International Journal for Philosophy of Religion 53: 147–161, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.
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The historical argument for the Christian faith: A response to Alvin Plantinga JASON COLWELL Department of Mathematics, Caltech 253-37, 1200 E, California Boulevard, Pasadena, CA 91125
Introduction In Chapter 8 of his book, Warranted Christian Belief, Alvin Plantinga critically discusses the historical argument for the Christian faith. Generally, he characterizes the historical argument as an evidentialist argument for the truth of Christianity. Specifically, he says that the argument claims to show that the conditional probability of the central claims of the Christian faith, given the truth of a certain body of background knowledge, is high. Historical arguments, in Plantinga’s view, rest on a sequence of propositions, beginning with the background knowledge assumed and ending with (the conjunction of) the central claims of the Christian faith. Each proposition in the sequence provides evidence for the next. In this way, he explains, the background knowledge provides evidence for the final proposition. More precisely, such a sequence of propositions provides a lower bound on the conditional probability of the final proposition (the truth of the central claims of Christianity) given the inital proposition (the background knowledge). Plantinga’s main point is that such a sequence of propositions provides a small lower bound, and thus he concludes that the historical argument provides weak evidence for the Christian faith. In this article, I wish to show that Plantinga’s considerations do not require us to dispose of the historical argument. I intend to argue that the lower bound may be significantly increased by simultaneous consideration of several different sequences of propositions. Supposing these requisite sequences can be found, the significant increase in the lower bound shows Plantinga’s conclusion to be false. (And as a matter of fact, many have argued for the truth of propositions comprising such sequences.) I am not claiming to show here that the historical argument is a good one. Rather, I am trying to demonstrate that the weakness Plantinga finds in the argument need not be fatal, as he thinks, but that it might be compensated
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for, in fact by a mathematical principle similar to the one he uses. It is interesting to note that Plantinga’s arguments in Warranted Christian Belief have a similar scope: he does not argue that Christian belief is warranted. Rather, he proposes a model whereby Christian belief could have warrant.
The historical argument The historical argument, says Plantinga, is an attempt to derive the conclusion that the central truths of Christianity are probable given the evidence from history available to us. I shall first look in detail at his explanation and negative evaluation of the historical argument. Then I shall make two obervations. My first and primary observation is that multiple sequences of propositions may strengthen the historical argument in a way that Plantinga has not considered. My second observation is that non-historical evidence might be used along with historical evidence to further strengthen the historical argument. The historical argument, explains Plantinga, rests on a sequence of propositions such as the following: K The things which we all take as background knowledge are indeed true. T God exists. A God would make some kind of revelation to humankind. This revelation could be of God or of certain aspects of him of which it is important for humankind to know. B Jesus’ teachings were such that they could be sensibly interpreted and extrapolated to G. C Jesus rose from the dead. D In raising Jesus from the dead, God endorsed his teachings. E The extension and extrapolation of Jesus’ teachings to G is true. G The central claims of the gospel are true. Here C must be taken to refer to a literal bodily resurrection. The argument then proceeds by claiming that the existence of God, T , is probable on K, our background knowledge. This (assumedly high) probability is denoted by P (T |K). Next, the argument asserts that A is probable on the conjunction T &K, i.e. that P (A|T &K) is high. Similarly, P (B|K&T &A), P (C|K&T &A&B), P (D|K&T &A&B&C), P (E|K& T &A&B&C&D), P (G|K&T &A&B&C&D&E) are taken to be high. Then the argument claims that P (G|K) is high, that is, that G is probable on K.
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The law of dwindling probabilities Plantinga exposes a flaw in this historical argument by noting that these probabilities have to be multiplied to obtain the probability P (G|K) which a proponent of the argument wishes to be high. By the usual arithmetic of conditional probabilities, we have the relations P (G|K) ≥ P (G|K&T &A&B&C&D&E) · P (T &A&B&C&D&E|K), P (T &A&B&C&D&E|K) = P (E|K&T &A&B&C&D) · P (T &A&B&C&D|K), P (T &A&B&C&D|K) = P (D|K&T &A&B&C) · P (T &A&B&C|K), P (T &A&B&C|K) = P (C|K&T &A&B) · P (T &A&B|K), P (T &A&B|K) = P (B|K&T &A) · P (T &A|K), and P (T &A|K) = P (A|K&T ) · P (T |K).
