, then he can be nothing other than what men call God.

... No, I presume I may say that we
more certainly know that there is a
God than that there is anything else without
us. When I say we know I mean there
is such knowledge within our reach which
we cannot miss, if we will but apply our
minds to that, as we do to several other
inquiries.

John Locke,
Chapter X of Essay Concerning Human Understanding

What if the Universe is Infinite?

Suppose, for the sake of argument, that the universe really has existed forever, without beginning. Although I have objections to this, I will concede it momentarily.

Imagine the universe exists without a beginning. Does this entail atheism? Of course not. There may have been a God who created an eternal universe. Does the existence of this possibility entail theism? No, of course not.

But if the universe exists eternally, certain cosmological arguments are undercut. For example, those that require that the universe had a beginning. My cosmological argument is one such, and would be undercut should it be shown that the universe is in fact infinite.

But cosmological (and ontological) arguments that only require the universe to be contingent are not undercut. Those atheists who posit an infinite universe still beg the question of why there exists a universe at all, rather than no universe. Such a universe would still require something logically prior to it.

Can't the universe exist by necessity? I posit 'no', as I commit no logical fallacy when I imagine a "world" in which nothing exists - no matter, no energy, no time, no space. Anselmian theists maintain that God is logically necessary, unlike the universe. Thus, He may be logically prior to the universe.

On Love

Love hath not to do with naught but the lover, nor hath it to do with naught but the beloved.

If the Hotel Can Have an Infinite Number of Rooms, Why Can't the Universe Have an Infinite Number of Days?

In my previous post, wherein I attempted to provide an undercutting defeater of Craig's Hilbert's Hotel argument for the impossibility of an actual infinite number of things, I allowed for the conception of a hotel, the set of whose rooms is infinite, and has a cardinality of aleph-null. And yet, I also provided a small argument at the end that I believe may better perform the same function as Hilbert's Hotel in the greater Kalam. But as I thought about what I had done, a possible reply came to mind: If the Hotel can have an infinite number of rooms, why can't the universe have an infinite number of days? I do not have a polished answer, buy I here journal my initial musings.

In the Hotel conception, I said that God built the hotel by the power of His word, and sustains it by His power. I don't actually believe that Hilbert's Hotel exists in this world, but I can conceive of it pretty good, and I think I have illustrated such a conception in a satisfactory way. At any rate, if one claims that he does not know whether he can conceive of such a hotel or not, I think I have made it more difficult to say that it is impossible to conceive of it, such that an argument for the impossibility of such a hotel, or any actual infinite number of things, is not as easy as pointing to the abnormal phenomena such a hotel might give rise to.

Nevertheless, it might appear incoherent for me to posit such a hotel and at the same time argue for the impossibility of an actual infinite number of days in the universe. After all, why can't God simply just create such a beginningless universe and sustain it by the power of His word? Such a question might be unfair for an atheistic infinite universe argument to utilize at face value, but really it is just a call for internal coherence on my part. Well, I believe that there is a fundamental difference between the Hotel and the number of days in the universe.

In the case of the hotel, the rooms are instantly built by God, such that there is no temporal transgression of an infinite spatio-temporal distance. One minute the Hotel is not, the next minute, God speaks such a structure into existence. The set A of all Hotel rooms is at T1 empty, and then the set B of all Hotel rooms is all at once at T2 infinite, and of the cardinality aleph-null.

But in the case of the days in the universe, they cannot exist all at once. Rather, this moment exists and naught else. Thus, by "days" we mean to denote a segment of temporal transgression made by temporally bound objects. There does not exist, "now", all moments in time. This view, Presentism, is something I hold but do not care to explicate and defend here. I am interested in researching it further, and perhaps writing on it someday. My Philosophy of Religion professor, Thomas Crisp, is also a presentist. I am not sure whether my argument for the beginning of the universe is altered whether or not Presentism is accepted, but I will go forward as if it is.

This difference is all that is necessary to establish why it is that a hotel with an infinite number of rooms is conceivable, but a universe whose temporal past is not. For, as was shown in my argument in the previous post about the Hotel, there is no room with the number -∞ (negative infinity). Nor is there a room with the number 'infinity' on its threshold. For infinity is the state of a set, not a number unto itself. Any given number is finite, while infinite sets of finite numbers may be considered.

Similarly, if 'now' is labeled "0", and yesterday "-1", then it is seen that there cannot be a day with the label "-∞". Any given day in history will have a finite label. But why can't the set of all past days be infinite? Because of the impossibility of transgressing an infinite spatio-temporal distance. Just as the present must transgress the moments in today to get to tomorrow, so it would have had to transgress the past in order to get to today. This is what was illustrated in my thought experiment by the runners who attempted to begin their race infinitely far away. They will begin by crossing room numbers 0 through -10, and then they will transgress rooms -10 through -20, and continue running for eternity, without ever finding a starting line from which to run back to room 0. This is a textbook example of a potential infinite. At any given time, the runners will be in front of a room with a finite number, and the cardinality of the set of rooms they will have transgressed will be ever-increasing. But a potentially infinite set will never become an infinite set. In the same way that even God, if He counts one number at a time, will never reach infinity. He will be counting forever, and the set of numbers He utters will be potentially infinite. For at any given time, He will be uttering a finite number. Not even God can transgress an infinite spatio-temporal distance.

The universe cannot have existed from infinity past because it is impossible to cross an infinite distance, or an infinite amount of time. The Hotel can have an infinite number of rooms, because its construction was instantaneous. This would be like God thinking of an infinite set of numbers all at once - something He is no doubt capable of doing.

An Argument Against Craig's Hilbert's Hotel Illustration and a Proposed Solution

Jon Wright pointed out to me that the prior post did not handle the particular type of transfinite subtraction Craig says cannot be done. Namely, subtraction involving infinite quantities. I spoke about this with my math professor, Matthew Weathers. I proposed my argument, and he helped clear up some concepts for me, and explained the nature of cardinalities in a helpful way. Generally drawing from that experience, while sitting here in a class called "Mission in Political Context", I here provide an undercutting argument against Craig's Hilbert's Hotel argument for the impossibility of the existence of an actually infinite number of things. Afterward, I propose an alterative argument that serves the same purpose in the overall Kalam.

In the broader context of the Kalam, Craig says,

Perhaps the best way to bring home the truth of (2.11) is by means of an illustration. Let me use one of my favorites, Hilbert's Hotel, a product of the mind of the great German mathematician, David Hilbert. Let us imagine a hotel with a finite number of rooms. Suppose, furthermore, that all the rooms are full. When a new guest arrives asking for a room, the proprietor apologizes, "Sorry, all the rooms are full." But now let us imagine a hotel with an infinite number of rooms and suppose once more that all the rooms are full. There is not a single vacant room throughout the entire infinite hotel. Now suppose a new guest shows up, asking for a room. "But of course!" says the proprietor, and he immediately shifts the person in room #1 into room #2, the person in room #2 into room #3, the person in room #3 into room #4 and so on, out to infinity. As a result of these room changes, room #1 now becomes vacant and the new guest gratefully checks in. But remember, before he arrived, all the rooms were full! Equally curious, according to the mathematicians, there are now no more persons in the hotel than there were before: the number is just infinite. But how can this be? The proprietor just added the new guest's name to the register and gave him his keys-how can there not be one more person in the hotel than before? But the situation becomes even stranger. For suppose an infinity of new guests show up the desk, asking for a room. "Of course, of course!" says the proprietor, and he proceeds to shift the person in room #1 into room #2, the person in room #2 into room #4, the person in room #3 into room #6, and so on out to infinity, always putting each former occupant into the room number twice his own. As a result, all the odd numbered rooms become vacant, and the infinity of new guests is easily accommodated. And yet, before they came, all the rooms were full! And again, strangely enough, the number of guests in the hotel is the same after the infinity of new guests check in as before, even though there were as many new guests as old guests. In fact, the proprietor could repeat this process infinitely many times and yet there would never be one single person more in the hotel than before.

