Paul Draper, “A Critique of the Kalam Cosmological Argument”
1. Arg from contingency (one version of Cosmo arg)
a. Every contingent being (including things infinitely old) has a cause of its existence
b. The universe is contingent
c. Thus, universe has a cause of its existence
2. Draper rejects arg from contingency
a. b. is clearly true (if contingent means “logically contingent”)
i. Isn’t the universe also physically contingent (on physical constants/laws necessary for its existence)?
b. Rejects a.
i. Something that is infinitely old has always existed
ii. Why would something that has always existed require a cause of its existence, even if it is logically possible that it might not have existed?
iii. Also not clear that an infinitely old thing could have had a cause of its existence
(1) Because causes must precede?
3. Kalam version of Cosmo argument
a. Everything that begins to exist has a cause of its existence
b. Universe began to exist
c. Thus, universe has a cause of its existence
d. Kalam argument’s key difference from other cosmological arguments
i. Conclusion that universe has a cause of its existence based on premise that universe began to exist a finite time ago
ii. Avoids weakness of argument from contingency by denying universe is infinitely old
iii. Claims universe needs a cause, not because contingent, but because it had a beginning
4. Draper on Kalam argument
a. a. is a very strong premise
b. b. is weak
5. Draper thinks
a. The argument does not prove universe had a beginning, and
b. Even if it did prove universe had a beginning, argument fails because it equivocates (uses “begins to exist” in two different ways) (begins within time or with time?)
c. Example of equivocation
i. A feather is light.
ii. What is light cannot be dark.
iii. Therefore, a feather cannot be dark.
6. Draper’s summary of Craig’s four arguments for b. (=the claim that universe began to exist)
i. First two arguments are philosophical and depend on distinction
(1) Potential infinite
(a) Series/collection that can increase forever w/o limit but is always finite
(i) Examples
(ii) Set of events occurred since the birth of his daughter
1) Set of completed years after 1000 BCE
(2) Actual infinite
(a) Set of discrete things (real or not) whose number is actually infinite
(b) E.g.: the set of natural numbers: 1, 2, 3, and so on
b. Arg one: Can’t be an infinite regress of events because actual infinites can’t exist in reality
c. Arg two: infinite regress of events is impossible because, even if actual infinites can exist in reality, they could not be formed by successive addition.
d. Arg three (Scientific): Evidence for big bang theory supports the view that the universe had a beginning
e. Arg four: 2nd Law of Thermodynamics supports idea that universe began to exist
i. 2nd law claims the amount of energy available to do mechanical work always decreases in a closed system
ii. Since universe as a whole is a closed system with a finite amount of such energy, an infinitely old universe is incompatible with the fact we have not yet run out of such energy
(1) Universe not yet reached its equilibrium end state
7. Note about 3rd and 4th arguments: Not just idea that science and religion are compatible but that science provides evidence for religion!
8. Draper statement of versions of arg two:
a. It claims: Infinite regress of events is impossible because, even if actual infinites can exist in reality, they could not be formed by successive addition
b. Kant’s related argument:
i. if the world had no beginning, then at any moment an eternity has elapsed, that is, an infinite series of successive states of things has happened
ii. But one can never complete an infinite by successive synthesis.
9. Draper’s evaluation of version two:
a. Summary: It assumes that an infinite past can only exist if one can form an infinite by adding one at a time to a finite past, but at no point in the past is it finite so one is really getting an infinite by adding one at a time to an infinite (and this is possible)
b. It is true that one can’t start with a finite collection and then by adding one member at a time turn it into an infinite collection (no matter how much time one has)
(1) What if one has an infinite amount of time?