Substituting each relation into the previous one, we obtain P (G|K) ≥ P (G|K&T &A&B&C&D&E) · · · · · ·
P (E|K&T &A&B&C&D) P (D|K&T &A&B&C) P (C|K&T &A&B) P (B|K&T &A) P (A|K&T ) P (T |K).
For the purpose of illustration, Plantinga then proceeds to assign approximate values to each of the probabilities on the right-hand side of the above equation. He notes that E entails G, so that the first probability is 1. (Equivalently, one could omit the first factor.) He assigns to the others values P (E|K&T &A&B&C&D) P (D|K&T &A&B&C) P (C|K&T &A&B) P (B|K&T &A) P (A|K&T ) P (T |K)
∈ = ∈ ∈ ∈ ∈
[0.7, 0.9] 0.9 [0.6, 0.8] [0.7, 0.9] [0.9, 1] [0.9, 1].
Then, although these probabilities each is reasonably high, their product, the value on the right-hand side of the above inequality is low: ≥0.21 if we choose the left endpoint of each interval, ≥0.35 if we choose the midpoint of each interval. Plantinga calls this phenomenon the “law of dwindling probabilities”.
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An observation about dwindling probabilities My main observation is that the law of dwindling probabilities also gives support for the historical argument in question. Specifically, one can apply, in a way Plantinga has not considered, the mathematical fact, the same one considered by Plantinga, that for events X1 , . . . , Xn , the probability P (X1 &X2 & . . . &Xn ) can be small even if the individual probabilities P (Xi ) are large. (The discussion here will be comfortably short on mathematical rigour, but more detailed calculations of probability can be found in Appendix A.) Suppose there is a set of n sequences of propositions, Y1,1 , Y1,2 , . . . Y1,m1 , Y2,1 , Y2,2 , . . . Y1,m2 , .. . Yn,1 , Yn,2 , . . . Yn,mn (of respective lengths m1 , m2 , . . . , mn ), each of which forms an argument for the truth of the gospel. That is, the ith argument can be represented as a chain of (claimed) implications: K
K&Yi,1
K&Yi,1 &Yi,2
.. .
K&Yi,1 & . . . &Yi,mi −1
K&Yi,1 & . . . &Yi,mi
G
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We have n sequences and thus n different arguments for G. In the ith argument, one would argue from K to Yi,1 , from K&Yi,1 to Yi,2 , from K&Yi,1 &Yi,2 to Yi,3 , and so on, until finally one would argue that G follows from K&Yi,1 &Yi,2 & . . . &Yi,mi . The situation can be depicted by the following diagram:
Y1,1
Y1,2
.. .
Y1,m1
K RRRR RRR RRR RRR RRR R) Yn,1 Y2,1 ···
ww ww w ww {w w
Y2,2
···
.. .
Y2,m2
GG lll GG lll l GG l ll GG G# lllll vl
Yn,2
.. .
Yn,mn
G
(The n sequences may not all be of the same length, as it might appear from the diagram.) Within each sequence, we consider the conditional statements Yi,1 | K, Yi,2 | K&Yi,1 , .. . Yi,mi | K&Yi,1 & . . . &Yi,mi −1 , G | K&Yi,1 & . . . &Yi,mi , which form an argument from our background knowledge K to our desired conclusion G. The essential idea is that although each of the n arguments may be weak on its own, they may be strong together. The chains may together provide good evidence for their common conclusion G. We shall assume that each of the n arguments is independent of each other argument. (The type of analysis which follows may also be done in the case where the sequences of propositions are dependent or even overlapping, though the calculations then are more complex. An example of such calculations is given in Appendix B.)