But Hilbert's Hotel is even stranger than the German mathematician gave it out to be. For suppose some of the guests start to check out. Suppose the guest in room #1 departs. Is there not now one less person in the hotel? Not according to the mathematicians-but just ask the woman who makes the beds! Suppose the guests in room numbers 1, 3, 5, . . . check out. In this case an infinite number of people have left the hotel, but according to the mathematicians there are no less people in the hotel-but don't talk to that laundry woman! In fact, we could have every other guest check out of the hotel and repeat this process infinitely many times, and yet there would never be any less people in the hotel. But suppose instead the persons in room number 4, 5, 6, . . . checked out. At a single stroke the hotel would be virtually emptied, the guest register reduced to three names, and the infinite converted to finitude. And yet it would remain true that the same number of guests checked out this time as when the guests in room numbers 1, 3, 5, . . . checked out. Can anyone sincerely believe that such a hotel could exist in reality? These sorts of absurdities illustrate the impossibility of the existence of an actually infinite number of things.

-http://www.leaderu.com/truth/3truth11.html

Now, his immediate premises and sub-premises are,

2 The universe began to exist.

2.1 Argument based on the impossibility of an
actual infinite.

2.11 An actual infinite cannot exist.

That the universe began to exist I agree with. That an actual infinite temporal regression of physical members such as days is impossible I agree with. But I believe that there are a potentially infinite number of physical terms, meaning that the set that contains each day of time is a potentially infinite set. Specifically, it has a beginning (creation), but it will not have an end. Thus, the cardinality of the set of days that exist or have existed is finite (it includes however many days have passed since creation), but its cardinality (the number of days in the set) will always be increased as days pass. God has no intention that I know of to stop creating and/or sustaining the passing of days.

But this is to say nothing of an actual infinite. If by denying the possibility of an actual infinite Craig is required to believe that the number line does not contain members that are real objects (and informed by his other writings we can be confident of this), then I disagree. I think that numbers are real, that they are objects, and that the set of all whole numbers is infinite, in fact, there are many infinite sets of numbers.

At any rate, I can give an example of a meaningful, coherent subtraction of an infinite set from another infinite set. Let's subtract all whole negative numbers from all whole numbers:

Set X {...-3, -2, -1, 0, 1, 2, 3...}
- Set Y {...-3, -2, -1}
= Set Z {0, 1, 2, 3..}

So the cardinality of X is aleph-null, and so is that of the sets Y and Z. Here is where I feel that Craig has misunderstood the nature of transfinite arithmetic. For by "the same number of guests" Craig really means 'the same cardinality of the set of guests'. Let me explain. I believe Craig's contrual is something like the following.

Aleph-null
- Aleph-null
= Aleph-null

Thus, the cardinality of the set produced by the difference in the cardinalities of the sets X and Y is the same as the cardinalities of each set. This would not be a problem, but for other instances of transfinite subtraction, and Craig gives a few. Consider another example,

Set X {...-3, -2, -1, 0, 1, 2, 3...}
- Set X {...-3, -2, -1, 0, 1, 2, 3...}
= Set Z' { }

The cardinality of X is aleph-null, and when X is subtracted, the resulting set Z' is empty, and therefore has a cardinality of 0:

Aleph-null
- Aleph-null
= Zero

Furthermore, we can construct all kinds of examples of subtracting infinite sets from other infinite sets such that the difference may be virtually any number. Consider,

Set A {1, 2, 3...}
- Set B {2, 3...}
= Set C {1}

The cardinality of A is alpeh-null, and the cardinality of B is aleph-null, but the cardinality of C is 1. Thus:

Aleph-null
- Aleph-null
= One

Therefore, subtracting an infinite set with a cardinality of aleph-null from another
set with a cardinality of aleph-null is an operation that is not well defined, and it is useless to us.

But is this the whole picture? Hold that thought, and follow me while I retrace a famous logical contradiction drawn from the principle of square roots:

√25 = 5
√25 = -5
∴ 5 = -5
But 5 ≠ -5

The above fallacy lies in the incompleteness of the statement √25 = 5, and the incompleteness of the statement √25 = -5. Rather, the two should be resolved with the statement √25 = ±5.

Similarly, I believe that Craig's fallacy is one of incompleteness. As I stated last time, one has not exhaustively defined a set if one has merely described its cardinality. Thus the operations within the ilk:

Aleph-null
- Aleph-null
= One

are not complete. While the unhelpful statement that 'aleph-null - aleph-null = 0 or 1 or 2 or n or aleph-null', isn't well defined, it is coherent. However, there is no reason to only perform transfinite arithmetic at the level of cardinalities. In fact, I can think of a very good reason not to perform transfinite arithmetic at the level of cardinalities...

In the last post I gave an application of the set theory paradigm that went like this

If the intersection of a set X and a set Y is empty, and the cardinality of X is 3, and the cardinality of Y is 2, then the cardinality of the union of X and Y is 5.

But, what if the intersection of X and Y is not empty? In such cases, even transfinite addition becomes undefined. For example, the intersection of a set X {1, 2, 3} and a set Y {2, 3, 4} is the set Z {2, 3} such that to add the cardinalities of X and Y would look like this:

3
+ 3
= 2

But we know that this is not a true equation. However, if the members of the set with a cardinality of 3 and the second set that also has a cardinality of 3 are defined, then the intersection of the two sets is coherent:

Set X {1, 2, 3}
∩ Set Y {2, 3, 4}
= Set Z {2, 3}

Thus, adding cardinalities is just as "absurd" as subtracting cardinalities. But this is exactly what Craig does when he subtracts 'an infinite number of guests' from 'an infinite number of guests' to get 'an infinite number of guests'. He calls an absurdity what is in reality an undefined expression. He should rephrase his expression to say that 'there is some infinite set D such that a proper infinite subset E of D may be subtracted from D, resulting in a third infinite subset F'.

I believe I have given an example of such an operation:

Set X {...-3, -2, -1, 0, 1, 2, 3...}
- Set Y {...-3, -2, -1}
= Set Z {0, 1, 2, 3..}

While Craig believes that Hilbert's Hotel is absurd, I can imagine such a hotel as existing. Picture this:

You are standing, facing the hotel. You look to the left, and you can see the building extending beyond sight. You look to the right and sure enough, the hotel rooms continue on beyond your visual range. God has constructed this hotel by the power of His word, and He sustains its existence. You walk straight ahead, which leads you to room #0, which is the clerks office. She tells you that all the room #'s are occupied, but she thinks she can squeeze you in. She makes an announcement over the loud speaker that every occupant of a room with a positive number is to move to the room with the number one above his. You walk outside and turn around to face the hotel again. Now you begin to see every occupant in the rooms to your right open their doors, walk farther right, and enter into the next rooms. This leaves room #1 open, and you walk in and place your luggage on the fold-out table you remove from the closet. Hilbert's 'Hotel is a strange place' you think, but you're sure they make their money.

In set theory terms, the cardinality of the set containing all room numbers is aleph-null. Moreover, the cardinality of the set containing all guests is aleph-null, and when you check in, the resulting set has an additional member (you), but it also has the cardinality aleph-null. And yet, just like in the examples I gave above, this phenomenon is coherent (and now even conceivable). But am I failing to handle his argument in its full force?

