Suppose there is a hotel and the hotel contains an infinite number of rooms, but all the infinite rooms are full with a guest. Someone approaches the hotel and wants a room. This should not be a problem for the manager who has an infinite amount of rooms, so he simply shifts every occupant up a room so that the guest in Room #1 goes to Room #2, the guest in Room #2 moves into Room #3, and so on through infinity. So Room #1 is now empty, but before the additional guest showed up the hotel was full. How can this be?

Apparently the situation can be complicated further. Suppose an infinite amount of guests show up and want to check in to this infinite hotel. The manager simply tells each guest to double his room number, and that new number will be the guest’s new room, so that the guest in Room #2 will move to Room #4, the guest in Room #3 will move to Room #6, and so on. Since any number multiplied by two is an even number, the original guests are all in even-numbered rooms, leaving the odd-numbered rooms to the infinite amount of new guests. The manager could even do this an infinite number of times if he or she wanted, but the rooms, we said, were already full before the guests arrived and now they’re full…again. But even if some guests or an infinite amount of guests left, the hotel would still be full. How can this be?

There are a couple problems with this illustration. First, we start off by stating that there is an infinite amount of rooms. Do we really mean that, or do we wink when we propose that, believing that that is impossible? If we do not really mean what we state, do we start out with a meaningless or weakened version of “infinite” from the start? Let us try another method and start out by sticking to our guns when we claim something is infinite. There is a hotel with an infinite amount of rooms – really. Although we cannot picture this, and although it would be impossible to measure and count, this hotel does have an infinite number of rooms for the sake of argument. But in this reality we have to say that if all the hotel rooms are occupied; then if there is a hotel room there necessarily is a guest that occupies that space. So based on our beginning criterion of every room within this series being occupied, there would be no empty rooms for any member of the infinite amount of guests to move into. In other words, having every guest “shift over into the next room is the part that is absurd and impossible, not the actual infinite that we assume from the beginning. This also eliminates the problem of anyone else showing up and looking for rooms, whether it be just one guest or an infinite amount of guests. There are no vacant hotel rooms in this infinite set, regardless of who shows up.

But this example doesn’t at all prove that an actual infinite is possible, it only demonstrates that if you do not assume its impossibility from the outset then you can find where the absurdity lies within the illustration. What about removing a member of an actual infinite set? If one guest among an infinite amount checks out from one of the infinite amount of hotel rooms, we still have an infinite amount of hotel rooms but not an infinite amount of guests. So the question is, can we meaningfully even talk about “infinity minus one”? It does not appear so, because we know that after subtracting one guest from the infinite set, we can’t just add that guest back to the set to make it infinite. So either there really can be an actual infinite that can sustain its infinite amount even when it is subtracted from (although talk of these implications sounds absurd), or the difficulties in talking about an actual infinite being subtracted from make its existence absurd. Craig lightly addresses these concerns and objections, recognizing that if these conditions existed then these absurdities would also occur, but assumes that the illustration demonstrates the need to deny the reality of an actual infinite from the get-go. More work needs to be done on this, or more reading on this needs to be done by me.

My concern lies more with how this illustration has been used to argue for the cosmological argument. Let us take this hotel illustration and look at it as an analogy. What is argued is that the universe must have had a beginning because an actual infinite series of events is absurd, as demonstrated by illustrations like Hilbert’s hotel. If we take the hotel example and understand the universe to be the hotel rooms and the series of events within the universe to be the guests, a significant problem arises. What would it look like to “remove” an event in the universe from its infinite series of events? To put it another way, we can picture and speak of removing hotel guests within an infinite series of guests from an infinite series of hotel rooms, but can we meaningfully speak of removing an event in the universe from an infinite series within the universe? How would an event be removed? There seems to be a category mistake or a quality that differentiates the two scenarios, disconnecting the supposed analogy. At any rate, it would need to be demonstrated how the two scenarios are analogous or related.

The purpose here is not to dismiss or completely discount the cosmological argument, but merely to anticipate objections an unbeliever might propose given the cosmological argument’s own set of rules, conditions, and logical parameters.

photo courtesy of Brent

Kant, considered by many to be the father of modern philosophy, is a figure theologians should be familiar with. His influence upon the theological world can scarcely be overstated. In this lecture, Keith Ward speaks about Kant’s triumph of idealism.

1. Every Thought Captive by Richard Pratt, Jr.
2. The Battle Belongs to the Lord by K. Scott Oliphint
3. Always Ready by Greg Bahnsen
4. Institutes of the Christian Religion by John Calvin (especially Book I – you’ll have to listen to the discussion to hear why this is on the list)
5. Presuppositional Apologetics: Stated and Defended by Greg Bahnsen
6. Van Til’s Apologetic by Greg Bahnsen (contains large portions of Van Til’s writings)
7. Christian Apologetics by Cornelius Van Til annotated by William Edgar
8. The Defense of the Faith, 3rd edition by Cornelius Van Til annotated by K. Scott Oliphint
9. A Christian Theory of Knowledge by Cornelius Van Til
10. Survey of Christian Epistemology by Cornelius Van Til
11. Common Grace and the Gospel by Cornelius Van Til
12. Introduction to Systematic Theology by Cornelius Van Til annotated by William Edgar

Therefore, when we speak of God as an absolute personality, we mean that God is a person who is neither dependent upon nor derivative of any other person or thing.  He is a se and exists entirely self-sufficiently without need of any external reference or relationship.  As such, God is absolute.  As with God’s other essential attributes, this absoluteness extends to his personality since it is entirely self-sufficient, underived and without reference to any other personality.  God’s personality is the perfect embodiment of personality.  His self-consciousness and essence are coterminous.

This means that the world is intensely personal.  Van Til sought to explore the implications of this insight by applying it to epistemology.  Interestingly, various strands of philosophy have picked up on this same notion.  Andrew Seth Pringle-Pattison saw absolute personality as a necessary precondition for a viable epistemology.  Working in the milieu of early 20th British absolute idealism, Pringle-Pattison moved the systems of F. H. Bradley and Bernard Bosanquet toward a personal solution.  Though it may be considered an improvement of sorts, Van Til pointed out the failures of Pringle-Pattison’s system.

For Van Til, nothing less than the absolute, personal and Trinitarian God of the Bible can provide the foundation for epistemology.  This is a driving factor behind Van Til’s discussion of God as a person in his unity – not simply in his diversity (i.e. the one person/three person discussion).  Working with the Trinitarian formulations of Charles Hodge, A. A. Hodge and Herman Bavinck, Van Til sought to show how only an orthodox Trinitarian doctrine of perichoresis (mutual indwelling, interpenetration, coinherence of the Father, Son and Spirit) could provide the “solution” to philosophy’s epistemological questions.