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For any fixed i, Plantinga’s analysis is correct. Precisely, suppose that P (G | K&Yi,1 & . . . &Yi,mi ) ·P (Yi,mi | K&Yi,1 & . . . &Yi,mi −1 ) .. . ·P (Yi,2 | K&Yi,1 ) ·P (Yi,1 | K), which we denote by Pi , is small (even while, as Plantinga allows, each multiplicand may be large). We have P (G|K) ≥ P (G|K&Yi,1 & . . . &Yi,mi ) ·P (Yi,mi |K&Yi,1 & . . . &Yi,mi −1 ) .. . ·P (Yi,2 |K&Yi,1 ) ·P (Yi,1 |K) = Pi , which gives a weak lower bound on P (G|K). That is, for each i, it is probable that the ith argument fails. But we can apply the law of dwindling probabilities to {1 − Pi }1≤i≤n , the set of probabilities of the respective chains of (claimed) implications failing. It says that although each 1 − Pi (the probability that the ith chain fails) is large, the product (1 − P1 )(1 − P2 ) · · · (1 − Pn ) (the probability that all the chains fail) may be small. Equivalently, although Pi (the probability that the ith chain succeeds) is small, 1 − (1 − P1 )(1 − P2 ) · · · (1 − Pn ) (the probability that at least one of the chains succeeds) may be large. If suitable propositions {Yi,j }i,j can be found, then there will be a large lower bound for the probability of G: P (G|K) ≥ 1 − (1 − P1 )(1 − P2 ) · · · (1 − Pn )
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An example supporting the historical argument The following example illustrates that this method can be deployed in support of the historical argument. For ease of notation, let us rename the propositions T , A, B, C, D, E already used, writing Y1,1 = T , Y1,2 = A, Y1,3 = B, Y1,4 = C, Y1,5 = D, and Y1,6 = E. This sequence of propositions will be used along with two other sequences now to be defined. The first of these two other sequences is the following: Y2,1 The Old Testament prophecies were in fact written well in advance of Jesus’ life. Y2,2 The Old Testament prophecies predicted the coming of a Messiah. Y2,3 The Old Testament prophecies were fulfilled in the person of Jesus of Nazareth. Y2,4 This fulfillment of prophecy demonstrated that Jesus was divine, and that the things he taught were true. The first proposition, Y2,1 , is reasonably certain. The next, Y2,2 , is also fairly certain, though many Jews today do not wait for a personal Messiah, and take the passages to be figurative. There is much evidence for Y2,3, assuming Y2,1 and Y2,2. Moishe Rosen argues, using the Jewish calendar and calculations of the periods of time given in the Book of Daniel, that the prophecies of Daniel were fulfilled in Jesus.1 Finally, Y2,4 might also be well argued for, assuming that the previous three statements are true. We now turn to a third sequence of propositions. This one concerns the church which sprang up, both in Palestine and as far away as India, by the work of Jesus’ apostles. Nine or ten of the twelve (all but Judas and John, and possibly Matthew) were martyred for their faith. They died refusing to deny their beliefs in Jesus and his teachings. They also claimed to have personally seen him after his resurrection. Following, then, are the propositions we shall consider: Y3,1 Jesus had apostles who spread the message of Christianity after his death. Y3,2 Nine of them died for that message. Y3,3 They died claiming what the book of Acts records: that Jesus appeared to numerous people in bodily form after his death. Y3,4 They were not mistaken or insane, and would not all have died for what they knew was a lie. The plan of the argument (which is composed of three separate arguments) can be depicted as follows:
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Y1,1
Y1,2
Y1,3
Y1,4
KE EE zz EE z z EE z z E" z z| Y2,1
Y2,2
Y2,3
Y2,4
Y3,1
Y3,2
Y3,3
Y3,4
Y1,5 Y1,6 DD DD DD DD "
G I will not attempt to assign values to the conditional probabilities involved in these sequences of assertions. Instead, I will assume that P2 and P3 are comparable to Plantinga’s moderate estimate, 0.35, for P1 . Under this assumption, we discover that the probability of G on K is at least 1 − (1 − P1 )(1 − P2 )(1 − P3 ) = 1 − (1 − 0.35)(1 − 0.35)(1 − 0.35) 0.725. This is certainly an improvement, and demonstrates how the law of dwindling probabilities, though working against the argument in one way, can work for it in another way. I claim that the mathematical principle which appears to weaken the historical argument bears upon the argument not only by weakening each sequence of propositions, but also by combining the strengths of multiple sequences of propositions. The essential principle involved is that whereas the law of dwindling probabilities decreases the probability of a conjunction, it increases the probability of a disjunction. But perhaps we can do better still with a another observation. I am not referring to the finding of more independent sequences of historical claims,