Let's explore Craig's illustration a little more. One example of absurdity he gives is:

But Hilbert's Hotel is even stranger than the German mathematician gave it out to be... Suppose the guest in room #1 departs. Is there not now one less person in the hotel? Not according to the mathematicians-but just ask the woman who makes the beds!

I judge Craig to be accurate when he says that there is "one less person in the hotel". But he is mistaken when he accuses "the mathematicians" of disagreeing. What I think he means is that mathematicians would maintain (and I think rightly so) that the cardinality of the resulting set is the same as the initial set. But this does not mean that the initial set didn't lose a member! What Craig should say is something like 'in the set H containing all the hotel room numbers {-1, 0, 1, 2, 3...}, the guest in room #1 leaves, represented by the removal of the set I, {1} from H, resulting the set J {-1, 0, 2, 3...}. And yet, the cardinality of H is aleph-null, and the cardinality of the set J is also aleph-null, even though J contains one less member than H (J is a proper subset of H)'. Allow me to express this in a linear fashion:

Aleph-null
- One
= Aleph-null

As I demonstrated earlier, this is not a logical contradiction, for the subtraction of a finite number from aleph-null results in aleph-null. More specifically, the subtraction of a finite number of members from an infinite set with the cardinality of aleph-null results in an infinite set with the cardinality of aleph-null as well, even though the resulting set is a proper subset of the original set. In the example Craig gives:

Set H {...-3, -2, -1, 0, 1, 2, 3...}
- Set I {1}
= Set J {...-3, -2, -1, 0, 2, 3...}

So the guest in room #1 may leave, and this is not absurd. But that was just the subtraction of a finite number of members from an infinite set. Can we also meaningfully subtract an infinite number of members from an infinite set? Craig says

Suppose the guests in room numbers 1, 3, 5, . . . check out. In this case an infinite number of people have left the hotel, but according to the mathematicians there are no less people in the hotel-but don't talk to that laundry woman! In fact, we could have every other guest check out of the hotel and repeat this process infinitely many times, and yet there would never be any less people in the hotel

By this I understand Craig to be expressing a phenomenon that goes something like 'in the set H containing all the hotel room numbers {-1, 0, 1, 2, 3...}, the guests in rooms with odd numbers leave, represented by the removal of the set L {1, 3, 5...} from H, resulting in the set M {-1, 0, 2, 4, 6...}. And yet, the cardinality of H is aleph-null, and the cardinality of the set L is also aleph-null, and the resulting set M has a cardinality of aleph-null even though M contains less members than H (specifically, M is a proper subset of H). Thus, the difference between the infinite set H and the infinite set L is another infinite set'. Allow me to express this in a linear fashion:

Aleph-null
- Aleph-null
= Aleph-null

As I demonstrated earlier, this is not a logical contradiction either, for just as the square root of 25 is 5 or -5, so the subtraction of aleph-null from aleph-null may be 0 or 1 or 2 or n or aleph-null. And although this is coherent but not meaningful, meaning may be added by simply defining the members in each infinite set:

Set H {...-3, -2, -1, 0, 1, 2, 3...}
- Set L {1, 3, 5...}
= Set M {...-3, -2, -1, 0, 2, 4, 6...}

Thus, Craig's argument is demonstrated to be unsuccessful in revealing any absurdity. As far as a clear and persuasive argument for the fact that the universe had a beginning, permit a modest formulation of my own. I have offered such arguments before, but will briefly indulge once again.

The morning after your first night's stay in Hilbert's Hotel, you put on your pajamas and open your door to pick up the copy of the L. A. Times whose thump against your door woke you up. You look up, and with the hotel to your back, you look to your right and see a crowd of runners gathered in front of the clerk's office. You inquire as to the event, and your neighbor in room #2 explains that there is to be a race, whose participants will start the race in front of room #-∞. 'How can they ever get started?' you ask. 'They will never stop walking down the line of negative numbered rooms' you assert. 'And as soon as they decide to turn around and begin the race, the room in front of which they do so will necessarily be finite, not infinite!' you argue, beginning to get concerned. 'There is no room whose number is -∞. Each room has a finite number, but the set of all rooms is infinite! Even if God Himself allows them to run toward the clerks office where the finish line is while He constantly pulls them in the direction of the negatively numbered rooms, their running will be in vain, for whatever progress they make will be more than cancelled out by God's pull - they can neither start nor finish the race'. You try to warn the runners, but they ignore you and take off toward the infinite. You feel sorry for the runners, whose racetrack is the set of rooms with negative numbers {...-3, -2, -1}. And furthermore, to get started, they have to cross that same track while searching for the starting line! How can they cross a distance that consists of a set of rooms with the cardinality aleph-null? How can they cross it twice?

Such a mental exercise demonstrates the absurdity of positing a universe whose temporal past extends infinitely. While it is coherent to posit a universe with a beginning and no end, it is incoherent to say that the universe never got started - never had a beginning. For, with today as the finish line of the race (and indeed, today has come to pass), the cursor of history - the ontological "now" - will have to transgress a set of days whose cardinality is aleph-null. This is logically impossible.

Therefore, while Craig's Hotel argument is susceptible to an undercutting defeater, there is another argument that may take its place, rendering his overall cosmological argument stronger.

A Novice Argument for the Utility and Coherence of Transfinite Subtraction

Below I lay out a set of definitions that I currently understand to constitute the basic paradigm of set theory. I then construct an argument, using those definitions, for the coherence and utility of transfinite subtraction. I can identify no logical contradiction so far, and I find the argument of interest because Craig says that one "cannot do inverse operations like subtraction in transfinite arithmetic with infinite quantities". I happen to believe that my objection to this point in Craig's "Kalam Cosmological Argument" is not fatal, but I shall not explicate that position here.

DEFINITIONS
Set – A collection of members
Member or Element – An object in a set
Proper subset – A set X whose every member belongs to another set Y, while Y includes members who do not belong to X
Equality – The state of a set X with another set Y, while X contains every one of and only the members of Y
Cardinality – The size of a set
Finite – The state of a set X whose members may be put into a one to one correspondence with the set {1, 2, 3… n}
Potential infinity – The state of a set X whose members may be put into a one to one correspondence with the set {1, 2, 3… n}, but whose cardinality may always be increased
Infinite – The state of a set X whose members may not be put into a one to one correspondence with the set {1, 2, 3… n}
Aleph-null or Aleph-naught – The cardinality of the set containing all rational numbers
Aleph-one – The cardinality of the set containing all real numbers
Aleph-n – The cardinality of the set containing the next higher cardinality than the set whose cardinality is aleph-(n-1).
Union – The set of the members of a set X and the members of a set Y
Intersection – The set of the members of a set X who also belong to a set Y
Power set – A set X of all possible subsets of a set Y. The set of a powerset has a larger cardinality than any subset of the set Y.

AN EXAMPLE OF ADDITION UNDER THE SET THEORY PARADIGM
If the intersection of a set X and a set Y is empty, and the cardinality of X is 3, and the cardinality of Y is 2, then the cardinality of the union of X and Y is 5.