ii. But this is not required for the past to be infinite
c. For if temporal regress of events is infinite, then the universe has never had a finite number of past events
i. Rather it has always been the case that the collection of past events is infinite
ii. So rather than an infinite formed by successively adding to a finite collection
iii. It is an infinite formed by successively adding to an infinite collection
iv. And one can form an infinite that way
10. Draper thinks Craig’s first argument is better
11. Craig’s first argument
a. Temporal regress of physical events must be finite–there must have been a first physical event
b. For actual infinite can’t exist in reality
c. Infinite temporal regress of events is an actual infinite
d. First physical event can’t be preceded by an eternal absolute quiet physical universe
12. No set of real things can be actual infinite because to so assume has paradoxical implications
a. Hilbert’s hotel
b. Library could have infinitely many black books (assigned even number) and add infinitely may red books (odd number) and not increase number of books at all (still an infinite)
13. Draper’s argument against Craig argument that an actual infinite is impossible because assuming so leads to paradoxes
14. The paradoxes result from three inconsistent statements and Craig just assumes we must reject one of them (existence of actual infinites, Three below), but we might instead reject one of the others (One or Two)
a. One: A set has more members than any of its proper subsets
i. A proper subset is one that has some members of a set but not all of them
ii. This is why we think that Hilbert’s hotel has more people after we move person in room one to room two (etc.) and put the new guy in room one (the set of occupants before the move is a proper subset of the set of occupants after the move)
iii. Note: Mathematicians reject One (proper subsets can have just as many members as the set)
b. Two: If the members of two sets can be placed in one to one correspondence, then neither set has more members than the other
i. The set of people in Hilbert’s hotel before and after the move can be put in one to one correspondence and thus there are no more people after the move
ii. One might argue that intuitively the set of natural numbers (1,2,3, ...) is bigger that the set of even numbers (2, 4, 6...) even though they can be put into one to one correspondence.
c. Three: There are actual infinite sets
15. So Craig has not shown Three is false, because we might instead reject One of Two
16. Two implies that since the set of even numbers and natural numbers can be put in one to one correspondence, one can add infinitely many red books to the library and it still have the same number of books
17. One implies that so adding books would increase number of books (as even numbered books is a proper subset)
18. This is a contradiction, so Craig has us reject (three) idea there are actual infinite sets
19. But why reject Three and not Two (or One, as mathematicians do)?
a. “Why is it more reasonable to believe that actually infinite libraries are impossible than to believe that, although they are possible, one such library can have more books than a second despite the fact that the books in the first can be placed in one-to-one correspondence with the books in the second?”
b. Craig gives us no reason for this.
20. Draper argues that Craig’s Kalam argument equivocates on the phrase “begins to exist” and thus fails
a. To equivocate is to use the same word but with different meanings
b. Example of argument that equivocates
i. A feather is light
ii. What is light cannot be dark
iii. Therefore, a feather cannot be dark
c. Even if Craig shown that the universe did begin to exist, argument fails as other premise (what begins to exist has a cause) uses “begins to exist” in a different way
21. Two senses of “begins to exist”
a. One: Begins within (or in) time
i. To begin to exist means to begin within time (with time already existing)
(1) It implies that there was a time at which X did not exist and then later time at which X does exist
b. Two: Begins with time
i. To begin to exist with time
(1) Time began with the thing beginning, so there was not a time that existed prior to its beginning
(2) Not a time at which X did not exist, as X began with time
22. Kalam cosmological arg formulation
a. Premise One: Whatever begins to exist (within time) has a cause
i. Premise Two: The universe began to exist (with time)
ii. Conclusion: Universe has a cause
23. Craig equivocates between the sense of “begins to exist” in premise one (begins within time) and the sense of begins to exist in premise two (begins with time)
a. So the argument commits the fallacy of equivocation
24. Premise two: The universe “began to exist” here means began to exist with time.
25. Premise one is only plausible if we mean begins to exist within time
a. For we have only experienced things being causally brought into exist within time
b. We have no intuitions about the causality of things that begin to exist with time (for we have never experienced such things)
i. Such things would require timeless causes, and we have no experience of this
26. Further it is far from obvious that a universe that begins to exists with time needs a cause of its existence
a. Like an infinitely old universe, a universe that begins to exist with time has always existed:
i. Never a time at which this universe did not exist
b. Not clear that something that has always existed requires a cause for its existence
c. Not even clear that such a thing could have a cause of its existence