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though that may be possible. Instead, let us consider other evidence, such as personal sensory experience (here “sense” is intended not to include the sensus divinitatis) and accounts of miracles in modern times. We may apply the same reasoning to this whole set of evidence (including the historical evidence just discussed). Of course these experiences and reports would have to be specific enough to lead us to conclude the truth of Christianity or of fundamental claims thereof. But such may exist, and the law of dwindling probabilities would give us, even for six independent sequences of propositions, each chain of conditionals yielding alone a probability of 0.35, a resulting estimated chance of 1 − (1 − 0.35)6 0.925 that the claims of the gospel are true. With this argument, I do not mean to suggest that faith is unnecessary for the acceptance of the central truths of Christianity, that the need for faith is removed by the use of reason. Plantinga says that there is within every human being a capability to perceive God directly, which he calls the sensus divinitatis. “The sensus divinitatis is a disposition or set of dispositions to form theistic beliefs in various circumstances, in response to the sorts of conditions or stimuli that trigger the working of this sense of divinity.”2 The sensus divinitatis, says Plantinga, is damaged or impeded by sin and must be restored to proper function by faith and the working of the Holy Spirit. Further to Plantinga’s exposition, perhaps our fallen state makes us unable to follow (unaided) the deliverances of our reason when they would lead us into humble submission to God. Indeed, the Apostle Paul speaks in Romans 7 of sin “living” in him, making him unable to do even the good he wants to do. Romans 7:23 says: “. . . but I see another law at work in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin at work within my members.” The matter of the need for faith is raised with a question at the beginning of Plantinga’s discussion of the historical argument. “But given that recalibration [of your affections, aims, and intentions], couldn’t you then see and appreciate the historical case for the truth of the main lines of Christianity without any special work of the Holy Spirit?”3 Not necessarily; because although historical evidence may well function as part of a strong argument for the truth of the Christian faith, the internal instigation of the Holy Spirit may still be necessary to bring someone to believe that truth.
Conclusion The historical argument attempts to show that the central claims of Christianity are probable given the evidence available to us from history. In the historical argument, a sequence of propositions is used, each of which is
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probable given the truth of the previous propositions. Accordingly, from the sequence of propositions a chain of conditionals is constructed which leads from background knowledge consisting of propositions commonly assumed to be true, to the desired conclusion that the gospel is true. Plantinga illustrates the fact that even if each conditional in the chain is very likely true, the whole chain of conditionals may provide weak evidence for the Christian faith. I respond by pointing out that if several sequences of propositions are used, the historical argument may be much strengthened. I consider the set of chains of conditionals constructed, each chain being constructed from a sequence. Standard calculations of probability are used to show that the multiple chains of conditionals combine disjunctively. That is, the (perhaps high) probabilities of each chain having at least one of its conditionals false – this is the conclusion of Plantinga’s argument – are multiplied to give a low probability that all of the chains so fail. In Plantinga’s considerations, the probabilities of the statements in a conjuction (the probabilities that each of the conditionals in a chain is true) are multiplied. In my considerations, the probabilities of the negations of the statements in a disjunction (that is, the probabilities that the chains fail) are multiplied. Then it is seen to be likely that at least one of the chains has all its conditionals true. Thus, we obtain a reasonably high lower bound for the probability that the claims of the gospel are true. Based upon the argument from dwindling probabilities associated with one chain of historical evidence, one might be tempted to think it unprofitable to try to find support for the gospel in the historical argument. Such a thought, however, would be mistaken because, as I have shown in this article, multiple chains of historical evidence may be deployed to provide strong support for the central claims of the Christian faith. There is no reason to become discouraged about the strength of the historical argument.4 Appendix A: Detailed calculations of probability While this section is not necessary for a basic understanding of my argument, it justifies rigourously my reasoning concerning the n sequences of propositions. Suppose there is a doubly indexed collection {Yi,j }1≤i≤n,1≤j ≤mi ∀i of propositions. For each i, we consider the conditional statements Yi,1 | K, Yi,2 | K&Yi,1 , .. . Yi,mi | K&Yi,1 & . . . &Yi,mi −1 , G | K&Yi,1 & . . . &Yi,mi ,
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which form an argument from our background knowledge K to our desired conclusion G. Again, the diagram which depicts the situation is: K RRRR RRR vv v RRR vv RRR v v RRR v {v R) Y1,1 Yn,1 Y2,1 ··· Y1,2
Y2,2
.. .
.. .
.. .