ARGUMENT FOR THE UTILITY AND COHERENCE OF TRANSFINITE SUBTRACTION
One has not exhaustively defined a set if one has merely described its cardinality. For example, the set X, containing the members {1, 2, 3} has a cardinality of 3, and the set Y, containing the members {4, 5, 6}, also has a cardinality of 3. However, X is not equal to Y. “Infinity” is not a number; it is the state of any infinite set. Thus, the union of the set A whose member is {-1} and the set B whose members include zero and all positive whole numbers {0, 1, 2, 3…}, is to produce a set C with the members {-1, 0, 1, 2, 3…}. B and C are both infinite sets. However, C includes one member who is not in B, namely, {-1}. Therefore, C has a larger cardinality. It is therefore not a logical contradiction to say ‘infinity plus one is infinity’. Such a statement is unclear however, as it does not specify the members of either infinite set referenced, or the specific member (e.g. 1, 2, or 3) who is being added to the first infinite set.

Thus informed, transfinite subtraction becomes possible. For example, the above mentioned infinite set C minus the member -1 is the infinite set B. Thus, ‘infinity minus one is infinity’ is merely the statement ‘there is some infinite set D, that contains some member E, such that E may be subtracted from D, and D remains in the state infinite’.

[Update: I know blog at Philosophia Swingrovia.]

the barbarian sees red!

I had a discussion with my new found friend Tim; a guy I met at my Starbucks. Of the many discussions and disagreements we’ve gotten into, one of them is the following. I questioned the assumption many people seem to think is obviously true; namely, the proposition that “one cannot know a thing unless one has something else to compare it to.” Why think this is true? And the reply went something like, “because without the ability to make a distinction between any two things, one cannot be aware of anything in particular.” So I went experimenting in my thoughts and came up with the following scenario:

Imagine there is a barbarian (by ‘barbarian’ I mean a man who knows no language nor any language users) who lives in a rainforest paradise with birds and trees and all sorts of other wonderful created things, but unlike most rainforests known to man this particular rainforest and everything in it is colored red, and no thing in the forest is any color besides red, and all things in the forest are the same hue or red. Imagine further that our barbarian has the same sort of vision, lighting conditions, and neural network, such that, everything going on with us when we see red also goes on with our barbarian. So the question is, does our barbarian know the forest is red? I imagine he would be seeing the same thing we do when we see red, but of course he wouldn’t know there is other possible colors than red, or even further that there is such a thing as natural-kind ‘colors,’ since anyone who knows about the natural kind colors would have to be aware of at least two. Bust despite all of this, isn’t it the case that our barbarian sees red when he looks at everything in the forest? Would he have a name for phenomenon of red? Probably not, since I think in most cases words are created in response to distinctions, and our barbarian knows of no other color to distinguish the color he sees. So if we asked him, “Mr. Barbarian, do you see red?” He probably wouldn’t know what we are referring to, because the thing we’re referring too (the red he sees) would be so universally manifested that he would unconsciously assume that the red he sees is not something distinct from everything else in the rainforest. But despite all this, is he not seeing the same hue of red we see when we see the same hue of red he sees? He’s got to be seeing the red in the forest, and this is true despite the fact he wouldn’t be able to communicate his knowledge to us. To claim that “one cannot know a thing unless one has something else to compare it to”, one must show how the above stated scenario is not only improbably but logically impossible. And good luck showing that…

Proverbs 19:11

Good sense makes one slow to anger,
and it is his glory to overlook an offense.

Romans 12:18

If possible, so far as it depends on you, live peaceably with all.

Does an Uncaused Universe Prove Atheism?

Suppose Quentin Smith succeeds in demonstrating that the actual universe began to exist without being caused to exist. Does this entail atheism?

An easy counter-example: there exists a theistic God, who did not cause the unviverse, and yet the universe began to exist.

The inability of a Quentonian argument to constitute positive proof of atheism does not prove theism, it just undercuts the potency of such an atheistic argument. If his argument is successful however, it will undercut all cosmological arguments, decreasing the reasons that some theists have for believing that God exists.

The difficulty in positively proving atheism is cited by some atheists as a point of persuasion, as if to say, "sure, my argument does not logically entail atheism proper, but no argument can, so give me a break". I have not been persuaded that it is necessarily the case that no argument can prove atheism, or theism for that matter. This is a point whose converse I am willing to grant for the sake of argument however.

My main point? Arguments that undercut theistic arguments do not entail atheism and vice versa.

My question to you: what types of enterprises seem likely candidates to succesfully provide positive evidence for atheism?

Patience and Freedom

Patience is an aspect of the fruit of the Spirit (Gal. 5:22).
Love is patient (1 Cor. 13:4).

Can we conclude then, that God, whose nature and charatcer contain the maximal degree of every good attribute, is patient?

What does it mean to be patient? The Oxford American Dictionary defines it as "able to wait without becoming annoyed or anxious". This will suffice.

What does it mean for God to be patient? If God's nature, character, and decisions are causally sufficient to determine the existence and behavior of each and every object, and there exists no object outside of God or that which He sufficiently determines to exist and behave, then the only possible way for God to be patient is for Him to be patient with Himself.

However, doesn't the essence of patience require that the patient respectfully endure the existence or action of an object outside himself? For calling God "patient" implies the temptation of annoyance ar anxiety. But how can God be tempted to be annoyed or anxious with Himself? Is God schizophrenic?

I answer "no". I think God is patient with objects who act independently of Him and contrary to His will. I am forced to conclude that their power to do so was given them by God for a good reason, and they are only permitted to act by God's decree. But just as Jesus emptied Himself (Phil. 5-11), and sovereignly chose to not apply His power and right to be equal with God, so I believe God soveriengly choses to not apply His power and right to sufficiently determine every event. No, He allows persons the dangerous and yet beautiful and enabling power of free will.

Your thoughts? Does the Divine attribute of patience imply the free will of persons?

concerning my progress as a catechumen.

This is a letter I wrote to Father Michael, my priest at St. Luke's Orthodox Church, and in it I explain some of the things I am struggling with on my journey to Orthodoxy.
____________



Father Michael,

I hope you got my email about why I wasn’t there for my Chrismation on Lazarus Saturday. I mentioned that I wasn’t able to make it because I planned a vacation with Noelle and my family last week because it was Noelle’s spring break and I didn’t think I would miss Pascha since it’s usually a week after the Latin Church’s Easter. I found out that I was wrong after I had already bought my plane tickets and paid for the hotels and so on. But despite all this I realized, somewhat to my own disappointment, that this wasn’t the whole story. For if it was, I would never miss my chrismation for the sake of a vacation, or nearly anything else for that matter. If I really was looking forward to my chrismation in the Orthodox Church like I ought to be I simply wouldn’t miss it for the world. So back when I realized I wasn’t going to make it I thought it somewhat odd that I was willing to miss it, and the truth is that I was, and this is not because it doesn’t mean to me what it should, but quite the contrary. I was willing to miss it because my heart isn’t completely settled on it, and that’s because I’m not completely ready, and I think you would agree that I ought to be nothing short of completely ready for the Rite of chrismation to be all that God has designed it to be. So because it means to me what it ought to, I mustn’t go through with it until I have my heart in the right place. I hope you don’t take offense to any of this, and please forgive me if my words betray my intent. I suppose I could make things clearer by explaining why I think I might not be ready.
The most immediate and less theological reason why my heart is not where it should is that going through with my chrismation will bind me either explicitly or implicitly to rejecting some of my past. For instance, in the chrismation confession, I am to pronounce that I renounce “all heretical associations, traditions, rules, and all teachers and their doctrines contrary to the Holy Eastern Orthodox Church, and cast them off.” (63) And further, that I “renounce all ancient modern apostasies, heresies, and founders of heresies, and cast them off because they are contrary to God.” (64) And again, that I “believe and confess that power has been given by Christ the Savoir to the Orthodox-Catholic Church, to bind and to loose. And that whatever, through that power, is bound or loosed on earth will be bound and loosed in Heaven.” (66) The difficulty here is that I became a Christian, and I am confident that I am in communion with invisible Church in part by the preaching of the Baptists (who are the theological decedents of the Anabaptists), and the teachings of the Anabaptists are officially condemned by the Eastern Churches. Now this isn’t to say that I am an Anabaptist, for as I have told you I have independently (and by the grace of God) come to the same theological positions that the Eastern Church espouses, so clearly I am no Baptist or Anabaptist. The problem is that my conversion into the Invisible Church was brought about by the presentation of the Gospel by the preaching of Baptists, and the things they preached, the doctrines that gave the doctrinal basis and context of my legitimate conversion and baptism, I am now called to renounce to a substantial degree, and I find myself vexed and disconcerted by this. Since the Eastern Church in fact recognizes the legitimacy of my conversion and baptism by the work of Baptists (this must be the case because I am to be chrismed only, and not re-baptized) I cannot with good conscience renounce their traditional as heretical, or even mostly heretical, for clearly they have been an instrument of Grace in my life, and in the lives of many others.
But maybe I have misinterpreted what I have read. I’m thinking that even though I am to affirm and confess “…that power has been given by Christ the Savoir to the Orthodox-Catholic Church, to bind and to loose. And that whatever, through that power, is bound or loosed on earth will be bound and loosed in Heaven,” it maybe doesn’t mean that no other visible Church, such as the Evangelical Baptists, have not received a portion of such power? For surely if my conversion and baptism, which was performed by Evangelical Baptists, is legitimate (again, as the Eastern Church seems to implicitly recognize this by not requiring me to be baptized again), then it must be the case that such Evangelical Baptists had the power, at the time of my conversion and baptism, to “bind and to loose.” Until God grants me peace with this issue, affirming these statements I am slated to confess without being sure that my statements, namely the Baptists too may have the power to “bind and to loose,” I cannot help thinking and feeling that I would in effect be denying the authenticity of my conversion and baptism, as well as the good work of many co-laborers of the Kingdom, and maybe even that my Christian brothers and sisters who are dear to me might not in fact be my brothers and sisters because they are not “in communion with the Eastern Church.” I am seeking communion with the Eastern Church in part because I know that I have become part of Christ’s Eternal Kingdom, and I did so outside of the visible communion with the Eastern Church, and unless I can combine this process into a cohesive story, my major reason for wanting to Commune with Eastern Church is strongly undercut.
The second, more theological worry is the issue of doctrinal authority and the Canon of Scripture. I am well aware that the Canon of the New Testament didn’t pop into existence ex nihilo but was pieced together by the combined efforts of God directing the hearts of both the Eastern and Latin Church Fathers. The Bible, as the collection of divinely inspired texts, was put together and sealed with Divine Authority. The fact that the Eastern (and Western) Church were the vessels to which God ordained the Cannon, it’s a natural move for someone like myself who trusts the Bible as the most reliable source for sound teaching to seek to commune with the tradition who bequeathed it. It’s no wonder then that by studying the Bible I’ve come to have the hold the same theological positions as the Church Fathers.
My criteria for what I believe about God has always been the Bible, and I come to understand the things I have by using the reason God has given me and by reading the Bible with the guidance of the Holy Spirit. I think a good case could be made that Early Church thought the Bible to be sufficiently authoritative on its own behalf. For instance when speaking about the Gospel of Jesus Christ, the Apostle’s Creed states that Jesus Christ “for us men and for our salvation came down from Heaven, and was incarnate of the Holy Spirit, and the Virgin Mary, and became man. And he was crucified for us under Pontius Pilate, and suffered, and was buried. And the third day He rose again, according to the Scriptures, and ascended into Heaven…” Notice that it doesn’t say anything like “because this is the teachings of the Church,”or that “the Fourth Ecumenical Council has decided” that Jesus did these things, but that it simply takes the Scriptures as the authority on the matter, as if it were sufficient. I think this is correct, but this isn’t the end of the story. The same Church that has been the vessel for the Holy Scriptures is also a tradition that has passed down doctrines that the Bible doesn’t directly address. For instance, the Church states that Mary never had sexual intercourse throughout her life, that she was the Ever Virgin Mary. Now I don’t have Biblical objections to such a doctrine, because the Bible nowhere contradicts it. The Bible emphasizes the fact that she was a Virgin when Christ was conceived by the Holy Spirit in her womb, and has no comment about whether she remained a Virgin throughout the rest of her life. But being Eastern Orthodox means that you affirm that she did in fact remain a Virgin for the rest of her life. And I’m perplexed about how I am supposed to affirm it when I don’t know if it’s true or not. I don’t have any reason to think it’s false, but not having a reason to think that something is false doesn’t imply that it’s true either. The Church, I think, says that I should believe it because the Church is directed by the hand of God, and therefore ought to be trusted in its proclamations of faith. But that is a difficult thing for me to swallow whole heartedly, for the historical Church wasn’t without it’s own schisms and divisions through the first thousand years of Ecumenical activity. For instance, St. Gregory of Nazianzus and St. Basil the Great both thought that St. Gregory of Nyssa was wrong about the latter’s teaching on universal salvation (that all mankind will eventually be saved). I suppose this instance of Church Father disagreement is beyond the scope of the Ecumenical Councils, and so it doesn’t represent division among the essentials of Orthodox Doctrine. Fair enough, but who’s to say that something like the doctrine of the Ever Virginity of Mary is something that is debatable in the same way St. Gregory of Nyssa’s universalism is, in which case it might be viewed as an open question? I think the response to this suggestion of the Eastern Church is that the Church teaches that the Virgin Mary was ever so, and so it’s not an open question. And then my next question becomes, well, how do I know that? How do I know that the Eastern Church and what it teaches is always correct? And I think the only response that could be given to me is something like, “The voice of God will be heard through the Church,” or “If you seek the voice of God, and you are one of His children, then you will naturally trust His Church.” What else could the response be? I actually think this a decent response, the problem for myself is that I haven’t heard such a confirmation from God yet, and maybe I need to be more patient and maybe need to open my heart, and keep seeking. And that’s exactly what I plan to do, but for now I’m not there yet.
I’m sorry Father Michael if I might be guilty of pride for demanding to know all these things. The thirst for knowledge often ends in pride and arrogance, and I’m open to the possibility that I’m seeking with my mind more than my heart, I really am. I know that I’m supposed to love God with all my heart, all my mind, and all my soul; it’s just difficult to guide my heart when I don’t see where I’m going, and I’ll be more than willing when my heart tells me to trust more than I can figure out on my own. I’m just not there yet.

An Old Journal of My Introduction to General and Special Relativity Wherein My Skepticism and Dogmatic Newtonianism Was Dissolved

Forward:
Dear Derek, in the presence of many witnesses, in light of our brief conversation earlier, I here submit to you some of my thoughts from a Physical Science class I took in Fall of 2005. One of the assignments involved thorough interaction with a chapter of choice in Hewitt’s, Suchocki’s, and Hewitt’s, Conceptual Physical Science. I selected a chapter we hadn’t gone over in class: Chapter 35: Special and General Relativity. Please keep in mind that I have learned a lot since this writing, that this writing is a direct summary and response to a chapter of a textbook, and that this was a general ed, non-science major class.

I also highly recommend these two resources:
http://www.pbs.org/wgbh/nova/elegant/
Zero: The Biography of a Dangerous Idea

•••

Original Writing:
35.1 Summary: To record the state of something we use three dimensions, which have no robust meaning unless we also state the time that the dimensional descriptions applied to the object in question. This seems to indicate that space and time may be bound. Einstein’s theories support this; that things exist in a space-time continuum.
35.1 Comments: I have seen the PBS special “The Elegant Universe”, so I am going into this chapter with a little bit of background information about the theories of relativity, but not much. I have some speculations of my own, which begin with critiques of contemporary explanations of “space-time” observations. I would therefore like to note my initial hesitance to calling space and time, or matter and energy, the same thing; no matter how intimately they may be connected.