Y1,m1
Y2,m2
Yn,mn
···
l GG lll GG lll GG l l l GG G# lllll vl G
Yn,2
The essential idea is that although each of the n arguments may be weak on its own, they may be strong together. The chains may together provide good evidence for their common conclusion G. Precisely, denoting by Yi the conjunction Yi,1 &Yi,2 & . . . &Yi,mi , it is the case that the statements {G&Yi |K}1≤i≤n may each be improbable while their disjunction may be probable. (The truth of this disjunction would in particular imply the truth of G given K.) Assume that for any i0 = i1 , j0 , j1 , the statements Yi0 ,j0 +1 |K&Yi0 ,1 & . . . &Yi0 ,j and Yi0 ,j1 +1 |K&Yi1 ,1 & . . . &Yi1 ,j are independent. Put another way, we shall assume that each of the n arguments is independent of each other argument. (The type of analysis which follows may also be done in the case where the sequences of conditional statements Yi,j +1 |K&Yi,1 & . . . &Yi,j are dependent, and will be shown by example in Appendix B.) For any fixed i, Plantinga’s analysis is correct. Precisely, suppose that the expression
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P (G|K&Yi,1 & . . . &Yi,mi −1 &Yi,mi ) m i −1
·
P (Yi,j +1 |K&Yi,1 & . . . &Yi,j )
j =1
· P (Yi,1 |K), which we denote by Pi , is small (even while, as Plantinga allows, each multiplicand may be large). We have P (G|K) ≥ P (G&Yi |K) = P (G|K&Yi,1 & . . . &Yi,mi −1 &Yi,mi ) ·
m i −1
P (Yi,j +1 |K&Yi,1 & . . . &Yi,j )
j =1
·P (Yi,1 |K) = Pi , which gives a weak lower bound on P (G|K). But we can apply the law of dwindling probabilities to the set of probabilities {P (¬(G&Yi )|K)}1≤i≤n . It says that although each P (¬(G&Yi )|K) = 1 − Pi is large, P (¬(G&Y1 )&¬(G&Y2 )& . . . &¬(G&Yn )|K) n = P (¬(G&Yi )|K) =
i=1 n
(1 − Pi )
i=1
may be small. Equivalently, P ((G&Y1 ) ∨ (G&Y2 ) ∨ . . . ∨ (G&Yn )|K) = 1 − P (¬((G&Y1 ) ∨ (G&Y2 ) ∨ . . . ∨ (G&Yn ))|K) = 1 − P (¬(G&Y1 )&¬(G&Y2 )& . . . &¬(G&Yn )|K) n = 1 − (1 − Pi ) i=1
may be large even if each P (G&Yi |K) = Pi
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is small. If suitable propositions {Yi,j }i,j can be found, then there will be a large lower bound for the probability of G: P (G|K) ≥ P (G&(Y1 ∨ Y2 ∨ . . . ∨ Yn )|K) = P ((G&Y1 ) ∨ (G&Y2 ) ∨ . . . ∨ (G&Yn )|K) n = 1 − (1 − Pi ) i=1
Again, the idea is that though each ith chain may have a high probability 1 − Pi of failing, the probability that they all fail is ni=1 (1 − Pi ), which may be low.
Appendix B: Overlapping sequences of propositions Overlapping sequences of propositions could also be used to strengthen the historical argument. (There is likely to be overlap among the sequences of propositions we would actually use.) For example, we might use the propositions God would make himself widely known to the world. Y1,3 Y1,4 Christianity is the religion today which has the best claim to historical accuracy. The plan of the argument would be depicted
Y1,1
y yy y yy |y y
RRR K E EE RRR EE RRR EE RRRR E" RRR ( Y2,1 Y3,1
Y1,2
CC CC CC CC !