35.2 Summary: Einstein’s Special Theory of Relativity, based on Newtonian principles, states first that “Observers can never detect their uniform motion except relative to other objects”. A restatement of this postulate is that “All laws of nature are the same in all uniformly moving reference frames”. An example is given of being able to pour coffee while flying through the air on a jet plane. This is supported by any experiment that has been carried out. If it has been carried out on earth, the fact that the earth is in motion, and the experiment was carried out as if there was not any acceleration of the location it was carried out in (indeed, there was not any relative motion of the lab relative to the earth and its atmosphere), then it becomes more and more clear that if the entire frame of reference is moving relative to an outside object, then relative motion inside the reference frame is only relative to other objects inside the reference frame – the motion of objects outside the reference frame are not factors in the motion of the objects inside.
The second postulate is that “The speed of light in free space will have the same value to all observers, regardless of the motion of the source or the motion of the observer. The speed of light is a constant.” This postulate is confirmed by our measurements of the speed of light. If both postulates accurately describe reality, then when two observers in relative motion to each other and a light source disagree about the time of a certain event, they may both be correct – the only thing to budge in the equation is time. A note is made that points in space and time are both quantized, i.e. there are fundamental units for them.
35.3 Comments: I like that the wording of the first postulate does not deny objective uniform motion or location. It does not affirm them either. If you start with relative motion, you will get relative motion. In other words, if we measure motion relatively, or call motion “change in position relative to a frame of reference” then of course we will conclude that motion is relative. Rather, the postulate simply states that it is impossible to detect uniform motion (if it is a phenomenon that actually occurs in our universe). I am however, skeptical of even this. What, logically, was Einstein’s reason for believing that humans will never discover a universally objective frame of reference, nor be able to develop the technology to measure motion in relationship to it?
I have also wondered about the famous experiment involving two clocks on two airplanes flying in opposite directions around the world. Their clocks showed a difference in displayed time at the end. But couldn’t that have been due merely to the physical strain exerted upon the inner workings of the clocks during the experiment? I would wonder then, what were the clocks measuring? Is it possible that what we call “time” is actually two different things: ‘age’ and ‘time’. ‘Age’ being the physical change or decay of an object, and ‘time’ being the objective, steady progression of events in this world. Time might be the cursor of history marking where everything is. How else would it be that the pilots of the planes could see each other after the flight? Wouldn’t they be living in two different planes of reality – different “times”? One would be a few split seconds ahead of the other! Or perhaps at the end of the day they both wound up in the same time plane, but traveled through less “time” to get there. I wonder then, what the nature of the “time” is that they traveled through; could they have seen each other during their journeys? How much of the Special Theory has to do with mere perception, and how much of it with the actual bending of time? Could it be that our methods for measurement are flawed?

35.3 Summary: The notion that time can be stretched is called “time dilation”. A very compelling illustration is given. Suppose that we could observe a light flash bounce between two mirrors inside a transparent spaceship. An observer onboard the spaceship, and an observer on the ground would both measure the speed of light as the same rate, denoted c. Yet to the observer onboard the spaceship, the flash of light is only moving up and down (which it is – relative to the environment of the spaceship). However to the observer on the ground, the flash of light will actually be moving up and down, and horizontally as well (in a zig-zag pattern). This is because the entire spaceship, including the mirrors and the light flash, are moving parallel to the ground. To the observer on the ground, the flash of light will then be covering more distance than to the observer on the spaceship. If speed is equal to distance divided by time, and the speed of light is constant, and the distance stretches, then the time must logically be stretching, or dilating, as well. This occurrence can be expressed mathematically.
The text then contends that time is actually dilating, there is nothing unusual about the functioning of a clock itself, as indeed there is nothing unusual about clocks here on earth now, though they are all whizzing through space (because the earth on which they are is whizzing through space). Next the text explains that as a result of time dilation, according to the measurements we have made, as speeds approach the speed of light, time slows down and seems to approach zero. A mass at the velocity of light, c, takes an infinite amount of time to elapse one second, and zero amount of time to travel an infinite distance. Thankfully, the Law of the universe has set c to be a type of cosmic speed limit such that it is impossible to reach or exceed c. It is important to note that time dilation, to be perfectly accurate, most be taken into account even for small masses and slow accelerations. It is also important to note that as speeds approach c, mass approaches infinity, length approach zero. However light, which moves at c, will always be measured to be moving at c, regardless of your frame of reference.
Space travel is also discussed in this chapter. At high speeds it would be theoretically possible to spend 5 years traveling at 99.999 % of c, and return to earth only to find that 1100 years have passed for it and its inhabitants.
35.3 Comments: This chapter hasn’t mentioned it yet, but c is only the speed at which light moves in a “vacuum”. Light moves significantly slower in gas, even slower in liquid, and slower still through solids (if at all). This chapter coaxes another question. If Einstein is right, then why can light go the speed of light? Isn’t light made up of photons? Why are they exempt from the c speed limit? Well, if photons have zero mass, then perhaps it is not so absurd. I would also like to note that this section does not assert that time can be turned backwards. It can be sped and slowed (relatively), but there is nothing in this section that argues for bending and twisting time like a pretzel, or going back in time. In fact on page 845 it says that time accelerated astronauts will not be able to go backward in time.

35.4 Summary: Length contraction is related to time dilation. As was mentioned, as a mass approaches the speed of light, its length approaches zero, when measured by an observer who is not traveling relative to a common frame of reference. This contraction only takes place in the direction of motion. This phenomenon is related to time dilation, as distances will flatten to zero when a mass approaches them at c. In this way, one could travel an infinite distance in zero amount of time. Furthermore, if a mass approaches the speed of light, its length does not change relative to itself. Rather, the time it has to travel through in order to reach its destination is collapsing. However from the perspective of an outside observer, lengths are contracting.

35.5 Summary: In this chapter relativistic momentum is explained. The speed of any mass has a limit: c. However, momentum may increase without limit. This is illustrated by Einstein’s new equation for calculating momentum, which accounts for the Lorentz factor. Therefore as speed approaches c, momentum approaches ∞. With any progress toward c, objects appear to increase in mass, because they display an increase in inertia. Einstein however, seemed to think later in his life that mass is the same in all frames of reference, but space-time changes with speed.
35.5 Comments: It seems to me that if you accept Einstein’s initial premises, then all of this follows logically. To be honest, I think I might just have a lot of emotional struggles with accepting all of this.

35.6 Summary: Einstein asserts that matter and energy may be exchanged according to the expression E=mc2; E being energy, m being mass, and c being the familiar uninhibited speed of light. When fuel is used to produce energy, the system will afterward be found to be less some mass, in accordance with Einstein’s equation!