Y1,3
Y1,4
Y2,2
Y1,3
Y1,4
Y2,3
Y2,4
Y3,2
Y3,3
Y1,5 Y1,6 EE EE EE EE " G
Y3,4
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and the probability P (G|K) would have a calculated lower bound of 1−(1−P (Y1,1|K) ·P (Y1,2 |K&Y1,1 ) ·(1− (1− P (Y1,3 |K&Y1,1 &Y1,2 ) ·P (Y1,4 |K&Y1,1 &Y1,2 &Y1,3 ) ·P (Y1,5 |K&Y1,1 &Y1,2 &Y1,3 &Y1,4 ) ·P (Y1,6 |K&Y1,1 &Y1,2 &Y1,3 &Y1,4 &Y1,5 ) ·P (G|K&Y1,1 &Y1,2 &Y1,3 &Y1,4 &Y1,5 &Y1,6 )) |K&Y &Y ) ·(1−P (Y1,3 1,1 1,2 |K&Y &Y &Y ) ·P (Y1,4 1,1 1,2 1,3 &Y )))) ·P (G|K&Y1,1 &Y1,2 &Y1,3 1,4 ·(1−P (Y2,1 |K) ·P (Y2,2 |K&Y2,1 ) ·P (Y2,3 |K&Y2,1 &Y2,2 ) ·P (Y2,4 |K&Y2,1 &Y2,2 &Y2,3 ) ·P (G|K&Y2,1 &Y2,2 &Y2,3 &Y2,4 )) ·(1−P (Y3,1 |K) ·P (Y3,2 |K&Y3,1 ) ·P (Y3,3 |K&Y3,1 &Y3,2 ) ·P (Y3,4 |K&Y3,1 &Y3,2 &Y3,3 ) ·P (G|K&Y3,1 &Y3,2 &Y3,3 &Y3,4 )), which would be an improvement over the previously calculated lower bound, 1−(1−P (Y1,1|K) ·P (Y1,2 |K&Y1,1 ) ·P (Y1,3 |K&Y1,1 &Y1,2 ) ·P (Y1,4 |K&Y1,1 &Y1,2 &Y1,3 ) ·P (Y1,5 |K&Y1,1 &Y1,2 &Y1,3 &Y1,4 ) ·P (Y1,6 |K&Y1,1 &Y1,2 &Y1,3 &Y1,4 &Y1,5 ) ·P (G|K&Y1,1 &Y1,2 &Y1,3 &Y1,4 &Y1,5 &Y1,6 )) ·(1−P (Y2,1 |K) ·P (Y2,2 |K&Y2,1 ) ·P (Y2,3 |K&Y2,1 &Y2,2 ) ·P (Y2,4 |K&Y2,1 &Y2,2 &Y2,3 ) ·P (G|K&Y2,1 &Y2,2 &Y2,3 &Y2,4 )) ·(1−P (Y3,1 |K) ·P (Y3,2 |K&Y3,1 ) ·P (Y3,3 |K&Y3,1 &Y3,2 ) ·P (Y3,4 |K&Y3,1 &Y3,2 &Y3,3 ) ·P (G|K&Y3,1 &Y3,2 &Y3,3 &Y3,4 )). To see this, observe that 1− (1− P (Y1,3 |K&Y1,1&Y1,2 )
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·P (Y1,4 |K&Y1,1&Y1,2 &Y1,3 ) ·P (Y1,5 |K&Y1,1&Y1,2 &Y1,3 &Y1,4 ) ·P (Y1,6 |K&Y1,1&Y1,2 &Y1,3 &Y1,4 &Y1,5 ) ·P (G|K&Y1,1 &Y1,2 &Y1,3 &Y1,4 &Y1,5 &Y1,6 )) |K&Y &Y ) ·(1−P (Y1,3 1,1 1,2 |K&Y &Y &Y ) ·P (Y1,4 1,1 1,2 1,3 &Y )) ·P (G|K&Y1,1 &Y1,2 &Y1,3 1,4 is greater than or equal to 1− (1− P (Y1,3 |K&Y1,1&Y1,2 ) ·P (Y1,4 |K&Y1,1&Y1,2 &Y1,3 ) ·P (Y1,5 |K&Y1,1&Y1,2 &Y1,3 &Y1,4 ) ·P (Y1,6 |K&Y1,1&Y1,2 &Y1,3 &Y1,4 &Y1,5 ) ·P (G|K&Y1,1 &Y1,2 &Y1,3 &Y1,4 &Y1,5 &Y1,6 )), which equals P (Y1,3 |K&Y1,1&Y1,2 ) ·P (Y1,4 |K&Y1,1&Y1,2 &Y1,3 ) ·P (Y1,5 |K&Y1,1&Y1,2 &Y1,3 &Y1,4 ) ·P (Y1,6 |K&Y1,1&Y1,2 &Y1,3 &Y1,4 &Y1,5 ) ·P (G|K&Y1,1 &Y1,2 &Y1,3 &Y1,4 &Y1,5 &Y1,6 ).
Notes 1. Moishe Rosen, Y’shua (Chicago: Moody Press, 1982). 2. Alvin Plantinga, Warranted Christian Belief (New York: Oxford University Press, 2000), p. 173. 3. Ibid., p. 271. 4. I wish to thank Gary Colwell for his helpful comments, and an anonymous referee for a useful suggestion.