35.7 Summary: A desire to describe nature using standard forms and perspectives motivated Einstein to pursue a description of the phenomena he was examining, which came to be know as his theory of General Relativity. By thinking about a spaceship accelerating at g, the principle of equivalence became manifest, that “local observations made in an accelerated frame of reference cannot be distinguished from observations made in a Newtonian gravitational field”. A few thought experiments quickly establish this theory as reasonable, but Einstein elaborates on it by saying that, (in a free environment) because the trajectory of a beam of light relative to an accelerated mass is identical to the trajectory of an additional object relative to the same accelerated mass, space-time itself curves. He contends that matter and energy are two aspects of the same thing.
Euclidean geometry produces accurate results when dealing with objects on a flat surface. However, Einstein’s observations and calculations argued for a four dimensional warping of space-time. This is seen when the shortest distances between three planets form a triangle whose angles add up to greater than 180 degrees. The lines making up the legs of triangles such as this are called geodesics. The lines are technically not straight, but they are short. If this curving of space-time is positive throughout the universe, then the universe is warped like a sphere. If it is negative, then it is shaped more like a Pringles potato chip. This curvature of space-time causes what we perceive as gravity, and is proportional to mass. This principle is seen when we calculate the effect of large masses as they change position. It would seem that, rather than a sudden ceasing of gravitational force on other masses, a large mass that changes position creates gravity waves, similar to the waves made on the surface of a waterbed when a bowling ball is rolled across it.
Einstein’s calculations, when applied to planets in Our Solar System predicted precessing orbits. When Newtonian physics were used to predict the orbits of the planets it pretty much worked out – except for the missing 43 seconds of arc that Mercury displayed. Einstein’s equations had produced the right predictions.
Another confirmation of Einstein’s theory occurred in 1919 when a solar eclipse revealed that his predictions about the exact arc beams from distant stars display when passing near the Sun where dead on.
A third test confirms General Relativity, and it becomes clear that in General Relativity, the gravitational “red shift” is relative to location rather than speed (because c is a constant). It is also important to note that time is never sped or slowed for an object relative to itself (obviously). This is to say that though an object may pass through time more slowly than another relative to it, its lifespan is never extended from its own perspective.
35.7 Comments: I heard once that Einstein responded with a complete lack of surprise when his predictions about starlight arc were shown to be accurate. He said something about being certain from his equations alone; observation is secondary.

Concluding Thoughts:
This chapter has brought many questions and ideas to mind. For example, if God has no mass, then (if Einstein is right), He is not subject to time. Perhaps He can interact with this universe in the ontological now, all the while being atemporal and eternal. Maybe that photons have no mass somehow plays into a facet of God’s foreknowledge or omniscience.
This in turn raises thoughts concerning humans and the resurrection. If human souls have no mass, maybe it is so that, upon death (separation of body and soul), a soul zooms to resurrection day, upon which it meets its body and enters into temporality again. I understand this to be a much bigger scriptural and scientific topic to be researched than is feasible here, but it is interesting to be introduced to such musings.
I cannot keep from thinking about the implications of God stretching out the heavens. Could this skew our observations of the age of the universe? What if our solar system was accelerated altogether such that the age of our solar system is different than the age of another? I have heard some compelling arguments for a very young earth, and some for a very young solar system. But I have also heard about evidence that seems to support an older universe. Could it be that when God stretched out the heavens, galactic clocks spun at different rates relative to each other?

Consider:
Job 9:8 “[God] stretches out the heavens”
Ps. 104:2 “stretching out heaven like a tent curtain”1
Isa. 40:22 “He ... stretches out the heavens like a curtain and spreads them out like a tent”1
Isa. 42:5 “... God the Lord, who created the heavens and stretched them out”
Isa. 44:24 “I, the Lord, am the maker of all things, stretching out the heavens by Myself”
Isa. 45:12 “It is I who made the earth and created man upon it. I stretched out the heavens with My hands”
Isa. 48:13 “Surely My hand founded the earth and My right hand spread out the heavens.”
Isa. 51:13 “the Lord your Maker, Who stretched out the heavens and laid the foundations of the earth”
Jer. 10:12 “He has stretched out the heavens”
Jer. 51:15 “He stretched out the heavens”
Zech. 12:1 “the Lord who stretches out the heavens”

Please also see:
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html
http://www.creationscience.com/onlinebook/FAQ111.html#wp1885480
http://www.cosmicfingerprints.com/

Lastly, I would like to leave the reader with the following thought. When God destroys nature, and recreates it (Rev. 21:2), will he do so with a new set of universal constants, quantities, and forces? Did the fall of Adam knock a lot of forces and constants off track? Humans have the opportunity to seek the answers, but let us give glory to God, above all.

is God possibly subtle?

The atheistic argument from Divine Hiddeness:

Assume the following:

1. God exists
2. God made man in his image
3. Necessarily, if God made man in his image, then it’s God’s duty to make Himself known to the creatures whom bear his image in any circumstance whatever.
4. God didn’t make himself known to me.
5. God doesn’t exist (since 3 entails the necessity of God making myself known to me if he exists, and I don’t know he exists, then necessarily God cannot exist).

The rebuttal to the argument from Divine Hiddeness: the argument from Divine Subtlety, which finds premise three suspect:

Surely premise 3. is too strong to be prima facie true. Imagine a possible world where God is subtle, where he only makes Himself known to those who have the eyes to see, ears to hear, and a pure heart. Imagine that God is such that only those who are willing to discern His existence are able to see that he exists. If such a world is even possible then premise 3 is necessarily false.

So is it possible that God is subtle? There’s no contradiction in the above description, so it’s at least logically possible. But is it metaphysically possible? Maybe despite the logical possibility of it being true, maybe it must be ruled out for metaphysical reasons. But what would such a reason look like?

Maybe the following:

6. God so loves his creatures that He would never not let them know that He exists.

Is 6 blatantly obvious? No, for maybe God has reasons for being subtle, like

7. God so loves His creatures He wouldn’t force them to believe He exists unless they wanted to believe.

Is 7 possible true? Surely, for

8. Love never moves the beloved if the beloved must be moved against the beloved’s will.

8 seems obviously true, and I’d invite anyone to find an exception. Since 8 is true, then 6 and 3 are false, and so the argument from Divine Hiddeness collapses.

The Economy of Mercy

There's just two ways to lose yourself in this life
And neither way is safe
In my dreams I see visions of the future
But today we have today
And where will I find You?

In the economy of mercy
I am a poor and begging man
In the currency of Grace
Is where my song begins
In the colors of Your goodness
In the scars that mark your skin
Is where my song begins

These carbon shells
These fragile dusty frames
House canvases of souls
We are bruised and broken masterpieces
But we did not paint ourselves
And where will I find You?

Where was I when the world was made?
Where was I?

I'm lost without You here
Yes, I'm lost without You near me
I'm lost without You here
You knew my name when the world was made

History of Creationism

the MarioKart argument.

Imagine (although this has actually happened to me once) that you’re playing Mariokart for Nintendo Gamecube with a few friends. The light turns green and you start racing, and the buggy you think you are controlling does all the things you have to do via your controller input; your character speeds up, rounds corners, shoots the occasional shell, as well as takes the secret short cut you intend on taking. Imagine further that the character you thought was yours (the buggy with the Princess and Mario) is actually someone else’s (Judah Dorn’s) (yours is actually the one with Wario and Boo) and it just so happened Judah Dorn did everything you thought you were doing, but of course it was Judah who did what you thought you were doing, and not you (your buggy with Wario and Boo are a few turns behind everyone else in the race slamming into a wall because, as we have already seen and established, your controller was controlling Wario and Boo’s buggy and not the Princess and Mario’s, and there was actually a few things that Judah did with his buggy that you didn’t do with yours (unbeknownst to yourself at the time), and so on. Now what can be said about such a scenario? The following facts are worthy of reflection:

(1) You didn’t do what you thought you were doing, which is to say you didn’t cause anything to happen in the way you thought you did.

(2) Despite the fact of (1), since it was the case you thought you were doing something, you were able to

(3) Identify with what you thought you were doing in such a way that you would have taken responsibility for what Judah’s buggy was doing even though you had nothing to do with it.

These are the facts of the story, and we need to take one more step to make it extremely pertinent to a certain discussion. Could you, if facts (1)-(3) obtain, take responsibility for the actions of Judah’s buggy even if you knew after the fact that it wasn’t you who did it? In the very least you would have to concede that you intended the events that actually took place, and so were responsible in at least that sense (is this enough for responsibility? Perhaps it is). But never mind what you would accept or not, I know that when this situation actually happened to me I asked myself if I were willing to take responsibility for my actions even thought I didn’t actually do anything I thought I did at the time, and I told myself I would be willing to take responsibility. But how could I take responsibility for something I didn’t actually do? Well, quite simply, I willingly intended everything I thought I was doing, and so am responsible in a significant sense; and this is true despite the facts of the matter!

So, let’s abstract these phenomenon a bit. Say the world and its causal order is such that the future is closed and nothing that is, was, or is going to happen could happen otherwise than how it is, was, and is going to happen (determinism is true!). Well, does this mitigate against responsibility, that is, could the possible truth of determinism remove the possibility of responsibility of agents? Given my video game experience and what I learned from it, it seems I must say that responsibility and determinism are compossible in so far as the agents identify with what they think they’re doing even if they aren’t doing what they think they are.

A slight caveat: I think this example is indifferent to whatever is the source any determinism in any possible world, which is to say it matters not which things are the source or cause of determinism whether it be the laws of the universe or God or mad scientists. The question of the compossibility of responsibility is narrow enough to ignore such a discussion. Nevertheless if we were to change topics and ask if other things besides humans are responsible in the worlds where both determinism and responsibility cohabitate, the following seems to be true.

In the worlds where there is just physical laws, matter, minds capable of deliberation, determinism and responsibility, then minds are the only things could be responsible (in the moral sense), for they are the things that have good and bad intentions, and so on.

In the worlds where everything is as just described with the addition of a (theistic) God, then it seems there are now two types of things which can be called responsible, man and God- for God is also such that he can deliberate and have good intentions (although he can’t have evil ones, according to Classical Theism). Notice that in the worlds where a deistic God exists he wouldn’t be morally responsible, but just causally responsible, since, in order for him to be morally responsible he would have to have intentions of sorts, and deistic Gods don’t have intentions, they would be more like physical laws (if the existed) since they do things unconsciously. But in the worlds where the theistic God exists, then it is the case that what he causes to exist in any possible world are not just things he thinks he’s causing, or else He wouldn’t be God, but something else would. So in the worlds where a theistic God exists he would be in fact causing everything you think you are doing but nevertheless identify with, and in such worlds where there is evil done through agents who think they do it, it would be God who is doing it, which means that in such worlds God would be responsible for evil, which is impossible. Therefore if theism is true and there is evil in the world then compatibilism is false.

But back to what we were saying. How might a libertarian (someone who thinks determinism and responsibility are not compossible) respond to all of this? Well, L S* has an argument, and I’d like to paraphrase him here: So what if I identified with something that something else caused; that’s not even the question, and so these sorts of Frankfurt-style counterexamples to alternate possibility requirements for responsibility simply beg questions. Even if it is the case that everything I intended to do took place in ways I identified with, I could have intended to do other than which I thought I did. Since it is me who has the power and control of intending to do otherwise, and not Judah Dorn, this is what grounds the possibility of me identifying with anything whatever. To have the power to intend otherwise is having the power to engage an alternate possibility other than that which has happened, and so alternate possibilities are still required for responsibility ascriptions. So much for poo-poo compatibilism!

The meta-compatibilist response: Look, imagine that Judah Dorn’s controller can not only be hooked up to a Gamecube but your mind as well. Assuming that is conceivable (if not, why not, and remember that all things are possible through Christ who…etc.), then Judah could cause you to intend whatever you intend when every you do, and so long you as you in fact identify with what you think you’re intending but are in fact not, you could just as easily and in the same way be responsible. So much for the poo-poo need for alternate possibilities!

So, any thoughts?





* Unpublished voice mail left on my phone, 02/24/07.

Spiritual Gifting, Not Spiritual Gifts

For years, I have wrestled (internally) with my views on “spiritual gifts.” My ecclesiastical tradition has had much to say on the matter (especially in recent days).

So the long and short of my answer is this…Believers do not have spiritual gifts.

Allow me to continue. Our individualistic mindset has vastly distorted our concept of spiritual gifts. We, and by we I mean most evangelicals, see them as something believers have. Believing as such, we see it was an irrevocable gift from God. It is also commonplace to believe that having a spiritual gift is an indicator of how God has uniquely blessed us as individuals for his church. Perhaps we are far from the Biblical understanding of this subject.

A spiritual gift is a gifting of the Spirit in the lives of the elect for the benefit of the church.

Common Questions Answered:
1. When does some one receive their Spiritual Gift(s)?
One is given abilities in varying stages of life but these abilities are only “spiritual” when empowered by the Holy Spirit for the common edification of the local church.

2. Does everyone “have” a Spiritual Gift?
Everyone has gifts that are all given by God but the gifts, talents, and abilities are not always and at all times used by God.

3. Can I lose my gift?
God is the giver of every good gift and is certainly able to take these gifts or abilities away. Spiritual gifts are not possessions that believers own. When the gifts and abilites that God has given are used by the Spirit they become our spiritual gifting.

4. Are those gifts listed in Scripture (and those often mentioned in the OT) exhaustive lists?*
Definitely not! They are ways in which the Spirit of God was manifesting Himself through the people of God for a particular time.

5. What about the “cessation” of gifts? Are there gifts that are no longer present?
Yes and No. The Holy Spirit no longer manifests himself to believers in such a way to create “new prophecy.” However, we cannot deny that other “miraculous giftings” exist as the Spirit determines necessary.

6. Is this a consistent theology for the Old Testament?
The Holy Spirit was present in the lives of OT saints for a special anointing in which He worked for the good of His people. Often times the working of the Spirit was to bring His people to repentance. The Holy Spirit was also present using abilities of men and women for leadership and for even manual tasks such as constructing tabernacles, temples, and walls.

7. Are there “non-spiritual” gifts?
There are abilities that are God-given and other talents that are not from God. Certainly, God is able to use all human experiences to bless His people, but it is unreasonable to consider certain abilities, especially those pertaining to skillful sinning, to be in anyway spiritual in nature.

8. Is there one spiritual gift(ing) that all believers have? Do they have a responsibility to use that gift?
Yes! As I read 1 Corinthians, the one gift that we all have is love. Jesus, Himself, said, “By this all men will know that you are my disciples….” The love of Christ is one thing the Holy Spirit gives ALL believers. This spiritual gift is and should always be present in the manifestations of the Spirit’s gifting of believers for service.

9. How can Christians discover their “spiritual gifts”?
As defined above, spiritual gifts are the ways in which the Spirit of God uses both supernatural and natural abilities to bring about His purposes. Therefore, the best way to discover how God uses someone is to ask others in the body how they have been recipients of God’s work through them.

10. So why make the distinction between spiritual gifts and spiritual gifting?
We must not loose site of the most important thing. It is not the gifts and abilities that we have that are spiritual; but, the use of those gifts by the Holy Spirit that make them spiritual. Our gifts are not ours to keep. God has gifted his children for giving themselves to the community of faith for the building up of others. When we give our gifts and the Spirit uses them—we are exercising our spiritual gifting.


**(1 Cor. 12:28, 1 Cor. 12:8-10, Eph. 4:11, Rom. 12:6-8, 1 Cor 7:7, 1 Peter 4:11)